Electromagnetic bubbles that are sealed by themselves. Sounds like ball lighting to me.
Hello Confused2
Electromagnetic bubbles that are sealed by themselves. Sounds like ball lighting to me.
Electromagnetic bubbles that are sealed by themselves. Sounds like ball lighting to me.
Hello Montec,
I need to go smaller, much smaller.
Best wishes,
Confused2.
I need to go smaller, much smaller.
Best wishes,
Confused2.
All,
The illustration of a Parker Spiral is just too good to let go. I tried to link the .gif directly, but it didn't work. (anyone who can link this directly, please do)
Here is the web page that it is on: helios.gsfc.nasa.gov/solarmag
Here is the link to the NASA page, one more time; be sure to watch "REEL 2".
REEL 2
It is important to note, there is NO soap in these bubbles. The natural surface tension and molecular bonding holds pure water in a ~300 micron film bound by a wire loop. This removes the "diffraction" and "interference" of the "impurities" (vibrations) of the soap, and the limitations of the "waveguide" of the thinner than the full spectrum (octave) distance of visible light, of the film. The soapy film is "stretched" too thin, and is under un-natural tension. The pure water is able to form a thin film, a lens, and a sphere, all from a 2 dimensional boundary, and in the same environment.
Space station science officer Don Pettit, perhaps with "tongue in cheek", declares ..here at the space station lab, we have discovered the true color of the Universe (a "dull" green). His "uneasiness" in the fact that, on "live" (recorded) tape, he just poked a hole in current theory. Back at "the control room", they edit this for the printed transcripts to say "he jokingly states that.." . I'll take the real "picture" over their words. (spin)
Gadfly, have a great time, we'll see you when you get back!
TRoc
The illustration of a Parker Spiral is just too good to let go. I tried to link the .gif directly, but it didn't work. (anyone who can link this directly, please do)
Here is the web page that it is on: helios.gsfc.nasa.gov/solarmag
Here is the link to the NASA page, one more time; be sure to watch "REEL 2".
REEL 2
It is important to note, there is NO soap in these bubbles. The natural surface tension and molecular bonding holds pure water in a ~300 micron film bound by a wire loop. This removes the "diffraction" and "interference" of the "impurities" (vibrations) of the soap, and the limitations of the "waveguide" of the thinner than the full spectrum (octave) distance of visible light, of the film. The soapy film is "stretched" too thin, and is under un-natural tension. The pure water is able to form a thin film, a lens, and a sphere, all from a 2 dimensional boundary, and in the same environment.
Space station science officer Don Pettit, perhaps with "tongue in cheek", declares ..here at the space station lab, we have discovered the true color of the Universe (a "dull" green). His "uneasiness" in the fact that, on "live" (recorded) tape, he just poked a hole in current theory. Back at "the control room", they edit this for the printed transcripts to say "he jokingly states that.." . I'll take the real "picture" over their words. (spin)
Gadfly, have a great time, we'll see you when you get back!
TRoc
Hello All,
- TRoc - yippee bubbles!
I'd like to announce da da
Confused2's first law of bubbles.
Energy will be equally divided between the field that is contained and the field that contains it.
A bit difficult to prove without working through every possible sort of bubble (there may be exceptions I haven't thought of) but examples..
Finite bubble
Soap bubble, the energy required to create the film will be the same as the energy held by the excess pressure of the gas inside - (proof left to the reader)
Infinite bubble..
A point charge. Work out the energy of the field from infinity up to but excluding the point charge. The PROOF.. remove the charge and the field collapses back to zero. The point charge had exactly the same energy as the field it created.
IF Confused2's first bubble law is correct then it's a bit of a burden for a bubble theory because half the energy of whatever you are thinking about is going to zap straight into the bubble - the bubble becomes an intimate part of the problem.
Confused2's second law of bubbles will attempt to deal with quantised bubbles and may take some time to arrive ( ! )
Best wishes,
Confused2.
- TRoc - yippee bubbles!
I'd like to announce da da
Confused2's first law of bubbles.
Energy will be equally divided between the field that is contained and the field that contains it.
A bit difficult to prove without working through every possible sort of bubble (there may be exceptions I haven't thought of) but examples..
Finite bubble
Soap bubble, the energy required to create the film will be the same as the energy held by the excess pressure of the gas inside - (proof left to the reader)
Infinite bubble..
A point charge. Work out the energy of the field from infinity up to but excluding the point charge. The PROOF.. remove the charge and the field collapses back to zero. The point charge had exactly the same energy as the field it created.
IF Confused2's first bubble law is correct then it's a bit of a burden for a bubble theory because half the energy of whatever you are thinking about is going to zap straight into the bubble - the bubble becomes an intimate part of the problem.
Confused2's second law of bubbles will attempt to deal with quantised bubbles and may take some time to arrive ( ! )
Best wishes,
Confused2.
Hi confused2, TRoc and Gadfly,
That second movie was very interesting and quite obviously mostly "unexpected". These properties are what "real surfaces" and real bubbles have. I have watched it a few times and it is still fascinating.
Just an aside... I wrote a private paper about 5 years ago on traveling EM disturbances just like that one in the NASA diagram.
The Parker spiral
I can visualize that a new form of electromagnetic wave can be produced... at the time I called it gramophone radiation because it traced a similar radiation pattern to EM radiation but formed one single wavefront. This was to be produced by two oppositely statically charged spheres connected by a "bar" and "spun" at the center at a high angular frequency. These field disturbances "spread" at the speed of light but it is not "spawned" like propagating EM radiation as intact "Tori". The spiral connects every point in the space via transverse propagative fields. AM Disturbances at the source should "instantly" communicate to all other points in the total spiral... everywhere. This is unlike the Tori where the energy processes are confined to the "rings" of propagation of the photons by the speed of light and the field reversals.
The longer you wait the influence spreads and "fills" space out to the range of C*t... where t is the time after switch-on. As long as the system is "maintained" it may be possible to "signal" faster than the speed of light since the entire wave is only one simple wavefront. The catch is the effect dies off rapidly with distance since the dumbbells cannot travel faster than light. It may be possible to simulate super-luminal velocity by an EM "chaser arrangement" of energizing... a "festive" solution.. he he he!. . It would be interesting to reshape this "object" with negative refractive materials and concentrate it along a narrow beam to reduce spreading. Then you could set up instantaneous communication to other star systems.... as long as the transmitter remains "on". You would modulate the source "dumb bells" of opposite charges with an AM signal. I have some old diagrams if you would like to see them.
Cheers
That second movie was very interesting and quite obviously mostly "unexpected". These properties are what "real surfaces" and real bubbles have. I have watched it a few times and it is still fascinating.
Just an aside... I wrote a private paper about 5 years ago on traveling EM disturbances just like that one in the NASA diagram.
The Parker spiral
I can visualize that a new form of electromagnetic wave can be produced... at the time I called it gramophone radiation because it traced a similar radiation pattern to EM radiation but formed one single wavefront. This was to be produced by two oppositely statically charged spheres connected by a "bar" and "spun" at the center at a high angular frequency. These field disturbances "spread" at the speed of light but it is not "spawned" like propagating EM radiation as intact "Tori". The spiral connects every point in the space via transverse propagative fields. AM Disturbances at the source should "instantly" communicate to all other points in the total spiral... everywhere. This is unlike the Tori where the energy processes are confined to the "rings" of propagation of the photons by the speed of light and the field reversals.
The longer you wait the influence spreads and "fills" space out to the range of C*t... where t is the time after switch-on. As long as the system is "maintained" it may be possible to "signal" faster than the speed of light since the entire wave is only one simple wavefront. The catch is the effect dies off rapidly with distance since the dumbbells cannot travel faster than light. It may be possible to simulate super-luminal velocity by an EM "chaser arrangement" of energizing... a "festive" solution.. he he he!. . It would be interesting to reshape this "object" with negative refractive materials and concentrate it along a narrow beam to reduce spreading. Then you could set up instantaneous communication to other star systems.... as long as the transmitter remains "on". You would modulate the source "dumb bells" of opposite charges with an AM signal. I have some old diagrams if you would like to see them.
Cheers
GE and All,
I have watched both videos several times too! They are very interesting.
I've read a little on Parker Spirals, but had never seen a 3D diagram before. Having given up on my drawing ability, I turned to building models with thin copper wire & colored beads, or pipe cleaners. Please, when you get a chance, post your work on these forms.
"Coupling" them, or starting 2 of these shapes in the same (or harmonic distance) space, with a 90 degree turn between the start of the 2 cycles (acceleration phase), creates a helix (double) shaped "phase waveguide" that maintains a "point" (a dualistic enclosure of a 1/2 phase +E and 1/2 phase -M) moving forward, over a straight line (preferred direction).
By measuring these coupled waves at COMPLETE cycles, by the standard of 1 cps = 1 Hz, we only see ONE side of the mechanical process, ONE side of a duality: the complete circle illusion. By looking at this process a half phase at a time, a more Fundamental model takes shape. An acceleration phase, and a coast phase, maintaining a constant velocity. Two Vibrations, coupled at 90 deg., producing a consistent spectrum of 2 parts less than 1 octave. The 2 parts then play the role as "neutrals", they always fall in the same position, and in numerical relation to the initial state (the tonic). In the visible range of frequencies, they are Green and Magenta.
continued...
TRoc
I have watched both videos several times too! They are very interesting.
I've read a little on Parker Spirals, but had never seen a 3D diagram before. Having given up on my drawing ability, I turned to building models with thin copper wire & colored beads, or pipe cleaners. Please, when you get a chance, post your work on these forms.
"Coupling" them, or starting 2 of these shapes in the same (or harmonic distance) space, with a 90 degree turn between the start of the 2 cycles (acceleration phase), creates a helix (double) shaped "phase waveguide" that maintains a "point" (a dualistic enclosure of a 1/2 phase +E and 1/2 phase -M) moving forward, over a straight line (preferred direction).
By measuring these coupled waves at COMPLETE cycles, by the standard of 1 cps = 1 Hz, we only see ONE side of the mechanical process, ONE side of a duality: the complete circle illusion. By looking at this process a half phase at a time, a more Fundamental model takes shape. An acceleration phase, and a coast phase, maintaining a constant velocity. Two Vibrations, coupled at 90 deg., producing a consistent spectrum of 2 parts less than 1 octave. The 2 parts then play the role as "neutrals", they always fall in the same position, and in numerical relation to the initial state (the tonic). In the visible range of frequencies, they are Green and Magenta.
continued...
TRoc
continued:
In order to tackle the "nature of electricity and magnetism", one must tackle the pattern that allows them to combine. This pattern should make itself apparent in other ways. This pattern should be similar to having just ONE of the same form of waves, moving in 3D. This pattern DOES make itself apparent in ALL vibrations measured in Hz, even where we stop defining them as EM. The center point of this pattern lies at the octave of the square root of ©. The actual value, 17314.515..,
does not appear however, because of the imbalance of magnetic and electric force. This point is BETWEEN the duality: the point where the change from accelerate to coast takes place, the line that divides "Yellow" from "Cyan"; at the opposite point, where coast changes to accelerate, "Magenta" forms the bridge between "Violet" and "Red". This means that every Single "photon" has the same degrees of freedom, and based on the relation to either another photon, as in a stream, or to the source of the Vibration itself, the Electron, can then "collapse" into a state which we define as a measured resulting frequency. Any simple Electron to Electron resonance will occur at the same frequency, giving the illusion that the "photon" itself is traveling at that frequency. It should be apparent, that a single frequency has no mechanism with which to propel itself along; no "medium". Coupling this Fundamental Vibration with itself manifests an "imbalance" with which to self-interact. This Fundamental process is the tendency to regain balance through the cycle by cycle reduction of the DIFFERENCE in VIBRATION: The Beat Frequency. Any "collapse" of the current BF results in the MEASUREMENT, or Beat Sum. Vibration can only "end" from being "summed" by the introduction of another frequency, which "collapses" BOTH and cause a new one; or, for the initial vibrations themselves (any 2 independent vibrations), for the MEASURED space to no longer contain both of them.
This is why the "state" we define as Energy, moves around my Triangle representation of the BB Curve, at the outside edge. BF's of "complex" mixing can happen SIMULTANEOUSLY, and PERPENDICULAR to the "time" line. This is not accounted for in current theory. Measurements of the "end state" can only be represented by "probabilities". Measurements of the ENTIRE list of states will predict the outcome. This does not mean that ALL PATHS are taken, it is just a result of the "model" we call Math. Mathematically, all BF's are computed, but this not make the "wave center" change course: it still has one direction. At the collapse, the distance from this "center line" will mimic the wavelength (inverse/duality) of the BS.
I should not have to say any more, and yet, have also just described the "strange" results of Young's double slit experiment, and its' adjusted counterparts.
I will be back to give empirical evidence to support a "unified color theory", which stems from Unified Vibration. We have revisited the Black Body experiment, only to find that, in the most Scientific terms, it is NOT reproducible. I have explained the mathematical results of the "special" curve that the measured state produces. We need to revisit Newton's Prism experiment, and see what we can glean there. Then to a remodel of the photoelectric effect. If the "dualistic" hood is removed from the wave, Gravitational effects should be a short "hop" away.
TRoc
In order to tackle the "nature of electricity and magnetism", one must tackle the pattern that allows them to combine. This pattern should make itself apparent in other ways. This pattern should be similar to having just ONE of the same form of waves, moving in 3D. This pattern DOES make itself apparent in ALL vibrations measured in Hz, even where we stop defining them as EM. The center point of this pattern lies at the octave of the square root of ©. The actual value, 17314.515..,
does not appear however, because of the imbalance of magnetic and electric force. This point is BETWEEN the duality: the point where the change from accelerate to coast takes place, the line that divides "Yellow" from "Cyan"; at the opposite point, where coast changes to accelerate, "Magenta" forms the bridge between "Violet" and "Red". This means that every Single "photon" has the same degrees of freedom, and based on the relation to either another photon, as in a stream, or to the source of the Vibration itself, the Electron, can then "collapse" into a state which we define as a measured resulting frequency. Any simple Electron to Electron resonance will occur at the same frequency, giving the illusion that the "photon" itself is traveling at that frequency. It should be apparent, that a single frequency has no mechanism with which to propel itself along; no "medium". Coupling this Fundamental Vibration with itself manifests an "imbalance" with which to self-interact. This Fundamental process is the tendency to regain balance through the cycle by cycle reduction of the DIFFERENCE in VIBRATION: The Beat Frequency. Any "collapse" of the current BF results in the MEASUREMENT, or Beat Sum. Vibration can only "end" from being "summed" by the introduction of another frequency, which "collapses" BOTH and cause a new one; or, for the initial vibrations themselves (any 2 independent vibrations), for the MEASURED space to no longer contain both of them.
This is why the "state" we define as Energy, moves around my Triangle representation of the BB Curve, at the outside edge. BF's of "complex" mixing can happen SIMULTANEOUSLY, and PERPENDICULAR to the "time" line. This is not accounted for in current theory. Measurements of the "end state" can only be represented by "probabilities". Measurements of the ENTIRE list of states will predict the outcome. This does not mean that ALL PATHS are taken, it is just a result of the "model" we call Math. Mathematically, all BF's are computed, but this not make the "wave center" change course: it still has one direction. At the collapse, the distance from this "center line" will mimic the wavelength (inverse/duality) of the BS.
I should not have to say any more, and yet, have also just described the "strange" results of Young's double slit experiment, and its' adjusted counterparts.
I will be back to give empirical evidence to support a "unified color theory", which stems from Unified Vibration. We have revisited the Black Body experiment, only to find that, in the most Scientific terms, it is NOT reproducible. I have explained the mathematical results of the "special" curve that the measured state produces. We need to revisit Newton's Prism experiment, and see what we can glean there. Then to a remodel of the photoelectric effect. If the "dualistic" hood is removed from the wave, Gravitational effects should be a short "hop" away.
TRoc
If bubbles can be formed then some theory I've forgotten about predicts that they will form, possibly at a rate related to the probability of formation and energy gap etc. If the process is reversible then they will have a lifetime that would have to be looked into. Choose your bubble, work out the probability - if probability greater than zero then you have bubbles. Plausibility would do for the present. 
-c2.
-c2.
All,
I hope some of you are wondering why I am bothering with such laborious breakdown of the range of frequencies in the visible light that manifests as what we call "color". The answer is simple: if there is a pattern there, then the same pattern should exist for all frequencies. It is (not ironically) the only visible display of vibration that we have. Most importantly, the current theory, while explained well enough to fit the (designed) experiment, DOES NOT cover all of the visible phenomena that we see. Finally, this is relevant to this thread because "light" is an electro-magnetic wave. Whatever properties that colored light (visible frequencies) has, the rest of the spectrum should have as well. Taking that even a step further, one can find the same pattern for ALL measurements of vibration (frequency or wavelength).
The first scientific mention of the "colors" was from Newton, and his prism experiment. This matched what we see in a rainbow, and apparently that was enough to convince the world that "white" light (misnomer) contains all colors. For obvious reasons, what does not exist as color, is not always white. "Clear" light would be a MUCH better word to use, and would have avoided many of the problems with a theory of color. The biggest problem with the current, and long standing (300 yrs) color theory is that there is NO MATH to it. That is "blasphemous" to the scientific world. What is the frequency of "white"? There is none! How can the "mother" of all colors, each having a specific frequency (with the exception of magenta) not also have a frequency? Does white light vibrate? Then at what rate? It is that simple; and there is no answer. The same goes for "black", is black not a "color"? I do not want this topic to wander off into the realm of biology, or perception; it is not really about color, it is about EM waves.
Simply put, and staying within the topic of light (and not pigments), white light does not exist. Black (darkness) is the absence of light. Now back to Newton's prism experiment. It is incomplete; it is not "complementary".
His experiment goes like this: light of random frequencies is allowed to flow through a small hole in a wall of an otherwise dark room. At an unspecified distance, this beam of light is guided through a prism, refracted, and then travels to a wall, where it is reflected and then travels back to the "observer". This results in a "rainbow", containing Red-Orange-Yellow-Green-Cyan-Blue-Violet. Magenta is not there; this color is defined as an equal mix of red and violet.
In simplified form, this is the process: refract-reflect-measure (or observe, collapse, etc). The most basic, and logical change to this experiment is to reverse the order. Complementarity means it will produce the same results in reverse. If you experiment in this order, reflect-refract-measure, you do NOT get the same results. Green will never be seen in this experiment; and magenta, with careful coaxing, will show her face. Aside from these two colors, the only other "match" to the first experiment is this: R & Y will ALWAYS appear together, and C & V will ALWAYS appear together (as they do in a rainbow). Also gone from the picture is O and B . These colors are obviously tertiary to R/Y, and C/V, respectively.
Remembering that we are talking about EM waves, one must begin to question if these pairs of oscillating dualities are representative of each other. An electric "field" oscillates between + & - ; a magnetic field, between N & S. In "color", we have a wave oscillating between R & Y, and another between C & V.
How did I coax magenta into visibility? Most interestingly, by reflecting light off of a black line or spot on a white background, and then refracting it, and then measure/observe while the EM wave is in the NEAR field (polarization by reflection). This is absolutely the exact opposite of the first experiment: from the wall's "point of view" (frame of reference), the light is going through a white spot (hole of light) into a black background (dark room). The other interesting thing is that, as you increase the distance between the refraction/observation (leave the near field), you can watch magenta "split" into red and violet. This is essentially the re-coupling of the E and the M waves; the 90 deg geometry defeating the 90 deg "polarity" of an EM wave.
The rules that can be determined from these experiments (and others) is that red and violet will ALWAYS face "darkness", and yellow and cyan will ALWAYS face the "lightness". This is a new "polarity" in light. When Y & C are "squeezed" together, you get green; when V & R are brought together, magenta appears. Green and magenta can NEVER appear together, they exist only from opposing frames of reference. Cyan and red NEVER face each other, nor will violet and yellow.
When you extrapolate these "color" rules onto circular measuring, you get a CONSISTENT 90 deg. relationship for these "couple-able", polarized dualities. The very same rules that control the relationship between electric and magnetic fields (rate of vibration / frequencies).
Adding "math" (by frequency/wavelength) to the pattern, you will find that yellow is the Dominant of red, and violet is the Dominant of cyan. Of course we know, in terms of energy, that this is true. This pattern was first put forth by Pythagoras 2500 yrs ago; I am extending it by accuracy of our modern technology. Unfortunately, because of the lack of accurate data in current theory, I am only 99% finished with my own theory. I do not want to post it quite just yet.
Electro-magnetic wave "anomalies" in frequencies of the visible light range:
1. Science has not been able to determine the wavelength of magenta.
2. Black-body radiation NEVER turns green (while changing from yellow to cyan)
3. R-B-G can NOT produce the color Violet; only wavelengths <410nm can.
4. In the near field, black REFLECTS magenta.
5. Green light (light through green glass) casts a MAGENTA shadow!
6. No accurate (monochromatic) color mixing experiment has EVER been done.
7. Filters DO NOT represent one color, they allow 1/3 of the "octave" (or spectrum) through; therefore any 3 filtered colors will complete the "circle" (clear light).
8. Reversing the "prism" experiment reverses the spectrum, and eliminates green. (Try looking at a shadow cast on the bottom of a pool of a rope floating on water; you will see Y-R>dark line/shadow<V-C.)
9. In causal, or reductive reasoning, green will always appear where the light IS, and magenta will always be where the light WAS. Therefore, if a EM wave is going away from you, you will see red; if it is coming towards you, you will see blue. (Doppler)
more later...
TRoc
I hope some of you are wondering why I am bothering with such laborious breakdown of the range of frequencies in the visible light that manifests as what we call "color". The answer is simple: if there is a pattern there, then the same pattern should exist for all frequencies. It is (not ironically) the only visible display of vibration that we have. Most importantly, the current theory, while explained well enough to fit the (designed) experiment, DOES NOT cover all of the visible phenomena that we see. Finally, this is relevant to this thread because "light" is an electro-magnetic wave. Whatever properties that colored light (visible frequencies) has, the rest of the spectrum should have as well. Taking that even a step further, one can find the same pattern for ALL measurements of vibration (frequency or wavelength).
The first scientific mention of the "colors" was from Newton, and his prism experiment. This matched what we see in a rainbow, and apparently that was enough to convince the world that "white" light (misnomer) contains all colors. For obvious reasons, what does not exist as color, is not always white. "Clear" light would be a MUCH better word to use, and would have avoided many of the problems with a theory of color. The biggest problem with the current, and long standing (300 yrs) color theory is that there is NO MATH to it. That is "blasphemous" to the scientific world. What is the frequency of "white"? There is none! How can the "mother" of all colors, each having a specific frequency (with the exception of magenta) not also have a frequency? Does white light vibrate? Then at what rate? It is that simple; and there is no answer. The same goes for "black", is black not a "color"? I do not want this topic to wander off into the realm of biology, or perception; it is not really about color, it is about EM waves.
Simply put, and staying within the topic of light (and not pigments), white light does not exist. Black (darkness) is the absence of light. Now back to Newton's prism experiment. It is incomplete; it is not "complementary".
His experiment goes like this: light of random frequencies is allowed to flow through a small hole in a wall of an otherwise dark room. At an unspecified distance, this beam of light is guided through a prism, refracted, and then travels to a wall, where it is reflected and then travels back to the "observer". This results in a "rainbow", containing Red-Orange-Yellow-Green-Cyan-Blue-Violet. Magenta is not there; this color is defined as an equal mix of red and violet.
In simplified form, this is the process: refract-reflect-measure (or observe, collapse, etc). The most basic, and logical change to this experiment is to reverse the order. Complementarity means it will produce the same results in reverse. If you experiment in this order, reflect-refract-measure, you do NOT get the same results. Green will never be seen in this experiment; and magenta, with careful coaxing, will show her face. Aside from these two colors, the only other "match" to the first experiment is this: R & Y will ALWAYS appear together, and C & V will ALWAYS appear together (as they do in a rainbow). Also gone from the picture is O and B . These colors are obviously tertiary to R/Y, and C/V, respectively.
Remembering that we are talking about EM waves, one must begin to question if these pairs of oscillating dualities are representative of each other. An electric "field" oscillates between + & - ; a magnetic field, between N & S. In "color", we have a wave oscillating between R & Y, and another between C & V.
How did I coax magenta into visibility? Most interestingly, by reflecting light off of a black line or spot on a white background, and then refracting it, and then measure/observe while the EM wave is in the NEAR field (polarization by reflection). This is absolutely the exact opposite of the first experiment: from the wall's "point of view" (frame of reference), the light is going through a white spot (hole of light) into a black background (dark room). The other interesting thing is that, as you increase the distance between the refraction/observation (leave the near field), you can watch magenta "split" into red and violet. This is essentially the re-coupling of the E and the M waves; the 90 deg geometry defeating the 90 deg "polarity" of an EM wave.
The rules that can be determined from these experiments (and others) is that red and violet will ALWAYS face "darkness", and yellow and cyan will ALWAYS face the "lightness". This is a new "polarity" in light. When Y & C are "squeezed" together, you get green; when V & R are brought together, magenta appears. Green and magenta can NEVER appear together, they exist only from opposing frames of reference. Cyan and red NEVER face each other, nor will violet and yellow.
When you extrapolate these "color" rules onto circular measuring, you get a CONSISTENT 90 deg. relationship for these "couple-able", polarized dualities. The very same rules that control the relationship between electric and magnetic fields (rate of vibration / frequencies).
Adding "math" (by frequency/wavelength) to the pattern, you will find that yellow is the Dominant of red, and violet is the Dominant of cyan. Of course we know, in terms of energy, that this is true. This pattern was first put forth by Pythagoras 2500 yrs ago; I am extending it by accuracy of our modern technology. Unfortunately, because of the lack of accurate data in current theory, I am only 99% finished with my own theory. I do not want to post it quite just yet.
Electro-magnetic wave "anomalies" in frequencies of the visible light range:
1. Science has not been able to determine the wavelength of magenta.
2. Black-body radiation NEVER turns green (while changing from yellow to cyan)
3. R-B-G can NOT produce the color Violet; only wavelengths <410nm can.
4. In the near field, black REFLECTS magenta.
5. Green light (light through green glass) casts a MAGENTA shadow!
6. No accurate (monochromatic) color mixing experiment has EVER been done.
7. Filters DO NOT represent one color, they allow 1/3 of the "octave" (or spectrum) through; therefore any 3 filtered colors will complete the "circle" (clear light).
8. Reversing the "prism" experiment reverses the spectrum, and eliminates green. (Try looking at a shadow cast on the bottom of a pool of a rope floating on water; you will see Y-R>dark line/shadow<V-C.)
9. In causal, or reductive reasoning, green will always appear where the light IS, and magenta will always be where the light WAS. Therefore, if a EM wave is going away from you, you will see red; if it is coming towards you, you will see blue. (Doppler)
more later...
TRoc
Hi Troc - sorry still not drawn - you seem to be looking at the sensitivity of the human eye - lizards would see it differently but still share the same planet with us quite happily, at least I hope they are happy.
Good_Elf - something has been bubbling away at the top of the planet (
) for some time - I may be the only one trying to seal bubbles from the inside - I see other people trying to seal the universe from the inside and I ask - why so? Bit of a flyer here but how about nice normal spacetime packages up the bubbles - quantisation happens because spacetime simply permits nothing else?
de Broglie
lambda(wavelength) = h / p = h / (mv) * sqrt(1- sqr(v/c))
Point is this is mass and it's got planck's constant in it - not EM at all.
E = h * f <<<< Planck again. Mass in bendy space does it, photons when they radiate do it. let's do it, let's quantize space. (it had to scan a liitle bit)
Best wishes, Confused2.
Good_Elf - something has been bubbling away at the top of the planet (
) for some time - I may be the only one trying to seal bubbles from the inside - I see other people trying to seal the universe from the inside and I ask - why so? Bit of a flyer here but how about nice normal spacetime packages up the bubbles - quantisation happens because spacetime simply permits nothing else? de Broglie
lambda(wavelength) = h / p = h / (mv) * sqrt(1- sqr(v/c))
Point is this is mass and it's got planck's constant in it - not EM at all.
E = h * f <<<< Planck again. Mass in bendy space does it, photons when they radiate do it. let's do it, let's quantize space. (it had to scan a liitle bit)
Best wishes, Confused2.
Hi Confused2,
The energy of inflation of the universe into "space-time" (3D + T) is "incredible". Though "disputable" the amount of energy stored through inflation in an empty glass in outer space is equivalent to an inscribed sphere, radius - the radius of the Earth's orbit filled with water then converted to pure energy. This makes space-time very "stiff" and bubbles are out of the question (usually). On the "Up" side... It happily allows the Universe to be quite large "on the inside". "Big Bubbles... no trouble". He he he!
Practically speaking we are making "bubbles" all the time in our Universe (as you have noted) but not "in" space-time but "on" space-time. As you said... "bendy space". This (IMHO according to my interpretation) is in the "Uberspace" which is the six vestigial dimensions "connected" at every point in space-time but on a greater Riemann Manifold of at least 10 and more dimensions. Six of them are indeed "accessible" easily without too much of an energy penalty... even single photons can "blow bubbles " there. These dimensions are (from our perspective) invisible (the realm of the quantum and tends to hide events in there from our experience... intimately connected with h) but connected to our space-time. They are "empty" now due to "symmetry breaking" long ago. Nowadays they now contain only "unbroken symmetry" ... the quanta. I have said a little more in this "controversial" thread...
After Death... Good Elf
Read around it a little... Relativity is Electromagnetism compatible and "already unified" and it is an expression of symmetry (rotation) with EM. You have been looking at that thread on de Broglie and good for you. Note that mass enters as a relation between the phase and group velocity of a particle via an "internal process". Very understated but dead right.
Cheers
The energy of inflation of the universe into "space-time" (3D + T) is "incredible". Though "disputable" the amount of energy stored through inflation in an empty glass in outer space is equivalent to an inscribed sphere, radius - the radius of the Earth's orbit filled with water then converted to pure energy. This makes space-time very "stiff" and bubbles are out of the question (usually). On the "Up" side... It happily allows the Universe to be quite large "on the inside". "Big Bubbles... no trouble". He he he!
Practically speaking we are making "bubbles" all the time in our Universe (as you have noted) but not "in" space-time but "on" space-time. As you said... "bendy space". This (IMHO according to my interpretation) is in the "Uberspace" which is the six vestigial dimensions "connected" at every point in space-time but on a greater Riemann Manifold of at least 10 and more dimensions. Six of them are indeed "accessible" easily without too much of an energy penalty... even single photons can "blow bubbles " there. These dimensions are (from our perspective) invisible (the realm of the quantum and tends to hide events in there from our experience... intimately connected with h) but connected to our space-time. They are "empty" now due to "symmetry breaking" long ago. Nowadays they now contain only "unbroken symmetry" ... the quanta. I have said a little more in this "controversial" thread...
After Death... Good Elf
Read around it a little... Relativity is Electromagnetism compatible and "already unified" and it is an expression of symmetry (rotation) with EM. You have been looking at that thread on de Broglie and good for you. Note that mass enters as a relation between the phase and group velocity of a particle via an "internal process". Very understated but dead right.
Cheers
Hi!
Here is something that might help on:
These people are doing experiments that perhaps they could do for you that might shed some light.
A Scanned Perturbation Technique For Imaging Electromagnetic Standing Wave Patterns of Microwave Cavities.
jal
Here is something that might help on:
QUOTE
Green will never be seen in this experiment; and magenta, with careful coaxing, will show her face.
These people are doing experiments that perhaps they could do for you that might shed some light.
A Scanned Perturbation Technique For Imaging Electromagnetic Standing Wave Patterns of Microwave Cavities.
jal
Hi Jal and TRoc, Confused2, gadfly, Montec
I am sure TRoc will have his own reply but I found your paper and associated images fascinating and needed to say something.
I found your reference very similar in content to the Circuit QED experiments. Specially developed "atoms" are "constructed" to trap photons without recourse to actual bending dimensions at all. This is the first step in developing higher dimensional engineering. The synthetic atoms emit and absorb the same photon over and over into its own structure. I was particularly taken by your 8th and 9th Gif Image in that article you posted. We are seeing a Schrodinger solution in a cavity....
Look at this reference where I bring a few threads together... connect with the the tread "Light's Clock" by Qwerty in the post below...
Particles have mass, HOW?, Higgs or ? - Good Elf (1)
Then look into the link to Circuit QED here...
Particles have mass, HOW?, Higgs or ? - Good Elf (2)
I think that I will "post" that 8th Image to show the amazing picture that is recorded there from a real cavity...
Amazing picture of a Schrodinger Waveguide Cavity recorded by an actual probe
This process lacks the natural trapping mechanism inside the electronic structure of "atoms". You can connect the dots with my references above and the links I have there. Cavities in higher dimensions "exist" around the nuclei of atoms but in a higher dimensional space. These cavities trap photons and electrons "equally". Once trapped these particles no longer "feel" the influence of the charged nucleus. They are simply affected by the higher geometry they are forced to travel in. The equations are unaltered for this "interpretation" so the heresy is limited to a conceptual one.
Your images in that paper indicate that there are "real" cavities as well as the wall of the waveguide. Obviously there are no "nuclear" sources in the waveguide. I would like to see other interesting examples of dimensional bubbles "attached" to some "synthetic nucleus". Thought would need to be given to the way the charge is "suspended". Clearly to test relativity and its influence on such a nuclear system this experiment would need to be done in "microgravity" to see if the system indeed curves "Uberspace". Just a point everyone... how do you all think that the nucleus of atoms are 'suspended" centrally inside a freely floating atom and its associated shell? Any "absolute" clues to this process? Is a simple static charge a sufficient analog of the charge in nucleii to "fool" the Universe into thinking it is an atom of some kind? What value would the charge need to be... scaled to be a central point but providing the same EM gradients in relative magnitude and charge gradient.
Cheers
I am sure TRoc will have his own reply but I found your paper and associated images fascinating and needed to say something.
I found your reference very similar in content to the Circuit QED experiments. Specially developed "atoms" are "constructed" to trap photons without recourse to actual bending dimensions at all. This is the first step in developing higher dimensional engineering. The synthetic atoms emit and absorb the same photon over and over into its own structure. I was particularly taken by your 8th and 9th Gif Image in that article you posted. We are seeing a Schrodinger solution in a cavity....
Look at this reference where I bring a few threads together... connect with the the tread "Light's Clock" by Qwerty in the post below...
Particles have mass, HOW?, Higgs or ? - Good Elf (1)
Then look into the link to Circuit QED here...
Particles have mass, HOW?, Higgs or ? - Good Elf (2)
I think that I will "post" that 8th Image to show the amazing picture that is recorded there from a real cavity...
Amazing picture of a Schrodinger Waveguide Cavity recorded by an actual probe
This process lacks the natural trapping mechanism inside the electronic structure of "atoms". You can connect the dots with my references above and the links I have there. Cavities in higher dimensions "exist" around the nuclei of atoms but in a higher dimensional space. These cavities trap photons and electrons "equally". Once trapped these particles no longer "feel" the influence of the charged nucleus. They are simply affected by the higher geometry they are forced to travel in. The equations are unaltered for this "interpretation" so the heresy is limited to a conceptual one.
Your images in that paper indicate that there are "real" cavities as well as the wall of the waveguide. Obviously there are no "nuclear" sources in the waveguide. I would like to see other interesting examples of dimensional bubbles "attached" to some "synthetic nucleus". Thought would need to be given to the way the charge is "suspended". Clearly to test relativity and its influence on such a nuclear system this experiment would need to be done in "microgravity" to see if the system indeed curves "Uberspace". Just a point everyone... how do you all think that the nucleus of atoms are 'suspended" centrally inside a freely floating atom and its associated shell? Any "absolute" clues to this process? Is a simple static charge a sufficient analog of the charge in nucleii to "fool" the Universe into thinking it is an atom of some kind? What value would the charge need to be... scaled to be a central point but providing the same EM gradients in relative magnitude and charge gradient.
Cheers
Greetings!
jal, thanks for the link to the paper, it is an interesting experiment. It isn't quite in line with the quote you include of mine. An experiment with Parametric Down Conversion is probably closer. It could lend support to the theory (Planck) that there is a zeropoint field that is not being accounted for in these types of experiments. When I said "The other interesting thing is that, as you increase the distance between the refraction/observation (leave the near field), you can watch magenta "split" into red and violet. This is essentially the re-coupling of the E and the M waves; the 90 deg geometry defeating the 90 deg "polarity" of an EM wave." it can be further supported by a semi-recent paper on "Parametric UP Conversion, and a "satellite" rainbow that is produced. [The zeropoint field — no longer a ghost.]
confused2, when I said "I do not want this topic to wander off into the realm of biology, or perception; it is not really about color, it is about EM waves." , I did so with clarity. One can never reduce Physics to something other than our perception. Can you name any major, foundational theory that wasn't ultimately "collapsed" into the human eye??? Science is the reporting of what we see, and predicting what we will see. When you get to lizards, or whatever, you are being specific as to the "eye".
I realize that when I say "red", for example, some ambiguity may arise. This is not my fault; Science has yet to define specific frequencies/wavelengths to the spectrum. THEY leave it to our perceptive agreement; that is tragic in my opinion. When I say "red", or whatever, you can BET that I am talking about a specific frequency.
Anyone with helpful input as to explaining the "anomalies" that I listed would be greatly appreciated.
Recall the color experiment done in the space station by NASA; away from the "inductive" fields, and atmospheric limitations of the Earth, green was the result of multiple color mixing. I would LOVE (and predict) to see a simultaneous "capture" of the entangled opposing view of the thin film he was holding up for the cameras... I'll bet it would appear magenta to us.
Good Elf, can we revisit to the bubble/em connection, specifically, the equations from way back on page one?
"Laplace's Equation" for a spherical bubble and is:
σ = PR/2
where:
σ = surface tension
P = internal pressure
R = radius of bubble
The surface tension is a measure of the energy stored in the bubble. We see that it is proportional to the internal pressure P and R, the bubble radius. The surface area of the bubble is
A = 4piR
Bubbles can be made to resonate and the frequency of resonance is given by this equation...
here
f is the frequency and R is the radius. we see the frequency of oscillation of the bubble is proportional to 1/R smaller bubbles have higher resonant frequencies.
For a de Broglie particle lets assume that the circumference of the bubble is 2R equals n so we have...
f 1/R =2/n
constant = f which is an expression of a velocity.
and
here
You will probably have to fill in the equations, this system won't even copy an equation from a previous page.
TRoc
jal, thanks for the link to the paper, it is an interesting experiment. It isn't quite in line with the quote you include of mine. An experiment with Parametric Down Conversion is probably closer. It could lend support to the theory (Planck) that there is a zeropoint field that is not being accounted for in these types of experiments. When I said "The other interesting thing is that, as you increase the distance between the refraction/observation (leave the near field), you can watch magenta "split" into red and violet. This is essentially the re-coupling of the E and the M waves; the 90 deg geometry defeating the 90 deg "polarity" of an EM wave." it can be further supported by a semi-recent paper on "Parametric UP Conversion, and a "satellite" rainbow that is produced. [The zeropoint field — no longer a ghost.]
confused2, when I said "I do not want this topic to wander off into the realm of biology, or perception; it is not really about color, it is about EM waves." , I did so with clarity. One can never reduce Physics to something other than our perception. Can you name any major, foundational theory that wasn't ultimately "collapsed" into the human eye??? Science is the reporting of what we see, and predicting what we will see. When you get to lizards, or whatever, you are being specific as to the "eye".
I realize that when I say "red", for example, some ambiguity may arise. This is not my fault; Science has yet to define specific frequencies/wavelengths to the spectrum. THEY leave it to our perceptive agreement; that is tragic in my opinion. When I say "red", or whatever, you can BET that I am talking about a specific frequency.
Anyone with helpful input as to explaining the "anomalies" that I listed would be greatly appreciated.
Recall the color experiment done in the space station by NASA; away from the "inductive" fields, and atmospheric limitations of the Earth, green was the result of multiple color mixing. I would LOVE (and predict) to see a simultaneous "capture" of the entangled opposing view of the thin film he was holding up for the cameras... I'll bet it would appear magenta to us.
Good Elf, can we revisit to the bubble/em connection, specifically, the equations from way back on page one?
"Laplace's Equation" for a spherical bubble and is:
σ = PR/2
where:
σ = surface tension
P = internal pressure
R = radius of bubble
The surface tension is a measure of the energy stored in the bubble. We see that it is proportional to the internal pressure P and R, the bubble radius. The surface area of the bubble is
A = 4piR
Bubbles can be made to resonate and the frequency of resonance is given by this equation...
here
f is the frequency and R is the radius. we see the frequency of oscillation of the bubble is proportional to 1/R smaller bubbles have higher resonant frequencies.
For a de Broglie particle lets assume that the circumference of the bubble is 2R equals n so we have...
f 1/R =2/n
constant = f which is an expression of a velocity.
and
here
You will probably have to fill in the equations, this system won't even copy an equation from a previous page.
TRoc
Hi!
TRoc, the acticle, [The zeropoint field — no longer a ghost.]
support what you have said... what I was implying/trying to say was ... perhaps by combining the two experiments the missing "color" could be seen to be missing .
I'll now shut up, listen and learn.
jal
TRoc, the acticle, [The zeropoint field — no longer a ghost.]
support what you have said... what I was implying/trying to say was ... perhaps by combining the two experiments the missing "color" could be seen to be missing .
I'll now shut up, listen and learn.
jal
Hi TRoc, jal & Good_Elf (Montec too?),
Jal - useful link - thanks.
TRoc - OK, sorry again, I have to keep trying. I am genuinely colour blind which might explain why it means less to me than some others. I do agree that once you cease to observe (anything) you start to lose the plot.
Good_Elf -
Stephen Hawking (book ? ) tries to suggest (I think) that (if the universe were reversible) the sum total of 'everything' would be zero - maybe a throwaway line but even so - maybe you don't have to pay for the inflation because you're (effectively) only borrowing it. I don't quite follow your 'stiff' spacetime result - one point being that we (my assumption) are blowing bubbles in already inflated space - we don't have to blow 'em from scratch - I agree that would be a challenge.
Anything 'in' space is automatically relativity compatible - anything 'on' space would seem to duplicate the existing unification problems - hence my enthusiasm for an 'in' solution - it doesn't have to be good - just plausible will do for now.
Note that mass enters as a relation between the phase and group velocity of a particle via an "internal process". Very understated but dead right.
I've posted this elsewhere.. but .. I maintain that the phase and group velocity are purely artifacts of the maths chosen to analyse the 'mass' and have no absolutely no physical significance. It may give the right answer to the 'right' question but QM (eg electron mass) is not the right question for it, I suggest the problem lies with the maths not the mass.
I suspect String and Elf theory are looking for tight (perfect) coupling between QM and relativity - I'm looking at 'loose' coupling - where spacetime is totally uncritical of anything that is properly wrapped and may also take part in the wrapping process. Very Xmassy.
I've posted this elsewhere.. but .. I maintain that the phase and group velocity are purely artifacts of the maths chosen to analyse the 'mass' and have no absolutely no physical significance. It may give the right answer to the 'right' question but QM (eg electron mass) is not the right question for it, I suggest the problem lies with the maths not the mass.
I suspect String and Elf theory are looking for tight (perfect) coupling between QM and relativity - I'm looking at 'loose' coupling - where spacetime is totally uncritical of anything that is properly wrapped and may also take part in the wrapping process. Very Xmassy.
Good_Elf..
how do you all think that the nucleus of atoms are 'suspended" centrally inside a freely floating atom and its associated shell? Any "absolute" clues to this process? Is a simple static charge a sufficient analog of the charge in nucleii to "fool" the Universe into thinking it is an atom of some kind? What value would the charge need to be... scaled to be a central point but providing the same EM gradients in relative magnitude and charge gradient.
This is intended as a provoker..
Taking hydrogen .. Gauss's Law suggests a charge acts from it's centre however big it is so that takes care of the nucleus - I'd go for the probability of the electron being 'anywhere' around the nucleus is sufficient to cover up the +ve charge with -ve charge. I suspect hydrogen does have unusually bald spots at the top and bottom.. (hence hydrogen bonds?). I've a nasty feeling I've seen that the electron does quantum swoops right into the nucleus in some atoms..???
Best wishes, C2.
Jal - useful link - thanks.
TRoc - OK, sorry again, I have to keep trying. I am genuinely colour blind which might explain why it means less to me than some others. I do agree that once you cease to observe (anything) you start to lose the plot.
Good_Elf -
Stephen Hawking (book ? ) tries to suggest (I think) that (if the universe were reversible) the sum total of 'everything' would be zero - maybe a throwaway line but even so - maybe you don't have to pay for the inflation because you're (effectively) only borrowing it. I don't quite follow your 'stiff' spacetime result - one point being that we (my assumption) are blowing bubbles in already inflated space - we don't have to blow 'em from scratch - I agree that would be a challenge.
Anything 'in' space is automatically relativity compatible - anything 'on' space would seem to duplicate the existing unification problems - hence my enthusiasm for an 'in' solution - it doesn't have to be good - just plausible will do for now.
QUOTE
Note that mass enters as a relation between the phase and group velocity of a particle via an "internal process". Very understated but dead right.
I've posted this elsewhere.. but .. I maintain that the phase and group velocity are purely artifacts of the maths chosen to analyse the 'mass' and have no absolutely no physical significance. It may give the right answer to the 'right' question but QM (eg electron mass) is not the right question for it, I suggest the problem lies with the maths not the mass.
I suspect String and Elf theory are looking for tight (perfect) coupling between QM and relativity - I'm looking at 'loose' coupling - where spacetime is totally uncritical of anything that is properly wrapped and may also take part in the wrapping process. Very Xmassy.
QUOTE (->
| QUOTE |
Note that mass enters as a relation between the phase and group velocity of a particle via an "internal process". Very understated but dead right. |
I've posted this elsewhere.. but .. I maintain that the phase and group velocity are purely artifacts of the maths chosen to analyse the 'mass' and have no absolutely no physical significance. It may give the right answer to the 'right' question but QM (eg electron mass) is not the right question for it, I suggest the problem lies with the maths not the mass.
I suspect String and Elf theory are looking for tight (perfect) coupling between QM and relativity - I'm looking at 'loose' coupling - where spacetime is totally uncritical of anything that is properly wrapped and may also take part in the wrapping process. Very Xmassy.
Good_Elf..
how do you all think that the nucleus of atoms are 'suspended" centrally inside a freely floating atom and its associated shell? Any "absolute" clues to this process? Is a simple static charge a sufficient analog of the charge in nucleii to "fool" the Universe into thinking it is an atom of some kind? What value would the charge need to be... scaled to be a central point but providing the same EM gradients in relative magnitude and charge gradient.
This is intended as a provoker..
Taking hydrogen .. Gauss's Law suggests a charge acts from it's centre however big it is so that takes care of the nucleus - I'd go for the probability of the electron being 'anywhere' around the nucleus is sufficient to cover up the +ve charge with -ve charge. I suspect hydrogen does have unusually bald spots at the top and bottom.. (hence hydrogen bonds?). I've a nasty feeling I've seen that the electron does quantum swoops right into the nucleus in some atoms..???
Best wishes, C2.
Hi confused2,
Last point... gauss's law says that the "attraction" of the charge is due to only the "inscribed sphere" so for any uniformly charged sphere the transport of a test charge toward the center... the repulsion force decreases to zero at the center since the charge is all "outside" the test charge now. Similar to the principle of a van de graff generator where the sphere is hollow the charge resides on the outside and there is no effective charge inside. I have read in a lot of learned texts to the contrary and it is a load of manure.
If this is the case then the (for the sake of simplicity) the spherical electron cloud around the nucleus is uniformly distributed. The nucleus is an "opposite point charge" at the center surrounded by "equal charges" on opposite sides "everywhere". It is neither attracted nor repelled by the "symmetric" cloud. Yet according to the idea that there is attraction between the positive nucleus and the negative electron cloud, the electrons should be "sucked" into the nucleus. Force or no force? Probability density or a slow moving individual charges?... or neither?
Are those alarm bells ringing? Or tinnitus?
Last point... gauss's law says that the "attraction" of the charge is due to only the "inscribed sphere" so for any uniformly charged sphere the transport of a test charge toward the center... the repulsion force decreases to zero at the center since the charge is all "outside" the test charge now. Similar to the principle of a van de graff generator where the sphere is hollow the charge resides on the outside and there is no effective charge inside. I have read in a lot of learned texts to the contrary and it is a load of manure.
If this is the case then the (for the sake of simplicity) the spherical electron cloud around the nucleus is uniformly distributed. The nucleus is an "opposite point charge" at the center surrounded by "equal charges" on opposite sides "everywhere". It is neither attracted nor repelled by the "symmetric" cloud. Yet according to the idea that there is attraction between the positive nucleus and the negative electron cloud, the electrons should be "sucked" into the nucleus. Force or no force? Probability density or a slow moving individual charges?... or neither?
Are those alarm bells ringing? Or tinnitus?
Unnn... thats me. 
That point about "tension". Think of inflating an otherwise ordinary indestructible balloon. Blow it up until it has the size of our Universe now see if you can "pinch it". Check out how easy it is to deform an un-inflated balloon.
Phase and group velocity are real and are both real quantities not "imaginary" as you may think. Take a flashlight/laser pointer and aim it at one side of the moon and then immediately "flick" point to the opposite limb of the moon... the light spot on the surface of the moon can move faster than the "group velocity" of the speed of light. That is the "phase velocity". Everyday concept.
Cheers
That point about "tension". Think of inflating an otherwise ordinary indestructible balloon. Blow it up until it has the size of our Universe now see if you can "pinch it". Check out how easy it is to deform an un-inflated balloon.
Phase and group velocity are real and are both real quantities not "imaginary" as you may think. Take a flashlight/laser pointer and aim it at one side of the moon and then immediately "flick" point to the opposite limb of the moon... the light spot on the surface of the moon can move faster than the "group velocity" of the speed of light. That is the "phase velocity". Everyday concept.
Cheers
GE,
Does the Laplace equation work regardless of the medium that the bubble is in?
TRoc
Does the Laplace equation work regardless of the medium that the bubble is in?
TRoc
Hello Guest,
It is neither attracted nor repelled by the "symmetric" cloud. Yet according to the idea that there is attraction between the positive nucleus and the negative electron cloud, the electrons should be "sucked" into the nucleus. Force or no force? Probability density or a slow moving individual charges?... or neither?
Congratulations Guest - you've just discovered quantum mechanics ! Wiki links out so try
http://science.howstuffworks.com/atom7.htm - the whole site looks pretty good.
Best wishes, C2 .
QUOTE
It is neither attracted nor repelled by the "symmetric" cloud. Yet according to the idea that there is attraction between the positive nucleus and the negative electron cloud, the electrons should be "sucked" into the nucleus. Force or no force? Probability density or a slow moving individual charges?... or neither?
Congratulations Guest - you've just discovered quantum mechanics
! Wiki links out so try http://science.howstuffworks.com/atom7.htm - the whole site looks pretty good.
Best wishes, C2
.
Hello Good_Elf, Sorry I must have missed your post. Tension and origin of tension - I'm only suggesting a "don't care" zone rather than a full blown bubble - it doesn't work but it's ongoing. Phase and group - my efforts are made with some integrity - I do not wilfully seek to mislead. Best wishes, C2.
Hi confused2 and TRoc,
Confused2.... nobody has the answers to all this so we are simply pioneers in this operational way of thinking. You and me both have been warned off by several generations of "respectable" Physicists that such thinking is not to be pursued... eh!
TRoc... Gauss's Law or Laplace's Equation works for "sources" such as "electronic charges" or "mass" but propagating photons have neither mass nor charge. There is a kind of exception to the rule here. They spread "geometrically" into a different space.
Came across this pretty picture of a sodium atom... had to put it in...
Here the "orbitals" are symmetric and exhibit "charges" and "mass" of trapped electrons. Photons can also be trapped as well. The nucleus is obviously in the center... suspended apparently by "null" forces being inside a Faraday cage of surrounding charge??? Does the nucleus see any charge in this state at all? Yes this is Quantum Mechanics and it relates to de Broglie and the wavelength of particles.
Head hurts... something here... what it is I don't know. Related to this...
Particle-Wave duality
Confused2.... nobody has the answers to all this so we are simply pioneers in this operational way of thinking. You and me both have been warned off by several generations of "respectable" Physicists that such thinking is not to be pursued... eh!
TRoc... Gauss's Law or Laplace's Equation works for "sources" such as "electronic charges" or "mass" but propagating photons have neither mass nor charge. There is a kind of exception to the rule here. They spread "geometrically" into a different space.
Came across this pretty picture of a sodium atom... had to put it in...
Here the "orbitals" are symmetric and exhibit "charges" and "mass" of trapped electrons. Photons can also be trapped as well. The nucleus is obviously in the center... suspended apparently by "null" forces being inside a Faraday cage of surrounding charge??? Does the nucleus see any charge in this state at all? Yes this is Quantum Mechanics and it relates to de Broglie and the wavelength of particles.
Head hurts... something here... what it is I don't know. Related to this...
Particle-Wave duality
GE,
My point for asking about "where" Laplace is appropriate stems from this:
What is the relationship between surface tension and internal pressure of nucleation (bubbles) and the pressure of the medium that it is in?
Another question for you:
Do you think waves travel as bubbles, or are just measured with them (pi relations)?
TRoc
My point for asking about "where" Laplace is appropriate stems from this:
What is the relationship between surface tension and internal pressure of nucleation (bubbles) and the pressure of the medium that it is in?
Another question for you:
Do you think waves travel as bubbles, or are just measured with them (pi relations)?
TRoc
Hi TRoc,
QUOTE (TRoc Posted on Dec 28 2005+ 03:12 PM)
My point for asking about "where" Laplace is appropriate stems from this:
What is the relationship between surface tension and internal pressure of nucleation (bubbles) and the pressure of the medium that it is in?
Another question for you:
Do you think waves travel as bubbles, or are just measured with them (pi relations)?
Firstly TRoc, If I knew I probably would never have started this thread. It is thanks to you (and a couple of others) that I am able to keep some kind of "focus" on the topic. "Obviously" Laplace does have a lot to do with the problem of "bubbles".
Wikipedia: Laplace's equation
The traveling of waves as a problem for bubbles is difficult but obviously the electromagnetic expanding wavefront is a kind of expanding "bubble". The problem with photons as "branes" is that we are dealing with the light cone. Using the light cone as a frame of reference is a kind of "vehicle" to see things in the frame of the photon. Mathematicians would "immediately" convert this to light cone coordinates because this is "instinctive" to them.
Please look at this image which I consider the most accurate of the visualizations of the electric field in the Fresnel zone and near (evanescent) field of the dipole radiator. This is a section in the plane of the dipole. As the photon "bubble" is being created there is still a "dynamic" element about it but as it moves away from the near field and "pinches off"(electric field lines passing through zero)... launched into "free space" the pancakes retain the wavelength but become flattened and spread on the edge of its light cone. This is only a light cone distortion of this "otherwise" spherical bubble of the photon (actually many of these photons occupy this "template" all in phase and "marching" to the same drummer). In that "imaginary" frame the photon can be considered as a sphere whose entire surface topologically lies on a light cone with a "half twist" in the electric field... Full twist over an entire wavelength since a wavelength is actually two of those bubbles being launched (one with a positive excursion at the center and the next with a negative excursion at the center... repeat unit is two).. This has the same internal symmetry as the electron which is a "stationary particle" with mass. Notice that the bubble symmetry is "broken" because of our external view of the photon bubbles as "pancakes". Notice that internally the photon's light cone symmetry is not broken. The symmetry between these two distinct views is the symmetry of "Special Relativity" and thus it is no wonder that Electromagnetism is already Unified. When the photon reaches its final destination it will probably mostly undergo the reverse process to this "photon emission" as a symmetric "photon bubble" no longer on the surface of the light cone and interacting with a dipole absorber.
There are two aspects. The individual "corpuscles" of the particles being investigated can propagate "en masse" as a scatter gun inverse law spreading, each "corpuscle" being "on its own". Alternatively each individual "corpuscle" (on its own) also spreads. This process depends on the "appearance" of internal mass (and static charges). If it does not have any rest mass from our frame of reference it "spreads without limit" until absorbed as a "corpuscle". If it has rest mass de Broglie wavelength determines the way it spreads from our point of view. In higher dimensions it is still an unbroken symmetry.
Here is the real trick.... the photon (one complete wavelength) the electric field determined as a line that runs directly through the X-axis of the gif animation plotted as a sinusoidally varying electric field is a higher dimensional "coil" of which there are two polarizations possible and represents the photon spin of +1 or -1 over one wavelength. This cannot be shown simply in only a simple sinusoid, but we know that photons do exhibit this polarization.
This is all linked with Dirac's Party Trick and Balinese Candle Dancers being critical to the concept of internal spin.
You need to rotate a particle twice to bring it back into congruence with the original particle. Apparently "any" particle.
half-integral spins and Pauli Exclusion Principle
Now I point you at the excellent concepts of Lie Groups...
Topological groups, Lie groups : Selected topics at this site
Have a little "thinky" about the symmetry that the Standard Model has for spin.
Here is the other interesting site that discusses this phenomenon.
Spin, Statistics, CPT and All That Jazz : John Baez
Naturally this is linked with the property of "entanglement".
I can't say anything definite until I think more closely about all this and to consider the properties of Lie Groups and Physics. These are only my preliminary thoughts on the matter. I also think this has a strong influence on all other theories as well. What I know is I am not "functional" enough to resolve the problem mathematically so I resort to "imagery" here. Please bear with me.
Cheers
What is the relationship between surface tension and internal pressure of nucleation (bubbles) and the pressure of the medium that it is in?
Another question for you:
Do you think waves travel as bubbles, or are just measured with them (pi relations)?
Firstly TRoc, If I knew I probably would never have started this thread. It is thanks to you (and a couple of others) that I am able to keep some kind of "focus" on the topic. "Obviously" Laplace does have a lot to do with the problem of "bubbles".
Wikipedia: Laplace's equation
The traveling of waves as a problem for bubbles is difficult but obviously the electromagnetic expanding wavefront is a kind of expanding "bubble". The problem with photons as "branes" is that we are dealing with the light cone. Using the light cone as a frame of reference is a kind of "vehicle" to see things in the frame of the photon. Mathematicians would "immediately" convert this to light cone coordinates because this is "instinctive" to them.
Please look at this image which I consider the most accurate of the visualizations of the electric field in the Fresnel zone and near (evanescent) field of the dipole radiator. This is a section in the plane of the dipole. As the photon "bubble" is being created there is still a "dynamic" element about it but as it moves away from the near field and "pinches off"(electric field lines passing through zero)... launched into "free space" the pancakes retain the wavelength but become flattened and spread on the edge of its light cone. This is only a light cone distortion of this "otherwise" spherical bubble of the photon (actually many of these photons occupy this "template" all in phase and "marching" to the same drummer). In that "imaginary" frame the photon can be considered as a sphere whose entire surface topologically lies on a light cone with a "half twist" in the electric field... Full twist over an entire wavelength since a wavelength is actually two of those bubbles being launched (one with a positive excursion at the center and the next with a negative excursion at the center... repeat unit is two).. This has the same internal symmetry as the electron which is a "stationary particle" with mass. Notice that the bubble symmetry is "broken" because of our external view of the photon bubbles as "pancakes". Notice that internally the photon's light cone symmetry is not broken. The symmetry between these two distinct views is the symmetry of "Special Relativity" and thus it is no wonder that Electromagnetism is already Unified. When the photon reaches its final destination it will probably mostly undergo the reverse process to this "photon emission" as a symmetric "photon bubble" no longer on the surface of the light cone and interacting with a dipole absorber.
QUOTE
Do you think waves travel as bubbles, or are just measured with them (pi relations)?
There are two aspects. The individual "corpuscles" of the particles being investigated can propagate "en masse" as a scatter gun inverse law spreading, each "corpuscle" being "on its own". Alternatively each individual "corpuscle" (on its own) also spreads. This process depends on the "appearance" of internal mass (and static charges). If it does not have any rest mass from our frame of reference it "spreads without limit" until absorbed as a "corpuscle". If it has rest mass de Broglie wavelength determines the way it spreads from our point of view. In higher dimensions it is still an unbroken symmetry.
Here is the real trick.... the photon (one complete wavelength) the electric field determined as a line that runs directly through the X-axis of the gif animation plotted as a sinusoidally varying electric field is a higher dimensional "coil" of which there are two polarizations possible and represents the photon spin of +1 or -1 over one wavelength. This cannot be shown simply in only a simple sinusoid, but we know that photons do exhibit this polarization.
This is all linked with Dirac's Party Trick and Balinese Candle Dancers being critical to the concept of internal spin.
You need to rotate a particle twice to bring it back into congruence with the original particle. Apparently "any" particle.
half-integral spins and Pauli Exclusion Principle
Now I point you at the excellent concepts of Lie Groups...
Topological groups, Lie groups : Selected topics at this site
Have a little "thinky" about the symmetry that the Standard Model has for spin.
Here is the other interesting site that discusses this phenomenon.
Spin, Statistics, CPT and All That Jazz : John Baez
Naturally this is linked with the property of "entanglement".
I can't say anything definite until I think more closely about all this and to consider the properties of Lie Groups and Physics. These are only my preliminary thoughts on the matter. I also think this has a strong influence on all other theories as well. What I know is I am not "functional" enough to resolve the problem mathematically so I resort to "imagery" here. Please bear with me.
Cheers
Hello Good_Elf, Troc +?,
I've fired a bit of a broadside on another thread about a photon having a single frequency and energy which makes it difficult (or impossible) to analyse in the time domain and hopefully suggesting that there will be no spread in the frequency domain. In general a changing electrostatic field is sufficient to cause em (photon) radiation - wires are hardly required.
Please feel free to comment here ..
-C2.
I've fired a bit of a broadside on another thread about a photon having a single frequency and energy which makes it difficult (or impossible) to analyse in the time domain and hopefully suggesting that there will be no spread in the frequency domain. In general a changing electrostatic field is sufficient to cause em (photon) radiation - wires are hardly required.
Please feel free to comment here
..-C2.
Hi confused2,
QUOTE (Confused2 Posted on Dec 30 2005+ 11:05 PM)
I've fired a bit of a broadside on another thread about a photon having a single frequency and energy which makes it difficult (or impossible) to analyze in the time domain and hopefully suggesting that there will be no spread in the frequency domain. In general a changing electrostatic field is sufficient to cause em (photon) radiation - wires are hardly required... Please feel free to comment here
Interesting point. What I would like to add is it is difficult for me to visualize this entity. Consider a CW EM Wave propagating along some axis. If I "chop" a segment of this otherwise perfect wave causing it to be of a finite extent in time it becomes a packet. The truncation process changes the cosine wave modifying its Fourier series which is the cosine wave "multiplied" with a window function.
Notice the truncation introduces "sidebands".Now you are telling me you can do this trick without introducing those additional frequencies that would limit this otherwise "infinite long repeating period wave"? The only way I can this might be possible is that it becomes the snake that swallows its own tail? If this happens it would become a fermion of some kind. The topology is then "difficult" without some trick. The function you see there is the sinc function... impulse response function must be sinc function in the time domain,
(top right)
thus...
(bottom right)
Otherwise the sidebands "merge" with the central frequency and are unable to be discriminated for. This is the "uncertainty" in the frequency of the packet. Narrowing this band spread increases the time interval of the window function in exactly the same way as this... For time and frequency pair, the relation is stated as:
in other places stated as...
Wikipedia Heisenberg uncertainty principle ... see comment below.
A CW laser that runs uninterrupted for a very long time might exhibit a single frequency but individual photon packets (which is the way they are absorbed) are more than one frequency through discreteness. Please note that it is through the process of individual photon packet emission and absorption that we arrive at the relationship of...
E = hf.
We see h is the quanta of impulse or the impulse response function above and it is scaled by the frequency in all emission and absorption processes.
It is no magic it is a geometric factor alone and is related to "cavity" size. I have a pretty picture of that (request if you want to see it again).
Back to the CW laser... Clearly a process of phase cancellation for the unwanted extra frequencies occurs for CW lasers. This is often called "destructive interference" but nothing could be further from the truth. For a single photon which extends one wavelength the window is related to the speed of light and the frequency.
Here is an interesting statement from above...
Interesting point. What I would like to add is it is difficult for me to visualize this entity. Consider a CW EM Wave propagating along some axis. If I "chop" a segment of this otherwise perfect wave causing it to be of a finite extent in time it becomes a packet. The truncation process changes the cosine wave modifying its Fourier series which is the cosine wave "multiplied" with a window function.Notice the truncation introduces "sidebands".Now you are telling me you can do this trick without introducing those additional frequencies that would limit this otherwise "infinite long repeating period wave"? The only way I can this might be possible is that it becomes the snake that swallows its own tail? If this happens it would become a fermion of some kind. The topology is then "difficult" without some trick. The function you see there is the sinc function... impulse response function must be sinc function in the time domain,
(top right)thus...
(bottom right)Otherwise the sidebands "merge" with the central frequency and are unable to be discriminated for. This is the "uncertainty" in the frequency of the packet. Narrowing this band spread increases the time interval of the window function in exactly the same way as this... For time and frequency pair, the relation is stated as:
in other places stated as...
Wikipedia Heisenberg uncertainty principle ... see comment below.
A CW laser that runs uninterrupted for a very long time might exhibit a single frequency but individual photon packets (which is the way they are absorbed) are more than one frequency through discreteness. Please note that it is through the process of individual photon packet emission and absorption that we arrive at the relationship of...
E = hf.
We see h is the quanta of impulse or the impulse response function above and it is scaled by the frequency in all emission and absorption processes.
It is no magic it is a geometric factor alone and is related to "cavity" size. I have a pretty picture of that (request if you want to see it again).
Back to the CW laser... Clearly a process of phase cancellation for the unwanted extra frequencies occurs for CW lasers. This is often called "destructive interference" but nothing could be further from the truth. For a single photon which extends one wavelength the window is related to the speed of light and the frequency.
Here is an interesting statement from above...
QUOTE (Wikipedia Uncertainty Principle+)
An uncertainty relation arises between any two observable quantities that can be defined by non-commuting operators. This means that the uncertainty principle arises in measuring the position and the velocity of an object, or in measuring the position and momentum of an object, or in the measurement of energy and time of an object or a system.
The uncertainty principle does not just apply to position and momentum. In its general form, it applies to every pair of conjugate variables. An example of a pair of conjugate variables is the x-component of angular momentum (spin) vs. the y-component of angular momentum. In general, and unlike the case of position versus momentum discussed above, the lower bound for the product of the uncertainties of two conjugate variables depends on the system state.
The uncertainty principle does not just apply to position and momentum. In its general form, it applies to every pair of conjugate variables. An example of a pair of conjugate variables is the x-component of angular momentum (spin) vs. the y-component of angular momentum. In general, and unlike the case of position versus momentum discussed above, the lower bound for the product of the uncertainties of two conjugate variables depends on the system state.
QUOTE (Confused2 Posted on Dec 30 2005+ 11:05 PM)
In general a changing electrostatic field is sufficient to cause em (photon) radiation - wires are hardly required.
Just a point... it must exceed the work function of the surface. Could you elaborate on that point about wires... I think that is a symmetry point. I am speaking about the intrinsic spin quanta and its two polarizations when speaking about Balinese Candle Dancers etc. Each photon packet must have that characteristic (left or right spin in six dimensions... isospin). I may have confused your point a little.
http://en.wikipedia.org/wiki/Weak_isospin
http://en.wikipedia.org/wiki/Isospin
This is through SU(2) symmetry. You can see that strong force has isospin, weak force has weak isospin and electromagnetism has an allied spin in an unfolded topology of spin leading to the two polarizations. All variations on the same phenomena. The topology is "hidden" with photons SU(2) symmetry it is part of the closed brane of our Universe. Up close and "personal" this symmetry is the Unitary group ... this short exact sequence splits (see reference) so that U(n) may written as a semidirect product of SU(n) by U(1). Here the U(1) subgroup of U(n) and of SU(n)... Hidden version of SU(2) as well. Everything is "spin".
http://en.wikipedia.org/wiki/Unitary_group
I wish this was a proof of higher dimensions but it only proves the existence of curved (and closed) space-time on the scale of the Universe. Close but no Kewpie Doll.
There is a lot of unfinished business with this link (repeated in my previous post)..
Spin, Statistics, CPT and All That Jazz : John Baez
Naturally this is linked with the property of "entanglement". It also relates to article John Baez refers to in "the American Journal of Physics, Feb 1995, Roy Gould gives a nice heuristic argument for the spin statistics theorem - why spin 1/2 particles are fermions , and integer spin particles are bosons." This would give a justification to the Topological Electron - Photon paper of Williamson et al. That is with a little help from Balinese Candle Dancers and a few extra dimensions. What this all shows is a repeated symmetry motif that goes from the scale of the Universe to the smallest sub-atomic particle (SU(2)).
Have you got a reference to this phenomenon somewhere? It would be interesting to study it carefully. Your comments and interest appreciated.
Cheers
Just a point... it must exceed the work function of the surface. Could you elaborate on that point about wires... I think that is a symmetry point. I am speaking about the intrinsic spin quanta and its two polarizations when speaking about Balinese Candle Dancers etc. Each photon packet must have that characteristic (left or right spin in six dimensions... isospin). I may have confused your point a little.
http://en.wikipedia.org/wiki/Weak_isospin
http://en.wikipedia.org/wiki/Isospin
This is through SU(2) symmetry. You can see that strong force has isospin, weak force has weak isospin and electromagnetism has an allied spin in an unfolded topology of spin leading to the two polarizations. All variations on the same phenomena. The topology is "hidden" with photons SU(2) symmetry it is part of the closed brane of our Universe. Up close and "personal" this symmetry is the Unitary group ... this short exact sequence splits (see reference) so that U(n) may written as a semidirect product of SU(n) by U(1). Here the U(1) subgroup of U(n) and of SU(n)... Hidden version of SU(2) as well. Everything is "spin".
http://en.wikipedia.org/wiki/Unitary_group
I wish this was a proof of higher dimensions but it only proves the existence of curved (and closed) space-time on the scale of the Universe. Close but no Kewpie Doll.
There is a lot of unfinished business with this link (repeated in my previous post)..
Spin, Statistics, CPT and All That Jazz : John Baez
Naturally this is linked with the property of "entanglement". It also relates to article John Baez refers to in "the American Journal of Physics, Feb 1995, Roy Gould gives a nice heuristic argument for the spin statistics theorem - why spin 1/2 particles are fermions , and integer spin particles are bosons." This would give a justification to the Topological Electron - Photon paper of Williamson et al. That is with a little help from Balinese Candle Dancers and a few extra dimensions. What this all shows is a repeated symmetry motif that goes from the scale of the Universe to the smallest sub-atomic particle (SU(2)).
Have you got a reference to this phenomenon somewhere? It would be interesting to study it carefully. Your comments and interest appreciated.
Cheers
Hello Good_Elf,
I can't take a CW em wave and chop it into a packet - it's a bit like trying to make a pig out of sausages. I can try to make a CW em wave made out of packets seem reasonable - hopefully that will be just as good. I don't have a school chemistry book to hand but I do remember putting bits of stuff into the non-oxidizing bit of a candle flame and getting a characteristic colour for each element. Generally this is explained by collisions between atoms exciting the electrons into a particular state - when the electron falls back you get a characteristic colour (possibly colours if you're not colour blind) for the element. This would seem to be a 'one at a time' thing, a packetty, photonny, sort of a thing. Mercury vapour street lights do much the same and give a continuous orange (I think) glow. CW from photons seems OK for light.
http://home.earthlink.net/~lenyr/ntype-nr.htm
If we accept he really is making tunnel diodes (it looks good to me) - on the evidence of his photo of the curve tracer output - there are gaps (unlike Wikipedia) - the output is undefined in those regions and he probably has bursts of high frequencies which his scope can't display - very plausible.
He's making L-C oscillators with tunnel diodes (bless him!). The mechanism for tunnel diodes, as I understand it, is that each and every electron passing through the diode has a probability of gaining a certain (fixed) amount of energy (from the gap) - from the look of his circuit and scope he's pumping an LC network at not much more than a few kilohertz. Each electron through the diode is bumping up his energy states. With a very low frequency he doesn't need much energy (E) from each electron through the diode. It looks like a very quantum-mechanical wave generator to me - he just needs an aerial to start transmitting.
I would agree that a quantum mechanical origin doesn't prove anything stays quantized - but hopefully it seems a bit more plausible. Everybody (even Wikipedia) is very wave orientated because that's what we're used to.
http://www.answers.com/topic/photon-noise
http://webphysics.davidson.edu/Projects/An...lli/node40.html
--------------------------------------------------
Moving on to sidebands etc.
If I were an electronic engineer (er.. ) designing most sorts of transmitter one of my main aims would be to ensure that the fundamental oscillator in the system obeys the rule E = N x h x f where N is an integer, this would be so the frequency does not change with small changes (individual 'hfs') in the total energy in the 'main' oscillator - I want it to be stable. In general I would leave most of the energy in the oscillator and just sniff a bit of it which I would then amplify to become the transmitted signal. The whole caboodle is connected together with bits of wire within which the available 'quantum states' are either close or overlapping (another story) so they don't interact (much) with our original states. The final stage is obviously to fling our photons out as efficiently as possible (eg 1/2 wave dipole) into a hostile world.
Sooooooo .. To amplitude modulate our transmitter (say with music) we change the gain of at least one stage - the number of 'carrier' photons we send out is then varies with the peaks and troughs in the music. If ours was the only transmitter in the world we could just count the photons in our receiver. There is a problem with this counting process because we want the music not the total count of photons since we turned our transmitter on - we need to know how many photons we're getting 'now'. We can't do 'now' but we can do a count in a very short interval (a sample) .. so how short an interval do we need to take our count in?
I can't take a CW em wave and chop it into a packet - it's a bit like trying to make a pig out of sausages. I can try to make a CW em wave made out of packets seem reasonable - hopefully that will be just as good. I don't have a school chemistry book to hand but I do remember putting bits of stuff into the non-oxidizing bit of a candle flame and getting a characteristic colour for each element. Generally this is explained by collisions between atoms exciting the electrons into a particular state - when the electron falls back you get a characteristic colour (possibly colours if you're not colour blind) for the element. This would seem to be a 'one at a time' thing, a packetty, photonny, sort of a thing. Mercury vapour street lights do much the same and give a continuous orange (I think) glow. CW from photons seems OK for light.
http://home.earthlink.net/~lenyr/ntype-nr.htm
If we accept he really is making tunnel diodes (it looks good to me) - on the evidence of his photo of the curve tracer output - there are gaps (unlike Wikipedia) - the output is undefined in those regions and he probably has bursts of high frequencies which his scope can't display - very plausible.
He's making L-C oscillators with tunnel diodes (bless him!). The mechanism for tunnel diodes, as I understand it, is that each and every electron passing through the diode has a probability of gaining a certain (fixed) amount of energy (from the gap) - from the look of his circuit and scope he's pumping an LC network at not much more than a few kilohertz. Each electron through the diode is bumping up his energy states. With a very low frequency he doesn't need much energy (E) from each electron through the diode. It looks like a very quantum-mechanical wave generator to me - he just needs an aerial to start transmitting.
I would agree that a quantum mechanical origin doesn't prove anything stays quantized - but hopefully it seems a bit more plausible. Everybody (even Wikipedia) is very wave orientated because that's what we're used to.
http://www.answers.com/topic/photon-noise
http://webphysics.davidson.edu/Projects/An...lli/node40.html
--------------------------------------------------
Moving on to sidebands etc.
If I were an electronic engineer (er.. ) designing most sorts of transmitter one of my main aims would be to ensure that the fundamental oscillator in the system obeys the rule E = N x h x f where N is an integer, this would be so the frequency does not change with small changes (individual 'hfs') in the total energy in the 'main' oscillator - I want it to be stable. In general I would leave most of the energy in the oscillator and just sniff a bit of it which I would then amplify to become the transmitted signal. The whole caboodle is connected together with bits of wire within which the available 'quantum states' are either close or overlapping (another story) so they don't interact (much) with our original states. The final stage is obviously to fling our photons out as efficiently as possible (eg 1/2 wave dipole) into a hostile world.
Sooooooo .. To amplitude modulate our transmitter (say with music) we change the gain of at least one stage - the number of 'carrier' photons we send out is then varies with the peaks and troughs in the music. If ours was the only transmitter in the world we could just count the photons in our receiver. There is a problem with this counting process because we want the music not the total count of photons since we turned our transmitter on - we need to know how many photons we're getting 'now'. We can't do 'now' but we can do a count in a very short interval (a sample) .. so how short an interval do we need to take our count in?
see http://en.wikipedia.org/wiki/Shannon_sampling_theorem..
When sampling a band limited </wiki/Band limited> signal (e.g., through analog to digital conversion) the sampling frequency </wiki/Sampling_frequency> must be greater than twice the signal's bandwidth in order to be able to reconstruct the original perfectly from the sampled version.
This is the time domain equivalent of the frequency domain result
http://en.wikipedia.org/wiki/Anti-aliasing_filter
Most often, an anti-aliasing filter is a low-pass filter </wiki/Low-pass_filter>. However, this is not a requirement. The Shannon-Nyquist sampling theorem </wiki/Shannon-Nyquist_sampling_theorem> states that the sampling rate must be greater than twice the bandwidth, not maximum frequency, of the signal. For the types of signals that are bandwidth limited, but not centered at zero, a band-pass filter </wiki/Band-pass_filter> would be used as an anti-aliasing filter. For example, this could be done with a single-sideband modulated </wiki/Single-sideband_modulation> or frequency modulated </wiki/Frequency_modulated> signal. If one desired to sample an FM radio </wiki/FM_radio> broadcast on channel 200 </wiki/FM_broadcast_band>, then an appropriate anti-alias filter would be centered on 87.9 MHz </wiki/Megahertz> with 200 kHz bandwidth (or pass-band </wiki/Pass-band> of 87.8 MHz to 88.0 MHz), and the sampling rate would be no less than 400 kHz. (In this case not the audio of the broadcast is sampled, but the actual transmission signal itself , which is not very common.[my emphasis] )
One can see that the term bandwidth and similar problems apply whether one deals with the problem in the time domain (by counting or sampling) or the frequency domain.
I'm sure it all sounded odd - I suggest this is only because you're used to waves.
Uncertainty principle --------
One can see that the term bandwidth and similar problems apply whether one deals with the problem in the time domain (by counting or sampling) or the frequency domain.
I'm sure it all sounded odd - I suggest this is only because you're used to waves.
Uncertainty principle --------
http://en.wikipedia.org/wiki/Uncertainty_principle
Contributor 1
The Heisenberg uncertainty principle provides a quantitative relationship between the uncertainties of p and x as measured by their standard deviations in the following way: If the particle state is such that the first measurement yields a dispersion of values Δx, then the second measurement will have a distribution of values whose dispersion Δp is at least inversely proportional to Δx.
IMHO contributor 1 has hit the nail on the head.. the uncertainty is statistical.. when dealing with a small number of events it is not possible to map out the uncertainty. Only with a large number of photons will the uncertainty appear as you describe.
wiki/Standard_deviation
The standard deviation is a measure of the degree of dispersion of the data from the mean value. Stated another way, the standard deviation is simply the "average" or "expected" variation around an average (i.e., square all individual deviations around the average, add these up, divide by N, then take the square root. You then have the root of the mean squared deviation (RMS </wiki/Root_mean_square>, in a very simple sense the average or expected variation around the average). In fact the standard deviation is sometimes called the expected deviation, though this may be confusing as the expected value </wiki/Expected_value> of the deviation is instead the average absolute deviation </wiki/Average_absolute_deviation>.
A large standard deviation indicates that the data points are far from the mean and a small standard deviation indicates that they are clustered closely around the mean.
http://en.wikipedia.org/wiki/Uncertainty_principle
Contributor 2
Only quantum mechanics can provide the answer stating that the particle will have an uncertainty in position according to the Heisenberg Uncertainty Principle already discussed, such that it might not really reach the singularity and thus escape the possible collapse to infinite density.
Contributor 2 does not seem to have understood the implication of what was written by contributor 1. I don't think QM has an answer to the problem of two particles sitting on top of each other or even one sitting on top of itself.
As far as I am concerned the problem lies with trying to quantize something that was already quantized - As you open your gate you get an amount of energy anything between 0 and N x hf where N may be very large. When N is large the quantum analysis will merge with the frequency domain analysis.
I've enjoyed the challenge ! I'll try again on any bit (all?) if you like.
Best wishes, C2.
(Quotes working thanks to Good_Elf!)
Looking at the animations posted by Good_Elf (01/01/06) .. worth the effort..
Assuming the maths behind them is good (no reason not to)..
A smoothly changing probability distribution is interesting in itself , raising the question - what is it that stops the electron probability distribution from smoothly changing to a distribution where the electrons spend all their time in the nucleus and never come out? It's a slippery slope. One is invited to accept that these changing probability distributions correspond to movements of fractional electronic charges - possibly another slippery slope. What governs the rate at which these probability distributions change? Any thoughts?
-C2.
QUOTE
Good_Elf..
Consider a CW EM Wave propagating along some axis. If I "chop" a segment of this otherwise perfect wave causing it to be finite in time it becomes a packet
Consider a CW EM Wave propagating along some axis. If I "chop" a segment of this otherwise perfect wave causing it to be finite in time it becomes a packet
I can't take a CW em wave and chop it into a packet - it's a bit like trying to make a pig out of sausages. I can try to make a CW em wave made out of packets seem reasonable - hopefully that will be just as good. I don't have a school chemistry book to hand but I do remember putting bits of stuff into the non-oxidizing bit of a candle flame and getting a characteristic colour for each element. Generally this is explained by collisions between atoms exciting the electrons into a particular state - when the electron falls back you get a characteristic colour (possibly colours if you're not colour blind) for the element. This would seem to be a 'one at a time' thing, a packetty, photonny, sort of a thing. Mercury vapour street lights do much the same and give a continuous orange (I think) glow. CW from photons seems OK for light.
http://home.earthlink.net/~lenyr/ntype-nr.htm
If we accept he really is making tunnel diodes (it looks good to me) - on the evidence of his photo of the curve tracer output - there are gaps (unlike Wikipedia) - the output is undefined in those regions and he probably has bursts of high frequencies which his scope can't display - very plausible.
He's making L-C oscillators with tunnel diodes (bless him!). The mechanism for tunnel diodes, as I understand it, is that each and every electron passing through the diode has a probability of gaining a certain (fixed) amount of energy (from the gap) - from the look of his circuit and scope he's pumping an LC network at not much more than a few kilohertz. Each electron through the diode is bumping up his energy states. With a very low frequency he doesn't need much energy (E) from each electron through the diode. It looks like a very quantum-mechanical wave generator to me - he just needs an aerial to start transmitting.
I would agree that a quantum mechanical origin doesn't prove anything stays quantized - but hopefully it seems a bit more plausible. Everybody (even Wikipedia) is very wave orientated because that's what we're used to.
http://www.answers.com/topic/photon-noise
http://webphysics.davidson.edu/Projects/An...lli/node40.html
--------------------------------------------------
Moving on to sidebands etc.
If I were an electronic engineer (er.. ) designing most sorts of transmitter one of my main aims would be to ensure that the fundamental oscillator in the system obeys the rule E = N x h x f where N is an integer, this would be so the frequency does not change with small changes (individual 'hfs') in the total energy in the 'main' oscillator - I want it to be stable. In general I would leave most of the energy in the oscillator and just sniff a bit of it which I would then amplify to become the transmitted signal. The whole caboodle is connected together with bits of wire within which the available 'quantum states' are either close or overlapping (another story) so they don't interact (much) with our original states. The final stage is obviously to fling our photons out as efficiently as possible (eg 1/2 wave dipole) into a hostile world.
Sooooooo .. To amplitude modulate our transmitter (say with music) we change the gain of at least one stage - the number of 'carrier' photons we send out is then varies with the peaks and troughs in the music. If ours was the only transmitter in the world we could just count the photons in our receiver. There is a problem with this counting process because we want the music not the total count of photons since we turned our transmitter on - we need to know how many photons we're getting 'now'. We can't do 'now' but we can do a count in a very short interval (a sample) .. so how short an interval do we need to take our count in?
QUOTE (->
| QUOTE |
| Good_Elf.. Consider a CW EM Wave propagating along some axis. If I "chop" a segment of this otherwise perfect wave causing it to be finite in time it becomes a packet |
I can't take a CW em wave and chop it into a packet - it's a bit like trying to make a pig out of sausages. I can try to make a CW em wave made out of packets seem reasonable - hopefully that will be just as good. I don't have a school chemistry book to hand but I do remember putting bits of stuff into the non-oxidizing bit of a candle flame and getting a characteristic colour for each element. Generally this is explained by collisions between atoms exciting the electrons into a particular state - when the electron falls back you get a characteristic colour (possibly colours if you're not colour blind) for the element. This would seem to be a 'one at a time' thing, a packetty, photonny, sort of a thing. Mercury vapour street lights do much the same and give a continuous orange (I think) glow. CW from photons seems OK for light.
http://home.earthlink.net/~lenyr/ntype-nr.htm
If we accept he really is making tunnel diodes (it looks good to me) - on the evidence of his photo of the curve tracer output - there are gaps (unlike Wikipedia) - the output is undefined in those regions and he probably has bursts of high frequencies which his scope can't display - very plausible.
He's making L-C oscillators with tunnel diodes (bless him!). The mechanism for tunnel diodes, as I understand it, is that each and every electron passing through the diode has a probability of gaining a certain (fixed) amount of energy (from the gap) - from the look of his circuit and scope he's pumping an LC network at not much more than a few kilohertz. Each electron through the diode is bumping up his energy states. With a very low frequency he doesn't need much energy (E) from each electron through the diode. It looks like a very quantum-mechanical wave generator to me - he just needs an aerial to start transmitting.
I would agree that a quantum mechanical origin doesn't prove anything stays quantized - but hopefully it seems a bit more plausible. Everybody (even Wikipedia) is very wave orientated because that's what we're used to.
http://www.answers.com/topic/photon-noise
http://webphysics.davidson.edu/Projects/An...lli/node40.html
--------------------------------------------------
Moving on to sidebands etc.
If I were an electronic engineer (er.. ) designing most sorts of transmitter one of my main aims would be to ensure that the fundamental oscillator in the system obeys the rule E = N x h x f where N is an integer, this would be so the frequency does not change with small changes (individual 'hfs') in the total energy in the 'main' oscillator - I want it to be stable. In general I would leave most of the energy in the oscillator and just sniff a bit of it which I would then amplify to become the transmitted signal. The whole caboodle is connected together with bits of wire within which the available 'quantum states' are either close or overlapping (another story) so they don't interact (much) with our original states. The final stage is obviously to fling our photons out as efficiently as possible (eg 1/2 wave dipole) into a hostile world.
Sooooooo .. To amplitude modulate our transmitter (say with music) we change the gain of at least one stage - the number of 'carrier' photons we send out is then varies with the peaks and troughs in the music. If ours was the only transmitter in the world we could just count the photons in our receiver. There is a problem with this counting process because we want the music not the total count of photons since we turned our transmitter on - we need to know how many photons we're getting 'now'. We can't do 'now' but we can do a count in a very short interval (a sample) .. so how short an interval do we need to take our count in?
see http://en.wikipedia.org/wiki/Shannon_sampling_theorem..
When sampling a band limited </wiki/Band limited> signal (e.g., through analog to digital conversion) the sampling frequency </wiki/Sampling_frequency> must be greater than twice the signal's bandwidth in order to be able to reconstruct the original perfectly from the sampled version.
This is the time domain equivalent of the frequency domain result
QUOTE
http://en.wikipedia.org/wiki/Anti-aliasing_filter
Most often, an anti-aliasing filter is a low-pass filter </wiki/Low-pass_filter>. However, this is not a requirement. The Shannon-Nyquist sampling theorem </wiki/Shannon-Nyquist_sampling_theorem> states that the sampling rate must be greater than twice the bandwidth, not maximum frequency, of the signal. For the types of signals that are bandwidth limited, but not centered at zero, a band-pass filter </wiki/Band-pass_filter> would be used as an anti-aliasing filter. For example, this could be done with a single-sideband modulated </wiki/Single-sideband_modulation> or frequency modulated </wiki/Frequency_modulated> signal. If one desired to sample an FM radio </wiki/FM_radio> broadcast on channel 200 </wiki/FM_broadcast_band>, then an appropriate anti-alias filter would be centered on 87.9 MHz </wiki/Megahertz> with 200 kHz bandwidth (or pass-band </wiki/Pass-band> of 87.8 MHz to 88.0 MHz), and the sampling rate would be no less than 400 kHz. (In this case not the audio of the broadcast is sampled, but the actual transmission signal itself , which is not very common.[my emphasis] )
One can see that the term bandwidth and similar problems apply whether one deals with the problem in the time domain (by counting or sampling) or the frequency domain.
I'm sure it all sounded odd - I suggest this is only because you're used to waves.
Uncertainty principle --------
QUOTE (->
| QUOTE |
| http://en.wikipedia.org/wiki/Anti-aliasing_filter Most often, an anti-aliasing filter is a low-pass filter </wiki/Low-pass_filter>. However, this is not a requirement. The Shannon-Nyquist sampling theorem </wiki/Shannon-Nyquist_sampling_theorem> states that the sampling rate must be greater than twice the bandwidth, not maximum frequency, of the signal. For the types of signals that are bandwidth limited, but not centered at zero, a band-pass filter </wiki/Band-pass_filter> would be used as an anti-aliasing filter. For example, this could be done with a single-sideband modulated </wiki/Single-sideband_modulation> or frequency modulated </wiki/Frequency_modulated> signal. If one desired to sample an FM radio </wiki/FM_radio> broadcast on channel 200 </wiki/FM_broadcast_band>, then an appropriate anti-alias filter would be centered on 87.9 MHz </wiki/Megahertz> with 200 kHz bandwidth (or pass-band </wiki/Pass-band> of 87.8 MHz to 88.0 MHz), and the sampling rate would be no less than 400 kHz. (In this case not the audio of the broadcast is sampled, but the actual transmission signal itself , which is not very common.[my emphasis] ) |
One can see that the term bandwidth and similar problems apply whether one deals with the problem in the time domain (by counting or sampling) or the frequency domain.
I'm sure it all sounded odd - I suggest this is only because you're used to waves.
Uncertainty principle --------
http://en.wikipedia.org/wiki/Uncertainty_principle
Contributor 1
The Heisenberg uncertainty principle provides a quantitative relationship between the uncertainties of p and x as measured by their standard deviations in the following way: If the particle state is such that the first measurement yields a dispersion of values Δx, then the second measurement will have a distribution of values whose dispersion Δp is at least inversely proportional to Δx.
IMHO contributor 1 has hit the nail on the head.. the uncertainty is statistical.. when dealing with a small number of events it is not possible to map out the uncertainty. Only with a large number of photons will the uncertainty appear as you describe.
QUOTE
wiki/Standard_deviation
The standard deviation is a measure of the degree of dispersion of the data from the mean value. Stated another way, the standard deviation is simply the "average" or "expected" variation around an average (i.e., square all individual deviations around the average, add these up, divide by N, then take the square root. You then have the root of the mean squared deviation (RMS </wiki/Root_mean_square>, in a very simple sense the average or expected variation around the average). In fact the standard deviation is sometimes called the expected deviation, though this may be confusing as the expected value </wiki/Expected_value> of the deviation is instead the average absolute deviation </wiki/Average_absolute_deviation>.
A large standard deviation indicates that the data points are far from the mean and a small standard deviation indicates that they are clustered closely around the mean.
QUOTE (->
| QUOTE |
| wiki/Standard_deviation The standard deviation is a measure of the degree of dispersion of the data from the mean value. Stated another way, the standard deviation is simply the "average" or "expected" variation around an average (i.e., square all individual deviations around the average, add these up, divide by N, then take the square root. You then have the root of the mean squared deviation (RMS </wiki/Root_mean_square>, in a very simple sense the average or expected variation around the average). In fact the standard deviation is sometimes called the expected deviation, though this may be confusing as the expected value </wiki/Expected_value> of the deviation is instead the average absolute deviation </wiki/Average_absolute_deviation>. A large standard deviation indicates that the data points are far from the mean and a small standard deviation indicates that they are clustered closely around the mean. |
http://en.wikipedia.org/wiki/Uncertainty_principle
Contributor 2
Only quantum mechanics can provide the answer stating that the particle will have an uncertainty in position according to the Heisenberg Uncertainty Principle already discussed, such that it might not really reach the singularity and thus escape the possible collapse to infinite density.
Contributor 2 does not seem to have understood the implication of what was written by contributor 1. I don't think QM has an answer to the problem of two particles sitting on top of each other or even one sitting on top of itself.
As far as I am concerned the problem lies with trying to quantize something that was already quantized - As you open your gate you get an amount of energy anything between 0 and N x hf where N may be very large. When N is large the quantum analysis will merge with the frequency domain analysis.
I've enjoyed the challenge
! I'll try again on any bit (all?) if you like.Best wishes, C2.
(Quotes working thanks to Good_Elf!)
Hi confused2,
While the Universe is not composed of CW laser emission, the principle is still a good one. A resonant cavity tuned to a particular frequency will "chop" the "apparent" CW into "bite" sized packets.
With light it is a boson so there is one difference to pigs and bosons is they can "overlap" each other and they stitch seamlessly. I guess it depends on where you believe quantization comes from. If you think quantization comes from beneath the quantum limit then there is something "deterministic" about the process. If you think as I do that quantization arises at the moment of emission or absorption and it is determined by the physical parameters at the level of the system producing the quanta then it becomes a manifestation of geometry.
Emission and absorption change the systems that are doing the emission and absorption. I believe they are "elastic" and therefore the cavity changes "tune" as it absorbs the photon. This prevents the reverse process too readily occurring. I have a related page I found here that illustrates the "internal" emission and absorption of a single quanta. This is a big ask to jump from this to higher dimensions but please consider that the surfaces shown are "hypersurfaces" and have complex quantities related to higher dimensions.
This paper How a Photon Is Created or Absorbed is really brilliant with animations as well.
This article illustrates the information that is needed to fill in the gaps between what is taught and what is actually occurring in atomic transitions. This shows the importance of the time dependent component of the transitions.
There are two animations (approx 1.8 Mb Quicktime MOV each) on the page that indicate in very graphical terms what is happening and to the quantity of energy involved in the processes being transferred. Well worth the download to actually see what research has produced (I have quoted extensively from the Original Article: J. Chem. Educ. 1979, 56, 631-634.)....
The time evolution of a hydrogen atom undergoing a dipole forbidden (2s -> 1s) transition is animated with a cross section of the charge density encoded as intensity on the left side. The quantum dynamics of the charge density are depicted as a rendered isosurface on the right side. Since the charge density for this process is spherically symmetrical, there is no persistent electric dipole to couple with the surrounding radiation.
The second one is similar but with more detail and more dramatic...
The time evolution of a hydrogen atom undergoing a dipole allowed (2p -> 1s) transition is animated with a cross section of the charge density encoded as intensity on the left side. The quantum dynamics of the charge density are depicted as a rendered isosurface on the right side. These oscillations are driven at the expense of the atom's energy (depicted by the "energy gauge") as the charge density contracts. The atom behaves as a miniature transmitter in which the oscillating electric dipole creates an electromagnetic pulse known as a photon.
The myth of quantum "instantaneous" leaps is obvious here. The actual ejection/transition process takes time. What is happening is a dynamic process that is responding through an "impulse" to the transition from one eigen state to the other. The impulse is not "instantaneous" but has an area under the curve that takes an extended time and this is equivalent to the sync function mentioned previously. Planck's constant is then related to the cavity size and the photon is scaled by a frequency multiplier.
I realize this takes a bit more than what is shown here in the paper but emission and absorption between different atoms should be visualized using this process and then you see what is supposed to be happening. It is really not as mysterious a process as is claimed. Notice also we are not speaking about psi-squared but actual charge density which is a "measurable". I suggest that HUP is not statistics but is underpinned by a more structured process which we are unable to actually measure but nonetheless does occur (check out the process in the article). I do not deny that statistics are important in any measuring process but we must try to read what is behind statistics... you know what they say... "there are lies... damn lies and then there is statistics"...
After that demo it may be easier to see my point of view.
Cheers
While the Universe is not composed of CW laser emission, the principle is still a good one. A resonant cavity tuned to a particular frequency will "chop" the "apparent" CW into "bite" sized packets.
QUOTE
I can't take a CW em wave and chop it into a packet - it's a bit like trying to make a pig out of sausages. I can try to make a CW em wave made out of packets seem reasonable - hopefully that will be just as good.
With light it is a boson so there is one difference to pigs and bosons is they can "overlap" each other and they stitch seamlessly. I guess it depends on where you believe quantization comes from. If you think quantization comes from beneath the quantum limit then there is something "deterministic" about the process. If you think as I do that quantization arises at the moment of emission or absorption and it is determined by the physical parameters at the level of the system producing the quanta then it becomes a manifestation of geometry.
Emission and absorption change the systems that are doing the emission and absorption. I believe they are "elastic" and therefore the cavity changes "tune" as it absorbs the photon. This prevents the reverse process too readily occurring. I have a related page I found here that illustrates the "internal" emission and absorption of a single quanta. This is a big ask to jump from this to higher dimensions but please consider that the surfaces shown are "hypersurfaces" and have complex quantities related to higher dimensions.
This paper How a Photon Is Created or Absorbed is really brilliant with animations as well.
This article illustrates the information that is needed to fill in the gaps between what is taught and what is actually occurring in atomic transitions. This shows the importance of the time dependent component of the transitions.
There are two animations (approx 1.8 Mb Quicktime MOV each) on the page that indicate in very graphical terms what is happening and to the quantity of energy involved in the processes being transferred. Well worth the download to actually see what research has produced (I have quoted extensively from the Original Article: J. Chem. Educ. 1979, 56, 631-634.)....
The time evolution of a hydrogen atom undergoing a dipole forbidden (2s -> 1s) transition is animated with a cross section of the charge density encoded as intensity on the left side. The quantum dynamics of the charge density are depicted as a rendered isosurface on the right side. Since the charge density for this process is spherically symmetrical, there is no persistent electric dipole to couple with the surrounding radiation.
The second one is similar but with more detail and more dramatic...
The time evolution of a hydrogen atom undergoing a dipole allowed (2p -> 1s) transition is animated with a cross section of the charge density encoded as intensity on the left side. The quantum dynamics of the charge density are depicted as a rendered isosurface on the right side. These oscillations are driven at the expense of the atom's energy (depicted by the "energy gauge") as the charge density contracts. The atom behaves as a miniature transmitter in which the oscillating electric dipole creates an electromagnetic pulse known as a photon.
The myth of quantum "instantaneous" leaps is obvious here. The actual ejection/transition process takes time. What is happening is a dynamic process that is responding through an "impulse" to the transition from one eigen state to the other. The impulse is not "instantaneous" but has an area under the curve that takes an extended time and this is equivalent to the sync function mentioned previously. Planck's constant is then related to the cavity size and the photon is scaled by a frequency multiplier.
I realize this takes a bit more than what is shown here in the paper but emission and absorption between different atoms should be visualized using this process and then you see what is supposed to be happening. It is really not as mysterious a process as is claimed. Notice also we are not speaking about psi-squared but actual charge density which is a "measurable". I suggest that HUP is not statistics but is underpinned by a more structured process which we are unable to actually measure but nonetheless does occur (check out the process in the article). I do not deny that statistics are important in any measuring process but we must try to read what is behind statistics... you know what they say... "there are lies... damn lies and then there is statistics"...
After that demo it may be easier to see my point of view.
Cheers
[QUOTE=Confused2,Jan 1 2006, 07:55 PM]to sample an FM radio </wiki/FM_radio> broadcast on channel 200 </wiki/FM_broadcast_band>, then an appropriate anti-alias filter would be centered on 87.9 MHz </wiki/Megahertz> with 200 kHz bandwidth (or pass-band </wiki/Pass-band> of 87.8 MHz to 88.0 MHz), and the sampling rate would be no less than 400 kHz. (In this case not the audio of the broadcast is sampled, but the actual transmission signal itself , which is not very common.[my emphasis] )
[/quote]
[/QUOTE]
200 kHz bandwidth (or pass-band </wiki/Pass-band> of 87.8 MHz to 88.0 MHz), and the sampling rate would be no less than 400 kHz. (In this case not the audio of the broadcast is sampled, but the actual transmission signal itself , which is not very [QUOTE]
i thought shannon / nyquist used the upper and lower frequencies to determin bandwidth and not the actual number of frequency steps that make up the bandwidth.
tim
[/quote]
[/QUOTE]
200 kHz bandwidth (or pass-band </wiki/Pass-band> of 87.8 MHz to 88.0 MHz), and the sampling rate would be no less than 400 kHz. (In this case not the audio of the broadcast is sampled, but the actual transmission signal itself , which is not very [QUOTE]
i thought shannon / nyquist used the upper and lower frequencies to determin bandwidth and not the actual number of frequency steps that make up the bandwidth.
tim
Hi Phaze,
Yes - absolutely right - thanks.
Hi Good_Elf,
While I go through the whole of your excellent post - many thanks - can we try a simple experiment?
Of sausages and pigs..
We need a laser, an optical attenuator and two photodiodes L and R which produce pulses of voltage and a click when they detect a photon, they detect with 100% detection efficiency.
We setup the laser with the beam spread somewhat. Initially the two photodiodes are at exactly the same distance from the laser.
Please say where you disagree
1) With the optical attenuator set at maximum we get random clicks from both diodes. Sausages.
2) We increase the intensity so the clicks are almost continuous - there is still no correlation between the clicks from L and R. Sausages.
3) We increase the intensity a lot, so the clicks appear continuous (10^4 clicks/sec) - but in reality there is still no correlation between the clicks from L and R. Still sausages.
4) We increase the intensity hugely, the clicks appear continuous - C2 predicts no correlation but I believe GE theory predicts at some point L and R will be effectively picking up the same wave - the sausages have merged.
5) We move one photodiode a fraction further away from the (spreading) source, the moved diode now clicks less often. GE theory is left to suggest how to match the part of the beam with more sausages in to the part of the beam with less. If L gives 1 click per second less than R - then we've lost a sausage. Would the missing click be CLICK one elephant CLICK one elephant CLICK one elephant etc or 'random'? "CLICK one elephant" suggests new frequency components have appeared in our beam (?) and random would seem diagnostic of an absence of correllation between the beams picked up by the two diodes - or something else?
C2 instinct suggests the inverse square law wouldn't work if photons stitched together in the way you seem to suggest.
Best wishes, C2.
Afterthought..
At some point I think we should decide, for the purposes of this thread, whether Minkowski space is 'real' or imaginery and whether or not 'uncertainty' extends into it.
QUOTE
I thought Shannon / Nyquist used the upper and lower frequencies to determine bandwidth and not the actual number of frequency steps that make up the bandwidth.
Yes - absolutely right - thanks.
Hi Good_Elf,
While I go through the whole of your excellent post - many thanks - can we try a simple experiment?
Of sausages and pigs..
We need a laser, an optical attenuator and two photodiodes L and R which produce pulses of voltage and a click when they detect a photon, they detect with 100% detection efficiency.
We setup the laser with the beam spread somewhat. Initially the two photodiodes are at exactly the same distance from the laser.
Please say where you disagree
1) With the optical attenuator set at maximum we get random clicks from both diodes. Sausages.
2) We increase the intensity so the clicks are almost continuous - there is still no correlation between the clicks from L and R. Sausages.
3) We increase the intensity a lot, so the clicks appear continuous (10^4 clicks/sec) - but in reality there is still no correlation between the clicks from L and R. Still sausages.
4) We increase the intensity hugely, the clicks appear continuous - C2 predicts no correlation but I believe GE theory predicts at some point L and R will be effectively picking up the same wave - the sausages have merged.
5) We move one photodiode a fraction further away from the (spreading) source, the moved diode now clicks less often. GE theory is left to suggest how to match the part of the beam with more sausages in to the part of the beam with less. If L gives 1 click per second less than R - then we've lost a sausage. Would the missing click be CLICK one elephant CLICK one elephant CLICK one elephant etc or 'random'? "CLICK one elephant" suggests new frequency components have appeared in our beam (?) and random would seem diagnostic of an absence of correllation between the beams picked up by the two diodes - or something else?
C2 instinct suggests the inverse square law wouldn't work if photons stitched together in the way you seem to suggest.
Best wishes, C2.
Afterthought..
At some point I think we should decide, for the purposes of this thread, whether Minkowski space is 'real' or imaginery and whether or not 'uncertainty' extends into it.
Hi Good Elf
The paper "How a Photon Is Created or Absorbed" was very interesting. Just another clue in my search to find out how photons impart momentum to atoms as described towards the end of this article about Cavity Quantum Electrodynamics (CQED) http://physicsweb.org/articles/world/13/12/10/1
The paper "How a Photon Is Created or Absorbed" was very interesting. Just another clue in my search to find out how photons impart momentum to atoms as described towards the end of this article about Cavity Quantum Electrodynamics (CQED) http://physicsweb.org/articles/world/13/12/10/1
Hi Montec,
Glad you enjoyed it. I have only just latched on to that one. It has the benefit of illustrating a single atom dynamics.
Previously I have "promoted" a less pure but interesting series of articles on the Web about Circuit QED. I would point out the cavity is nothing like that in nature but is fine for short periods. In this experiment we can see the hardware and the dynamics of a "synthetic" atom and how it manages a single photon. Maybe this article is a little more recent...
Circuit QED Project - photon in a can.
This site has heaps of illuminating details about this process... (see publications)
There is an illuminating pair of equation on the top of page three here...
The resemblances in mathematical structures between the optical constants of artificial electromagnetic media and some physical phenomena in field theory - Jian Qi Shen
This is all very illuminating regards the process of photon emission and capture.
Cheers
QUOTE
The paper "How a Photon Is Created or Absorbed" was very interesting. Just another clue in my search to find out how photons impart momentum to atoms as described towards the end of this article about Cavity Quantum Electrodynamics (CQED) http://physicsweb.org/articles/world/13/12/10/1
Glad you enjoyed it. I have only just latched on to that one. It has the benefit of illustrating a single atom dynamics.
Previously I have "promoted" a less pure but interesting series of articles on the Web about Circuit QED. I would point out the cavity is nothing like that in nature but is fine for short periods. In this experiment we can see the hardware and the dynamics of a "synthetic" atom and how it manages a single photon. Maybe this article is a little more recent...
Circuit QED Project - photon in a can.
This site has heaps of illuminating details about this process... (see publications)
There is an illuminating pair of equation on the top of page three here...
The resemblances in mathematical structures between the optical constants of artificial electromagnetic media and some physical phenomena in field theory - Jian Qi Shen
This is all very illuminating regards the process of photon emission and capture.
Cheers
Looking at the animations posted by Good_Elf (01/01/06) .. worth the effort..
Assuming the maths behind them is good (no reason not to)..
A smoothly changing probability distribution is interesting in itself , raising the question - what is it that stops the electron probability distribution from smoothly changing to a distribution where the electrons spend all their time in the nucleus and never come out? It's a slippery slope. One is invited to accept that these changing probability distributions correspond to movements of fractional electronic charges - possibly another slippery slope. What governs the rate at which these probability distributions change? Any thoughts?
-C2.
Hello Good_Elf,
Have we reached the point where neither of us can see what the other is seeing?
My view - the transition is a single energy transition and produces a photon of energy E ( = h * f) - making f a single frequency. I see nothing to gate until there is a frequency to gate - if there were many photons per transition then there would be something to gate - but imho there is only one photon per transition.
??
Have we reached the point where neither of us can see what the other is seeing?
My view - the transition is a single energy transition and produces a photon of energy E ( = h * f) - making f a single frequency. I see nothing to gate until there is a frequency to gate - if there were many photons per transition then there would be something to gate - but imho there is only one photon per transition.
??
Hi confused2,
QUOTE (Confused2 Posted on Jan 3 2006+ 04:24 PM)
One is invited to accept that these changing probability distributions correspond to movements of fractional electronic charges - possibly another slippery slope. What governs the rate at which these probability distributions change? Any thoughts?
I would slightly correct that... it is supposed to illustrate charge density. This is not "quite" the same as probability. Probability will not "fluctuate' since probability is related to the time "independent" solutions. In a way it is a bit meaningless to discuss the value of psi squared dV since this is the instantaneous changes in "something".
Dirac's Equation shows that this equation is a function that can be interpreted as probability density flow and can be converted into a current. Check out this reference...
Dirac Equation - Wikipedia
What it really means is up to you to decide.
I would slightly correct that... it is supposed to illustrate charge density. This is not "quite" the same as probability. Probability will not "fluctuate' since probability is related to the time "independent" solutions. In a way it is a bit meaningless to discuss the value of psi squared dV since this is the instantaneous changes in "something".
Dirac's Equation shows that this equation is a function that can be interpreted as probability density flow and can be converted into a current. Check out this reference...
Dirac Equation - Wikipedia
What it really means is up to you to decide.
QUOTE (From How a Photon Is Created or Absorbed: Giles Henderson Eastern Illinois University+ Charleston, IL 61920)
More recently, the analogous transient nutation effect (8, 9) and so called "photon echoes" (10-12) have been observed in molecular spectra using pulsed coherent laser radiation. These experiments confirm that there are no "quantum jumps" in the non-stationary state; rather there are smooth, continuous periodic changes in the magnetic and electric properties of a system undergoing a transition.
I suppose this statement is contestable, I can see no reason to do that, sounds pretty "good" to me. This following thread may help with the understanding of charge in particles... specifically an electron. The paper "hints" at demonstrating how all charged particles might be "created" from photons.
The altering of time, Is it possible for someone to do so?
This is a sort of "Party Clown" view of HEP where you make everything in the Universe from sub-atomic particle membranes using a "twist" here and a "boost" there and you get a "daschund"... he he he!
from... P343, "A First Course in String Theory" by B. Zwiebach
The mere fact that the "photon echoes" can be detected in these Molecular Orbitals suggests strongly that more is happening than was formerly understood.
"So what governs the rate?" I would say "tension" in the dimensional brane as it might in a balloon... that energy that keeps space open. Each time one of these pockets in higher dimensions are created a little extra volumetric space in our Universe is created... at least temporarily (in the case of photons) but more persistently in the case of electrons.
There is a strange fact that states that fermions need to be rotated twice before they are returned to their congruent state... this goes with everything, while a photon only needs to be rotated once to be congruent. This must be related to the different kinds of space they exist in and the way the particles are connected to the rest of the Universe. In the case of an electron positron pair I am sure that if the electron and positron were free to move, that in their own frames of rest the charges would 'disappear" while they were falling toward each other. Mind you this would create an inertial imbalance due to the high electromagnetic forces which are disproportionate to the masses involved. It is interesting to think of massless electrons falling freely as to what that may mean. Alternatively you could think of a suitable twist in the interior of the electron that nullifies the charge such as a spin 2 particle... he he he!
Have you ever wondered about why the Nucleus and the Electron shells just "happen" to look and behave like each other? Why should this be? Are they terrible twins (not identical twins). Perhaps they are "reciprocal space" views of each other. One a boson and the other a fermion (wave and impulse) carrying the Fourier idea into everything. Why do particles and antiparticles destroy each other and why do electrons and protons do not suck each other in... These particles all have the concept of charge and they are all sources of charge but as in magnetism where is the "return loop" for the electric field lines going from positive to negative charges... Is the particle embedded in higher dimensional space and the return loop is via higher dimensions and this is the fundamental reason why fermions require two twists to return the particle to a congruent state? This would mean that magnetic particles lie "on" space-time and the return loop is already in ordinary space. This is a party trick I would like to do is take a bar magnet and rotate it through pi/2 radians in hyperspace and convert it into a big "charged particle".
Pay no serious attention to these ideas since they are just "ramblings" from elves.
Cheers
I suppose this statement is contestable, I can see no reason to do that, sounds pretty "good" to me. This following thread may help with the understanding of charge in particles... specifically an electron. The paper "hints" at demonstrating how all charged particles might be "created" from photons.
The altering of time, Is it possible for someone to do so?
This is a sort of "Party Clown" view of HEP where you make everything in the Universe from sub-atomic particle membranes using a "twist" here and a "boost" there and you get a "daschund"... he he he!
from... P343, "A First Course in String Theory" by B. Zwiebach
The mere fact that the "photon echoes" can be detected in these Molecular Orbitals suggests strongly that more is happening than was formerly understood.
"So what governs the rate?" I would say "tension" in the dimensional brane as it might in a balloon... that energy that keeps space open. Each time one of these pockets in higher dimensions are created a little extra volumetric space in our Universe is created... at least temporarily (in the case of photons) but more persistently in the case of electrons.
There is a strange fact that states that fermions need to be rotated twice before they are returned to their congruent state... this goes with everything, while a photon only needs to be rotated once to be congruent. This must be related to the different kinds of space they exist in and the way the particles are connected to the rest of the Universe. In the case of an electron positron pair I am sure that if the electron and positron were free to move, that in their own frames of rest the charges would 'disappear" while they were falling toward each other. Mind you this would create an inertial imbalance due to the high electromagnetic forces which are disproportionate to the masses involved. It is interesting to think of massless electrons falling freely as to what that may mean. Alternatively you could think of a suitable twist in the interior of the electron that nullifies the charge such as a spin 2 particle... he he he!
Have you ever wondered about why the Nucleus and the Electron shells just "happen" to look and behave like each other? Why should this be? Are they terrible twins (not identical twins). Perhaps they are "reciprocal space" views of each other. One a boson and the other a fermion (wave and impulse) carrying the Fourier idea into everything. Why do particles and antiparticles destroy each other and why do electrons and protons do not suck each other in... These particles all have the concept of charge and they are all sources of charge but as in magnetism where is the "return loop" for the electric field lines going from positive to negative charges... Is the particle embedded in higher dimensional space and the return loop is via higher dimensions and this is the fundamental reason why fermions require two twists to return the particle to a congruent state? This would mean that magnetic particles lie "on" space-time and the return loop is already in ordinary space. This is a party trick I would like to do is take a bar magnet and rotate it through pi/2 radians in hyperspace and convert it into a big "charged particle".
Pay no serious attention to these ideas since they are just "ramblings" from elves.
Cheers
Hi!
Interesting... Are you getting any thoughts about what would be the size range for a photon?
jal
Interesting... Are you getting any thoughts about what would be the size range for a photon?
jal
Hi jal,
QUOTE (jal Posted on Jan 5 2006+ 03:43 PM)
Hi!
Interesting... Are you getting any thoughts about what would be the size range for a photon?jal
The size of any particle is a bit of a problem since the waves all scoot around inside the shell and sometimes they add and other times they subtract. They are a soliton. You will need Java for the next two illustrations.
Quantum Mechanical Scattering
Try the different barriers and wells. Notice they show the complex values but none of these "targets" can contain the particle.
In this next demo you can see what is happening to particles over longer periods of time in various atomic orbits...
Quantum Gaussian electron in classical "orbit"
This is the electron starting out as an undispersed packet then getting spread around over time. The scale is obviously the radius of the 1S orbital...
Here is a theoretical writing capacity "on" a single atomic orbital manipulating the 2500 angular momentum states of an electron for n=50...
The caption says...
Interesting... Are you getting any thoughts about what would be the size range for a photon?jal
The size of any particle is a bit of a problem since the waves all scoot around inside the shell and sometimes they add and other times they subtract. They are a soliton. You will need Java for the next two illustrations.
Quantum Mechanical Scattering
Try the different barriers and wells. Notice they show the complex values but none of these "targets" can contain the particle.
In this next demo you can see what is happening to particles over longer periods of time in various atomic orbits...
Quantum Gaussian electron in classical "orbit"
This is the electron starting out as an undispersed packet then getting spread around over time. The scale is obviously the radius of the 1S orbital...
Here is a theoretical writing capacity "on" a single atomic orbital manipulating the 2500 angular momentum states of an electron for n=50...
The caption says...
QUOTE (Writing on an Atom from [URL=http://www.optics.rochester.edu:8080/users/stroud/+)
http://www.optics.rochester.edu:8080/users/stroud/[/URL]]This picture is actually a graph of an atomic electron wave function made up of a superposition of the 2500 angular momentum states that make up the n = 50 Rydberg manifold of hydrogen. The states are mostly localized on a spherical surface of radius 2500 Bohr radii. The phase of the wave function at each point is mapped onto hue (color) while the amplitude of the wave function is mapped onto saturation (brightness). This picture illustrates the fact that a single atom has an enormous information capacity - if one can control it well enough to write and readout the encoded information.
Here is everything you ever wanted to know about atoms but were too bored to know... he he he! (Java again)
This java applet displays the wave functions (orbitals) of the hydrogen atom
Cheers
Here is everything you ever wanted to know about atoms but were too bored to know... he he he! (Java again)
This java applet displays the wave functions (orbitals) of the hydrogen atom
Cheers
Good Elf...
Love the applets... I'll study them... thanks!
jal
Love the applets... I'll study them... thanks!
jal
Hi Good_Elf , Jal, et al,
I have spent a considerable amount of time looking for support for my views about the nature of photons and wavepackets - none whatsoever - either I am a very clever bunny or a not so smart bunny 
, even I have to admit the latter seems the most probable. Regardless..
Looking at the first applet..
http://www.sgi.com/fun/java/john/wave-sim.html
There is a high frequency component 'under' a gaussian distribution curve - this looks 'reasonable' - the chances of detecting the photon varies with the distance from the centre of the wavepacket - the problem I have is that there would appear to be five or more photons in the wavepacket - as an aid to analysis this may work perfectly but my feeling is that it is somewhat flawed as a picture of a single photon. For what it's worth (!) my own 'interpretation' is that there is a single photon which cannot be located precisely - the gaussian distribution is (probably) correct but what is under it isn't. In general this would be no more than a big endian v. little endian problem - the result is the same - but in the particular case of launching and detecting individual photons it seems fairly crucial (at least to me). A previous applet has shown the process of launching (apparently) the same sort of clump of photons. A less attractive alternative to the clump and gauss picture would be to suggest that an amount of energy (the photon, one of it ) is genuinely not located precisely in time and space - the 'size' being a property of space not of photons as such- the end result is the same but the probability doesn't have to be built into the structure of the photon - perhaps it doesn't matter.
Final fling! - C2.
I have spent a considerable amount of time looking for support for my views about the nature of photons and wavepackets - none whatsoever - either I am a very clever bunny
or a not so smart bunny , even I have to admit the latter seems the most probable. Regardless..Looking at the first applet..
http://www.sgi.com/fun/java/john/wave-sim.html
There is a high frequency component 'under' a gaussian distribution curve - this looks 'reasonable' - the chances of detecting the photon varies with the distance from the centre of the wavepacket - the problem I have is that there would appear to be five or more photons in the wavepacket - as an aid to analysis this may work perfectly but my feeling is that it is somewhat flawed as a picture of a single photon. For what it's worth (!) my own 'interpretation' is that there is a single photon which cannot be located precisely - the gaussian distribution is (probably) correct but what is under it isn't. In general this would be no more than a big endian v. little endian problem - the result is the same - but in the particular case of launching and detecting individual photons it seems fairly crucial (at least to me). A previous applet has shown the process of launching (apparently) the same sort of clump of photons. A less attractive alternative to the clump and gauss picture would be to suggest that an amount of energy (the photon, one of it ) is genuinely not located precisely in time and space - the 'size' being a property of space not of photons as such- the end result is the same but the probability doesn't have to be built into the structure of the photon - perhaps it doesn't matter.
Final fling! - C2.
Hi confused2,
QUOTE (Confused2 Posted on Jan 7 2006+ 11:15 AM)
I have spent a considerable amount of time looking for support for my views about the nature of photons and wave packets - none whatsoever - either I am a very clever bunny or a not so smart bunny , even I have to admit the latter seems the most probable. Regardless..
I disagree, this sort of information is changing almost daily. To give an example of how many particles are in one place you can't really have a straight answer. Here is a quote from a recent article on atomic "bilocation"....
I disagree, this sort of information is changing almost daily. To give an example of how many particles are in one place you can't really have a straight answer. Here is a quote from a recent article on atomic "bilocation"....
QUOTE ( Schroedinger's Cation:Physicists prove that an atom can be in two different places at once 1996+)
...The question is, at what point, or scale, do the probabilistic rules of the quantum realm give way to the deterministic laws that govern the macroscopic world? This question has been brought into vivid relief by the recent work done by the NIST team, which includes Christopher Monroe, Dawn Meekhof, Brian King and Dave Wineland. The group confined a charged beryllium atom in a tiny electromagnetic cage and then cooled it with a laser to its lowest energy state. In this state the position of the atom and its "spin" (a quantum property that is only metaphorically analogous to spin in the ordinary sense) could be ascertained to within a very high degree of accuracy, limited by Heisenberg's uncertainty principle. The workers then stimulated the atom with a laser just enough to change its wave function; according to the new wave function of the atom, it now had a 50 percent probability of being in a "spin-up" state in its initial position and an equal probability of being in a "spin-down" state in a position as much as 80 nanometers away, a vast distance indeed for the atomic realm. In effect, the atom was in two different places, as well as two different spin states, at the same time--an atomic analog of a cat both living and dead.
(The clinching evidence that the NIST researchers had achieved their goal came from their observation of an interference pattern; that phenomenon is a telltale sign that a single beryllium atom produced two distinct wave functions that interfered with each other.)
http://www.sciam.com/article.cfm?articleID...B81809EC588EF21
I have subsequently seen other experiments that duplicate this phenomenon with other atoms and it is really all about the wave function. There is usually a place where the atom is and a place that simulates all the properties of the atom including the "chemical bonding properties" but the atom is not there. I have mentioned this phenomena before but I can't find where it was stated. There were accompanying "atomic force micrographs" that showed a little elliptical corral of conductive atoms surrounding where the test atom was situated at an "optical" focal point and at the other focus ... sure enough another "image" was sitting "pretty". It is therefore still possible to view events in this "multiple superimposed" and "entangled" way, and even have the images displaced spatially.
When I am putting up a case, I usually put it in a very strong way... perhaps too strong. Like lawyers in court, I only plead the case for my "client". I guess the issue is what is the "real meaning" of these phenomena. What I suspect is that the new evidence for "spooky stuff" does throw old data into new light.
I would like to offer a "kind of resolution" of this phenomenon. That is the "observation" is in no way "absolute". What I mean is like the phenomenon of Einstein's Rings, the Universe throws up multiple images of the one event, these are optical "resolutions of the state of the system. These "images" are made up of a summation of dynamic wave functions and these are related to "strings" and what is observed are not simply images but they are expressions of the state of the system. So a real particle may appear to be in several places at once but when push comes to shove... it will "actually" be in one place and this is not a matter of chance in the end but represents the way existence actually works. The other places are not just plain old images but a dynamic bit of the whole like the way your reflection in a still pool of water, if disturbed, may show parts of you existing in many different places and multiplely so (not a one to one relationship)... this does not mean that you are in several different places but you are actually observed in those several different places at once. Now is this because we are a coherent phenomena that can actually sustain this plastic shimmering in space or is the shimmering a "surface phenomena" and the "solid" reality lies beneath? I prefer the idea that we are energy phenomena and that we have no "exact" location. The energy inductively "returns" to the source from which it emanates (as an evanescent field) and this is because of the processes I have discussed before.
Space-time is not the source of the "disturbances" it is the phenomena itself that is the source of the disturbance. Space-time may be featureless and we impress this vibrant energy structure "on top" of it. A "shimmering vibrating" essence embedded in the "still" Universe? Not a "shimmering vibrating" Universe with a "still" essence embedded in it... he he he! In some ways these two views are similar but the epistemological significance is not inconsiderable.
The underlying mapping is the problem but the Universe "solves" this "spontaneously". The trouble is "reality" is what most people believe they "observe" and sometimes the reality is actually hidden from us by the chaotic "surface" of phenomena and I believe that the surface of that "reality" hides much of what is going on "behind the scenes". This may be in higher dimensions.
Like your comment on that! No "final flings" please.
Cheers
(The clinching evidence that the NIST researchers had achieved their goal came from their observation of an interference pattern; that phenomenon is a telltale sign that a single beryllium atom produced two distinct wave functions that interfered with each other.)
http://www.sciam.com/article.cfm?articleID...B81809EC588EF21
I have subsequently seen other experiments that duplicate this phenomenon with other atoms and it is really all about the wave function. There is usually a place where the atom is and a place that simulates all the properties of the atom including the "chemical bonding properties" but the atom is not there. I have mentioned this phenomena before but I can't find where it was stated. There were accompanying "atomic force micrographs" that showed a little elliptical corral of conductive atoms surrounding where the test atom was situated at an "optical" focal point and at the other focus ... sure enough another "image" was sitting "pretty". It is therefore still possible to view events in this "multiple superimposed" and "entangled" way, and even have the images displaced spatially.
When I am putting up a case, I usually put it in a very strong way... perhaps too strong. Like lawyers in court, I only plead the case for my "client". I guess the issue is what is the "real meaning" of these phenomena. What I suspect is that the new evidence for "spooky stuff" does throw old data into new light.
I would like to offer a "kind of resolution" of this phenomenon. That is the "observation" is in no way "absolute". What I mean is like the phenomenon of Einstein's Rings, the Universe throws up multiple images of the one event, these are optical "resolutions of the state of the system. These "images" are made up of a summation of dynamic wave functions and these are related to "strings" and what is observed are not simply images but they are expressions of the state of the system. So a real particle may appear to be in several places at once but when push comes to shove... it will "actually" be in one place and this is not a matter of chance in the end but represents the way existence actually works. The other places are not just plain old images but a dynamic bit of the whole like the way your reflection in a still pool of water, if disturbed, may show parts of you existing in many different places and multiplely so (not a one to one relationship)... this does not mean that you are in several different places but you are actually observed in those several different places at once. Now is this because we are a coherent phenomena that can actually sustain this plastic shimmering in space or is the shimmering a "surface phenomena" and the "solid" reality lies beneath? I prefer the idea that we are energy phenomena and that we have no "exact" location. The energy inductively "returns" to the source from which it emanates (as an evanescent field) and this is because of the processes I have discussed before.
Space-time is not the source of the "disturbances" it is the phenomena itself that is the source of the disturbance. Space-time may be featureless and we impress this vibrant energy structure "on top" of it. A "shimmering vibrating" essence embedded in the "still" Universe? Not a "shimmering vibrating" Universe with a "still" essence embedded in it... he he he! In some ways these two views are similar but the epistemological significance is not inconsiderable.
The underlying mapping is the problem but the Universe "solves" this "spontaneously". The trouble is "reality" is what most people believe they "observe" and sometimes the reality is actually hidden from us by the chaotic "surface" of phenomena and I believe that the surface of that "reality" hides much of what is going on "behind the scenes". This may be in higher dimensions.
Like your comment on that! No "final flings" please.
Cheers
Hi!
Good Elf...Confused2....
If I may make a few comments....
I'm not a master of communication... some of you guys can really nail/communicate an idea very clearly. I want to say that I agree with both of you. I tried to say the same thing with my thread.
You said,
You conclude,"This may be in higher dimensions."
I conclude, "it's in the shape of spacetime/"spot" and how it is put together (packed) and how it is moving. BECAUSE I HAVE BEEN TAUGHT THAT:
Everything is happening in space. Everything is suppose to be following the shape of space.
You said,
You conclude,"This may be in higher dimensions."
I conclude, "it's in the shape of spacetime/"spot" and how it is put together (packed) and how it is moving. BECAUSE I HAVE BEEN TAUGHT THAT:
Everything is happening in space. Everything is suppose to be following the shape of space.
You said,
... is genuinely not located precisely in time and space - the 'size' being a property of space not of photons as such- the end result is the same but the probability doesn't have to be built into the structure of the photon - perhaps it doesn't matter. ...
As far as the math.... to describe how EMF/particle act/interact....it would not change much if any IF the probability was built into the structure of spacetime.
I did specify in my thread that the "spot" was the indivisible amount ..of space, (2pi)... of time, (2pi)... and of action contained within 2pi.
Hawkins called it an instanton.
I drew a picture.
You said,
Yes, it is not inconsiderable.
Are you ready to abandon the idea that the sun is not going around the earth?
I apologize, if I am detracting rather then helping.
jal
Good Elf...Confused2....
If I may make a few comments....
I'm not a master of communication... some of you guys can really nail/communicate an idea very clearly. I want to say that I agree with both of you. I tried to say the same thing with my thread.
You said,
QUOTE
The trouble is "reality" is what most people believe they "observe" and sometimes the reality is actually hidden from us by the chaotic "surface" of phenomena and I believe that the surface of that "reality" hides much of what is going on "behind the scenes" .
You conclude,"This may be in higher dimensions."
I conclude, "it's in the shape of spacetime/"spot" and how it is put together (packed) and how it is moving. BECAUSE I HAVE BEEN TAUGHT THAT:
Everything is happening in space. Everything is suppose to be following the shape of space.
You said,
QUOTE (->
| QUOTE |
| The trouble is "reality" is what most people believe they "observe" and sometimes the reality is actually hidden from us by the chaotic "surface" of phenomena and I believe that the surface of that "reality" hides much of what is going on "behind the scenes" . |
You conclude,"This may be in higher dimensions."
I conclude, "it's in the shape of spacetime/"spot" and how it is put together (packed) and how it is moving. BECAUSE I HAVE BEEN TAUGHT THAT:
Everything is happening in space. Everything is suppose to be following the shape of space.
You said,
... is genuinely not located precisely in time and space - the 'size' being a property of space not of photons as such- the end result is the same but the probability doesn't have to be built into the structure of the photon - perhaps it doesn't matter. ...
As far as the math.... to describe how EMF/particle act/interact....it would not change much if any IF the probability was built into the structure of spacetime.
I did specify in my thread that the "spot" was the indivisible amount ..of space, (2pi)... of time, (2pi)... and of action contained within 2pi.
Hawkins called it an instanton.
I drew a picture.
You said,
QUOTE
...Spacetime.... In some ways these two views are similar but the epistemological significance is not inconsiderable."...
Yes, it is not inconsiderable.
Are you ready to abandon the idea that the sun is not going around the earth?
I apologize, if I am detracting rather then helping.
jal
Hi jal, confused2, TRoc and yquantum,
QUOTE (jal Posted on Jan 7 2006+ 06:03 PM)
Are you ready to abandon the idea that the sun is not going around the earth?
As we elves often say..."I am all ears!"
I hope not! I think that was ironic... the bit about the Sun eh! He he he. Yes it is a very near thing and the idea has to be "nailed down" because so much is riding on this concept. What is reality? What is to be found at the Planck Length? What does this wave and particle duality really mean? I believe there is an answer.
As we elves often say..."I am all ears!"
I hope not! I think that was ironic... the bit about the Sun eh! He he he. Yes it is a very near thing and the idea has to be "nailed down" because so much is riding on this concept. What is reality? What is to be found at the Planck Length? What does this wave and particle duality really mean? I believe there is an answer.QUOTE (Good Elf Posted on Jan 7 2006+ 05:25 PM)
The trouble is "reality" is what most people believe they "observe" and sometimes the reality is actually hidden from us by the chaotic "surface" of phenomena and I believe that the surface of that "reality" hides much of what is going on "behind the scenes" .
Not just photons but also even atomic particles, as illustrated in my last post, as well (we are all made of collections of atoms), need to be viewed in the context of higher dimensions if there are any HD's to consider at all. In three dimensions you have your particle and you have its momentum space, as yquantum has recently stated in another thread. They are really one and the same entity in only three dimensions (no higher dimensions... there is nothing extra to consider here). In higher dimensions the particle and this "indeterminacy" of position and momentum (or energy and time) may not be a property of the particle in "hyperspace". As you (jal) pointed out...
Not just photons but also even atomic particles, as illustrated in my last post, as well (we are all made of collections of atoms), need to be viewed in the context of higher dimensions if there are any HD's to consider at all. In three dimensions you have your particle and you have its momentum space, as yquantum has recently stated in another thread. They are really one and the same entity in only three dimensions (no higher dimensions... there is nothing extra to consider here). In higher dimensions the particle and this "indeterminacy" of position and momentum (or energy and time) may not be a property of the particle in "hyperspace". As you (jal) pointed out...
QUOTE (Confused2 Posted on Jan 7 2006+ 11:15 AM)
... A less attractive alternative to the clump and gauss picture would be to suggest that an amount of energy (the photon, one of it ) is genuinely not located precisely in time and space - the 'size' being a property of space not of photons as such- the end result is the same but the probability doesn't have to be built into the structure of the photon - perhaps it doesn't matter.
This is a very subtle point and it why I went on with my "nit picking". Confused2 has a valid point... the "size in 3D space" is not necessarily connected with the particle itself, but connected with the observers measurements of the particle. The "shimmering surface" (I am speaking figuratively about the observation) that is connected with the particle and its position is the "patch" in 3D space-time defined "approximately" by...
or...
The inner product being a representation of a "mathematical space"... not a spatial space here. But this exists in a spatial space. As to what confused2 said about it "not mattering..." it really does matter as you have emphasized and I am sure this was only an expression of "indecision" by confused2 (C2 correct me if I am wrong here). Obviously "probing" this surface in three dimensions with more and more precise location finding and resolving instruments will "kick" the image around a lot, not only in size but in the distortions of the "images" rendered in it. Notice the second equation above leads to time dependent interpretations to this "shimmering surface". Does it represent the particle or the surface? I (of course) lean toward the latter.
You can see that if this is "reality" and we are trying to model the real particle on the basis of the dynamically distorted and spread image we are in for "problems". This is the interface to Bohmian Mechanics and the interpretation configuration space may be very complex.
This is just a one dimensional configuration space... remember we have six of them to deal with (or perhaps three complex ones).
http://www.phys.port.ac.uk/fpweb%20dell/configur.htm
There may be "hidden variables" there due to the act of the projection... the very nature of the quantum and what we think it is depends on just what we see in that imperfect "mirror".
I value both of your inputs here (and any others). Please feel free to add your insights here. I believe we are looking into higher dimensions... "through a glass darkly" (...Biblical Physics here...).
This is a very subtle point and it why I went on with my "nit picking". Confused2 has a valid point... the "size in 3D space" is not necessarily connected with the particle itself, but connected with the observers measurements of the particle. The "shimmering surface" (I am speaking figuratively about the observation) that is connected with the particle and its position is the "patch" in 3D space-time defined "approximately" by...
or...
The inner product being a representation of a "mathematical space"... not a spatial space here. But this exists in a spatial space. As to what confused2 said about it "not mattering..." it really does matter as you have emphasized and I am sure this was only an expression of "indecision" by confused2 (C2 correct me if I am wrong here). Obviously "probing" this surface in three dimensions with more and more precise location finding and resolving instruments will "kick" the image around a lot, not only in size but in the distortions of the "images" rendered in it. Notice the second equation above leads to time dependent interpretations to this "shimmering surface". Does it represent the particle or the surface? I (of course) lean toward the latter.
You can see that if this is "reality" and we are trying to model the real particle on the basis of the dynamically distorted and spread image we are in for "problems". This is the interface to Bohmian Mechanics and the interpretation configuration space may be very complex.
This is just a one dimensional configuration space... remember we have six of them to deal with (or perhaps three complex ones).
http://www.phys.port.ac.uk/fpweb%20dell/configur.htm
There may be "hidden variables" there due to the act of the projection... the very nature of the quantum and what we think it is depends on just what we see in that imperfect "mirror".
I value both of your inputs here (and any others). Please feel free to add your insights here. I believe we are looking into higher dimensions... "through a glass darkly" (...Biblical Physics here...).
QUOTE (1 Cor. xiii V11-12: First Epistle of Paul to the Corinthians+)
When I was a child, I spake as a child,
I understood as a child, I thought as a child:
but when I became a man, I put away
childish things. For now we see through a
glass, darkly; but then face to face: now
I know in part; but then shall I know even
as also I am known.
Cheers
I understood as a child, I thought as a child:
but when I became a man, I put away
childish things. For now we see through a
glass, darkly; but then face to face: now
I know in part; but then shall I know even
as also I am known.
Cheers
Hi!
Good Elf Posted on Jan 7 2006, 05:53 PM
...and mathematically...must be treated as if there are 10???
I'll stop and listen.
jal
ps. everybody loves bunnies
Good Elf Posted on Jan 7 2006, 05:53 PM
QUOTE
remember we have six of them to deal with (or perhaps three complex ones).
...and mathematically...must be treated as if there are 10???
I'll stop and listen.
jal
ps. everybody loves bunnies
Hello Good_Elf, Jal et al,
Thanks for your wonderfully informed and creative approaches .. I would not be attempting this without it..
"Anyone who thinks they understand quantum mechanics hasn't really understood it" - Niels Bohr (probably)
Good_Elf has correctly diagnosed indecision/confusion.. the internal problem lies with relativity and QM - the photon is obviously at the interface between the two worlds.
I am at the stage of having some small understanding of conventional models and no understanding of my own model - the best I can explain at the moment is that it seems to involve replacing the internal probability of a photon with the external probability of everything else - it may well be complete nonsense but I'm putting a bit of time into it just in case. It looks vaguely plausible in my own little world of wires and transistors but at some point it's going to have to go through empty space and agree with experimental results - at the moment I don't see how it can which either means wrong or that I need better glasses.
http://forum.physorg.com/index.php?showtop...t=0&#entry51364 gives an indication of the type of 'smooth' universe I am trying to launch these ridiculous and totally incompatible probabilities into - I have yet to make any sense of it myself.
With apologies for the delay in response..
Re beryllium atom in two places
http://www.sciam.com/article.cfm?articleID...B81809EC588EF21
(The clinching evidence that the NIST researchers had achieved their goal came from their observation of an interference pattern; that phenomenon is a telltale sign that a single beryllium atom produced two [my emphasis] distinct wave functions that interfered with each other.)
http://en.wikipedia.org/wiki/Stern-Gerlach_apparatus ). Spin is either up or down .. no gradual merging.. if the atoms had 'oscillated' (in a classical sense) between the two points I would fall on my sword and admit defeat.. but they report two distinct wave functions (as I would have 'expected').
Imagine the earth revolving around another body of the same size and mass - they revolve around the centre of mass .. at the centre of mass there is either nothing (holding two planets together) or a huge flux of Higgs Bosons or something else.
Good_Elf might like this (for fun)..
As we reduce a mass the uncertainty about it's position increases towards infinity - at zero mass - a theoretical photon - it could be anywhere. If we allow the uncertainty to extend into Minkowski space (just for fun) it could be anywhere at any time. If we give it a tiny bit of mass we compress the uncertainty and the Minkowski space removes the possibility of detecting it twice - it is never in two places at the same time. By introducing 'other factors' we can squeeze the uncertainty into new shapes (but never eliminate it) .. bubbles. If charge introduces twist, I don't know how and I don't know why but it seems to.. knit yourself a daschund if you wish. The Minkowski space allows a single particle to hide another without too many absurdities.. the whole thing is locked together by Planck's constant (somehow!). If a bubble bursts..
(EDIT- I should make clear that the above comes directly from Good_Elf postings earlier in this thread (possibly other threads) .. not my ideas - I'm not responsible!)
Unfortunately Confused2 theory is looking much less plausible.
Many thanks,
-C2.
PS .. GE - Benzene is a bit of an oddity but the water seems a bit muddy - too many atoms and chemists involved from what I can find,
Thanks for your wonderfully informed and creative approaches .. I would not be attempting this without it..
"Anyone who thinks they understand quantum mechanics hasn't really understood it" - Niels Bohr (probably)
Good_Elf has correctly diagnosed indecision/confusion.. the internal problem lies with relativity and QM - the photon is obviously at the interface between the two worlds.
I am at the stage of having some small understanding of conventional models and no understanding of my own model - the best I can explain at the moment is that it seems to involve replacing the internal probability of a photon with the external probability of everything else - it may well be complete nonsense but I'm putting a bit of time into it just in case. It looks vaguely plausible in my own little world of wires and transistors but at some point it's going to have to go through empty space and agree with experimental results - at the moment I don't see how it can which either means wrong or that I need better glasses.
http://forum.physorg.com/index.php?showtop...t=0&#entry51364 gives an indication of the type of 'smooth' universe I am trying to launch these ridiculous and totally incompatible probabilities into - I have yet to make any sense of it myself.
With apologies for the delay in response..
Re beryllium atom in two places
http://www.sciam.com/article.cfm?articleID...B81809EC588EF21
QUOTE
(The clinching evidence that the NIST researchers had achieved their goal came from their observation of an interference pattern; that phenomenon is a telltale sign that a single beryllium atom produced two [my emphasis] distinct wave functions that interfered with each other.)
http://en.wikipedia.org/wiki/Stern-Gerlach_apparatus ). Spin is either up or down .. no gradual merging.. if the atoms had 'oscillated' (in a classical sense) between the two points I would fall on my sword and admit defeat.. but they report two distinct wave functions (as I would have 'expected').
Imagine the earth revolving around another body of the same size and mass - they revolve around the centre of mass .. at the centre of mass there is either nothing (holding two planets together) or a huge flux of Higgs Bosons or something else.
Good_Elf might like this (for fun)..
As we reduce a mass the uncertainty about it's position increases towards infinity - at zero mass - a theoretical photon - it could be anywhere. If we allow the uncertainty to extend into Minkowski space (just for fun) it could be anywhere at any time. If we give it a tiny bit of mass we compress the uncertainty and the Minkowski space removes the possibility of detecting it twice - it is never in two places at the same time. By introducing 'other factors' we can squeeze the uncertainty into new shapes (but never eliminate it) .. bubbles. If charge introduces twist, I don't know how and I don't know why but it seems to.. knit yourself a daschund if you wish. The Minkowski space allows a single particle to hide another without too many absurdities.. the whole thing is locked together by Planck's constant (somehow!). If a bubble bursts..
(EDIT- I should make clear that the above comes directly from Good_Elf postings earlier in this thread (possibly other threads) .. not my ideas - I'm not responsible!)
Unfortunately Confused2 theory is looking much less plausible.
Many thanks,
-C2.
PS .. GE - Benzene is a bit of an oddity but the water seems a bit muddy - too many atoms and chemists involved from what I can find,
Well, it's been a long time since I felt like I could contribute to this thread, but I think I might actually have something worthwhile to say....
QUOTE (Confused2+Jan 8 2006, 10:04 AM)
As we reduce a mass the uncertainty about it's position increases towards infinity
Not exactly. It's momentum and/or energy that, as we increase our certainty, will lead to a corresponding uncertainty in position. So really the accuracy of Confused2's statement depends on whether he is talking about rest mass or relativistic mass. If he was talking about relativistic mass, then he might be correct, because relativistic mass accounts for kinetic energy. But I don't know off-hand if it also accounts for other potential energies, such as gravitational or EM.... Can an "expert" weigh in on that???
Not exactly. It's momentum and/or energy that, as we increase our certainty, will lead to a corresponding uncertainty in position. So really the accuracy of Confused2's statement depends on whether he is talking about rest mass or relativistic mass. If he was talking about relativistic mass, then he might be correct, because relativistic mass accounts for kinetic energy. But I don't know off-hand if it also accounts for other potential energies, such as gravitational or EM.... Can an "expert" weigh in on that???
QUOTE (Confused2+Jan 8 2006, 10:04 AM)
at zero mass - a theoretical photon - it could be anywhere.
Even at zero rest mass, a photon still has a non-zero energy/momentum (and, to come back to the above points, a non-zero relativistic mass). So the probability of a zero mass can be unity, while still having an uncertainty regarding its energy/momentum. Which means that uncertainty about it's location need not be unbounded simply by reason of its zero rest mass.
Since energy is proportional to wavelength/frequency we can derive another uncertainty equation from the above one based on one of those instead of one based on mass, if we so desire.
...Just some thoughts. If it turns out that wasn't worthwhile, and I've made a mistake, I would happily be corrected.
Even at zero rest mass, a photon still has a non-zero energy/momentum (and, to come back to the above points, a non-zero relativistic mass). So the probability of a zero mass can be unity, while still having an uncertainty regarding its energy/momentum. Which means that uncertainty about it's location need not be unbounded simply by reason of its zero rest mass.
Since energy is proportional to wavelength/frequency we can derive another uncertainty equation from the above one based on one of those instead of one based on mass, if we so desire.
...Just some thoughts. If it turns out that wasn't worthwhile, and I've made a mistake, I would happily be corrected.
Hi Waterbreath,
Most welcome comments.. thanks.
I for one would be delighted if you looked back at least as far as
http://forum.physorg.com/index.php?showtopic=3003&st=120
(the previous page) and commented from there.. there are some splendid applets if nothing else..
I think we're all TOE orientated and trying out ideas - my own 'drift' at this point happens to be trying to get relativity to work on quantum type phenomenon
Not exactly. It's momentum and/or energy that, as we increase our certainty, will lead to a corresponding uncertainty in position. So really the accuracy of Confused2's statement depends on whether he is talking about rest mass or relativistic mass.
My argument being simply as m->0 then p-> 0 then delta p -> 0 therefore delta x -> infinity. The essence of the problem being that h doesn't scale down to suit us when we want it to. As m->0 it appears (to me) that the thing is turning into a photon of zero frequency and infinite wavelength. You draw attention (I suspect accidentally - but that's the value of saying something instead of nothing ) to the point that the bird doesn't fly away at zero mass - it has been flying away for some time.
I suspect we've been here before on another thread - if the mass is relative then the energy in the photon must also be relative.. comment most welcome.
My argument being simply as m->0 then p-> 0 then delta p -> 0 therefore delta x -> infinity. The essence of the problem being that h doesn't scale down to suit us when we want it to. As m->0 it appears (to me) that the thing is turning into a photon of zero frequency and infinite wavelength. You draw attention (I suspect accidentally - but that's the value of saying something instead of nothing ) to the point that the bird doesn't fly away at zero mass - it has been flying away for some time.
I suspect we've been here before on another thread - if the mass is relative then the energy in the photon must also be relative.. comment most welcome.
Since energy is proportional to wavelength/frequency we can derive another uncertainty equation from the above one based on one of those instead of one based on mass, if we so desire.
We have been looking at giving birth to a photon..
One contraversial option (that would be me) is that photons are 'born' as the result of a quantum 'change of state' - a single event which is as indivisible as (say) spin reversal. This is my preferred option. Under these circumstances the concept of wavelength can only be reduced to a concept of probability of detection which varies with time and distance (if these are not the same under the circumstances). I would interpret detection, perhaps incorrectly, as a similar 'change of state'. Given that one of these photons is going to be identical to any other photon born in the same way it is extrememly hard to play games with their phase and group velocities, among other things. They are not convenient, they are not classical, they are what I am looking at now and I'm not sure whether or not I can do the maths or even what the maths is.
Another option is that photons are born in a process that relates very closely to their eventual frequency - there will be oscillations within the atom as the state change occurs and the photons develop as something very close to a series of classical em sinewaves gated with the length of time it takes them to emerge. Photons produced in this way are conveniently ready for their life as sinewaves, where E=hf, in the electromagnetic spectrum.
Suggestions and criticism, classical or otherwise, are most welcome.
Best wishes, C2.
Most welcome comments.. thanks.
I for one would be delighted if you looked back at least as far as
http://forum.physorg.com/index.php?showtopic=3003&st=120
(the previous page) and commented from there.. there are some splendid applets if nothing else..
I think we're all TOE orientated and trying out ideas - my own 'drift' at this point happens to be trying to get relativity to work on quantum type phenomenon
QUOTE
Not exactly. It's momentum and/or energy that, as we increase our certainty, will lead to a corresponding uncertainty in position. So really the accuracy of Confused2's statement depends on whether he is talking about rest mass or relativistic mass.
My argument being simply as m->0 then p-> 0 then delta p -> 0 therefore delta x -> infinity. The essence of the problem being that h doesn't scale down to suit us when we want it to. As m->0 it appears (to me) that the thing is turning into a photon of zero frequency and infinite wavelength. You draw attention (I suspect accidentally - but that's the value of saying something instead of nothing ) to the point that the bird doesn't fly away at zero mass - it has been flying away for some time.
I suspect we've been here before on another thread - if the mass is relative then the energy in the photon must also be relative.. comment most welcome.
QUOTE (->
| QUOTE |
Not exactly. It's momentum and/or energy that, as we increase our certainty, will lead to a corresponding uncertainty in position. So really the accuracy of Confused2's statement depends on whether he is talking about rest mass or relativistic mass. |
My argument being simply as m->0 then p-> 0 then delta p -> 0 therefore delta x -> infinity. The essence of the problem being that h doesn't scale down to suit us when we want it to. As m->0 it appears (to me) that the thing is turning into a photon of zero frequency and infinite wavelength. You draw attention (I suspect accidentally - but that's the value of saying something instead of nothing ) to the point that the bird doesn't fly away at zero mass - it has been flying away for some time.
I suspect we've been here before on another thread - if the mass is relative then the energy in the photon must also be relative.. comment most welcome.
Since energy is proportional to wavelength/frequency we can derive another uncertainty equation from the above one based on one of those instead of one based on mass, if we so desire.
We have been looking at giving birth to a photon..
One contraversial option (that would be me) is that photons are 'born' as the result of a quantum 'change of state' - a single event which is as indivisible as (say) spin reversal. This is my preferred option. Under these circumstances the concept of wavelength can only be reduced to a concept of probability of detection which varies with time and distance (if these are not the same under the circumstances). I would interpret detection, perhaps incorrectly, as a similar 'change of state'. Given that one of these photons is going to be identical to any other photon born in the same way it is extrememly hard to play games with their phase and group velocities, among other things. They are not convenient, they are not classical, they are what I am looking at now and I'm not sure whether or not I can do the maths or even what the maths is.
Another option is that photons are born in a process that relates very closely to their eventual frequency - there will be oscillations within the atom as the state change occurs and the photons develop as something very close to a series of classical em sinewaves gated with the length of time it takes them to emerge. Photons produced in this way are conveniently ready for their life as sinewaves, where E=hf, in the electromagnetic spectrum.
Suggestions and criticism, classical or otherwise, are most welcome.
Best wishes, C2.
QUOTE (Confused2+Jan 8 2006, 04:19 PM)
Hi Waterbreath,
Most welcome comments.. thanks.
I for one would be delighted if you looked back at least as far as
http://forum.physorg.com/index.php?showtopic=3003&st=120
(the previous page) and commented from there..
I will do that, probably within a few hours. I do not have time at the moment, but wanted to acknowledge the response. Thank you.
Regarding the mass thing... I am not sure where our disconnect is. Maybe looking at the back posts will clear that up for me, so I won't comment too deeply right now. But basically, I don't see how the mass going to zero can cause the "release" of the photon by way of the Uncertainty Principle, because I don't think we can say that as m->0, p->0... Unless you're saying you think there needs to be a modification to the UP as it now stands.
Again, I will try to come back later, within a few hours, but can't make any guarantees. And again, thanks for taking the time to respond.
Most welcome comments.. thanks.
I for one would be delighted if you looked back at least as far as
http://forum.physorg.com/index.php?showtopic=3003&st=120
(the previous page) and commented from there..
I will do that, probably within a few hours. I do not have time at the moment, but wanted to acknowledge the response. Thank you.
Regarding the mass thing... I am not sure where our disconnect is. Maybe looking at the back posts will clear that up for me, so I won't comment too deeply right now. But basically, I don't see how the mass going to zero can cause the "release" of the photon by way of the Uncertainty Principle, because I don't think we can say that as m->0, p->0... Unless you're saying you think there needs to be a modification to the UP as it now stands.
Again, I will try to come back later, within a few hours, but can't make any guarantees. And again, thanks for taking the time to respond.
Well, I went back and read a bunch of that stuff, and did my best to understand it all.
All I could really conclude is that I need to study topology, abstract algebra, and maybe some calc as well, before any of this stuff is going to make much sense to me.
All I could really conclude is that I need to study topology, abstract algebra, and maybe some calc as well, before any of this stuff is going to make much sense to me.
Hi all!
I am looking for opinions/inputs on my thread. You all seem to be looking for answers too. Some people have all the answers, I don't. Would you leave a comment on my thread... makes sense!...could be!....impossible!...would be sufficient.
I'm definitely looking at things from a different point of view.
jal
I am looking for opinions/inputs on my thread. You all seem to be looking for answers too. Some people have all the answers, I don't. Would you leave a comment on my thread... makes sense!...could be!....impossible!...would be sufficient.
I'm definitely looking at things from a different point of view.
jal
Hi all,
Waterbreath - thanks for looking anyway, I agree there is a lot of n dimensional hand waving going on.
jal - I've already posted as much as I can on your thread .
For the purposes of this thread.. in the nice continuous relativistic type space that we all (well some of us) know and love..
Would it be safe to say the the photon count will decline as 1/r^2 as we move away from a point source which randomly emits large number of photons? As we reduce the photon intensity there will be a smooth transition to the point where we say the probability of detecting a photon will still be given by 1/r^2 ?
Now you see why I had to write such nice things about Good_Elf on another thread
.
Best wishes, - C2.
Edit - GE re (?) I think we have to proceed as though there are no hidden variables (ie not look for them) because we can only hope to deal with that which is 'revealed'.
Waterbreath - thanks for looking anyway, I agree there is a lot of n dimensional hand waving going on.
jal - I've already posted as much as I can on your thread
.For the purposes of this thread.. in the nice continuous relativistic type space that we all (well some of us) know and love..
Would it be safe to say the the photon count will decline as 1/r^2 as we move away from a point source which randomly emits large number of photons? As we reduce the photon intensity there will be a smooth transition to the point where we say the probability of detecting a photon will still be given by 1/r^2 ?
Now you see why I had to write such nice things about Good_Elf on another thread
.Best wishes, - C2.
Edit - GE re (?) I think we have to proceed as though there are no hidden variables (ie not look for them) because we can only hope to deal with that which is 'revealed'.
Hi Confused2,
The "elf" button has been pressed!
Does this mean you prefer "postulates" for which there is not the tiniest bit of evidence of a reason... just to make things work for you (that is the worst kind of "hidden variable")? Its the Clayton's Theory... the Theory you have when you don't have a Theory. The only reason we use them is because they work (fair ... but not entirely convincing). Quantum Postulates - they are everywhere.. Just because there are some hidden variables this means that you are still "allowed" to look for them. The "built in" postulates remove the chance of finding out the real meaning of "stuff" forever. I kid you not! Are we so outraged that some things are hidden from our gaze that we have this need to have theories that disguise the fact from our gullible pupils? Mankind claiming that we are all knowing gods again eh? Remember "hidden variable" theories do not mean there are no answers in them.
Does this mean you prefer "postulates" for which there is not the tiniest bit of evidence of a reason... just to make things work for you (that is the worst kind of "hidden variable")? Its the Clayton's Theory... the Theory you have when you don't have a Theory. The only reason we use them is because they work (fair ... but not entirely convincing). Quantum Postulates - they are everywhere.. Just because there are some hidden variables this means that you are still "allowed" to look for them. The "built in" postulates remove the chance of finding out the real meaning of "stuff" forever. I kid you not! Are we so outraged that some things are hidden from our gaze that we have this need to have theories that disguise the fact from our gullible pupils? Mankind claiming that we are all knowing gods again eh? Remember "hidden variable" theories do not mean there are no answers in them.
For the purposes of this thread.. in the nice continuous relativistic type space that we all (well some of us) know and love..
Hey... go have a look at who started this thread. There is a "revelation" that may surprise... and I say it's a fair cop! Oh well... if you are talking "revelation"... then ask your "source" (the great golden horned bull Om I suppose) what the hidden variables are and everything will be "peachy"! No doubt this "god" is "the god" worshipped by all "impatient" Physicists.
... now I see why you were "buttering me up" I got you down for a sack of coal next Xmas with Santa. 
(...come to think of it...actually that is probably more than you got from him this last year! )
Just kidding!
Cheers
You fox
I'm not going to let you go that easy.
I'm thinking.
We could all be bubbling with laughter if we could only understand each other.
jal
The "elf" button has been pressed!
QUOTE
Edit - GE re (?) I think we have to proceed as though there are no hidden variables (ie not look for them) because we can only hope to deal with that which is 'revealed'.
Does this mean you prefer "postulates" for which there is not the tiniest bit of evidence of a reason... just to make things work for you (that is the worst kind of "hidden variable")? Its the Clayton's Theory... the Theory you have when you don't have a Theory. The only reason we use them is because they work (fair ... but not entirely convincing). Quantum Postulates - they are everywhere.. Just because there are some hidden variables this means that you are still "allowed" to look for them. The "built in" postulates remove the chance of finding out the real meaning of "stuff" forever. I kid you not! Are we so outraged that some things are hidden from our gaze that we have this need to have theories that disguise the fact from our gullible pupils? Mankind claiming that we are all knowing gods again eh? Remember "hidden variable" theories do not mean there are no answers in them.
QUOTE (->
| QUOTE |
| Edit - GE re (?) I think we have to proceed as though there are no hidden variables (ie not look for them) because we can only hope to deal with that which is 'revealed'. |
Does this mean you prefer "postulates" for which there is not the tiniest bit of evidence of a reason... just to make things work for you (that is the worst kind of "hidden variable")? Its the Clayton's Theory... the Theory you have when you don't have a Theory. The only reason we use them is because they work (fair ... but not entirely convincing). Quantum Postulates - they are everywhere.. Just because there are some hidden variables this means that you are still "allowed" to look for them. The "built in" postulates remove the chance of finding out the real meaning of "stuff" forever. I kid you not! Are we so outraged that some things are hidden from our gaze that we have this need to have theories that disguise the fact from our gullible pupils? Mankind claiming that we are all knowing gods again eh? Remember "hidden variable" theories do not mean there are no answers in them.
For the purposes of this thread.. in the nice continuous relativistic type space that we all (well some of us) know and love..
Hey... go have a look at who started this thread. There is a "revelation" that may surprise... and I say it's a fair cop! Oh well... if you are talking "revelation"... then ask your "source" (the great golden horned bull Om I suppose) what the hidden variables are and everything will be "peachy"!
No doubt this "god" is "the god" worshipped by all "impatient" Physicists.... now I see why you were "buttering me up"
I got you down for a sack of coal next Xmas with Santa. (...come to think of it...actually that is probably more than you got from him this last year! )Just kidding!
Cheers
Hello Good_Elf,
I appreciate you have been under a lot of strain recently - the presents were good and the wrapping was excellent - thank you.
I have summarized my lack of evidence here and given what I hope you will agree is a fair summary of yours here. I have listed what I see as the main points of dispute here. I am at present too busy to be outraged by anything - I would like to use the time that I have as constructively as possible. I certainly have no wish to be drawn into discussions about the nature and power of Om.
I should confess that at present my main (and selfish) interest is trying to prove that any time or frequency domain phenomen can be dealt with in what I would call the 'probability domain'. Because it's me the maths and concepts would have to be easy - a much simplified Schrodinger - by starting with 'phenomena' the ideas don't have to cover everything in the way Schrodinger does. If I fail it doesn't prove the idea is wrong - if I succeed then maybe it will shed some light on bubbles/not bubbles, nature/size of bubbles etc. A book cannot argue it's point so I need some sort of sentient creature to try this out on. At present we don't seem to have any agreement on any phenomenon. I had hoped the inverse square law would be a non-contraversial starting point. I have no objections to any set of hidden variables that do not affect the result, maybe setting Ubersensitivity to zero would be good?
Best wishes, Confused2.
I appreciate you have been under a lot of strain recently - the presents were good and the wrapping was excellent - thank you.
QUOTE
Good_Elf
I believe that there is a 'continuum" there. Why?... because there is not a shred of evidence to the contrary.
I believe that there is a 'continuum" there. Why?... because there is not a shred of evidence to the contrary.
I have summarized my lack of evidence here and given what I hope you will agree is a fair summary of yours here. I have listed what I see as the main points of dispute here. I am at present too busy to be outraged by anything - I would like to use the time that I have as constructively as possible. I certainly have no wish to be drawn into discussions about the nature and power of Om.
I should confess that at present my main (and selfish) interest is trying to prove that any time or frequency domain phenomen can be dealt with in what I would call the 'probability domain'. Because it's me the maths and concepts would have to be easy - a much simplified Schrodinger - by starting with 'phenomena' the ideas don't have to cover everything in the way Schrodinger does. If I fail it doesn't prove the idea is wrong - if I succeed then maybe it will shed some light on bubbles/not bubbles, nature/size of bubbles etc. A book cannot argue it's point so I need some sort of sentient creature to try this out on. At present we don't seem to have any agreement on any phenomenon. I had hoped the inverse square law would be a non-contraversial starting point. I have no objections to any set of hidden variables that do not affect the result, maybe setting Ubersensitivity to zero would be good?
Best wishes, Confused2.
GE & C2,
Elf mode "ON"; Ubersensitivity levels set to "0".
Ready?
I am ready to surrender to the following premise:
Electric and Magnetic waves (coupled/vector) have no spherical solutions, therefore we must give up our bubble-wands, or make fundamental changes to Maxwell's field theories.
My "gut" says to keep the spherical scalars and move on.
TRoc
Elf mode "ON"; Ubersensitivity levels set to "0".
Ready?
I am ready to surrender to the following premise:
Electric and Magnetic waves (coupled/vector) have no spherical solutions, therefore we must give up our bubble-wands, or make fundamental changes to Maxwell's field theories.
My "gut" says to keep the spherical scalars and move on.
TRoc
Hi Troc and Good_Elf,
Ubersensitivity set to zero.
Nice one Troc.
There is no classical explanation for a photon. As far as I am concerned we should boldly go as far as Good_Elf wishes. There is something to be found and if we stop looking we will never find it .
-C2 .
Ubersensitivity set to zero.
Nice one Troc.
There is no classical explanation for a photon. As far as I am concerned we should boldly go as far as Good_Elf wishes. There is
something to be found and if we stop looking we will never find it .-C2
.
GE, C2
GE's page 1
I think bringing the electron into this discussion would be quite relevant. What if the "bubble" is NOT infinitely flexible? If it had a lower limit, the bubble would burst at high energies, leading to pair production. Then, after a short period, recombine through conservation of energy by longest wavelength principle.
However, given just the right amount of energy, the sending electron, and the receiving electron would set up a zero point field / scalar spherical wave / resonant standing wave / de Broglie matter wave (take your pick) between them. Thinking in "flatland" terms, the straight line between them could travel across "90 deg" lines the whole way - or along homogeneous field lines offering the "zero resistance" of maximum permittivity of space. Everywhere else, the space is filled with warping / distortions, that would change the frequency; so the "photon" is forced to take the path of least resistance, and arrives "Beat" free resonant.
Consider the strong-coupling regime in QED. Recent experiments coherently coupling a "single photon" with a "single superconducting qubit" demonstrate a "peculiar" coherent superposition of 2 simultaneous possibilities: the excited state of the atom and the photon become indistinguishable. [Nature 9/9/2004] This must be the best example of zero BeatFrequency that I have seen. Such pure resonance allows us to see the harmonics that exist in all vibrations; Science refers to these as vacuum Rabi peaks. This reduction of path length or width (the qubit in the cavity) obviously is key to producing this highly resonant state.
The "collapsing" of the wavefunction prematurely would catch a "harmonic" of the original wavelength, which then Sums to its' original state, by the reduction of path length. Reducing the path width, as in the double slit experiment, produces the same effect. The harmonics always have a Beat that is 1/2 wavelength, which is the same thing as phase, which is what shows up on the screen. Note that the more resonant / coherent the wave, the more that this effect can be seen.
Now back to bubbles / spherical waves. As you mentioned, the increase in energy results in a decrease in radius. In terms of amplitude, the wave fronts become more dense in a given area as the radius shrinks. Doppler is a good way to visualize this: velocity will do the same thing to a traveling spherical wave packet. The other way to look at that is the dualistic opposite of the ISL: the density of "field lines" increases with the decrease in distance, or path length.
So, look at our 2 electrons (sender/receiver), and the matter waves between them. They are going to be symmetric no matter what the distance. This translates to a consistently measured velocity between frames of reference.
While you have the image of the 2 Doppler waves facing each other, draw a line from the center out, in any direction. Now draw a second line 90 deg to the first. You can see that they will cross the same number of "field lines". Now complete the square, and measure over time, and you get perfect symmetry. This is the MM experiment, and why it couldn't measure a shift. (the same should apply to LIGO)
In the room I am sitting in, a level placed on the floor says that I am on level, flat ground. It does not matter how many times I repeat this, trying to mimic an increase in distance. The fact remains that I am measuring with a path length that is too short to demonstrate that I am on the surface of a sphere. The ratio of the length of my point A to B measurement to the radius is too great. The same goes for the "width" of the straight line between our 2 electrons, and their spherical matter waves. To each radius that is crosses, it crosses at 90 deg, which establishes the homogeneous, un-warped medium.
It should also be noted that these ever "density increasing in a given area" waves would have an ultimate "point like" measurement. As long as you were dealing with a finite radius, "infinities" would not be produced at this "singularity" (just a phase shift, and spin & direction change).
Looking at the ways in which spontaneous cavitation occurs, we see 1. by the local pressure dropping below the vapor pressure, and 2. to increase the local flow velocity. Vapor pressure is temperature dependent, so an increase in temperature will produce #1 as well. Temperature ultimately being an exchange of radiation / waves between the hotter (more energy, freq) to the colder (longer wavelength). If we imagine the density of the space medium being the sum of all matter waves, along Mach's principle, then the stable electron can represent the smallest radius in the medium in an equilibrium state. Add energy, in the form of a wave of specific frequency, increasing the temperature, and dropping local "equilibrium" pressure down, and producing a bubble that would be "squeezed" along the homogeneous straight line to the next resonant electron.
Comments are all appreciated.
TRoc
GE's page 1
QUOTE
This resonant object must store energy as a "frequency" too. If you "excite a bubble" assuming it is "infinitely" flexible and will not "burst" the surface area will depend on how much energy this frequency that is pumped into the bubble has. Think of the bubble surface "undulating" at the frequency of the natural vibration rate of the "cavity". This effectively increases the surface area of the bubble by deformation. . The total energy of the "bubble" is the sum of all these "modes" and I would ask you to think of other branes too. Luckily you can excite these bubbles this way and not "burst".
I think bringing the electron into this discussion would be quite relevant. What if the "bubble" is NOT infinitely flexible? If it had a lower limit, the bubble would burst at high energies, leading to pair production. Then, after a short period, recombine through conservation of energy by longest wavelength principle.
However, given just the right amount of energy, the sending electron, and the receiving electron would set up a zero point field / scalar spherical wave / resonant standing wave / de Broglie matter wave (take your pick) between them. Thinking in "flatland" terms, the straight line between them could travel across "90 deg" lines the whole way - or along homogeneous field lines offering the "zero resistance" of maximum permittivity of space. Everywhere else, the space is filled with warping / distortions, that would change the frequency; so the "photon" is forced to take the path of least resistance, and arrives "Beat" free resonant.
Consider the strong-coupling regime in QED. Recent experiments coherently coupling a "single photon" with a "single superconducting qubit" demonstrate a "peculiar" coherent superposition of 2 simultaneous possibilities: the excited state of the atom and the photon become indistinguishable. [Nature 9/9/2004] This must be the best example of zero BeatFrequency that I have seen. Such pure resonance allows us to see the harmonics that exist in all vibrations; Science refers to these as vacuum Rabi peaks. This reduction of path length or width (the qubit in the cavity) obviously is key to producing this highly resonant state.
The "collapsing" of the wavefunction prematurely would catch a "harmonic" of the original wavelength, which then Sums to its' original state, by the reduction of path length. Reducing the path width, as in the double slit experiment, produces the same effect. The harmonics always have a Beat that is 1/2 wavelength, which is the same thing as phase, which is what shows up on the screen. Note that the more resonant / coherent the wave, the more that this effect can be seen.
Now back to bubbles / spherical waves. As you mentioned, the increase in energy results in a decrease in radius. In terms of amplitude, the wave fronts become more dense in a given area as the radius shrinks. Doppler is a good way to visualize this: velocity will do the same thing to a traveling spherical wave packet. The other way to look at that is the dualistic opposite of the ISL: the density of "field lines" increases with the decrease in distance, or path length.
So, look at our 2 electrons (sender/receiver), and the matter waves between them. They are going to be symmetric no matter what the distance. This translates to a consistently measured velocity between frames of reference.
While you have the image of the 2 Doppler waves facing each other, draw a line from the center out, in any direction. Now draw a second line 90 deg to the first. You can see that they will cross the same number of "field lines". Now complete the square, and measure over time, and you get perfect symmetry. This is the MM experiment, and why it couldn't measure a shift. (the same should apply to LIGO)
In the room I am sitting in, a level placed on the floor says that I am on level, flat ground. It does not matter how many times I repeat this, trying to mimic an increase in distance. The fact remains that I am measuring with a path length that is too short to demonstrate that I am on the surface of a sphere. The ratio of the length of my point A to B measurement to the radius is too great. The same goes for the "width" of the straight line between our 2 electrons, and their spherical matter waves. To each radius that is crosses, it crosses at 90 deg, which establishes the homogeneous, un-warped medium.
It should also be noted that these ever "density increasing in a given area" waves would have an ultimate "point like" measurement. As long as you were dealing with a finite radius, "infinities" would not be produced at this "singularity" (just a phase shift, and spin & direction change).
Looking at the ways in which spontaneous cavitation occurs, we see 1. by the local pressure dropping below the vapor pressure, and 2. to increase the local flow velocity. Vapor pressure is temperature dependent, so an increase in temperature will produce #1 as well. Temperature ultimately being an exchange of radiation / waves between the hotter (more energy, freq) to the colder (longer wavelength). If we imagine the density of the space medium being the sum of all matter waves, along Mach's principle, then the stable electron can represent the smallest radius in the medium in an equilibrium state. Add energy, in the form of a wave of specific frequency, increasing the temperature, and dropping local "equilibrium" pressure down, and producing a bubble that would be "squeezed" along the homogeneous straight line to the next resonant electron.
Comments are all appreciated.
TRoc
Hi Confused2, TRoc et al,
This stuff must be taken with some good humour... elves must at least have a laugh about these issues.
OK... you have a good point C2 about the "Inverse square Law" being easy to start with. Something simple... Lets think about the similarity between a small amount of water and light... these are as different as you can get but they are excellent to think about. I will use the analogy of "space-time" of being a "flexible " sheet. First consider space-time as flat as it is possible to be... with 1 gee gravity (perpendicular) and the sheet stretching from here to Pluto. Not the slightest deviation from flatness can be detected. This is of course a Gedanken Experiment. I now have a glass of "idealized" water and some "unusual" light that likes "hugging" two dimensional surfaces but other than that is quite normal... it travels at the speed of light etc. Now this surface is stiffer than steel and it is "perfect" to use tensors on this surface since it is elastic but definitely not "rubber" since rubber is definitely not elastic. Do you get my drift?
I pour the glass of water on the surface and it spreads but because water has some mass it has very slightly almost infinitesimally curved this sheet of 2D space-time and though it spreads ultimately for miles it eventually "pools". Being ideal water the "dip" in the center of the sheet of "steel" is less than the thickness of a single atom (lucky this water is ideal) but it is something and eventually this "depression" is sufficient to ultimately cause the water to "come to rest" and pool. A very special "optical technique" can plot this curvature on the sheet as concentric circular curves with the maximum value in the center where the water was released. This "depression" surprisingly goes clear out to the edge of the sheet (and potentially beyond) since this has caused a bend in the "figure" as an inverse square law ... all the way to "infinity". The effect is "never" gone away and the "figure" is always perfect.
When I mean at rest I am assuming that the idealized particles do not have enough thermal energy to overcome surface tension etc... Only under these extreme conditions will Tensors work at all since it is a theory of "linear" deformation and though you may want to use complex maths to describe the properties with first second and third order derivatives of things such as in General Relativity, these deformation must remain smaller than can be seen for the maths to work correctly. Not my idea you can check this out.
The reason this "ideal water" pooled was because it had some mass which caused the natural depression and all the rest followed due to the "mathematically ideal" properties of this "stiff" but "ideal" membrane.
I carefully clean up... every slightest bit and I start again. This time with my special light that is constrained to "hug the surface" of the sheet. The light has no rest mass. This literally means that it only travels at "one speed"... the speed of light. This speed is so high that no hill is too high for it to not get over. The only thing that potentially could arrest its motion is a black hole and this sheet is once again "perfect" and there is no curve in it at all. I drop my glass of special light at the center of the surface of the sheet. It is "up and running instantly" and it has no rest mass because it has no "rest velocity" but it did impart momentum to the surface of the model "space-time". From the sheets point of view it is a flash at the center that spreads as if it was an impulse in the surface of a very stiff pond. There is no "nett depression" since the "impulse" produces a plus and minus transverse oscillation always of equal effect that "spreads" at the speed of light. Special cameras record this event for our later scrutiny. We see interference zones at some angles and the initial conditions make a lot of difference to the positioning and frequency of these "zones". But because it was just a single impulse the disturbance is of limited duration and it travels to the edge of the sheet with the height of the overall disturbance falling off as an inverse square law relationship.
Accounting is done on this process and we note that we can calculate an energy function at all times in this surface and this "one off" event produced "packets" where the energy was a maximum on this wavefront as it spread "classically" (at the speed of light). Since it was "perfectly elastic" the total energy of these "packets" remained constant as it spread... just becoming more and more spread. An accurate accounting of the "geometric figure" of the sheet noticed that when all the positive excursions and the negative excursions of this "one off ripple" were added up... there was never a time when there was any "nett" depression or anti-depression in the surface except at T=0 in a small zone around the origin. This effect quickly "dissipated" and did not travel far from the center. After that initial impulse this effect was not noticed again. This was an "anti-symmetric" disturbance for all but an instant when it was created.
We then went back over the figures for the water and noticed the same phenomenon. Similar ripples but because of the constant mass of the water there was a "permanent" lowering of the central energy of the system (depression) and the velocity was very much slower because of its inherent mass and the waves dissipated toward the edge and reflected off the boundary always near the maximum spread of the "pool", surging back and forth radially with time... luckily the amplitude was exceedingly small and the deformations in the underlying surface were even smaller being in that very stiff material. Because this "liquid" was ideal these oscillations continued on and on... quivering and returning to the source periodically, the boundary fluctuating. Somehow eventually the "vibrations" quietened down and the oscillations were damped away to zero and the pool was "still". This meant that the more elastic surface of the (pseudo) 2D space-time sheet was even more ideal and the phenomena continued there longer than the time it took to be damped down in the bulk of the ideal water itself. In the end the energy function showed a "symmetric" figure and never once had "zero" energy except at the beginning near T=0 where a fluctuation did show some "one sided character for a brief instant. This was a 'symmetric".. one sided function.
The light on the other hand could not be retained by the sheet and it "escaped" off the edge in one "cycle". In both cases the "fluids" obeyed inverse square law "propagation" but they were different. The water responded to a permanent depression at the center and "pooled"... this was due to the nett effect of a one sided "mass function" at that center. All the material was retained within a certain distance from the center and oscillations in the fluid had a temporal and a harmonic effect... these were surging radially then converging radially... like a breathing... and the waves formed a series of nodes and anti-nodes in the surface as a standing pattern which eventually dissipated.
A third experiment was also performed where the "underside of this surface at its center was "weighted" by a constant mass of considerable value. This formed an inverse square law depression in the overall surface, not unlike the water only constant and bigger. The special light was again released from the center of this depression. What was noticed was a similar wave phenomenon formed with just one small modification... the effect of the extra depression (which went out to infinity) added an "extra" inverse square law "force" to the light. The symmetric elastic depression apparently "slowed" the light in its travels to the periphery by a couple of percent. Examination showed that this was the elastic deformation had increased the actual distances traveled by the light (successive circumferences showed an excess in area and an apparent modification of the value of pi). Careful accounting showed that it was most noticeable near the center where the mass was and was a constant problem "out to infinity". Concentric circles indicate the light's energy passed them at later times than in the first light experiment due to the greater physical distance the light had to travel due to this deformation (the speed of the light remained constant). While this "retardation" was observed the effect of "full on" electromagnetic "induction" was never noticed, where the energy surged back and forth, where the analogy of the water puddle seemed a better model for the phenomenon. No matter what the deformation of the surface within the elastic bounds... all that seemed to happen was a slowing of the speed of light was occurring. Though this was "light" the laws of electromagnetism did not show the same result as indicated in "real" experiments. There was something wrong with this "surface"... it was not able to produce the known inductive effects. The "ripples" produced much of the effect of "propagation" but failed to realize the full effects of induction. It also did not work with "cavity" phenomena either never being able to trap the electromagnetic wave at all.
This "story" ends with the Physicists becoming frustrated with the process and they say ... to hell with it... lets propose that it does all the right things and we call these "postulates"... the maths is too nice to disturb. What is "obvious" is you can't deform the surface sufficiently to form cavities where the energy can "pool" and "surge". If you do deform the surface sufficiently your tensor mathematics will no longer describe the non-linear functions found there. Also forming "cavities" in space-time was tanamount to producing "mini-black holes" and requires vast machines sort of like those at Cern.
Practical experiments done in the 21st Century indicate that "mechanical" models of oscillation and atomic like properties can be performed using closed cavity resonators. These do not "naturally" form in space-time. Every attempt to "quantize" this surface fails. It is shown by mathematical analysis that the very process of this effort is mathematically flawed. Yet "we all know" that space-time is "quantized" don't we?
The gedanken experiment continues... Mechanical systems using artificial "shells" of 2D space-time allow the special light to spread indefinitely on an inner surface of a sphere rather than these unrealistic flat planes. Somewhere between the flat planes and the small distances where these "shells" seem to crop up the geometry changes quite a bit... wonder why?
Do you see the issues here? Do we agree at least to this much? Do we understand also why a simple 2D description of the 3D surfaces will not work?
Cheers
This stuff must be taken with some good humour... elves must at least have a laugh about these issues.
OK...
you have a good point C2 about the "Inverse square Law" being easy to start with. Something simple... Lets think about the similarity between a small amount of water and light... these are as different as you can get but they are excellent to think about. I will use the analogy of "space-time" of being a "flexible " sheet. First consider space-time as flat as it is possible to be... with 1 gee gravity (perpendicular) and the sheet stretching from here to Pluto. Not the slightest deviation from flatness can be detected. This is of course a Gedanken Experiment. I now have a glass of "idealized" water and some "unusual" light that likes "hugging" two dimensional surfaces but other than that is quite normal... it travels at the speed of light etc. Now this surface is stiffer than steel and it is "perfect" to use tensors on this surface since it is elastic but definitely not "rubber" since rubber is definitely not elastic. Do you get my drift?I pour the glass of water on the surface and it spreads but because water has some mass it has very slightly almost infinitesimally curved this sheet of 2D space-time and though it spreads ultimately for miles it eventually "pools". Being ideal water the "dip" in the center of the sheet of "steel" is less than the thickness of a single atom (lucky this water is ideal) but it is something and eventually this "depression" is sufficient to ultimately cause the water to "come to rest" and pool. A very special "optical technique" can plot this curvature on the sheet as concentric circular curves with the maximum value in the center where the water was released. This "depression" surprisingly goes clear out to the edge of the sheet (and potentially beyond) since this has caused a bend in the "figure" as an inverse square law ... all the way to "infinity". The effect is "never" gone away and the "figure" is always perfect.
When I mean at rest I am assuming that the idealized particles do not have enough thermal energy to overcome surface tension etc... Only under these extreme conditions will Tensors work at all since it is a theory of "linear" deformation and though you may want to use complex maths to describe the properties with first second and third order derivatives of things such as in General Relativity, these deformation must remain smaller than can be seen for the maths to work correctly. Not my idea you can check this out.
The reason this "ideal water" pooled was because it had some mass which caused the natural depression and all the rest followed due to the "mathematically ideal" properties of this "stiff" but "ideal" membrane.
I carefully clean up... every slightest bit and I start again. This time with my special light that is constrained to "hug the surface" of the sheet. The light has no rest mass. This literally means that it only travels at "one speed"... the speed of light. This speed is so high that no hill is too high for it to not get over. The only thing that potentially could arrest its motion is a black hole and this sheet is once again "perfect" and there is no curve in it at all. I drop my glass of special light at the center of the surface of the sheet. It is "up and running instantly" and it has no rest mass because it has no "rest velocity" but it did impart momentum to the surface of the model "space-time". From the sheets point of view it is a flash at the center that spreads as if it was an impulse in the surface of a very stiff pond. There is no "nett depression" since the "impulse" produces a plus and minus transverse oscillation always of equal effect that "spreads" at the speed of light. Special cameras record this event for our later scrutiny. We see interference zones at some angles and the initial conditions make a lot of difference to the positioning and frequency of these "zones". But because it was just a single impulse the disturbance is of limited duration and it travels to the edge of the sheet with the height of the overall disturbance falling off as an inverse square law relationship.
Accounting is done on this process and we note that we can calculate an energy function at all times in this surface and this "one off" event produced "packets" where the energy was a maximum on this wavefront as it spread "classically" (at the speed of light). Since it was "perfectly elastic" the total energy of these "packets" remained constant as it spread... just becoming more and more spread. An accurate accounting of the "geometric figure" of the sheet noticed that when all the positive excursions and the negative excursions of this "one off ripple" were added up... there was never a time when there was any "nett" depression or anti-depression in the surface except at T=0 in a small zone around the origin. This effect quickly "dissipated" and did not travel far from the center. After that initial impulse this effect was not noticed again. This was an "anti-symmetric" disturbance for all but an instant when it was created.
We then went back over the figures for the water and noticed the same phenomenon. Similar ripples but because of the constant mass of the water there was a "permanent" lowering of the central energy of the system (depression) and the velocity was very much slower because of its inherent mass and the waves dissipated toward the edge and reflected off the boundary always near the maximum spread of the "pool", surging back and forth radially with time... luckily the amplitude was exceedingly small and the deformations in the underlying surface were even smaller being in that very stiff material. Because this "liquid" was ideal these oscillations continued on and on... quivering and returning to the source periodically, the boundary fluctuating. Somehow eventually the "vibrations" quietened down and the oscillations were damped away to zero and the pool was "still". This meant that the more elastic surface of the (pseudo) 2D space-time sheet was even more ideal and the phenomena continued there longer than the time it took to be damped down in the bulk of the ideal water itself. In the end the energy function showed a "symmetric" figure and never once had "zero" energy except at the beginning near T=0 where a fluctuation did show some "one sided character for a brief instant. This was a 'symmetric".. one sided function.
The light on the other hand could not be retained by the sheet and it "escaped" off the edge in one "cycle". In both cases the "fluids" obeyed inverse square law "propagation" but they were different. The water responded to a permanent depression at the center and "pooled"... this was due to the nett effect of a one sided "mass function" at that center. All the material was retained within a certain distance from the center and oscillations in the fluid had a temporal and a harmonic effect... these were surging radially then converging radially... like a breathing... and the waves formed a series of nodes and anti-nodes in the surface as a standing pattern which eventually dissipated.
A third experiment was also performed where the "underside of this surface at its center was "weighted" by a constant mass of considerable value. This formed an inverse square law depression in the overall surface, not unlike the water only constant and bigger. The special light was again released from the center of this depression. What was noticed was a similar wave phenomenon formed with just one small modification... the effect of the extra depression (which went out to infinity) added an "extra" inverse square law "force" to the light. The symmetric elastic depression apparently "slowed" the light in its travels to the periphery by a couple of percent. Examination showed that this was the elastic deformation had increased the actual distances traveled by the light (successive circumferences showed an excess in area and an apparent modification of the value of pi). Careful accounting showed that it was most noticeable near the center where the mass was and was a constant problem "out to infinity". Concentric circles indicate the light's energy passed them at later times than in the first light experiment due to the greater physical distance the light had to travel due to this deformation (the speed of the light remained constant). While this "retardation" was observed the effect of "full on" electromagnetic "induction" was never noticed, where the energy surged back and forth, where the analogy of the water puddle seemed a better model for the phenomenon. No matter what the deformation of the surface within the elastic bounds... all that seemed to happen was a slowing of the speed of light was occurring. Though this was "light" the laws of electromagnetism did not show the same result as indicated in "real" experiments. There was something wrong with this "surface"... it was not able to produce the known inductive effects. The "ripples" produced much of the effect of "propagation" but failed to realize the full effects of induction. It also did not work with "cavity" phenomena either never being able to trap the electromagnetic wave at all.
This "story" ends with the Physicists becoming frustrated with the process and they say ... to hell with it... lets propose that it does all the right things and we call these "postulates"... the maths is too nice to disturb. What is "obvious" is you can't deform the surface sufficiently to form cavities where the energy can "pool" and "surge". If you do deform the surface sufficiently your tensor mathematics will no longer describe the non-linear functions found there. Also forming "cavities" in space-time was tanamount to producing "mini-black holes" and requires vast machines sort of like those at Cern.
Practical experiments done in the 21st Century indicate that "mechanical" models of oscillation and atomic like properties can be performed using closed cavity resonators. These do not "naturally" form in space-time. Every attempt to "quantize" this surface fails. It is shown by mathematical analysis that the very process of this effort is mathematically flawed. Yet "we all know" that space-time is "quantized" don't we?
The gedanken experiment continues... Mechanical systems using artificial "shells" of 2D space-time allow the special light to spread indefinitely on an inner surface of a sphere rather than these unrealistic flat planes. Somewhere between the flat planes and the small distances where these "shells" seem to crop up the geometry changes quite a bit... wonder why?
Do you see the issues here? Do we agree at least to this much? Do we understand also why a simple 2D description of the 3D surfaces will not work?
Cheers
QUOTE
I can offer very little that may advance your cause. I will suggest that you ponder the questions "what is the dualistic opposite of ISL?", and "what role does Pi play in that duality?" If nothing else, it may lead you to further insight to the geometry that you seek.
You fox I'm not going to let you go that easy.
I'm thinking.
We could all be bubbling with laughter if we could only understand each other.
jal
Hi TRoc and Confused2 et al,
Unfortunately our posts crossed paths. I needed to modify my answer a little to make it sensible. Refresh your browser.
I am having a little problem with the "visualization". I have been reading your "photon - photon" annihilation producing anti-particles. See second diagram here (e-p annihilation) ...
A photon is emitted from each of two electrons and they interact along a line drawn between them?" Is this the "experiment"? Since photons can pass through each other unaffected (Bose-Einstein Statistics) and all conservation laws are "respected" why did this occur to produce the new electron - positron pair? For this to work it seems we do not need to "burst bubbles" ... just "unravel" them, both these events are reversible. This also needs some "broken symmetry" for it to happen as well, perhaps an atom or other particle with mass.
Cheers
Unfortunately our posts crossed paths. I needed to modify my answer a little to make it sensible. Refresh your browser.
I am having a little problem with the "visualization". I have been reading your "photon - photon" annihilation producing anti-particles. See second diagram here (e-p annihilation) ...
A photon is emitted from each of two electrons and they interact along a line drawn between them?" Is this the "experiment"? Since photons can pass through each other unaffected (Bose-Einstein Statistics) and all conservation laws are "respected" why did this occur to produce the new electron - positron pair? For this to work it seems we do not need to "burst bubbles" ... just "unravel" them, both these events are reversible. This also needs some "broken symmetry" for it to happen as well, perhaps an atom or other particle with mass.
Cheers
TRoc?...Good Elf?....
Let's look at how it propagates
in/on
in/onit is elastic
Let's look at how it propagates
QUOTE
The reason this "ideal water" pooled was because it had some mass which caused the natural depression and all the rest followed due to the "mathematically ideal" properties of this "stiff" but "ideal" membrane.
in/on
QUOTE (->
| QUOTE |
| The reason this "ideal water" pooled was because it had some mass which caused the natural depression and all the rest followed due to the "mathematically ideal" properties of this "stiff" but "ideal" membrane. |
in/onit is elastic
the membrane.
After you explain, spread/propagate then I'll go to your final point.
After you explain, spread/propagate then I'll go to your final point.
Do we understand also why a simple 2D description of the 3D surfaces will not work?
Just to make things easier for you, put your drop at the bottom corner and explain the path of speading/propagation . You can go on the surfaces of the blue areas but not inside the blue areas because that is occupied by the membrane.
Remember, you said that the membrane is elastic/quivering (make it) by as much as 50%.
Go for it.
jal
What??? Good Elf just made a post
QUOTE
Since it was "perfectly elastic" the total energy of these "packets" remained constant as it spread... just becoming more and more spread
After you explain, spread/propagate then I'll go to your final point.
QUOTE (->
| QUOTE |
| Since it was "perfectly elastic" the total energy of these "packets" remained constant as it spread... just becoming more and more spread |
After you explain, spread/propagate then I'll go to your final point.
Do we understand also why a simple 2D description of the 3D surfaces will not work?
Just to make things easier for you,
put your drop at the bottom corner and explain the path of speading/propagation . You can go on the surfaces of the blue areas but not inside the blue areas because that is occupied by the membrane.Remember, you said that the membrane is elastic/quivering (make it) by as much as 50%.
Go for it.
jal
What??? Good Elf just made a post
All,
The legacy of modern science is a large collection of writings, written by hundreds of individuals, at different times along a 300 year time-line. Different languages, different specialties, and a large collection of self invoked symbols representing both observations, and predictive systems, loosely joined by a decimal oriented quantity group called "numbers". In the end that is why math plays such an important role in all this; to keep us "somewhere close" to the same page.
It is quite an experience to be part of this new, quasi REAL-TIME, sharing of thoughts oriented at explaining the world around us. This world has become both enormously smaller AND larger than what existed in the collective consciousness of our predecessors. Because of this, even though we have been adding to our collective knowledge base with unprecedented speed, the questions have kept pace with the answers.
Indeed, the challenge can be perceived as larger than before. I firmly believe that we have enough data collected to solve the puzzle. Sorting through the "miles of piles" of information, and agreeing on what to "throw out" and what to retain, is a huge task. Specialization has created monsters out of some of us; the more we know of "our branch", the less likely we believe an "outsider" will have relevant ideas. I think that specialization is counter-evolutionary; it is only by the "bringing together" of specialized data, and combining or generalizing it, do we make quantum leaps of knowledge. Since the Universities are not likely to start churning out Generalists anytime soon, the little box of light in front of you is the best hope that we have. Gone are the days when "men of great knowledge" can weigh in as experts in all Sciences.
OK, off the soap box !
jal, that was partly "just for you": I did not mean to "dodge your question", only that, what I had read of your work did not light up my thoughts enough to where I thought I could be of direct help. I won't give up if you won't !
Good Elf,
I was "changing gears" a bit on that last post: I mean to apply "bubble" thinking to the electron as well. No thorough discussion of the "photon" should be without a good run on the electron. So ALL of that was applying spherical wave / bubble analogies to the electron, as well as subsequent photo electron generation / reception.
Yes, we did "cross paths" there! Imagine how many hairs I scratched out trying to see how your post was in reply to mine !! I am going to have to read it a FEW more times to fully "gel" with it, but I am still with you.
TRoc
The legacy of modern science is a large collection of writings, written by hundreds of individuals, at different times along a 300 year time-line. Different languages, different specialties, and a large collection of self invoked symbols representing both observations, and predictive systems, loosely joined by a decimal oriented quantity group called "numbers". In the end that is why math plays such an important role in all this; to keep us "somewhere close" to the same page.
It is quite an experience to be part of this new, quasi REAL-TIME, sharing of thoughts oriented at explaining the world around us. This world has become both enormously smaller AND larger than what existed in the collective consciousness of our predecessors. Because of this, even though we have been adding to our collective knowledge base with unprecedented speed, the questions have kept pace with the answers.
Indeed, the challenge can be perceived as larger than before. I firmly believe that we have enough data collected to solve the puzzle. Sorting through the "miles of piles" of information, and agreeing on what to "throw out" and what to retain, is a huge task. Specialization has created monsters out of some of us; the more we know of "our branch", the less likely we believe an "outsider" will have relevant ideas. I think that specialization is counter-evolutionary; it is only by the "bringing together" of specialized data, and combining or generalizing it, do we make quantum leaps of knowledge. Since the Universities are not likely to start churning out Generalists anytime soon, the little box of light in front of you is the best hope that we have. Gone are the days when "men of great knowledge" can weigh in as experts in all Sciences.
OK, off the soap box !
jal, that was partly "just for you": I did not mean to "dodge your question", only that, what I had read of your work did not light up my thoughts enough to where I thought I could be of direct help. I won't give up if you won't !
Good Elf,
I was "changing gears" a bit on that last post: I mean to apply "bubble" thinking to the electron as well. No thorough discussion of the "photon" should be without a good run on the electron. So ALL of that was applying spherical wave / bubble analogies to the electron, as well as subsequent photo electron generation / reception.
Yes, we did "cross paths" there! Imagine how many hairs I scratched out trying to see how your post was in reply to mine !! I am going to have to read it a FEW more times to fully "gel" with it, but I am still with you.
TRoc
I hate talking to myself....I never get any new answers
jal
jal
So Jal? Its a wave pattern within a a lower demisonal packet?
Guest_Steve...
sorry.... I'm looking for a new answer.... you make it move/speading/propagation through space/fabric and tell me what happens.
jal
sorry.... I'm looking for a new answer.... you make it move/speading/propagation through space/fabric and tell me what happens.
jal
Hi Jal,
I see you are very intense about this concept. What about simple spreading volumetrically? Why do we need to have these little spheres? Why do we absolutely need this embellishment to the fabric of the Universe? The next question is ... is it some kind of stuck in place structure? I know there are a number of attempts to fill the Universe with crystalline forms. I do not think that this is the answer for the emptiness "out there".
The next question is what is the material these bubbles are made from? If the answer is "empty space"... how is this structure energetically supported? I fully realize that your idea may be ultimately right but it would be surprising to me to have this come up as a winner since it is not answering all the "great questions" it is only explaining a small aspect of the whole picture.
If you have a good reply to this already link to it and I might be able to pick up on it easier. You are sure giving it a big run for its money.
Cheers
I see you are very intense about this concept. What about simple spreading volumetrically? Why do we need to have these little spheres? Why do we absolutely need this embellishment to the fabric of the Universe? The next question is ... is it some kind of stuck in place structure? I know there are a number of attempts to fill the Universe with crystalline forms. I do not think that this is the answer for the emptiness "out there".
The next question is what is the material these bubbles are made from? If the answer is "empty space"... how is this structure energetically supported? I fully realize that your idea may be ultimately right but it would be surprising to me to have this come up as a winner since it is not answering all the "great questions" it is only explaining a small aspect of the whole picture.
If you have a good reply to this already link to it and I might be able to pick up on it easier. You are sure giving it a big run for its money.
Cheers
Hi!
Ever since the concept that space time was developed I was intrigued by the fact that here was a "material" with some kind of structure.
No matter where I looked, nobody was addressing how EMF and particles were moving/spreading/propagation through that "material". Nobody,(except LQG) were trying to find a shape, size or structure for that material.
See... you said, "....spreading volumetrically..." and you assumed that there was no mechanism or structure for the spreading to go "through".
Your next point, " ...stuck in place...", If you mean, stiff but elastic? I would go with that.
Next, they would have to be made of energy "bubbles". That is why they are "elastic".
The "bubble" explanation, above, was not contrary to a spacetime structure.
I wouldn't be surprise that it could be "a winner" of a description.
I do not want to detract from you main discussion ....if you want to call and end to this discussion...so be it.
jal
Ever since the concept that space time was developed I was intrigued by the fact that here was a "material" with some kind of structure.
No matter where I looked, nobody was addressing how EMF and particles were moving/spreading/propagation through that "material". Nobody,(except LQG) were trying to find a shape, size or structure for that material.
See... you said, "....spreading volumetrically..." and you assumed that there was no mechanism or structure for the spreading to go "through".
Your next point, " ...stuck in place...", If you mean, stiff but elastic? I would go with that.
Next, they would have to be made of energy "bubbles". That is why they are "elastic".
The "bubble" explanation, above, was not contrary to a spacetime structure.
I wouldn't be surprise that it could be "a winner" of a description.
I do not want to detract from you main discussion ....if you want to call and end to this discussion...so be it.
jal
Hi Jal,
I know your idea is the opposite to the way I am thinking about it but nobody can say who is a winner or not. Whenever you feel the urge to "contribute" feel free.
Cheers
I know your idea is the opposite to the way I am thinking about it but nobody can say who is a winner or not. Whenever you feel the urge to "contribute" feel free.
Cheers
Hi!
Nope, I think similar.
TRoc Posted: Sep 28 2005, 03:39 PM
And I used 2r to equate the whole phase and to be equal to time
TRoc Posted: Sep 30 2005, 01:53 PM
And I used 2r to equate the whole phase and to be equal to time
TRoc Posted: Sep 30 2005, 01:53 PM
At this point, we have shown that we can produce a plane wave within a spherical region centered at the origin, of radius as large as we want
TRoc Posted: Nov 11 2005, 09:14 AM
Good Elf Posted: Nov 12 2005, 09:54 AM
Good Elf Posted: Nov 12 2005, 09:54 AM
..."Space-time Bubbles"....
I think that they are still there making up spacetime
I could go on and on...I like what is being done here.... because I see a description of spacetime in action.
I'll hold back on my comments
jal
Nope, I think similar.
TRoc Posted: Sep 28 2005, 03:39 PM
QUOTE
The relationship of energy moving around the spiral to its' wavelength (= to 2r) would be ~ pi. Note here a departure on my part from the norm; I am not talking here about a wave packet, or a stream, etc., I am talking about the simple case of a single photon. Because only 1 phase of the wave exists at a time, I use 2r to equal half of the phase. The other half will exist in the next frame, at 1/2 wavelength distance away. So it is a circle cut in 1/2 and separated by time, and connected at the "node" in between the phases.
And I used 2r to equate the whole phase and to be equal to time
TRoc Posted: Sep 30 2005, 01:53 PM
QUOTE (->
| QUOTE |
| The relationship of energy moving around the spiral to its' wavelength (= to 2r) would be ~ pi. Note here a departure on my part from the norm; I am not talking here about a wave packet, or a stream, etc., I am talking about the simple case of a single photon. Because only 1 phase of the wave exists at a time, I use 2r to equal half of the phase. The other half will exist in the next frame, at 1/2 wavelength distance away. So it is a circle cut in 1/2 and separated by time, and connected at the "node" in between the phases. |
And I used 2r to equate the whole phase and to be equal to time
TRoc Posted: Sep 30 2005, 01:53 PM
At this point, we have shown that we can produce a plane wave within a spherical region centered at the origin, of radius as large as we want
TRoc Posted: Nov 11 2005, 09:14 AM
QUOTE
Almost every experiment I can think of takes place in a "medium" that is defined by the "user". This medium, like everything else, has a resonant frequency
Good Elf Posted: Nov 12 2005, 09:54 AM
QUOTE (->
| QUOTE |
| Almost every experiment I can think of takes place in a "medium" that is defined by the "user". This medium, like everything else, has a resonant frequency |
Good Elf Posted: Nov 12 2005, 09:54 AM
..."Space-time Bubbles"....
I think that they are still there making up spacetime
I could go on and on...I like what is being done here....
because I see a description of spacetime in action.I'll hold back on my comments
jal
Privet Good Elf !
Have we a 21st century Fermat in the person of Michael Munowitz?
The following outpouring, I fear, may turn your elven eyelids into lead weights, and make your beaming eyes glaze over. If you experience such symptoms, then please sprightly hop along to more interesting matters.
I deluge you and your fellow Phys Ogres with this wealth of redundant detail to quell any doubt that Dr. Munowitz, whom I myself had never heard of until yesterday, is indeed the Real McCoy as regards certain issues discussed with gusto and intelligence on this forum -- though not always with as wide a range of data as would be optimal.
So if you haven't yet come across Dr. Munowitz's ideas, please consider allocating a tiny crinkle or two in your Elrondishly elevated crenellated prefrontal hard drive, the better to store and process a few bytes, jots & tittles of Dr. Munowitz's scientific/metaphysical datapoints, as well as his recursive claim of qualification to such claims.
In the 80's Munowitz was a researcher in "particle chemistry" at the U.C. Lawrence Laboratories atop the glorious green Elvish hills of Lothlorien that tower above the quaint, desirous-at-all-costs-to-bow-out-of-history hobbit town of BerzerkelyShire. Munowitz's Lawrence Lab research led to publication of "non-trivial," still cited research articles -- articles that he believes, if more widely examined and understood, would "destructively interfere" with certain notions of paradox and mystery surrounding the FERMIONIC quantum microcosm. He's also authored a college Chemistry text considered by some to be the finest ever penned (keyboarded, dictated, etc.), but from the reader reviews, it may be somewhat too advanced for all save tenured Chemistry professors. Munowitz's PhD is in Chemistry, and as might be expected, was granted by the hegemonic H school by the Charles.
Munowitz's latest book is a work of popular science -- "Knowing : The Nature of Physical Law."
I squandered precious time yesterday flipping through its pages at a local B&N.
Now I think we (Good Elf and Tergiversating Dybbuk, among others) find "relatively" little challenge in covering with fig leafs any serious gaps in empirical data and scientific theory to explain supposed instances of alleged PHOTONIC quantum weirdness, such as:
( a ) The supposedly inscrutable "paradox" of PHOTONIC zebra striping that occurs when an EM interaction takes place within a well-tempered double slit camera obscura (a venerable Enlightenment device invented in much the same scientific spirit and at nearly the same historical moment as the high-tech improvements that so revolutionized the then burgeoning decapitation industry); and
( b ) the paradox of spooky coordinated entangled PHOTONIC action occurring at supposed "distances" allegedly accessible only via superluminal intercession.
The above is actually not too weird, hardly spooky enough, nor particularly paradoxical, at least insofar as EM-&-PHOTONS-&-Light Cones are concerned, since:
( c ) The smoking gun responsible for destructive interference and PHOTONIC cancellation is a feature -- or perhaps it's really a "bug," a bosonic auto-immune deficiency, I don't know -- expressed in roustabout EM's wavy gravy-ness whenever EM is roused into interaction. This feature -- or bug -- has been empirically detected, mathematically scrutinized, reflected upon & theorized over for two centuries since Thomas Young's day. As a result, a few precious EM trade secrets have been wrested from the BOOK and rendered unto WE the HUBRISTIC, the OVERABUNDANT, the MOST UNSAPIENT -- save for uncommonly rare good, better and great Elfs (and Ents, those that remain).
( d ) Likewise, by nature EM interacts invariantly apace at C, whose notable feature/bug is a quality of infinite Lorentz transformation, of forward length contraction, of advancing time dilation, and of light cones unto total nullity, from a relative point of view. Atemporal nonlocal PHOTONIC entanglement, it turns out, is another way of saying Special Relativity -- which is to say, an obvious, garden variety, C metric. Far less spooky, I should think, than, say, some freezing December night stumbling upon Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner and Blitzen all tangled up in blue.
However. . .
Houston. . .
We have a problem.
We've encountered a load of FERMIONS who are causing us a heap of grief.
Bohrian fatalism dictates that we surrender and give up the ghost in the face f the FERMION hordes. For:
(e) When it comes to a FERMIONIC quantum, Thomas Young's double slit device PERVERSELY continues to produce destructive interference; and
(f) And perhaps it should be recalled that Einstein et al.'s EPR gedanken exercise was spooky precisely because the animal who escaped the particle zoo to emerge from the quantum foam nonlocally and atemporally was NOT our old friend, Mr. PHOTON, but rather pesky LEPTON, a/k/a Kid Electron, to be exact.
What the heck are particles with rest masses doing thinking they can masquerade as infinitely Lorentzian transformed bosons.
Not cricket, I say.
Enter Michael Munowitz.
Says he, the problem was basically solved back in the 70's by the renowned Swedish mathematician Lars Hormander, who was awarded the Fields Medal in '62.
Munowitz doesn't have time to get into the details, however. Says he, the maths are just too complicated to fit into a book aimed at the general public.
Nor would the maths fit in the margins -- fair guess, doncha think?
Munowitz doesn't use the taboo word "pilot wave."
Nor is the infidel who advanced that heresy mentioned in the index.
But Munowitz is unambiguous that there is a wave of "information" associated with WE fermions -- and decades of experiments have shown that fermions at the quantum level engage in destructive interference and entanglement just as any civilized rest mass zero boson would.
So did Lars the Math Guy really demonstrate that there exists a wave that is not only undetectable whilst in light cone mode, but whose emission and absorption are equally undectable. . . yet it exists.
Well, I got no problemo whatsoever with Pilot Waves and such.
But it's not something I can discuss except with fellow Gnostics.
You see, there ain't no fig leaf that I can figure out here.
Good Elf. . . maybe your superior Elfish cognition can come up with some insight into what Munowitz was saying about Hormander.
If you google, here's a key phrase from the relevant section of Munowitz's book:
"microlocal analysis"
Also, Munowitz was saying something about propagation of the information wave being governed by a quadratic equation in regards to how it expands, as inferred (nothing is detected) from our humble FERMIONIC viewpoint.
++++++++++++++++++++++++++
Munowitz writings & links:
1. Knowing : The Nature of Physical Law (Hardcover)
* Hardcover: 432 pages
* Publisher: Oxford University Press, USA (November 1, 2005)
* Language: English
* ISBN: 0195167376
Book Description
We ask question after question of an indifferent universe that would just as soon remain mute; and slowly, patiently, one sentence at a time, we write our own version of the book of nature. It is called science, from the Latin word for knowledge, and it is a book everybody should read.
With simplicity and elegance, "Knowing" interprets the book of nature for curious readers of all sorts--but especially for those hoping to appreciate the beauty of physics without getting lost in the mathematics. Indeed, there is a world of scientific understanding in the pages of this gracefully written and inviting book, where hundreds of little diagrams substitute for the equations that physicists otherwise need to tell their tale. Readers will discover the way things work: how big things (like Earth or Moon) come from small things (like quarks and electrons), how tiny particles push and pull, and how the world hangs in the balance. We learn how an "unbiased" observer and a fixed speed of light, nothing else, conjure up E=mc2 and four-dimensional space-time. We see how Newton's clockwork universe of unwavering determination differs (but not in every respect) from Heisenberg's quantum universe of hazy uncertainty. And we see how a world of chaos throws a wrench into everybody's mechanical ideal.
From tiny atoms to vast galaxies, the universe is ours to explore and to know: its particles, its interactions, its laws, its unending surprises. Heavily illustrated with explanatory drawings and diagrams--perhaps no other science book for general readers uses diagrams so extensively--Knowing takes us to the edge of modern science, allowing us to peer in further than we would have dreamed possible.
II. COHERENCE and NMR
Michael Munowitz, PhD (Harvard --
Wiley-Interscience; 1 edition (September 19, 1988)
ISBN: 0-471-61523-4
Hardcover
289 pages
October 1988
From publisher's website:
Table of Contents and
http://www.wiley.com/WileyCDA/WileyTitle/p...html?print=true
Book Description:
http://www.wiley.com/WileyCDA/WileyTitle/p...html?print=true
Places into perspective the role of quantum dynamics in NMR (Nuclear Magnetic Resonance) -- addresses characterization of a system of particles with spin (or any other quantum mechanical property), how such a system changes with time, and broader applications to chemistry, physics, and other fields. Also ties together the various manifestations of NMR in solids and liquids -- using as a common language the unitary transformation of a system's density operator under the Hamiltonian -- revealing the underpinnings of what might be called manipulative NMR: experiments in which the time-dependent (Erwin) Schrödinger equation is controlled externally in a non-trivial fashion.
++++++++++++++++++++++
From Amazon ( http://www.amazon.com/gp/product/0471615234/
)
One comment.
5 Stars -- OUTSTANDING TREATMENT WITH A PHYSICAL INSIGHT TO COHERENCE, August 30, 1998
The connection between the physical motion of nuclear spins in a magnetic field and the mathematics that describes their interactions is a difficult one for the spectroscopist. It is common for a modern NMR spectroscopist to understand the elements of a complex NMR pulse sequence in terms of product operators or the density matrix. I have written numerous pulse sequences myself, but always had difficulty in picturing how the nuclear vectors were able to transfer information about their phase or component amplitudes onto a coupling partner. This book is the first I have read which clarifies the coherence transfer process with physcial desriptions of the interactions of the Cartesian components of the angular momentum.
+++++++++++++++++++++++
III. MULTIPLE-QUANTUM DYNAMICS IN SOLID STATE NMR
THE JOURNAL OF CHEMICAL PHYSICS -- September 1, 1985 -- Volume 83, Issue 5, pp. 2015-2025
http://scitation.aip.org/getabs/servlet/Ge...=cvips&gifs=yes
By J. Baum, M. MUNOWITZ, A. N. Garroway, and A. Pines
Department of Chemistry, University of California, Berkeley and Materials and Molecular Research Division, Lawrence Berkeley Laboratory, Berkeley, CA
Abstract:
Recently developed solid state multiple-quantum NMR methods are applied to extended coupling networks, where direct dipole-dipole interactions can be used to create coherences of very high order (~100). . . [W]e treat the distribution of coherence in a multiple-quantum spectrum as Gaussian, and characterize a spectrum obtained for a given preparation time by its variance. The variance of the distribution is associated roughly with the number of coupled spins effectively interacting, and its steady growth with time reflects the continual expansion of the system under the action of the dipolar interactions. The increase in effective system "size" is accounted for by a random walk model for the time development of the density operator.
+++++++++++++++++++++++
[Munowitz's '85 paper seems to have laid a solid foundation for work now in the news concerning sustained chain reaction quantum entanglement]
IV. TWELVE-SPIN "SCHRÖDINGER CAT"
By: A. K. Khitrin, PhD - Associate Professor, Chemistry faculty, Materials Science division, Kent State, Ohio [ http://dept.kent.edu/chemistry/Faculty/Research/khitrin.htm ]
and
Jae-Seung Lee, Post-Doctoral Fellow, Kent State, OH [http://mrm.kaist.ac.kr/members/galley/galley.html ]
http://arxiv.org/ftp/quant-ph/papers/0508/0508011.pdf
Abstract:
PSEUDOPURE "cat" state, a superposition of quantum states with all spins up and all spins down, is experimentally demonstrated for a system of twelve dipolar-coupled nuclear spins of fully 13C-labeled benzene molecule oriented in a liquid-crystalline matrix.
Excerpt:
Quantum entanglement, a form of non-classical correlation, has been an important issue in recent debates on the foundations of quantum mechanics.1 In quantum information science, the entanglement is considered as a physical resource, which plays a crucial role in quantum teleportation,2 quantum key distribution (3,4) and quantum computing. (5,6)
A cat state is a special case of entanglement: superposition of the two most distinct states (alive and dead). Building a cat state is a benchmark for controlling quantum systems. (7) The decoherence time of the cat state sets limitation on quantum computing because this state is supposed to be the most fragile among quantum states. Cat states are the central elements in high-precision spectroscopy, (8) amplified quantum detection (9,10) and measurement. (11) In such applications, possible gain from using the cat states is proportional to the number of particles which can be entangled.
In this letter, we describe an experiment on creating a pseudopure cat state of a system of twelve dipolar-coupled nuclear spins. At present, it is the largest and the most complex composite quantum system where manipulations with individual states have been performed.
The physical system is a 5% solution of fully labeled 13C6-benzene (Aldrich) in liquid crystalline solvent MLC-6815 (EMD Chemical). Each benzene molecule contains twelve nuclear spins, six 13C and six protons, coupled by residual dipole-dipole interactions. All intermolecular spin-spin interactions are averaged out by fast molecular motions. Therefore, the system is an ensemble of non-interacting spin clusters, where each benzene molecule contains twelve dipolar-coupled nuclear spins. The experiment has been performed with a Varian Unity/Inova 500 MHz NMR spectrometer.
[snipped]
Summary:
In summary, a twelve-spin cat state has been experimentally demonstrated in a system of dipolar-coupled nuclear spins of fully 13C-labeled benzene in liquid crystalline matrix. In terms of the number of qubits, it is the largest "Schrödinger cat" ever built.
++++++++++++++++
["CAT STATES" - really, now... what's NOT to like?]
V. RESURRECTION OF SCHRÖDINGER CAT
Jae-Seung Lee, A. K. Khitrin
Department of Chemistry, Kent State University, Kent OH
Abstract:
Quantum decoherence is the major obstacle in using the potential of engineered
quantum dynamics to revolutionize high-precision measurements, sensitive
detection, or information processing. Here we experimentally demonstrate that
quantum state of a system can be recovered after the state is destroyed by
uncontrollable natural decoherence. Physical system is a cluster of seven
dipolar-coupled nuclear spins of single-labeled 13C-benzene in liquid crystal. 13C spin plays a role of a device for measuring protons' "cat" state, a superposition of states with six spins up (alive) and six spins down (dead). Information about the state, stored in the 13C spin, is used to bring the protons' subsystem into the alive state, while the excess entropy produced by decoherence is transferred to the "measuring device", the 13C spin.
[snipped]
Summary:
Decoherence is the major obstacle in designing practical devices which will utilize the advantages of quantum dynamics in detection, measurement, or information processing. The experiment performed in this work demonstrates that destructive effect of decoherence can be minimized by using a scheme where information stored in one part of a system is used to restore quantum state of another part.
Have we a 21st century Fermat in the person of Michael Munowitz?
The following outpouring, I fear, may turn your elven eyelids into lead weights, and make your beaming eyes glaze over. If you experience such symptoms, then please sprightly hop along to more interesting matters.
I deluge you and your fellow Phys Ogres with this wealth of redundant detail to quell any doubt that Dr. Munowitz, whom I myself had never heard of until yesterday, is indeed the Real McCoy as regards certain issues discussed with gusto and intelligence on this forum -- though not always with as wide a range of data as would be optimal.
So if you haven't yet come across Dr. Munowitz's ideas, please consider allocating a tiny crinkle or two in your Elrondishly elevated crenellated prefrontal hard drive, the better to store and process a few bytes, jots & tittles of Dr. Munowitz's scientific/metaphysical datapoints, as well as his recursive claim of qualification to such claims.
In the 80's Munowitz was a researcher in "particle chemistry" at the U.C. Lawrence Laboratories atop the glorious green Elvish hills of Lothlorien that tower above the quaint, desirous-at-all-costs-to-bow-out-of-history hobbit town of BerzerkelyShire. Munowitz's Lawrence Lab research led to publication of "non-trivial," still cited research articles -- articles that he believes, if more widely examined and understood, would "destructively interfere" with certain notions of paradox and mystery surrounding the FERMIONIC quantum microcosm. He's also authored a college Chemistry text considered by some to be the finest ever penned (keyboarded, dictated, etc.), but from the reader reviews, it may be somewhat too advanced for all save tenured Chemistry professors. Munowitz's PhD is in Chemistry, and as might be expected, was granted by the hegemonic H school by the Charles.
Munowitz's latest book is a work of popular science -- "Knowing : The Nature of Physical Law."
I squandered precious time yesterday flipping through its pages at a local B&N.
Now I think we (Good Elf and Tergiversating Dybbuk, among others) find "relatively" little challenge in covering with fig leafs any serious gaps in empirical data and scientific theory to explain supposed instances of alleged PHOTONIC quantum weirdness, such as:
( a ) The supposedly inscrutable "paradox" of PHOTONIC zebra striping that occurs when an EM interaction takes place within a well-tempered double slit camera obscura (a venerable Enlightenment device invented in much the same scientific spirit and at nearly the same historical moment as the high-tech improvements that so revolutionized the then burgeoning decapitation industry); and
( b ) the paradox of spooky coordinated entangled PHOTONIC action occurring at supposed "distances" allegedly accessible only via superluminal intercession.
The above is actually not too weird, hardly spooky enough, nor particularly paradoxical, at least insofar as EM-&-PHOTONS-&-Light Cones are concerned, since:
( c ) The smoking gun responsible for destructive interference and PHOTONIC cancellation is a feature -- or perhaps it's really a "bug," a bosonic auto-immune deficiency, I don't know -- expressed in roustabout EM's wavy gravy-ness whenever EM is roused into interaction. This feature -- or bug -- has been empirically detected, mathematically scrutinized, reflected upon & theorized over for two centuries since Thomas Young's day. As a result, a few precious EM trade secrets have been wrested from the BOOK and rendered unto WE the HUBRISTIC, the OVERABUNDANT, the MOST UNSAPIENT -- save for uncommonly rare good, better and great Elfs (and Ents, those that remain).
( d ) Likewise, by nature EM interacts invariantly apace at C, whose notable feature/bug is a quality of infinite Lorentz transformation, of forward length contraction, of advancing time dilation, and of light cones unto total nullity, from a relative point of view. Atemporal nonlocal PHOTONIC entanglement, it turns out, is another way of saying Special Relativity -- which is to say, an obvious, garden variety, C metric. Far less spooky, I should think, than, say, some freezing December night stumbling upon Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner and Blitzen all tangled up in blue.
However. . .
Houston. . .
We have a problem.
We've encountered a load of FERMIONS who are causing us a heap of grief.
Bohrian fatalism dictates that we surrender and give up the ghost in the face f the FERMION hordes. For:
(e) When it comes to a FERMIONIC quantum, Thomas Young's double slit device PERVERSELY continues to produce destructive interference; and
(f) And perhaps it should be recalled that Einstein et al.'s EPR gedanken exercise was spooky precisely because the animal who escaped the particle zoo to emerge from the quantum foam nonlocally and atemporally was NOT our old friend, Mr. PHOTON, but rather pesky LEPTON, a/k/a Kid Electron, to be exact.
What the heck are particles with rest masses doing thinking they can masquerade as infinitely Lorentzian transformed bosons.
Not cricket, I say.
Enter Michael Munowitz.
Says he, the problem was basically solved back in the 70's by the renowned Swedish mathematician Lars Hormander, who was awarded the Fields Medal in '62.
Munowitz doesn't have time to get into the details, however. Says he, the maths are just too complicated to fit into a book aimed at the general public.
Nor would the maths fit in the margins -- fair guess, doncha think?
Munowitz doesn't use the taboo word "pilot wave."
Nor is the infidel who advanced that heresy mentioned in the index.
But Munowitz is unambiguous that there is a wave of "information" associated with WE fermions -- and decades of experiments have shown that fermions at the quantum level engage in destructive interference and entanglement just as any civilized rest mass zero boson would.
So did Lars the Math Guy really demonstrate that there exists a wave that is not only undetectable whilst in light cone mode, but whose emission and absorption are equally undectable. . . yet it exists.
Well, I got no problemo whatsoever with Pilot Waves and such.
But it's not something I can discuss except with fellow Gnostics.
You see, there ain't no fig leaf that I can figure out here.
Good Elf. . . maybe your superior Elfish cognition can come up with some insight into what Munowitz was saying about Hormander.
If you google, here's a key phrase from the relevant section of Munowitz's book:
"microlocal analysis"
Also, Munowitz was saying something about propagation of the information wave being governed by a quadratic equation in regards to how it expands, as inferred (nothing is detected) from our humble FERMIONIC viewpoint.
++++++++++++++++++++++++++
Munowitz writings & links:
1. Knowing : The Nature of Physical Law (Hardcover)
* Hardcover: 432 pages
* Publisher: Oxford University Press, USA (November 1, 2005)
* Language: English
* ISBN: 0195167376
Book Description
We ask question after question of an indifferent universe that would just as soon remain mute; and slowly, patiently, one sentence at a time, we write our own version of the book of nature. It is called science, from the Latin word for knowledge, and it is a book everybody should read.
With simplicity and elegance, "Knowing" interprets the book of nature for curious readers of all sorts--but especially for those hoping to appreciate the beauty of physics without getting lost in the mathematics. Indeed, there is a world of scientific understanding in the pages of this gracefully written and inviting book, where hundreds of little diagrams substitute for the equations that physicists otherwise need to tell their tale. Readers will discover the way things work: how big things (like Earth or Moon) come from small things (like quarks and electrons), how tiny particles push and pull, and how the world hangs in the balance. We learn how an "unbiased" observer and a fixed speed of light, nothing else, conjure up E=mc2 and four-dimensional space-time. We see how Newton's clockwork universe of unwavering determination differs (but not in every respect) from Heisenberg's quantum universe of hazy uncertainty. And we see how a world of chaos throws a wrench into everybody's mechanical ideal.
From tiny atoms to vast galaxies, the universe is ours to explore and to know: its particles, its interactions, its laws, its unending surprises. Heavily illustrated with explanatory drawings and diagrams--perhaps no other science book for general readers uses diagrams so extensively--Knowing takes us to the edge of modern science, allowing us to peer in further than we would have dreamed possible.
II. COHERENCE and NMR
Michael Munowitz, PhD (Harvard --
Wiley-Interscience; 1 edition (September 19, 1988)
ISBN: 0-471-61523-4
Hardcover
289 pages
October 1988
From publisher's website:
Table of Contents and
http://www.wiley.com/WileyCDA/WileyTitle/p...html?print=true
Book Description:
http://www.wiley.com/WileyCDA/WileyTitle/p...html?print=true
Places into perspective the role of quantum dynamics in NMR (Nuclear Magnetic Resonance) -- addresses characterization of a system of particles with spin (or any other quantum mechanical property), how such a system changes with time, and broader applications to chemistry, physics, and other fields. Also ties together the various manifestations of NMR in solids and liquids -- using as a common language the unitary transformation of a system's density operator under the Hamiltonian -- revealing the underpinnings of what might be called manipulative NMR: experiments in which the time-dependent (Erwin) Schrödinger equation is controlled externally in a non-trivial fashion.
++++++++++++++++++++++
From Amazon ( http://www.amazon.com/gp/product/0471615234/
)
One comment.
5 Stars -- OUTSTANDING TREATMENT WITH A PHYSICAL INSIGHT TO COHERENCE, August 30, 1998
The connection between the physical motion of nuclear spins in a magnetic field and the mathematics that describes their interactions is a difficult one for the spectroscopist. It is common for a modern NMR spectroscopist to understand the elements of a complex NMR pulse sequence in terms of product operators or the density matrix. I have written numerous pulse sequences myself, but always had difficulty in picturing how the nuclear vectors were able to transfer information about their phase or component amplitudes onto a coupling partner. This book is the first I have read which clarifies the coherence transfer process with physcial desriptions of the interactions of the Cartesian components of the angular momentum.
+++++++++++++++++++++++
III. MULTIPLE-QUANTUM DYNAMICS IN SOLID STATE NMR
THE JOURNAL OF CHEMICAL PHYSICS -- September 1, 1985 -- Volume 83, Issue 5, pp. 2015-2025
http://scitation.aip.org/getabs/servlet/Ge...=cvips&gifs=yes
By J. Baum, M. MUNOWITZ, A. N. Garroway, and A. Pines
Department of Chemistry, University of California, Berkeley and Materials and Molecular Research Division, Lawrence Berkeley Laboratory, Berkeley, CA
Abstract:
Recently developed solid state multiple-quantum NMR methods are applied to extended coupling networks, where direct dipole-dipole interactions can be used to create coherences of very high order (~100). . . [W]e treat the distribution of coherence in a multiple-quantum spectrum as Gaussian, and characterize a spectrum obtained for a given preparation time by its variance. The variance of the distribution is associated roughly with the number of coupled spins effectively interacting, and its steady growth with time reflects the continual expansion of the system under the action of the dipolar interactions. The increase in effective system "size" is accounted for by a random walk model for the time development of the density operator.
+++++++++++++++++++++++
[Munowitz's '85 paper seems to have laid a solid foundation for work now in the news concerning sustained chain reaction quantum entanglement]
IV. TWELVE-SPIN "SCHRÖDINGER CAT"
By: A. K. Khitrin, PhD - Associate Professor, Chemistry faculty, Materials Science division, Kent State, Ohio [ http://dept.kent.edu/chemistry/Faculty/Research/khitrin.htm ]
and
Jae-Seung Lee, Post-Doctoral Fellow, Kent State, OH [http://mrm.kaist.ac.kr/members/galley/galley.html ]
http://arxiv.org/ftp/quant-ph/papers/0508/0508011.pdf
Abstract:
PSEUDOPURE "cat" state, a superposition of quantum states with all spins up and all spins down, is experimentally demonstrated for a system of twelve dipolar-coupled nuclear spins of fully 13C-labeled benzene molecule oriented in a liquid-crystalline matrix.
Excerpt:
Quantum entanglement, a form of non-classical correlation, has been an important issue in recent debates on the foundations of quantum mechanics.1 In quantum information science, the entanglement is considered as a physical resource, which plays a crucial role in quantum teleportation,2 quantum key distribution (3,4) and quantum computing. (5,6)
A cat state is a special case of entanglement: superposition of the two most distinct states (alive and dead). Building a cat state is a benchmark for controlling quantum systems. (7) The decoherence time of the cat state sets limitation on quantum computing because this state is supposed to be the most fragile among quantum states. Cat states are the central elements in high-precision spectroscopy, (8) amplified quantum detection (9,10) and measurement. (11) In such applications, possible gain from using the cat states is proportional to the number of particles which can be entangled.
In this letter, we describe an experiment on creating a pseudopure cat state of a system of twelve dipolar-coupled nuclear spins. At present, it is the largest and the most complex composite quantum system where manipulations with individual states have been performed.
The physical system is a 5% solution of fully labeled 13C6-benzene (Aldrich) in liquid crystalline solvent MLC-6815 (EMD Chemical). Each benzene molecule contains twelve nuclear spins, six 13C and six protons, coupled by residual dipole-dipole interactions. All intermolecular spin-spin interactions are averaged out by fast molecular motions. Therefore, the system is an ensemble of non-interacting spin clusters, where each benzene molecule contains twelve dipolar-coupled nuclear spins. The experiment has been performed with a Varian Unity/Inova 500 MHz NMR spectrometer.
[snipped]
Summary:
In summary, a twelve-spin cat state has been experimentally demonstrated in a system of dipolar-coupled nuclear spins of fully 13C-labeled benzene in liquid crystalline matrix. In terms of the number of qubits, it is the largest "Schrödinger cat" ever built.
++++++++++++++++
["CAT STATES" - really, now... what's NOT to like?]
V. RESURRECTION OF SCHRÖDINGER CAT
Jae-Seung Lee, A. K. Khitrin
Department of Chemistry, Kent State University, Kent OH
Abstract:
Quantum decoherence is the major obstacle in using the potential of engineered
quantum dynamics to revolutionize high-precision measurements, sensitive
detection, or information processing. Here we experimentally demonstrate that
quantum state of a system can be recovered after the state is destroyed by
uncontrollable natural decoherence. Physical system is a cluster of seven
dipolar-coupled nuclear spins of single-labeled 13C-benzene in liquid crystal. 13C spin plays a role of a device for measuring protons' "cat" state, a superposition of states with six spins up (alive) and six spins down (dead). Information about the state, stored in the 13C spin, is used to bring the protons' subsystem into the alive state, while the excess entropy produced by decoherence is transferred to the "measuring device", the 13C spin.
[snipped]
Summary:
Decoherence is the major obstacle in designing practical devices which will utilize the advantages of quantum dynamics in detection, measurement, or information processing. The experiment performed in this work demonstrates that destructive effect of decoherence can be minimized by using a scheme where information stored in one part of a system is used to restore quantum state of another part.
Hi Tergiversating Dybbuk,
Your suggestion looks highly interesting. I like to head Good_Elf off at the pass and I'm too mean to buy the book. Google gets me stuff that is either mathematically or chemically incomprehensible - give us a break here..
-Confused2 .
Your suggestion looks highly interesting. I like to head Good_Elf off at the pass and I'm too mean to buy the book. Google gets me stuff that is either mathematically or chemically incomprehensible
- give us a break here..-Confused2
.
Hi Tergiversating Dybbuk,
I have never heard of Michael Munowitz but no doubt there is a great deal I have not heard. Would you do the honor of explaining his concepts here to not just myself but to all? I am downloading your data and I will have a look into it as well. I do not know how appropriate it is but I am very interested by what the abstract is saying... he he he!
Cheers
QUOTE
"When you see a leaf blown from a tree and whirled along the pathway, don't think it's an accident, for it's moved by the will of G-d!"
IBST
IBST
I have never heard of Michael Munowitz but no doubt there is a great deal I have not heard. Would you do the honor of explaining his concepts here to not just myself but to all? I am downloading your data and I will have a look into it as well. I do not know how appropriate it is but I am very interested by what the abstract is saying... he he he!
Cheers
Dear Elves & other Folks,
Confused2 writes,
Me to -- on both counts.
Me to -- on both counts.
Google gets me stuff that is either mathematically or chemically incomprehensible sad.gif - give us a break here...
Google proved next to useless (not quite 100%, but pretty close) in illuminating Dr. Munowtiz's evidence, theories or speculations re the utterly undetectable -- and from the perspective of fermionic earthlings -- perhaps forever ethereal quantum information waves by which fermionic substances play the same game of ( a ) entangled spooky-action-at-a-distance and ( b ) single-file-procession (one particle at at time) double-slit wave interference.
In the case of photons, we can blame this wierdness on the EM interaction, with which we are all familiar.
However, much to the chagrin of those allergic to cognitive dissonance, C state properties also appear to crop up amongst -- that is, are observable characteristics under certain conditions -- greater-than-null-rest-mass fermions (leptons, hadrons).
SR offers an interpretation (more or less) of such wierdness in the case of rest mass zero Bosons, since having no rest mass, C is their normal state, with the expected result, a la Lorentz, that forward distance and passing time are transformed full null.
No reading of SR, however, to my limited knowledge, offers a seat at the full null table to mass-bearing fermions.
And yet, whether observed buzzing single file through double slits, or entangled group-wise in "CAT" states, Fermions appear to jump the SR rope with insolence or aplomb (take your pick), seeming to shed their entire rest mass -- in a limited way or from a certain perspective -- and to conduct themselves as if in some respect they operate fully & nully in the guage-boson-only restricted C-zone.
Einstein, Podolsky and Rosen predicted just this result under QM for the fermionic, mass-endowed Electron. The outlandishness and impossibility of such a result was sufficient in and of itself to debunk QM, so they thought.
Turned out, however, that this particular piece of outlandishness is straight from the BOOK.
David Bohm thought he had intuited some further passages from BOOK on this subject, and tried to re-introduce de Broglie's long ridiculed notion that written into the genetic code of even oafish, dense, slow moving fermions is a C-rated pilot wave of "quantum information." The whole concept stumbled badly on the blockhead idea that there might exist associated with "matter" such a non-tangible, materially undetectable informational thingie.
Not exactly a spectacular career move for a young scientist to suggest in all seriousness that matter is governed by non-material forces that cannot even in principle be detected.
Given this background, I was more than a little surprised to read in Munowtiz's book that the issue was long since settled, and by a mathematcian no less: Fields Medal winner Lars Hormand. His solution described key differences in how, from the perspective of decohered fermionic entity (elf, man, dybbuk, cat or dog, for e.g.) the respective waves (EM vs Quantum Informational) would propogate differently. Of course, this is all old news, and besides, it wouldn't fit withing the margins of a popular science book, so it didn't really bear further discussion in Knowing : The Nature of Physical Law.
Good Elf writes,
Wasn't I abundantly clear in my earlier message?
Well, how about in my response to Confused2 above?
Lemme be clear about one thing, however -- Dr. Munowitz was about as clear as a delphic virgin in his won't-fit-in-the-margins tantalizing peek-a-boo.
Very odd that Bohm didn't get a tip of the hat in the index or otherwise, nor did such hoary terms as "pilot wave." Though I don't blame the writer for avoiding such references like the deadly hexes they are known to be. Knock on wood.
That much I got.
But I'm utterly stumped by the references to Dr. Hormand and microlocal analysis and quadratic hoo hoo as all being instrumental in solving, long ago, mind you, the riddle of a materially undetectable quantum information wave.
I prefer to wait until books come out in soft cover before parting with my precious, inflatable rubbles. Sometimes seriously marked down copies of new books are available on Half.com or Walmart.com. I'll see what's out there, but otherwise it may be some time before I put down any cash on the barrelhead. Though I could head back to B&N and take better notes, I s'pose.
Btw, googling the two names Hörmander and Schrödinger may pull up something useful for the mathematically literate, of whose esteemed number I count myself null.
There may also be something in the term "quadratic-scattering wavefront set."
For instance,
http://www-math.mit.edu/~rbm/abstracts/Wunsch/Wunsch.html :
Wasn't I abundantly clear in my earlier message?
Well, how about in my response to Confused2 above?
Lemme be clear about one thing, however -- Dr. Munowitz was about as clear as a delphic virgin in his won't-fit-in-the-margins tantalizing peek-a-boo.
Very odd that Bohm didn't get a tip of the hat in the index or otherwise, nor did such hoary terms as "pilot wave." Though I don't blame the writer for avoiding such references like the deadly hexes they are known to be. Knock on wood.
That much I got.
But I'm utterly stumped by the references to Dr. Hormand and microlocal analysis and quadratic hoo hoo as all being instrumental in solving, long ago, mind you, the riddle of a materially undetectable quantum information wave.
I prefer to wait until books come out in soft cover before parting with my precious, inflatable rubbles. Sometimes seriously marked down copies of new books are available on Half.com or Walmart.com. I'll see what's out there, but otherwise it may be some time before I put down any cash on the barrelhead. Though I could head back to B&N and take better notes, I s'pose.
Btw, googling the two names Hörmander and Schrödinger may pull up something useful for the mathematically literate, of whose esteemed number I count myself null.
There may also be something in the term "quadratic-scattering wavefront set."
For instance,
http://www-math.mit.edu/~rbm/abstracts/Wunsch/Wunsch.html :
Propagation of growth and singularities for Schrödinger operators
By J. Wunsch
We study the time-dependent Schrödinger equation ... on ... with an asymptotically Euclidean metric, or, more generally, on a manifold with boundary M, equipped with a ``scattering metric.'' Microlocal smoothness of ... turns out to be determined by growth properties of ... at ... . A sensible measure of both singularities and growth is the ``quadratic-scattering'' wavefront set, a generalization of Hörmander's wavefront set. We prove a propagation theorem for the quadratic-scattering wavefront set that describes singularities and growth of in terms of singularities and growth of . This theorem generalizes a similar result of Craig, Kappeler and Strauss.
Or
http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=05-201
Also
http://www.amazon.com/gp/product/3540006621/
Also
http://www.amazon.com/gp/product/3540006621/
The Analysis of Linear Partial Differential Operators I : Distribution Theory and Fourier Analysis (Classics in Mathematics) (Paperback)
by Lars Hörmander
Paperback: 440 pages
Publisher: Springer; 2 edition (August 13, 2003)
Language: English
ISBN: 3540006621
The definitive guide to micro-local analysis
Hormander's four volume guide to linear partial differential operators is the definitive guide to smooth micro-local analysis from the man who invented a large fraction of it.
Micro-local analysis is an approach to the analysis of singularities of variable coefficient linear partial differential equations based on the use of the Fourier transform and of symplectic geometry. Ideas from Hamiltonian physics and quantum theory also feature heavily. The fact that the subject is a mixture of analysis and geometry makes it beautiful and powerful.
The four volume set is hard work and in some ways is more useful as a reference work than as a learning book but on the other hand, all the material is there and the books do reward the reader who is willing to spend the time to study them carefully.
The first volume is the most accessible and the second paperback edition carries the added benefit of included exercises with partial answers which are often highly informative.
And
http://www-maths.swan.ac.uk/staff/at/research.html
Confused2 writes,
QUOTE
I like to head Good_Elf off at the pass and I'm too mean to buy the book.
Me to -- on both counts.
QUOTE (->
| QUOTE |
| I like to head Good_Elf off at the pass and I'm too mean to buy the book. |
Me to -- on both counts.
Google gets me stuff that is either mathematically or chemically incomprehensible sad.gif - give us a break here...
Google proved next to useless (not quite 100%, but pretty close) in illuminating Dr. Munowtiz's evidence, theories or speculations re the utterly undetectable -- and from the perspective of fermionic earthlings -- perhaps forever ethereal quantum information waves by which fermionic substances play the same game of ( a ) entangled spooky-action-at-a-distance and ( b ) single-file-procession (one particle at at time) double-slit wave interference.
In the case of photons, we can blame this wierdness on the EM interaction, with which we are all familiar.
However, much to the chagrin of those allergic to cognitive dissonance, C state properties also appear to crop up amongst -- that is, are observable characteristics under certain conditions -- greater-than-null-rest-mass fermions (leptons, hadrons).
SR offers an interpretation (more or less) of such wierdness in the case of rest mass zero Bosons, since having no rest mass, C is their normal state, with the expected result, a la Lorentz, that forward distance and passing time are transformed full null.
No reading of SR, however, to my limited knowledge, offers a seat at the full null table to mass-bearing fermions.
And yet, whether observed buzzing single file through double slits, or entangled group-wise in "CAT" states, Fermions appear to jump the SR rope with insolence or aplomb (take your pick), seeming to shed their entire rest mass -- in a limited way or from a certain perspective -- and to conduct themselves as if in some respect they operate fully & nully in the guage-boson-only restricted C-zone.
Einstein, Podolsky and Rosen predicted just this result under QM for the fermionic, mass-endowed Electron. The outlandishness and impossibility of such a result was sufficient in and of itself to debunk QM, so they thought.
Turned out, however, that this particular piece of outlandishness is straight from the BOOK.
David Bohm thought he had intuited some further passages from BOOK on this subject, and tried to re-introduce de Broglie's long ridiculed notion that written into the genetic code of even oafish, dense, slow moving fermions is a C-rated pilot wave of "quantum information." The whole concept stumbled badly on the blockhead idea that there might exist associated with "matter" such a non-tangible, materially undetectable informational thingie.
Not exactly a spectacular career move for a young scientist to suggest in all seriousness that matter is governed by non-material forces that cannot even in principle be detected.
Given this background, I was more than a little surprised to read in Munowtiz's book that the issue was long since settled, and by a mathematcian no less: Fields Medal winner Lars Hormand. His solution described key differences in how, from the perspective of decohered fermionic entity (elf, man, dybbuk, cat or dog, for e.g.) the respective waves (EM vs Quantum Informational) would propogate differently. Of course, this is all old news, and besides, it wouldn't fit withing the margins of a popular science book, so it didn't really bear further discussion in Knowing : The Nature of Physical Law.
Good Elf writes,
QUOTE
I have never heard of Michael Munowitz but no doubt there is a great deal I have not heard. Would you do the honor of explaining his concepts here to not just myself but to all? I am downloading your data and I will have a look into it as well. I do not know how appropriate it is but I am very interested by what the abstract is saying... he he he!
Wasn't I abundantly clear in my earlier message?
Well, how about in my response to Confused2 above?
Lemme be clear about one thing, however -- Dr. Munowitz was about as clear as a delphic virgin in his won't-fit-in-the-margins tantalizing peek-a-boo.
Very odd that Bohm didn't get a tip of the hat in the index or otherwise, nor did such hoary terms as "pilot wave." Though I don't blame the writer for avoiding such references like the deadly hexes they are known to be. Knock on wood.
That much I got.
But I'm utterly stumped by the references to Dr. Hormand and microlocal analysis and quadratic hoo hoo as all being instrumental in solving, long ago, mind you, the riddle of a materially undetectable quantum information wave.
I prefer to wait until books come out in soft cover before parting with my precious, inflatable rubbles. Sometimes seriously marked down copies of new books are available on Half.com or Walmart.com. I'll see what's out there, but otherwise it may be some time before I put down any cash on the barrelhead. Though I could head back to B&N and take better notes, I s'pose.
Btw, googling the two names Hörmander and Schrödinger may pull up something useful for the mathematically literate, of whose esteemed number I count myself null.
There may also be something in the term "quadratic-scattering wavefront set."
For instance,
http://www-math.mit.edu/~rbm/abstracts/Wunsch/Wunsch.html :
QUOTE (->
| QUOTE |
| I have never heard of Michael Munowitz but no doubt there is a great deal I have not heard. Would you do the honor of explaining his concepts here to not just myself but to all? I am downloading your data and I will have a look into it as well. I do not know how appropriate it is but I am very interested by what the abstract is saying... he he he! |
Wasn't I abundantly clear in my earlier message?
Well, how about in my response to Confused2 above?
Lemme be clear about one thing, however -- Dr. Munowitz was about as clear as a delphic virgin in his won't-fit-in-the-margins tantalizing peek-a-boo.
Very odd that Bohm didn't get a tip of the hat in the index or otherwise, nor did such hoary terms as "pilot wave." Though I don't blame the writer for avoiding such references like the deadly hexes they are known to be. Knock on wood.
That much I got.
But I'm utterly stumped by the references to Dr. Hormand and microlocal analysis and quadratic hoo hoo as all being instrumental in solving, long ago, mind you, the riddle of a materially undetectable quantum information wave.
I prefer to wait until books come out in soft cover before parting with my precious, inflatable rubbles. Sometimes seriously marked down copies of new books are available on Half.com or Walmart.com. I'll see what's out there, but otherwise it may be some time before I put down any cash on the barrelhead. Though I could head back to B&N and take better notes, I s'pose.
Btw, googling the two names Hörmander and Schrödinger may pull up something useful for the mathematically literate, of whose esteemed number I count myself null.
There may also be something in the term "quadratic-scattering wavefront set."
For instance,
http://www-math.mit.edu/~rbm/abstracts/Wunsch/Wunsch.html :
Propagation of growth and singularities for Schrödinger operators
By J. Wunsch
We study the time-dependent Schrödinger equation ... on ... with an asymptotically Euclidean metric, or, more generally, on a manifold with boundary M, equipped with a ``scattering metric.'' Microlocal smoothness of ... turns out to be determined by growth properties of ... at ... . A sensible measure of both singularities and growth is the ``quadratic-scattering'' wavefront set, a generalization of Hörmander's wavefront set. We prove a propagation theorem for the quadratic-scattering wavefront set that describes singularities and growth of in terms of singularities and growth of . This theorem generalizes a similar result of Craig, Kappeler and Strauss.
Or
http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=05-201
QUOTE
Propagation of singularities for Schrödinger equations on the Euclidean space with a scattering metric
Ito Kenichi
Abstract
June 6, 2005
Given a scattering metric on the Euclidean space. We consider the Schrödinger equation corresponding to the metric, and study the propagation of singularities for the solution in terms of the homogeneous wavefront set. We also prove that the notion of the homogeneous wavefront set is essentially equivalent to that of the quadratic scattering wavefront set introduced by J. Wunsch [21]. One of the main results in [21] follows
on the Euclidean space with a weaker, almost optimal condition on the potential.
Ito Kenichi
Abstract
June 6, 2005
Given a scattering metric on the Euclidean space. We consider the Schrödinger equation corresponding to the metric, and study the propagation of singularities for the solution in terms of the homogeneous wavefront set. We also prove that the notion of the homogeneous wavefront set is essentially equivalent to that of the quadratic scattering wavefront set introduced by J. Wunsch [21]. One of the main results in [21] follows
on the Euclidean space with a weaker, almost optimal condition on the potential.
Also
http://www.amazon.com/gp/product/3540006621/
QUOTE (->
| QUOTE |
| Propagation of singularities for Schrödinger equations on the Euclidean space with a scattering metric Ito Kenichi Abstract June 6, 2005 Given a scattering metric on the Euclidean space. We consider the Schrödinger equation corresponding to the metric, and study the propagation of singularities for the solution in terms of the homogeneous wavefront set. We also prove that the notion of the homogeneous wavefront set is essentially equivalent to that of the quadratic scattering wavefront set introduced by J. Wunsch [21]. One of the main results in [21] follows on the Euclidean space with a weaker, almost optimal condition on the potential. |
Also
http://www.amazon.com/gp/product/3540006621/
The Analysis of Linear Partial Differential Operators I : Distribution Theory and Fourier Analysis (Classics in Mathematics) (Paperback)
by Lars Hörmander
Paperback: 440 pages
Publisher: Springer; 2 edition (August 13, 2003)
Language: English
ISBN: 3540006621
The definitive guide to micro-local analysis
Hormander's four volume guide to linear partial differential operators is the definitive guide to smooth micro-local analysis from the man who invented a large fraction of it.
Micro-local analysis is an approach to the analysis of singularities of variable coefficient linear partial differential equations based on the use of the Fourier transform and of symplectic geometry. Ideas from Hamiltonian physics and quantum theory also feature heavily. The fact that the subject is a mixture of analysis and geometry makes it beautiful and powerful.
The four volume set is hard work and in some ways is more useful as a reference work than as a learning book but on the other hand, all the material is there and the books do reward the reader who is willing to spend the time to study them carefully.
The first volume is the most accessible and the second paperback edition carries the added benefit of included exercises with partial answers which are often highly informative.
And
http://www-maths.swan.ac.uk/staff/at/research.html
QUOTE
Research Interests of Prof. Aubrey Truman, Professor of Mathematics and Head of Dept., University of Wales Swansea
Prof. Truman has an extensive background in mathematical physics. In one of his first papers he generalised the tube theorems on the Laplace transforms of tempered distributions and showed how these results lead to the range of interaction in quantum field theories being h/mc, m being the mass of the least massive particle in the theory [1]. With David Elworthy at Warwick, using the oscillatory integrals of Hörmander, he originated what he feels is the best rigorous definition of Feynman path integrals in non relativistic quantum mechanics [2] proving that Feynman's original ideas on defining a path integral could be made mathematically respectable. This resulted in one of the first rigorous explanations of the origin of the Maslov indices for wave functions in harmonic oscillator type potentials and the simplest derivation of the classical mechanical limit of quantum mechanics as h -> 0.
Prof. Truman has an extensive background in mathematical physics. In one of his first papers he generalised the tube theorems on the Laplace transforms of tempered distributions and showed how these results lead to the range of interaction in quantum field theories being h/mc, m being the mass of the least massive particle in the theory [1]. With David Elworthy at Warwick, using the oscillatory integrals of Hörmander, he originated what he feels is the best rigorous definition of Feynman path integrals in non relativistic quantum mechanics [2] proving that Feynman's original ideas on defining a path integral could be made mathematically respectable. This resulted in one of the first rigorous explanations of the origin of the Maslov indices for wave functions in harmonic oscillator type potentials and the simplest derivation of the classical mechanical limit of quantum mechanics as h -> 0.
Hi Tergiversating Dybbuk, Confused2, TRoc, Bee, Jal et al,
You are indeed a very "naughty" Dybbuk. Here was I thinking you may be able to assist us all and lo... yours is a jolly "romp" down into a dark and dangerous woods... he he he!
Damn... should have known... trick or treat. I think I got the "trick".
Still... if you have something of a "treat" to tell... the invitation is still open.
In respect to the main theme of "bubbles" I have been pursuing (with the help of Confused2) a different tack on a different thread.
Electrostatic Attraction by Confused2
This will supply a new impetus to this thread as well. I just hope people "get it".
Cheers
You are indeed a very "naughty" Dybbuk. Here was I thinking you may be able to assist us all and lo... yours is a jolly "romp" down into a dark and dangerous woods... he he he!
QUOTE
Lemme be clear about one thing, however -- Dr. Munowitz was about as clear as a delphic virgin in his won't-fit-in-the-margins tantalizing peek-a-boo.
Damn... should have known... trick or treat. I think I got the "trick".
Still... if you have something of a "treat" to tell... the invitation is still open.
In respect to the main theme of "bubbles" I have been pursuing (with the help of Confused2) a different tack on a different thread.
Electrostatic Attraction by Confused2
This will supply a new impetus to this thread as well. I just hope people "get it".
Cheers
Hi Good Elf, Tergiversating Dybbuk, TRoc,Confused2 and all
I do hope that everyone is having a happy New Year.
I probably will NOT be able to participate in this forum more than once weekly [perhaps even less], but will try to contribute when possible.
I probably will NOT be able to participate in the topic/forum started by Confused2
Topic: Electrostatic attraction, How and why
Forum: Relativity, Quantum Mechanics, New Theories
Good Elf - why NOT move this topic The nature of "electricity" & "magnetism", are bubbles the answer? to the Forum Relativity, Quantum Mechanics, New Theories?
Oxford University Press:
About the Author(s)
“Michael Munowitz is a full-time science writer. A graduate of Yale University, he earned a Ph.D. in chemical physics from Harvard University and has held postdoctoral appointments at the University of Leiden and the University of California, Berkeley. He is the author most recently of Principles of Chemistry, described by one reviewer as "the best-written general chemistry book I have ever read." He lives in Naperville, Illinois.”
Reviews
"All those who are eager to understand how the world works but have been frustrated and discouraged by the forbidding mathematical language of physical science will welcome this fascinating, lucid, and satisfying account of what we know (and don't know) about this most profound of human endeavors. Munowitz has written 'physics without tears.'" --Christian de Duve, Nobel Prize Laureate in Physiology and Medicine [for discoveries concerning "the structural and functional organization of the cell" with two others]
http://www.oup.com/us/catalog/general/subj...T0wMTk1MTY3Mzc2
Amazon:
‘Knowing : The Nature of Physical Law’ (Hardcover) by Michael Munowitz
Buy this book with
‘The Road to Reality : A Complete Guide to the Laws of the Universe’ (Hardcover) by Roger Penrose [Hawking colleague, formulator of Spinors and Spin Network and Twistor and Twistor Space with an emphasis on helicity].
http://www.amazon.com/gp/product/019516737...glance&n=283155
Twistor Theory
Spinors and Spin Network
Twistor and Twistor Space
Connection to Quantum Theory
Twistor Gravity
Further Development
http://universe-review.ca/R15-19-twistor.htm
TWISTOR DIAGRAMS Website by Andrew Hodges
http://www.twistordiagrams.org.uk/
Twistor String Theory
Link to program and transparencies
THE MATHEMATICAL INSTITUTE University of Oxford
London Mathematical Society Workshop 10-14 January 2005
Abstract
“This meeting was organised to take stock of the rapid progress being made on twistor-string theory and to encourage further cross-fertilization between string-theory, twistor theory and perturbative gauge theory. Twistor string theory was introduced by Witten in hep-th/0312171 as a string theory in twistor space that makes contact with N=4 super Yang-Mills theory on space-time via a generalization of the Penrose-Ward transform augmented by certain D-instanton corrections. It promises to combine many of the most attractive features of string theory and twistor theory and has implications not only for Yang-Mills but also for (conformal) gravity. It has in particular led to major advances in the calculations of Yang-Mills scattering amplitudes with applications to collider physics.”
http://www.maths.ox.ac.uk/~lmason/Tws/
“Lars Valter Hörmander (born January 24, 1931) is a Swedish mathematician who has been called "the foremost contributor to the modern theory of linear partial differential equations". He was awarded the Fields Medal in 1962, and the Wolf Prize in 1988. His Analysis of Linear Partial Differential Operators I - IV is considered a standard work on the subject of linear partial differential operators.”
I: Distribution Theory and Fourier Analysis (Springer-Verlag)
II: Differential Operators with Constant Coefficients (Springer-Verlag)
III: Pseudo-Differential Operators (Springer-Verlag)
IV: Fourier Integral Operators (Springer-Verlag)
http://en.wikipedia.org/wiki/Lars_Hormander
Contrast and compare this with
http://www.britannica.com/eb/article-9048172
Sophus Lie 1842-1899
Norwegian mathematician who founded the theory of continuous groups and their applications to the theory of differential equations. His investigations led to one of the major branches of 20th-century mathematics, the theory of Lie groups and Lie algebras
The French scholar Jean Dieudonne said,
"Lie theory is in the process of becoming the most important part of modern mathematics. Little by little it became obvious that the most unexpected theories, from arithmetic to quantum physics, came to encircle this Lie field like a gigantic axis."
Guest reviewer Sigbjørn Hervik is a PhD student in the Gravitational and Relativity Group at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge
http://plus.maths.org/issue19/reviews/book3/
and with
Richard E. Borcherds one of the Fields medalists 1998
To conclude, as the automorphism group of a distinguished conformal field theory in the critical dimension 26, the monster is fundamentally related to string theory of theoretical physics. What seems amazing about the moonshine is that finite group theorists, interested in understanding finite simple groups, and theoretical physicists, interested in unifying the fundamental forces, have converged to similar mathematical structures, almost independently and around the same time.
C. S. Rajan, Tata Institute of Fundamental Research, Mumbai 400 005, India
http://www.iisc.ernet.in/~currsci/dec25/articles6.htm
There is an excellent website on ‘Geometric Algebra’ by David Hestenes physicist [emeritus] Arizona State University discussing ‘projective geometry, linear algebra and Lie groups.’
http://modelingnts.la.asu.edu/html/GeoAlg.html
Some of this may correlate or compete with the topic/forum started by TRoc
Topic: Burkhard Heim's Particle Structure Theory
Forum: Relativity, Quantum Mechanics, New Theories
There was a very interesting development that may relate to helicity.
‘Surface Story’ by Ivars Peterson: “Inspired by spiral soap films, mathematicians zero in on a novel, economical, and infinite helix.”
I do hope that everyone is having a happy New Year.
I probably will NOT be able to participate in this forum more than once weekly [perhaps even less], but will try to contribute when possible.
I probably will NOT be able to participate in the topic/forum started by Confused2
Topic: Electrostatic attraction, How and why
Forum: Relativity, Quantum Mechanics, New Theories
Good Elf - why NOT move this topic The nature of "electricity" & "magnetism", are bubbles the answer? to the Forum Relativity, Quantum Mechanics, New Theories?
Oxford University Press:
About the Author(s)
“Michael Munowitz is a full-time science writer. A graduate of Yale University, he earned a Ph.D. in chemical physics from Harvard University and has held postdoctoral appointments at the University of Leiden and the University of California, Berkeley. He is the author most recently of Principles of Chemistry, described by one reviewer as "the best-written general chemistry book I have ever read." He lives in Naperville, Illinois.”
Reviews
"All those who are eager to understand how the world works but have been frustrated and discouraged by the forbidding mathematical language of physical science will welcome this fascinating, lucid, and satisfying account of what we know (and don't know) about this most profound of human endeavors. Munowitz has written 'physics without tears.'" --Christian de Duve, Nobel Prize Laureate in Physiology and Medicine [for discoveries concerning "the structural and functional organization of the cell" with two others]
http://www.oup.com/us/catalog/general/subj...T0wMTk1MTY3Mzc2
Amazon:
‘Knowing : The Nature of Physical Law’ (Hardcover) by Michael Munowitz
Buy this book with
‘The Road to Reality : A Complete Guide to the Laws of the Universe’ (Hardcover) by Roger Penrose [Hawking colleague, formulator of Spinors and Spin Network and Twistor and Twistor Space with an emphasis on helicity].
http://www.amazon.com/gp/product/019516737...glance&n=283155
Twistor Theory
Spinors and Spin Network
Twistor and Twistor Space
Connection to Quantum Theory
Twistor Gravity
Further Development
http://universe-review.ca/R15-19-twistor.htm
TWISTOR DIAGRAMS Website by Andrew Hodges
http://www.twistordiagrams.org.uk/
Twistor String Theory
Link to program and transparencies
THE MATHEMATICAL INSTITUTE University of Oxford
London Mathematical Society Workshop 10-14 January 2005
Abstract
“This meeting was organised to take stock of the rapid progress being made on twistor-string theory and to encourage further cross-fertilization between string-theory, twistor theory and perturbative gauge theory. Twistor string theory was introduced by Witten in hep-th/0312171 as a string theory in twistor space that makes contact with N=4 super Yang-Mills theory on space-time via a generalization of the Penrose-Ward transform augmented by certain D-instanton corrections. It promises to combine many of the most attractive features of string theory and twistor theory and has implications not only for Yang-Mills but also for (conformal) gravity. It has in particular led to major advances in the calculations of Yang-Mills scattering amplitudes with applications to collider physics.”
http://www.maths.ox.ac.uk/~lmason/Tws/
“Lars Valter Hörmander (born January 24, 1931) is a Swedish mathematician who has been called "the foremost contributor to the modern theory of linear partial differential equations". He was awarded the Fields Medal in 1962, and the Wolf Prize in 1988. His Analysis of Linear Partial Differential Operators I - IV is considered a standard work on the subject of linear partial differential operators.”
I: Distribution Theory and Fourier Analysis (Springer-Verlag)
II: Differential Operators with Constant Coefficients (Springer-Verlag)
III: Pseudo-Differential Operators (Springer-Verlag)
IV: Fourier Integral Operators (Springer-Verlag)
http://en.wikipedia.org/wiki/Lars_Hormander
Contrast and compare this with
http://www.britannica.com/eb/article-9048172
Sophus Lie 1842-1899
Norwegian mathematician who founded the theory of continuous groups and their applications to the theory of differential equations. His investigations led to one of the major branches of 20th-century mathematics, the theory of Lie groups and Lie algebras
The French scholar Jean Dieudonne said,
"Lie theory is in the process of becoming the most important part of modern mathematics. Little by little it became obvious that the most unexpected theories, from arithmetic to quantum physics, came to encircle this Lie field like a gigantic axis."
Guest reviewer Sigbjørn Hervik is a PhD student in the Gravitational and Relativity Group at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge
http://plus.maths.org/issue19/reviews/book3/
and with
Richard E. Borcherds one of the Fields medalists 1998
To conclude, as the automorphism group of a distinguished conformal field theory in the critical dimension 26, the monster is fundamentally related to string theory of theoretical physics. What seems amazing about the moonshine is that finite group theorists, interested in understanding finite simple groups, and theoretical physicists, interested in unifying the fundamental forces, have converged to similar mathematical structures, almost independently and around the same time.
C. S. Rajan, Tata Institute of Fundamental Research, Mumbai 400 005, India
http://www.iisc.ernet.in/~currsci/dec25/articles6.htm
There is an excellent website on ‘Geometric Algebra’ by David Hestenes physicist [emeritus] Arizona State University discussing ‘projective geometry, linear algebra and Lie groups.’
http://modelingnts.la.asu.edu/html/GeoAlg.html
Some of this may correlate or compete with the topic/forum started by TRoc
Topic: Burkhard Heim's Particle Structure Theory
Forum: Relativity, Quantum Mechanics, New Theories
There was a very interesting development that may relate to helicity.
‘Surface Story’ by Ivars Peterson: “Inspired by spiral soap films, mathematicians zero in on a novel, economical, and infinite helix.”
I apparently violated flood control - to continue
There was a very interesting development that may relate to helicity.
‘Surface Story’ by Ivars Peterson: “Inspired by spiral soap films, mathematicians zero in on a novel, economical, and infinite helix.”
http://sciencenews.org/articles/20051217/bob9.asp
The Periodic Genus 1 Helicoid Family
http://www.msri.org/about/sgp/jim/geom/min...dg1p/index.html
Ending with my favorite quote -
“If we knew what it was we were doing, it would not be called research, would it?” Einstein
There was a very interesting development that may relate to helicity.
‘Surface Story’ by Ivars Peterson: “Inspired by spiral soap films, mathematicians zero in on a novel, economical, and infinite helix.”
http://sciencenews.org/articles/20051217/bob9.asp
The Periodic Genus 1 Helicoid Family
http://www.msri.org/about/sgp/jim/geom/min...dg1p/index.html
Ending with my favorite quote -
“If we knew what it was we were doing, it would not be called research, would it?” Einstein
Gadfly,
Bingo! links. Thank you.
I'm pleased to read that Penrose, having his "spinors" crushed and left to "twistor" in the wind for the past 35 years or so by his betters in mathematical physics, never deserted his post as prophet unheeded. . .
And by golly but whaddyaknow. . . Edward, Duke de Witten has now come round as an acolyte, a true believer of the Penrosian Gospel.
If proof of miracles and intelligent design were otherwise nugatory, behold this turn of events!
Nope, not a "random" mutation. Rather, in the LONG run . . . for which I have neither the patience nor the stamina nor the self-confidence (but then I'm no prophet either), THE TRUTH WILL (in its own good time) OUT.
Good Elf writes,
So Good Elf be neither of Rivendell, Lothlorien, nor Western Haven stock... but of the elven band who fled to Mirkwood in ages past, suspicious to the marrow of mithril enthralled dwarves and tergiversating dybbuks, are ye? Lemme assure ya, I can relate.
Sez Good Elf
So Good Elf be neither of Rivendell, Lothlorien, nor Western Haven stock... but of the elven band who fled to Mirkwood in ages past, suspicious to the marrow of mithril enthralled dwarves and tergiversating dybbuks, are ye? Lemme assure ya, I can relate.
Sez Good ElfStill... if you have something of a "treat" to tell... the invitation is still open.
Bingo! links. Thank you.
I'm pleased to read that Penrose, having his "spinors" crushed and left to "twistor" in the wind for the past 35 years or so by his betters in mathematical physics, never deserted his post as prophet unheeded. . .
And by golly but whaddyaknow. . . Edward, Duke de Witten has now come round as an acolyte, a true believer of the Penrosian Gospel.
If proof of miracles and intelligent design were otherwise nugatory, behold this turn of events!
Nope, not a "random" mutation. Rather, in the LONG run . . . for which I have neither the patience nor the stamina nor the self-confidence (but then I'm no prophet either), THE TRUTH WILL (in its own good time) OUT.
Good Elf writes,
QUOTE
Here was I thinking you may be able to assist us all and lo... yours is a jolly "romp" down into a dark and dangerous woods... Damn... should have known... trick or treat. I think I got the "trick".
So Good Elf be neither of Rivendell, Lothlorien, nor Western Haven stock... but of the elven band who fled to Mirkwood in ages past, suspicious to the marrow of mithril enthralled dwarves and tergiversating dybbuks, are ye? Lemme assure ya, I can relate.
Sez Good Elf
QUOTE (->
| QUOTE |
| Here was I thinking you may be able to assist us all and lo... yours is a jolly "romp" down into a dark and dangerous woods... Damn... should have known... trick or treat. I think I got the "trick". |
So Good Elf be neither of Rivendell, Lothlorien, nor Western Haven stock... but of the elven band who fled to Mirkwood in ages past, suspicious to the marrow of mithril enthralled dwarves and tergiversating dybbuks, are ye? Lemme assure ya, I can relate.
Sez Good ElfStill... if you have something of a "treat" to tell... the invitation is still open.
So too, my great Good Elf, do I extend my warm welcome and unctious embrace.
But enough whimsy!
It does indeed look like there's been some very interesting developments in the Realm where Bohm would have been King... but developments 'neath the radar that even Good Elves might not necessarily espy.
Seems the problem has been an age old one . . . MacDonalds vs Campbells, Orange vs Green, Mars & Venus -- that is to say: Mathematicians and Physicists are at it again... as usual. . . unable to communicate, not even talking past each other... but on different continents, or planets.
Alors, mon ami!
Allons-y!
Basic, but not bad:
Tantalizing:
Tantalizing:Didier Robert: The semi-classical Van-Vleck formula -- Application to the Aharonov-Bohm effect
22 Oktober 1999
http://www.math.kth.se/braket/1999/991022_nr33.pdf
Abstract: At the very beginning of the quantum theory, Van-Vleck (1928) proposed a nice approximation formula for the integral kernel of the time-dependent propagator of the Schrödinger equation. This formula can be deduced from the Feynman path integral by a formal stationary phase argument. After works by Maslov and Hörmander on Fourier-integral operators, it is possible to give a rigorous mathematical proof of the Van-Vleck formula. Here we give a more direct and elementary proof, using propagation of coherent states. We apply this result to give a mathematical proof for the Aharonov-Bohm effect observed on the time-dependent propagator. This effect concerns a phase factor depending on the flux of a magnetic field, which can be non-trivial even if the particle never meets the magnetic field.
Hmmm, what dis?
Dense, but if you be a Pythagorean, heavenly!
Dense, but if you be a Pythagorean, heavenly!A Local-to-Global Singularity Theorem for Quantum Field Theory on Curved Space-Time
http://projecteuclid.org/Dienst/UI/1.0/Sum....cmp/1104287233
Communications in Mathematical Physics 180, 1-22 (1996)
Marek J. Radzikowski1*
(with an Appendix by Rainer Verch2)
1 Department of Mathematics, Texas A&M University, College Station, TX 77843, USA, and Department
of Mathematics, University of York, Heslington, York YO1 5DD, UK
2 II Institut fur Theoretische Physik, Universitat Hamburg, D - 22761 Hamburg, Germany
Received: 21 September 1994 / Accepted: 25 August 1995
To a special friend, who saved my life when I was younger, without whom I could not
have written this paper.
Abstract:
We prove that if a reference two-point distribution of positive type on
a time orientable curved space-time (CST) satisfies a certain condition on its wave
front set (the "class 0hii9 condition") and if any other two-point distribution (i) is of
positive type, (ii) has the same antisymmetric part as the reference modulo smooth
function and (iii) has the same local singularity structure, then it has the same global
singularity structure. In the proof we use a smoothing, positivity-preserving pseudodifferential operator the support of whose symbol is restricted to a certain conic
region which depends on the wave front set of the reference state. This local-toglobal
theorem, together with results published elsewhere, leads to a verification of a
conjecture by Kay that for quasi-free states of the Klein-Gordon quantum field on a
globally hyperbolic CST, the local Hadamard condition implies the global Hadamard
condition. A counterexample to the local-to-global theorem on a strip in Minkowski
space is given when the class &ht,g condition is not assumed.
[snip]
The main goal of this paper is to present a "local-to-global" theorem more general
than Kay's conjecture. Results published elsewhere [37, 38] are employed in showing
that Kay's conjecture is a special case of this local-to-global theorem. The language
of micro-local analysis is used throughout and is found to apply very naturally to this
problem and to yield a quite general answer. This is not the first paper on quantized
fields on curved space-time in which micro-local methods are used: Dimock's work
on the scattering operator for a scalar field on curved space-time [6] makes significant
use of the distinguished parametrix theory of Duistermaat and Hormander [8]. Also
see [35] for even earlier examples of papers in which pseudo-differential operators
were used in the context of quantum field theory on stationary and static space-times.
The "distributional approach" to quantized fields on curved space-time used
throughout this paper is outlined in Sect. 2. Section 3 presents a brief introduction
to micro-local analysis and lists some results that will be useful in later sections.
In Sect. 4 the class &hi,g condition for a time orientable CST (M, g) and the main
local-to-global singularity theorem are stated, followed by an outline of the proof of
this theorem, the proof being contained in Sects. 5, 6, 7, and 8. (These sections are
summarized in Sect. 4.) In Sect. 9, Kay's conjecture is verified using the existence of
globally Hadamard quasi-free states on an arbitrary globally hyperbolic curved spacetime and the equivalence (for quasi-free Klein-Gordon states) of the global Hadamard condition with a certain wave front set spectral condition (WFSSC) introduced in [37, 38] which is in turn stronger than the class &M,g condition. In fact an even stronger statement than Conjecture 1.1 is proven: any two-point distribution of positive type which has the local Hadamard singularity structure and whose commutator is i times the difference of the advanced and retarded fundamental solutions of the Klein-Gordon operator (modulo a smooth function) must have the global Hadamard singularity structure. (Note that we do not assume the quasi-free property or that the Klein-Gordon equation is satisfied.) In Sect. 10, we demonstrate the necessity for the reference state to satisfy the class &M,9 condition, by displaying a counterexample to the local-to-global theorem on a strip in Minkowski space when this condition is not assumed. Section 11 discusses some implications of the local-to-global theorem, in particular the strengthening of the belief that the Hadamard condition is physically distinguished, and a corollary displaying some dependence among the axioms
on curved space-time.
Getting drowsier & drowsier. . . this last one should assure you a sound slumber.
But enough whimsy!
It does indeed look like there's been some very interesting developments in the Realm where Bohm would have been King... but developments 'neath the radar that even Good Elves might not necessarily espy.
Seems the problem has been an age old one . . . MacDonalds vs Campbells, Orange vs Green, Mars & Venus -- that is to say: Mathematicians and Physicists are at it again... as usual. . . unable to communicate, not even talking past each other... but on different continents, or planets.
Alors, mon ami!
Allons-y!
Basic, but not bad:
QUOTE
RESULTS AND PROBLEMS IN DECOHERENCE THEORY
Received on 20 December, 2004
http://www.scielo.br/pdf/bjp/v35n2a/a02v352a.pdf
Roland Omnes -- Laboratoire de Physique Th´eorique, Universit´e de Paris-Sud, 91405 Orsay (France)
The main steps in the development of the ideas on decoherence are briefly reviewed, together with their present achievements. Unsolved problems are also pointed out . . .
Received on 20 December, 2004
http://www.scielo.br/pdf/bjp/v35n2a/a02v352a.pdf
Roland Omnes -- Laboratoire de Physique Th´eorique, Universit´e de Paris-Sud, 91405 Orsay (France)
The main steps in the development of the ideas on decoherence are briefly reviewed, together with their present achievements. Unsolved problems are also pointed out . . .
Tantalizing:
QUOTE (->
| QUOTE |
| RESULTS AND PROBLEMS IN DECOHERENCE THEORY Received on 20 December, 2004 http://www.scielo.br/pdf/bjp/v35n2a/a02v352a.pdf Roland Omnes -- Laboratoire de Physique Th´eorique, Universit´e de Paris-Sud, 91405 Orsay (France) The main steps in the development of the ideas on decoherence are briefly reviewed, together with their present achievements. Unsolved problems are also pointed out . . . |
Tantalizing:Didier Robert: The semi-classical Van-Vleck formula -- Application to the Aharonov-Bohm effect
22 Oktober 1999
http://www.math.kth.se/braket/1999/991022_nr33.pdf
Abstract: At the very beginning of the quantum theory, Van-Vleck (1928) proposed a nice approximation formula for the integral kernel of the time-dependent propagator of the Schrödinger equation. This formula can be deduced from the Feynman path integral by a formal stationary phase argument. After works by Maslov and Hörmander on Fourier-integral operators, it is possible to give a rigorous mathematical proof of the Van-Vleck formula. Here we give a more direct and elementary proof, using propagation of coherent states. We apply this result to give a mathematical proof for the Aharonov-Bohm effect observed on the time-dependent propagator. This effect concerns a phase factor depending on the flux of a magnetic field, which can be non-trivial even if the particle never meets the magnetic field.
Hmmm, what dis?
QUOTE
General Relativity and Microlocal Analysis
Last modified August 31, 2005 by Michael Kunzinger.
http://www.mat.univie.ac.at/~mike/research.php
Due to the inherent nonlinearities of the field equations, studying singularities in general relaivity by means of classical distributional methods soon runs into serious conceptual problems. In order to cope with such problems in a mathematically rigorous fashion one has to resort to some kind of distributional geometry allowing to carry out nonlinear operations with singular objects. As was already mentioned above the development of such a theory is one of the main current projects of our research group.
Together with R. Steinbauer we have studied geodesic and geodesic deviation equations in singular space times. In [J3] a satisfactory solution concept for such equations was developed and applied to the case of pp-Waves (plane fronted waves with parallel rays). For describing such waves Roger Penrose had used a discontinuous coordinate transformation turning the distributional form of the metric into a continuous form. While mathematically ill-defined (involving undefined nonlinear operations on distributions), this procedure provides physically equivalent descriptions of the situation (particle trajectories in both pictures coincide).
The key to understanding this behaviour lies in realizing that the Penrose transformation actually transports points of space time along (discontinuous) geodesics of the original (distributional) metric. By means of a global univalence result of Gale and Nikaido we were able to prove that the transformation is actually the distributional `shadow' of a Colombeau coordinate transformation. This also introduces a possibility of handling `discontinuous diffeomorphisms', see [J4]. The necessary tools for describing such transformations (which furnish an example of manifold-valued generalized functions) are presented in [J12].
Microlocal Analysis
Based on regularity theory for algebras of generalized functions (developed by M. Oberguggenberger), the aim of this joint project with G. Hörmann is an analysis of the interaction between nonlinear operations, singularities and differentiation from a microlocal point of view (in particular: propagation of singularities in nonlinear PDEs involving generalized functions). In [J8], microlocal properties of basic operations (multiplication and pullback) in the Colombeau algebra are analyzed. Although multiplication of distributions can be carried out unrestrictedly in the algebra, the wave front set of the product displays high sensitivity to the configuration of the factors' singularity structure. In case the wave front sets of the factors are in favorable position an extension of the classical inclusion relation (in the distributional setting) due to Hörmander is proven. Explicit examples are given showing that the inclusion relation will break down even in the Colombeau algebra if Hörmander's condition is violated.
Last modified August 31, 2005 by Michael Kunzinger.
http://www.mat.univie.ac.at/~mike/research.php
Due to the inherent nonlinearities of the field equations, studying singularities in general relaivity by means of classical distributional methods soon runs into serious conceptual problems. In order to cope with such problems in a mathematically rigorous fashion one has to resort to some kind of distributional geometry allowing to carry out nonlinear operations with singular objects. As was already mentioned above the development of such a theory is one of the main current projects of our research group.
Together with R. Steinbauer we have studied geodesic and geodesic deviation equations in singular space times. In [J3] a satisfactory solution concept for such equations was developed and applied to the case of pp-Waves (plane fronted waves with parallel rays). For describing such waves Roger Penrose had used a discontinuous coordinate transformation turning the distributional form of the metric into a continuous form. While mathematically ill-defined (involving undefined nonlinear operations on distributions), this procedure provides physically equivalent descriptions of the situation (particle trajectories in both pictures coincide).
The key to understanding this behaviour lies in realizing that the Penrose transformation actually transports points of space time along (discontinuous) geodesics of the original (distributional) metric. By means of a global univalence result of Gale and Nikaido we were able to prove that the transformation is actually the distributional `shadow' of a Colombeau coordinate transformation. This also introduces a possibility of handling `discontinuous diffeomorphisms', see [J4]. The necessary tools for describing such transformations (which furnish an example of manifold-valued generalized functions) are presented in [J12].
Microlocal Analysis
Based on regularity theory for algebras of generalized functions (developed by M. Oberguggenberger), the aim of this joint project with G. Hörmann is an analysis of the interaction between nonlinear operations, singularities and differentiation from a microlocal point of view (in particular: propagation of singularities in nonlinear PDEs involving generalized functions). In [J8], microlocal properties of basic operations (multiplication and pullback) in the Colombeau algebra are analyzed. Although multiplication of distributions can be carried out unrestrictedly in the algebra, the wave front set of the product displays high sensitivity to the configuration of the factors' singularity structure. In case the wave front sets of the factors are in favorable position an extension of the classical inclusion relation (in the distributional setting) due to Hörmander is proven. Explicit examples are given showing that the inclusion relation will break down even in the Colombeau algebra if Hörmander's condition is violated.
Dense, but if you be a Pythagorean, heavenly!
QUOTE (->
| QUOTE |
| General Relativity and Microlocal Analysis Last modified August 31, 2005 by Michael Kunzinger. http://www.mat.univie.ac.at/~mike/research.php Due to the inherent nonlinearities of the field equations, studying singularities in general relaivity by means of classical distributional methods soon runs into serious conceptual problems. In order to cope with such problems in a mathematically rigorous fashion one has to resort to some kind of distributional geometry allowing to carry out nonlinear operations with singular objects. As was already mentioned above the development of such a theory is one of the main current projects of our research group. Together with R. Steinbauer we have studied geodesic and geodesic deviation equations in singular space times. In [J3] a satisfactory solution concept for such equations was developed and applied to the case of pp-Waves (plane fronted waves with parallel rays). For describing such waves Roger Penrose had used a discontinuous coordinate transformation turning the distributional form of the metric into a continuous form. While mathematically ill-defined (involving undefined nonlinear operations on distributions), this procedure provides physically equivalent descriptions of the situation (particle trajectories in both pictures coincide). The key to understanding this behaviour lies in realizing that the Penrose transformation actually transports points of space time along (discontinuous) geodesics of the original (distributional) metric. By means of a global univalence result of Gale and Nikaido we were able to prove that the transformation is actually the distributional `shadow' of a Colombeau coordinate transformation. This also introduces a possibility of handling `discontinuous diffeomorphisms', see [J4]. The necessary tools for describing such transformations (which furnish an example of manifold-valued generalized functions) are presented in [J12]. Microlocal Analysis Based on regularity theory for algebras of generalized functions (developed by M. Oberguggenberger), the aim of this joint project with G. Hörmann is an analysis of the interaction between nonlinear operations, singularities and differentiation from a microlocal point of view (in particular: propagation of singularities in nonlinear PDEs involving generalized functions). In [J8], microlocal properties of basic operations (multiplication and pullback) in the Colombeau algebra are analyzed. Although multiplication of distributions can be carried out unrestrictedly in the algebra, the wave front set of the product displays high sensitivity to the configuration of the factors' singularity structure. In case the wave front sets of the factors are in favorable position an extension of the classical inclusion relation (in the distributional setting) due to Hörmander is proven. Explicit examples are given showing that the inclusion relation will break down even in the Colombeau algebra if Hörmander's condition is violated. |
Dense, but if you be a Pythagorean, heavenly!A Local-to-Global Singularity Theorem for Quantum Field Theory on Curved Space-Time
http://projecteuclid.org/Dienst/UI/1.0/Sum....cmp/1104287233
Communications in Mathematical Physics 180, 1-22 (1996)
Marek J. Radzikowski1*
(with an Appendix by Rainer Verch2)
1 Department of Mathematics, Texas A&M University, College Station, TX 77843, USA, and Department
of Mathematics, University of York, Heslington, York YO1 5DD, UK
2 II Institut fur Theoretische Physik, Universitat Hamburg, D - 22761 Hamburg, Germany
Received: 21 September 1994 / Accepted: 25 August 1995
To a special friend, who saved my life when I was younger, without whom I could not
have written this paper.
Abstract:
We prove that if a reference two-point distribution of positive type on
a time orientable curved space-time (CST) satisfies a certain condition on its wave
front set (the "class 0hii9 condition") and if any other two-point distribution (i) is of
positive type, (ii) has the same antisymmetric part as the reference modulo smooth
function and (iii) has the same local singularity structure, then it has the same global
singularity structure. In the proof we use a smoothing, positivity-preserving pseudodifferential operator the support of whose symbol is restricted to a certain conic
region which depends on the wave front set of the reference state. This local-toglobal
theorem, together with results published elsewhere, leads to a verification of a
conjecture by Kay that for quasi-free states of the Klein-Gordon quantum field on a
globally hyperbolic CST, the local Hadamard condition implies the global Hadamard
condition. A counterexample to the local-to-global theorem on a strip in Minkowski
space is given when the class &ht,g condition is not assumed.
[snip]
The main goal of this paper is to present a "local-to-global" theorem more general
than Kay's conjecture. Results published elsewhere [37, 38] are employed in showing
that Kay's conjecture is a special case of this local-to-global theorem. The language
of micro-local analysis is used throughout and is found to apply very naturally to this
problem and to yield a quite general answer. This is not the first paper on quantized
fields on curved space-time in which micro-local methods are used: Dimock's work
on the scattering operator for a scalar field on curved space-time [6] makes significant
use of the distinguished parametrix theory of Duistermaat and Hormander [8]. Also
see [35] for even earlier examples of papers in which pseudo-differential operators
were used in the context of quantum field theory on stationary and static space-times.
The "distributional approach" to quantized fields on curved space-time used
throughout this paper is outlined in Sect. 2. Section 3 presents a brief introduction
to micro-local analysis and lists some results that will be useful in later sections.
In Sect. 4 the class &hi,g condition for a time orientable CST (M, g) and the main
local-to-global singularity theorem are stated, followed by an outline of the proof of
this theorem, the proof being contained in Sects. 5, 6, 7, and 8. (These sections are
summarized in Sect. 4.) In Sect. 9, Kay's conjecture is verified using the existence of
globally Hadamard quasi-free states on an arbitrary globally hyperbolic curved spacetime and the equivalence (for quasi-free Klein-Gordon states) of the global Hadamard condition with a certain wave front set spectral condition (WFSSC) introduced in [37, 38] which is in turn stronger than the class &M,g condition. In fact an even stronger statement than Conjecture 1.1 is proven: any two-point distribution of positive type which has the local Hadamard singularity structure and whose commutator is i times the difference of the advanced and retarded fundamental solutions of the Klein-Gordon operator (modulo a smooth function) must have the global Hadamard singularity structure. (Note that we do not assume the quasi-free property or that the Klein-Gordon equation is satisfied.) In Sect. 10, we demonstrate the necessity for the reference state to satisfy the class &M,9 condition, by displaying a counterexample to the local-to-global theorem on a strip in Minkowski space when this condition is not assumed. Section 11 discusses some implications of the local-to-global theorem, in particular the strengthening of the belief that the Hadamard condition is physically distinguished, and a corollary displaying some dependence among the axioms
on curved space-time.
Getting drowsier & drowsier. . . this last one should assure you a sound slumber.
QUOTE
Conformal scattering and the Goursat problem : general ideas and what perspectives for black holes?
http://www.newton.cam.ac.uk/webseminars/pg...nicolas/all.pdf
Seminar, Newton Institute, Cambridge, 6th september 2005, 15:30.
1 Introduction
This talk is about time-dependent scattering in general relativity. Dietrich H¨afner has amply described the topic in his talk on friday. So let me just summarize the essential ideas.
• Fixed background space-time, Lorentzian metric, globally hyperbolic M= Rt × _,
_ 3-manifold with asymptotic ends.
• Study the behaviour in the asymptotic ends of solutions of covariant field equations onM. Does so usually by comparison with simplified dynamics (ideally asymptotic profiles, i.e. the flow of a null congruence) in each asymptotic region : construction of wave operators and completeness. The terminology "time-dependent" means that the construction is based on the dynamics (the evolution) and not on stationary solutions of the form ei!t_(x).
To this day, most of the works in this domain are constructions outside black holes : For Schwarzschild or other spherical black holes (approximately chronologically) J. Dimock [15], J. Dimock and B. Kay [16, 17, 18], A. Bachelot [1, 2, 3, 4, 5], A. Bachelot and A. Motet-Bachelot [6], J.-P. Nicolas [31], W.M. Jin [26], F. Melnyk [29, 30], T. Daud´e (PhD thesis, 2004) ; for Kerr or Kerr-Newmann (approximately chronologically) D. H¨afner [23], D. H¨afner and J.-P. Nicolas [24], T. Daud´e (PhD thesis, 2004).
As I just mentionned, time-dependent scattering in relativity deals with covariant field equations, i.e. equations that derive their structure entirely from that of the metric.
The fundamental information for studying the scattering properties of such
equations is therefore the asymptotics of the metric in the asymptotic ends of
_. All time-dependent scattering theories cited above are constructed following the same essential procedure :
( i ) Encoding of the fundamental information in an analytic expression of the metric via a choice of coordinate system and (for non scalar equations) of local frame. This step can already be quite critical (Schwarzschild, good choice of radial variable ; Kerr, example of our paper with Dietrich, we chose a tetrad that allows a spherically symmetric comparison without long range terms, which accounts for the fact that the effects of the rotation are short range).
( ii ) The information is then extracted via spectral techniques to obtain the scattering theory itself. These techniques are unstable with respect to time dependence of the coefficients of the equation : even for so-called time-dependent method, the time dependence allowed for the coefficients is very simple and means essentially that the methods can only be applied in stationary situations (or at least locally stationary, such as for the Kerr metric). This is a purely technical limitation, due to the methods used, not to the nature of the problem studied.
2. A geometrical alternative : "conformal scattering"
A different approach to scattering theory is to use the geometrical information of the asymptotics of the metric more directly to infer the asymptotic properties of the field. A natural tool for doing this is Penrose's conformal compactification. It allows us to interpret the complete scattering theory as the well-posedness of a Goursat problem on null infinity. Not a new idea : Goursat problem on null infinity studied by R. Penrose in 1963 [33].
First used in the framework of time dependent scattering by F.G. Friedlander [20, 21], for the wave equation on static spacetimes with regular conformal structure at spacelike infinity. Idea used also by J.C. Baez, I.E. Segal and Z.F. Zhou [7] for a non linear wave equation on flat spacetime. So this is all for static spacetimes.
Technique based on conformal compactifications, hence carries limitations of its own (these depend also of our understanding of the geometries studied and of the technique itself, there is therefore some hope that they will become less important) :
( i ) spacetimes whose asymptotic structure is well described by a conformal compactification and whose conformal metric is regular enough at infinity (essentially, in the present state of things, asymptotically simple space-times with enough regularity at null and timelike infinity) ;
( ii ) conformally invariant equations or at least conformally "controllable".
* But the technique is totally indifferent to time dependence. Generic time dependence can be allowed.
A first result has been published, in collaboration with L. Mason [28]. Work on
asymptotically simple space-times with regular null and timelike infinities. Construction of a scattering operator via conformal techniques : do a picture with a "vertical slice" of the compactified spacetime, a Cauchy hypersurface _0, data in C10 (_0), trace operators T± on I±, natural candidate for scattering operator is S := T+ (T-)-1. The whole work is therefore to show that T± are isomorphisms, i.e. to solve the Goursat problem. Note that the trace operators associate to the data only a part of the trace of the solution, called scattering data, that comes out naturally in the energy estimates needed to solve the Goursat problem. The construction is done for :
• massless Dirac fields : no restriction, conformally invariant closed 3-form ;
• Maxwell fields : closed 3-form but not conformally invariant, at least not fully, the normal vector field is not rescaled, not applicable for energy estimates involving I ; estimates are easy away from i0 because we have a symmetric hyperbolic system on a regular globally hyperbolic space-time ; near i0 we need an exact Killing vector field to have exactly conserved quantities, otherwise, the singularity is a problem ; our construction is valid only for the space-times of Chrusciel-Delay and Corvino-Schoen, the exact Killing vector field near i0 is useful for obtaining the energy estimates ;
• massless scalar fields : the construction is not quite complete, the Goursat problem is solved, it is easier than for Dirac and Maxwell, but for the energy estimates, we have a problem with the scalar curvature, it is said how to obtain them, but this is not done explicitely and again we need the exact symmetry near i0.
The construction for the wave equation is now complete. Extensions to nonlinear cases is in progress. The resolution of the Goursat problem is of course the fundamental construction in this work. It follows the ideas of a work by L. H¨ormander [25] in which he describes a technique based on energy estimates. His method is well adapted to scattering in that it gives convergences in minimum regularity spaces ; in addition, we slightly modify his approximation of solutions, this allows us to show the equivalence with an analytic scattering theory, defined in terms of classical wave operators whose comparison dynamics are asymptotic profiles.
In order to work with completely generic asymptotically simple space-times, without explicit symmetry near i0, one possibility is to handle the Goursat problem with very little regularity (at least at one point) since the metric is not much better than Lipschitz near i0. Also for the space-times of Christodoulou and Klainerman, that are the most general solutions (in terms of regularity) of the Einstein vacuum equations that are asymptotically simple (almost, not quite regular enough at I), we need weaker regularity for the Goursat problem.
3. H¨ormander's work (J.F.A. 1990)
What we describe is a slightly simplified version of H¨ormander's work for the fully characteristic Cauchy problem. His work in fact treats the Cauchy problem, the Goursat problem and anything in between where the initial data surface is allowed to be locally spacelike or null.
http://www.newton.cam.ac.uk/webseminars/pg...nicolas/all.pdf
Seminar, Newton Institute, Cambridge, 6th september 2005, 15:30.
1 Introduction
This talk is about time-dependent scattering in general relativity. Dietrich H¨afner has amply described the topic in his talk on friday. So let me just summarize the essential ideas.
• Fixed background space-time, Lorentzian metric, globally hyperbolic M= Rt × _,
_ 3-manifold with asymptotic ends.
• Study the behaviour in the asymptotic ends of solutions of covariant field equations onM. Does so usually by comparison with simplified dynamics (ideally asymptotic profiles, i.e. the flow of a null congruence) in each asymptotic region : construction of wave operators and completeness. The terminology "time-dependent" means that the construction is based on the dynamics (the evolution) and not on stationary solutions of the form ei!t_(x).
To this day, most of the works in this domain are constructions outside black holes : For Schwarzschild or other spherical black holes (approximately chronologically) J. Dimock [15], J. Dimock and B. Kay [16, 17, 18], A. Bachelot [1, 2, 3, 4, 5], A. Bachelot and A. Motet-Bachelot [6], J.-P. Nicolas [31], W.M. Jin [26], F. Melnyk [29, 30], T. Daud´e (PhD thesis, 2004) ; for Kerr or Kerr-Newmann (approximately chronologically) D. H¨afner [23], D. H¨afner and J.-P. Nicolas [24], T. Daud´e (PhD thesis, 2004).
As I just mentionned, time-dependent scattering in relativity deals with covariant field equations, i.e. equations that derive their structure entirely from that of the metric.
The fundamental information for studying the scattering properties of such
equations is therefore the asymptotics of the metric in the asymptotic ends of
_. All time-dependent scattering theories cited above are constructed following the same essential procedure :
( i ) Encoding of the fundamental information in an analytic expression of the metric via a choice of coordinate system and (for non scalar equations) of local frame. This step can already be quite critical (Schwarzschild, good choice of radial variable ; Kerr, example of our paper with Dietrich, we chose a tetrad that allows a spherically symmetric comparison without long range terms, which accounts for the fact that the effects of the rotation are short range).
( ii ) The information is then extracted via spectral techniques to obtain the scattering theory itself. These techniques are unstable with respect to time dependence of the coefficients of the equation : even for so-called time-dependent method, the time dependence allowed for the coefficients is very simple and means essentially that the methods can only be applied in stationary situations (or at least locally stationary, such as for the Kerr metric). This is a purely technical limitation, due to the methods used, not to the nature of the problem studied.
2. A geometrical alternative : "conformal scattering"
A different approach to scattering theory is to use the geometrical information of the asymptotics of the metric more directly to infer the asymptotic properties of the field. A natural tool for doing this is Penrose's conformal compactification. It allows us to interpret the complete scattering theory as the well-posedness of a Goursat problem on null infinity. Not a new idea : Goursat problem on null infinity studied by R. Penrose in 1963 [33].
First used in the framework of time dependent scattering by F.G. Friedlander [20, 21], for the wave equation on static spacetimes with regular conformal structure at spacelike infinity. Idea used also by J.C. Baez, I.E. Segal and Z.F. Zhou [7] for a non linear wave equation on flat spacetime. So this is all for static spacetimes.
Technique based on conformal compactifications, hence carries limitations of its own (these depend also of our understanding of the geometries studied and of the technique itself, there is therefore some hope that they will become less important) :
( i ) spacetimes whose asymptotic structure is well described by a conformal compactification and whose conformal metric is regular enough at infinity (essentially, in the present state of things, asymptotically simple space-times with enough regularity at null and timelike infinity) ;
( ii ) conformally invariant equations or at least conformally "controllable".
* But the technique is totally indifferent to time dependence. Generic time dependence can be allowed.
A first result has been published, in collaboration with L. Mason [28]. Work on
asymptotically simple space-times with regular null and timelike infinities. Construction of a scattering operator via conformal techniques : do a picture with a "vertical slice" of the compactified spacetime, a Cauchy hypersurface _0, data in C10 (_0), trace operators T± on I±, natural candidate for scattering operator is S := T+ (T-)-1. The whole work is therefore to show that T± are isomorphisms, i.e. to solve the Goursat problem. Note that the trace operators associate to the data only a part of the trace of the solution, called scattering data, that comes out naturally in the energy estimates needed to solve the Goursat problem. The construction is done for :
• massless Dirac fields : no restriction, conformally invariant closed 3-form ;
• Maxwell fields : closed 3-form but not conformally invariant, at least not fully, the normal vector field is not rescaled, not applicable for energy estimates involving I ; estimates are easy away from i0 because we have a symmetric hyperbolic system on a regular globally hyperbolic space-time ; near i0 we need an exact Killing vector field to have exactly conserved quantities, otherwise, the singularity is a problem ; our construction is valid only for the space-times of Chrusciel-Delay and Corvino-Schoen, the exact Killing vector field near i0 is useful for obtaining the energy estimates ;
• massless scalar fields : the construction is not quite complete, the Goursat problem is solved, it is easier than for Dirac and Maxwell, but for the energy estimates, we have a problem with the scalar curvature, it is said how to obtain them, but this is not done explicitely and again we need the exact symmetry near i0.
The construction for the wave equation is now complete. Extensions to nonlinear cases is in progress. The resolution of the Goursat problem is of course the fundamental construction in this work. It follows the ideas of a work by L. H¨ormander [25] in which he describes a technique based on energy estimates. His method is well adapted to scattering in that it gives convergences in minimum regularity spaces ; in addition, we slightly modify his approximation of solutions, this allows us to show the equivalence with an analytic scattering theory, defined in terms of classical wave operators whose comparison dynamics are asymptotic profiles.
In order to work with completely generic asymptotically simple space-times, without explicit symmetry near i0, one possibility is to handle the Goursat problem with very little regularity (at least at one point) since the metric is not much better than Lipschitz near i0. Also for the space-times of Christodoulou and Klainerman, that are the most general solutions (in terms of regularity) of the Einstein vacuum equations that are asymptotically simple (almost, not quite regular enough at I), we need weaker regularity for the Goursat problem.
3. H¨ormander's work (J.F.A. 1990)
What we describe is a slightly simplified version of H¨ormander's work for the fully characteristic Cauchy problem. His work in fact treats the Cauchy problem, the Goursat problem and anything in between where the initial data surface is allowed to be locally spacelike or null.
Gadfly wrote,
My humble apologies to Gadfly, Le Bon Elf and all others suited up for a spark- flying intellectual exchange concerning bubbles and EM, as well as to those in the peanut gallery soaking up the ambience and following this thread.
My lame excuse for rudely barging into the ongoing discussion is first, despite a year reading and enjoying the writings of the elvish, humanoid and various other participants in this forum, it hadn't seeped into my impervious cranial cavity that the better part of valor might be to start a new thread.
Moreover, I was swept away in a dual particle-wave-front of excited exuberance after stumbling upon Michael Munowitz's apparently well founded view that much of the mystery of the quantum has been deciphered via pure mathematics (building upon Schroedinger's surprising equations) , though these highly abstruse, essentially incomprehensible series of ever more subtle insights have yet to reach many ears in the Physics community, and hardly a soul amongst the enfeebled stratum of "general public" who fritter away their earthly evanescence in all-too-frequent contemplation of heavenly wonders -- as above, so below.
In sum, absolutely no disrespect was intended despite my in flagrante disregard of the forum's traditional decorum and customary politesse.
My bad ... now mortified ... hopefully to be assuaged, please, by your kind understanding.
Ever unctuous and obsequious,
Very truly yours,
Ter. Dybbuk
QUOTE
Good Elf - why NOT move this topic The nature of "electricity" & "magnetism", are bubbles the answer? to the Forum Relativity, Quantum Mechanics, New Theories?
My humble apologies to Gadfly, Le Bon Elf and all others suited up for a spark- flying intellectual exchange concerning bubbles and EM, as well as to those in the peanut gallery soaking up the ambience and following this thread.
My lame excuse for rudely barging into the ongoing discussion is first, despite a year reading and enjoying the writings of the elvish, humanoid and various other participants in this forum, it hadn't seeped into my impervious cranial cavity that the better part of valor might be to start a new thread.
Moreover, I was swept away in a dual particle-wave-front of excited exuberance after stumbling upon Michael Munowitz's apparently well founded view that much of the mystery of the quantum has been deciphered via pure mathematics (building upon Schroedinger's surprising equations) , though these highly abstruse, essentially incomprehensible series of ever more subtle insights have yet to reach many ears in the Physics community, and hardly a soul amongst the enfeebled stratum of "general public" who fritter away their earthly evanescence in all-too-frequent contemplation of heavenly wonders -- as above, so below.
In sum, absolutely no disrespect was intended despite my in flagrante disregard of the forum's traditional decorum and customary politesse.
My bad
... now mortified ... hopefully to be assuaged, please, by your kind understanding.Ever unctuous and obsequious,
Very truly yours,
Ter. Dybbuk
Hi Tergiversating Dybbuk,
Gadfly is only referring to a previous request to do this. It is not related to your contributions (to my knowledge) so don't worry ... you are not barging in. I am still trying to do a little research and answer other threads too. My "full-time" job is currently "mapping". This is a part time pursuit. I will be back soon....
Cheers
Gadfly is only referring to a previous request to do this. It is not related to your contributions (to my knowledge) so don't worry ... you are not barging in. I am still trying to do a little research and answer other threads too. My "full-time" job is currently "mapping". This is a part time pursuit. I will be back soon....
Cheers
Hi bad elf, radfly, td, c 4, RToc, pal & all
I was curious if hot liquid or temped metals were still magnetic (more or less mag), look deeper for clues about magnetism, gravity, heat and elec. Found this link interesting, cool mellow read for this topic. Haven't read the hole thread don't know if you have discussed this or it is old news.
http://www.science.ca/scientists/scientist...ile.php?pID=388
later…
I was curious if hot liquid or temped metals were still magnetic (more or less mag), look deeper for clues about magnetism, gravity, heat and elec. Found this link interesting, cool mellow read for this topic. Haven't read the hole thread don't know if you have discussed this or it is old news.
http://www.science.ca/scientists/scientist...ile.php?pID=388
later…
Hi Bee,
I take it you are referring to the bit in Taillefer saga about the "Cooper Pairs".
I take it you are referring to the bit in Taillefer saga about the "Cooper Pairs".
QUOTE (http://www.science.ca/scientists/scientistprofile.php?pID=388+)
4. Electrons have spin, which makes them into tiny little magnets. They also carry a negative charge. Like charges repel, so normally electrons strongly repel each other. However, in special circumstances, they may be drawn to each other to form so called "Cooper pairs". This occurs when the surrounding crystal matrix, made of positively charged atoms, is locally deformed by the passage of a single electron, which in turn attracts a second electron in its wake. Think of the way two people can be drawn together on a waterbed. It works something like that. In general, a Cooper pair of electrons "join" in such a way that their total spin cancels out. (i.e. the spin of one points up and the other points down, cancelling each other.) Because of this, a Cooper pair behaves like a single particle with spin 0 and mass twice that of a single electron. But Cooper pairs do not behave independently of each other like single electrons in a normal metal conductor. They form a single coherent quantum state, which means that instead of having random behaviour, they all behave in exactly the same way. In this sense, superconductivity is a large "macroscopic quantum phenomenon". To understand it properly you need to know the complicated mathematics of the superconducting wave function, which was developed by Bardeen, Cooper, and Schrieffer in 1957. Their BCS theory, a landmark achievement of 20th Century physics, won them the 1972 Nobel prize in physics. To put it simply superconductivity with Cooper pairs works like this. In a normal conductor it is very easy for a single electron to collide with crystal impurities leading to the metal having resistance. In a superconductor this does not happen because the coherent quantum state represents all electron pairs and makes it impossible to deflect the motion of one pair without involving all the others. Therefore collisions have no impact and there is no resistance. This is a pure quantum effect and there is nothing like it in classical physics. While conventional superconductors seem to follow this BCS Cooper pair theory, new high temperature superconducting materials cannot be explained this way. Taillefer and his colleagues feel that the mechanism for high temperature superconductors does not come from the deformation of the atomic lattice but from a purely electronic interaction, possibly involving the magnetic spin of the electrons. Current research is aimed at understanding these interactions.
This is very close to what he was speaking of earlier about...
This seems to be the origin (1957) of Peter Higg's concept of mass in the Higgs Field and the Higgs Boson's operation. That point I have discussed elsewhere in the "Particles have mass... HOW?" thread but obviously this is from another point of view. These combined electrons in quantum states are an idea worth thinking about, they are resulting in a spin zero state (nett). This proves that quantum phenomena are "system" parameters that share their properties with "assemblies". The Higgs Boson may be closely allied to some aspect of this because it too is supposed to be a "spin zero" state. Naturally the two electrons are "unable" to repel each other for reasons we have discussed previously... viewing electrons as a special type of topological "photon".
Good work Bee.
Cheers
This is very close to what he was speaking of earlier about...
QUOTE
Taillefer was attempting to measure the mass of electrons in a new class of materials called heavy electron metals, a potential superconductor of a completely new kind where electron interactions were known to be extraordinarily strong. This caused an electron mass increase, but nobody knew how much. Seeing the quantized oscillation would provide a direct measure of that mass. The Cambridge group was competing with other teams in Europe and United States who were all trying to see these effects. Everyone was (and still is) trying to understand what is going on inside heavy electron metals like uranium platinide, so there was a race to get the results.
This seems to be the origin (1957) of Peter Higg's concept of mass in the Higgs Field and the Higgs Boson's operation. That point I have discussed elsewhere in the "Particles have mass... HOW?" thread but obviously this is from another point of view. These combined electrons in quantum states are an idea worth thinking about, they are resulting in a spin zero state (nett). This proves that quantum phenomena are "system" parameters that share their properties with "assemblies". The Higgs Boson may be closely allied to some aspect of this because it too is supposed to be a "spin zero" state. Naturally the two electrons are "unable" to repel each other for reasons we have discussed previously... viewing electrons as a special type of topological "photon".
Good work Bee.
Cheers
Hi!
Still reading and learning.
I like the references, especially,
One-Loop Amplitudes In N=4 Super-Yang-Mills Theory
We are slowly converging on finding "the" spacetime structure/shape/topology.
jal
Still reading and learning.
I like the references, especially,
One-Loop Amplitudes In N=4 Super-Yang-Mills Theory
We are slowly converging on finding "the" spacetime structure/shape/topology.
jal
Hi Jal,
I am sure that is "great stuff" but the significance has gone right over the top of my beanie...
If you do understand this could you please explain to us why this is so...
"We are slowly converging on finding "the" spacetime structure/shape/topology"
Honestly I do what to know...
Cheers
I am sure that is "great stuff" but the significance has gone right over the top of my beanie...
If you do understand this could you please explain to us why this is so...
"We are slowly converging on finding "the" spacetime structure/shape/topology"
Honestly I do what to know...
Cheers
Hi!
I posted a reply at Yin_Yang of spacetime.
I did not want to litter you thread.
The Twistor Strings Workshop had some great presentations.
jal
I posted a reply at Yin_Yang of spacetime.
I did not want to litter you thread.
The Twistor Strings Workshop had some great presentations.
jal
Hi Good_Elf (I'm back!)
In March 1979, Catt, Walton, and Davidson published an article in Wireless World.
From wiki..
Catt claimed to have solved the paradox of electron spin by saying an electron is a trapped Heaviside energy current. His theory implies that gravitation traps the energy, like the bending of light by gravity. He then predicted that the size of the electron is then similar to a black-hole, far smaller than the Planck size suggested by "string theory". To test this, the gravity strength resulting from Catt's work can be calculated, and it appears correct.
It seems almost infinitely improbable - about the right level of improbability to match 'reality'.
Can you remember that far back? I haven't yet found the paper on Ivorcatt.com but it might be there.
-C2.
In March 1979, Catt, Walton, and Davidson published an article in Wireless World.
From wiki..
Catt claimed to have solved the paradox of electron spin by saying an electron is a trapped Heaviside energy current. His theory implies that gravitation traps the energy, like the bending of light by gravity. He then predicted that the size of the electron is then similar to a black-hole, far smaller than the Planck size suggested by "string theory". To test this, the gravity strength resulting from Catt's work can be calculated, and it appears correct.
It seems almost infinitely improbable - about the right level of improbability to match 'reality'.
Can you remember that far back? I haven't yet found the paper on Ivorcatt.com but it might be there.
-C2.
Guest = Confused2
Hi Confused2,
While I agree that the "idea" is right... the mechanism for trapping the photon is (IMHO) wrong. This is because in 3D + T space-time, too much energy is required to perform this operation. My opinion is that there are other dimensions which are more elastic than space-time (the six compact dimensions). These dimensions can perform the same functions (in every respect they are equivalent) but at much lower energy than the brane of our Universe which has been inflated too tight to easily cavitate (all that "tension"), let alone cavitate at the Planck Length or beyond. The smaller cavity is harder to produce. Consider the photon energy required to produce that "hole" ...
E = hf where f = C /
Have a look at just what Planck Units really mean...
Planck Units: Wikipedia
If we are speaking about "objects" below the Planck Length again we are "doomed" to never know if he is right or wrong. This is because these dimensions cannot be probed by human science ... thats not just in the next hounded years or so but "forever" since we would need the energy of a significant part of the "big bang" and an accelerator the size of a galaxy. I think that just about rules "us" out of it. I think that electromagnetism can trap your photon more easier since it is 10^41 stronger than gravity. The symmetry is wrong when you think in only three dimensions but in higher dimensions this is a "shoe in".
We know we can create electron pairs through "electromagnetic" processes at "reasonable" energies. I suspect this is the answer and it is just that we have no acceptable theory in 3D + T , and I agree... we need higher dimensions to trap photons in cavities.
Cheers
While I agree that the "idea" is right... the mechanism for trapping the photon is (IMHO) wrong. This is because in 3D + T space-time, too much energy is required to perform this operation. My opinion is that there are other dimensions which are more elastic than space-time (the six compact dimensions). These dimensions can perform the same functions (in every respect they are equivalent) but at much lower energy than the brane of our Universe which has been inflated too tight to easily cavitate (all that "tension"), let alone cavitate at the Planck Length or beyond. The smaller cavity is harder to produce. Consider the photon energy required to produce that "hole" ...
E = hf where f = C /
Have a look at just what Planck Units really mean...
Planck Units: Wikipedia
If we are speaking about "objects" below the Planck Length again we are "doomed" to never know if he is right or wrong. This is because these dimensions cannot be probed by human science ... thats not just in the next hounded years or so but "forever" since we would need the energy of a significant part of the "big bang" and an accelerator the size of a galaxy. I think that just about rules "us" out of it. I think that electromagnetism can trap your photon more easier since it is 10^41 stronger than gravity. The symmetry is wrong when you think in only three dimensions but in higher dimensions this is a "shoe in".
We know we can create electron pairs through "electromagnetic" processes at "reasonable" energies. I suspect this is the answer and it is just that we have no acceptable theory in 3D + T , and I agree... we need higher dimensions to trap photons in cavities.
Cheers
QUOTE (Good Elf+Jan 26 2006, 11:00 PM)
Have a look at just what Planck Units really mean...
If we are speaking about "objects" below the Planck Length again we are "doomed" to never know if he is right or wrong. This is because these dimensions cannot be probed by human science
From the Wikipedia page on Planck Length (link):
If we are speaking about "objects" below the Planck Length again we are "doomed" to never know if he is right or wrong. This is because these dimensions cannot be probed by human science
From the Wikipedia page on Planck Length (link):
QUOTE (Wikipedia+ emphasis mine)
The Planck length, Planck time, and Planck mass are units judiciously chosen so that c, G, and \hbar \ are all equal to 1 and thus disappear from equations of physical law that use those scaling factors.
This does not inherently suggest to me any real physical significance, as far as "laws" go. Only mathematical convenience and, as you noted, a certain resistance to "probing". I would think that quantum uncertainty would be a more fundamental obstacle to probing at these dimensions, though.
What if the theory can predict known phenomena, and maybe even as-yet-unobserved but "accessible" phenomena, in a way that is mathematically and conceptually simpler than competing theories that don't have the same inherent "unobservables". Under Occam's Razor, do the mathematical simplicities override the undesirableness of "unobservables"?
With that said, I remain critical of Catt's gravity-related proposal.
I'm curious what type of interaction could allow the gravitational trapping of a "current". Is he saying it's some sort of self-gravitation due to a high energy density? Or is he saying electrons are "compound" in that they have an extremely dense, but extremely small, central mass with an orbiting Heaviside current? What special situation arises that allows this, yet doesn't cause energy currents to gravitationally collapse all over the place and cause "real" particles to come popping out of space all the time?
(Edited for clarity.)
This does not inherently suggest to me any real physical significance, as far as "laws" go. Only mathematical convenience and, as you noted, a certain resistance to "probing". I would think that quantum uncertainty would be a more fundamental obstacle to probing at these dimensions, though.
What if the theory can predict known phenomena, and maybe even as-yet-unobserved but "accessible" phenomena, in a way that is mathematically and conceptually simpler than competing theories that don't have the same inherent "unobservables". Under Occam's Razor, do the mathematical simplicities override the undesirableness of "unobservables"?
With that said, I remain critical of Catt's gravity-related proposal.
I'm curious what type of interaction could allow the gravitational trapping of a "current". Is he saying it's some sort of self-gravitation due to a high energy density? Or is he saying electrons are "compound" in that they have an extremely dense, but extremely small, central mass with an orbiting Heaviside current? What special situation arises that allows this, yet doesn't cause energy currents to gravitationally collapse all over the place and cause "real" particles to come popping out of space all the time?
(Edited for clarity.)
Hi Waterbreath,
I think all three dimensional theories of particles fail the ultimate test of "confinement". In three dimensions plus time they will all reach the limit of function. This is why theories which have more dimensions "allow" new physics, they explore the natural extension of our Universe into unseen realms. It is technically possible to confine a particle using Gravitation in three dimensions (LQG). We already know this "particle" as a "Black Hole". I will maintain that not all material in the universe are made from matter dense enough to create confinement at that scale. Atomic particles are not all "Black Holes". Even if Black Hole particles could achieve confinement it would "evaporate" rapidly or "accrete" into one really big black hole as we already see in nature..
Catt's theory is a "first cut". When you want a theory that does not increase dimensions and you need to achieve confinement this would be the first "port of call". Once it is realized this is not the way, you must move on and still solve the problem.
What physics did in the early part of the last century was to say... yes we have confinement but we are not saying "how". This is then one quantum postulate... stated not demonstrated. You need several others to make this gambit work. A certain "protocol" has developed in science that says the best minds have looked into this problem... don't you worry your poor little heads about that ... shut up and calculate. Mankind make a very poor calculator in the age where a pocket calculator is far more efficient than man's unaided brain. It is certain that once you make sufficient "postulates" you will begin to have a theory that will fit in three dimensions. You simply take the "real" higher dimensional theory and flatten it by brute force into three dimensions (down from ten or more). We now have that and it has been lousy at predicting any physics beyond three dimensions (The Standard Model). You might ask why? It makes no apologies for it just patches over the cracks when they are found.
You point to Occam's Razor. Yes... the simplest theory will always be the best. But only the simplest theory possible... not a "simplified" theory that dumbs it down to a set of children's blocks on the flat table. It may be an excellent teaching tool, like those dreadful cuisenaire rods, but in the end you either adopt the ability to do actual mathematics and think in as many dimensions as is needed or you buy a calculator. I am sad to say that the latter course is the way modern students "progress". Any process that makes it "easy" is the acceptable theory. Well the World (maybe I should say the Universe) sometimes is not quite like the way man organizes his affairs.
Still... remove all the quantum postulates by one simple theory of adding dimensions and then go test it. I could already show you that most quantum theories "secretly" hold higher dimensions as necessary even though they work in lower dimensions. My specific theory might not be right but I will wager it will not be too far from the mark. Unlike many other string theories it is testable. It is "built" that way because I believe that to be Physics at all it must satisfy this criterion.
Cheers
I think all three dimensional theories of particles fail the ultimate test of "confinement". In three dimensions plus time they will all reach the limit of function. This is why theories which have more dimensions "allow" new physics, they explore the natural extension of our Universe into unseen realms. It is technically possible to confine a particle using Gravitation in three dimensions (LQG). We already know this "particle" as a "Black Hole". I will maintain that not all material in the universe are made from matter dense enough to create confinement at that scale. Atomic particles are not all "Black Holes". Even if Black Hole particles could achieve confinement it would "evaporate" rapidly or "accrete" into one really big black hole as we already see in nature..
Catt's theory is a "first cut". When you want a theory that does not increase dimensions and you need to achieve confinement this would be the first "port of call". Once it is realized this is not the way, you must move on and still solve the problem.
What physics did in the early part of the last century was to say... yes we have confinement but we are not saying "how". This is then one quantum postulate... stated not demonstrated. You need several others to make this gambit work. A certain "protocol" has developed in science that says the best minds have looked into this problem... don't you worry your poor little heads about that ... shut up and calculate. Mankind make a very poor calculator in the age where a pocket calculator is far more efficient than man's unaided brain. It is certain that once you make sufficient "postulates" you will begin to have a theory that will fit in three dimensions. You simply take the "real" higher dimensional theory and flatten it by brute force into three dimensions (down from ten or more). We now have that and it has been lousy at predicting any physics beyond three dimensions (The Standard Model). You might ask why? It makes no apologies for it just patches over the cracks when they are found.
You point to Occam's Razor. Yes... the simplest theory will always be the best. But only the simplest theory possible... not a "simplified" theory that dumbs it down to a set of children's blocks on the flat table. It may be an excellent teaching tool, like those dreadful cuisenaire rods, but in the end you either adopt the ability to do actual mathematics and think in as many dimensions as is needed or you buy a calculator. I am sad to say that the latter course is the way modern students "progress". Any process that makes it "easy" is the acceptable theory. Well the World (maybe I should say the Universe) sometimes is not quite like the way man organizes his affairs.
Still... remove all the quantum postulates by one simple theory of adding dimensions and then go test it. I could already show you that most quantum theories "secretly" hold higher dimensions as necessary even though they work in lower dimensions. My specific theory might not be right but I will wager it will not be too far from the mark. Unlike many other string theories it is testable. It is "built" that way because I believe that to be Physics at all it must satisfy this criterion.
Cheers
IMHO the thing that ties everything together is relativity - as far as I know every experiment shows that this 'works'. If you add extra dimensions you have to project into them "who's lookin at you now baby?" so that their effect becomes - let's be honest, - observer dependant. An ubermass that grabs everything travelling at more than 500mph but leaves the rest alone isn't going to work. People can fly past something with 26 variables at close to the speed of light and you don't really want to have tell them about this new set of 26 variables that they really ought to be working with. As far as I know the whole messy caboodle hangs together regardless of relative speed. Despite the mathematical inconvenience the whole thing is locked into three dimensions (+T) .. there is (as far as I know) no evidence of any free flying constants - they're locked, stuck, flattened into 3D + T.
-C2
-C2
Thanks for the response Good Elf.
I understand your criticisms of gravity-centric, 3D theories. This is the problem I was pointing to in my last paragraph. My questions regarding Occam's Razor, the simplicity of explanations, etc., were reflections of my own musings and uncertainties, not intended as argument for or against anything.
At any rate, I agree it doesn't seem feasible to create the types of confinement that we see with just gravity alone. The short-and-sweet of it seems to be that there is no balancing mechanism. It is either "too weak" and things eternally drift apart, or "too strong" and they collapse all to black holes which slowly decay into smaller bits that eternally drift apart.
Add another force, and/or another spatial dimension and you can do it, as you noted.
...
I had a long rant written out about the difference between mathematical models and prosaic explanations. But I've decided not to include it in full, as I'm sure no one in this thread needs to hear it. It was inspired by other threads, and only triggered by Good Elf's discussion of dimensions.
Suffice it to say, under the prosiac explanation of General Relativity, gravity warps spacetime. The mathematical model makes no such claims. It just says "in the vicinity of mass, energy does this...". Warping spacetime is our own prosaic interpretation of these equations, because of the similarity of the equations to those that would govern marbles, billiard balls, bowling balls, etc. rolling around on a stretchy rubber sheet.
Similarly, the Standard Model is a model. The number of dimensions it uses really depends on how you want to break out the equations, and it is also infinitely "patchable", both as Good Elf noted. The prose is used to "hide" the extra dimensions and make us more comfortable. But with each patch this monster becomes more complex, rigid, and limited, in the common prosaic explanation and the associated treatments of the underlying math. So, I'm with Good Elf. Something needs to give. We can't go on just feeling in the dark, relying on stubbed toes to tell us how the room looks. We have other faculties by which to figure this out, and we should use them. The prose of our theories is very useful in this respect. It can give us insight, inspire us and give us direction in how to amend the mathematical models predictively, rather than only for purposes of "damage control".
I understand your criticisms of gravity-centric, 3D theories. This is the problem I was pointing to in my last paragraph. My questions regarding Occam's Razor, the simplicity of explanations, etc., were reflections of my own musings and uncertainties, not intended as argument for or against anything.
At any rate, I agree it doesn't seem feasible to create the types of confinement that we see with just gravity alone. The short-and-sweet of it seems to be that there is no balancing mechanism. It is either "too weak" and things eternally drift apart, or "too strong" and they collapse all to black holes which slowly decay into smaller bits that eternally drift apart.
Add another force, and/or another spatial dimension and you can do it, as you noted.
...
I had a long rant written out about the difference between mathematical models and prosaic explanations. But I've decided not to include it in full, as I'm sure no one in this thread needs to hear it. It was inspired by other threads, and only triggered by Good Elf's discussion of dimensions.
Suffice it to say, under the prosiac explanation of General Relativity, gravity warps spacetime. The mathematical model makes no such claims. It just says "in the vicinity of mass, energy does this...". Warping spacetime is our own prosaic interpretation of these equations, because of the similarity of the equations to those that would govern marbles, billiard balls, bowling balls, etc. rolling around on a stretchy rubber sheet.
Similarly, the Standard Model is a model. The number of dimensions it uses really depends on how you want to break out the equations, and it is also infinitely "patchable", both as Good Elf noted. The prose is used to "hide" the extra dimensions and make us more comfortable. But with each patch this monster becomes more complex, rigid, and limited, in the common prosaic explanation and the associated treatments of the underlying math. So, I'm with Good Elf. Something needs to give. We can't go on just feeling in the dark, relying on stubbed toes to tell us how the room looks. We have other faculties by which to figure this out, and we should use them. The prose of our theories is very useful in this respect. It can give us insight, inspire us and give us direction in how to amend the mathematical models predictively, rather than only for purposes of "damage control".
QUOTE (Good Elf+)
Well the World (maybe I should say the Universe) sometimes is not quite like the way man organizes his affairs.
I'd go so far as to say that we can never really be at all certain that the prose of our theories represents the way the universe "really is". Many prosaic explanations can describe one mathematical model, but as you noted not all are equal in value. So let us also be wary of growing too attached to the prose of new ideas as well. We don't want to repeat our mistakes.
I'd go so far as to say that we can never really be at all certain that the prose of our theories represents the way the universe "really is". Many prosaic explanations can describe one mathematical model, but as you noted not all are equal in value. So let us also be wary of growing too attached to the prose of new ideas as well. We don't want to repeat our mistakes.
Hi Waterbreath, Confused2, TRoc et al,
I wanted to show you what I think happens schematically with the branes of particles undergoing relativistic spin on the edge of the light cone for the particle. This is a 2D drawing of what I think is happening in 6 dimensions. Some concessions were made to draw this.
The drawing represents a standing wave in the interior of a particle. The particle itself is spinning in the six extra-dimensions of space. The closure of the space around the particle which leads to confinement is purely relativistic remembering that photons always travel at the speed of light. I have drawn the radius vector equal to 1/R
(slight typo on figure) since this is in reciprocal space of a Fourier transform frequency and time and space with reciprocal space have been swapped. Seen from our "side" this is viewing the frequency domain from our perspective of the time domain of the particle. A "particle" has entered the brane with the right boundary conditions and is resonant. A photon or electron is now trapped (possibly some other rare exotic particles too). As 1/R -> 0 then R -> infinity. This means in this Hilbert Space the center of the particle is as big as you like and all processes there are asymptotically "free". For example the brane of the universe has R = 10 billion light years , maybe more. The brane of the universe spins once in 50 Billion years so the angular velocity of the "rim" of this sized particle barely rotates at all for the periphery to be traveling at the speed of light. Let this particle's angular frequency increase, the radius R falls dramatically but proportionally to E = hf and the brane has an angular frequency related to its de Broglie wavelength. We see the spin of the initial brane was initially related (in 6 dimensions) to the brane of our universe and has now shrunk in higher dimensions until the same angular momentum is resident in a particle the same size as the brane. This means the initial impulse is scaled by the frequency of the de Broglie particle. This is the energy.
This intrinsic spin on the brane wall is shown in the diagram in 2D diagrammatically as a interior wave and three zones. These actually map to nearly the same space but I have split them into 1, 2, 3. In zone one the string wave on the edge of the brane is undergoing relativistic length contraction "in the direction of motion". Actually what "really" happens is the wave is undergoing a "rotation" through an angle of arc sin (V/C). The closer to the edge of the light-cone the waves approaches the more it rotates relativistically. This appears as a rotation of the wave into another direction perpendicular to the three space the wave is currently propagating in (into zone 2). Since the particle is simply a photon in this frame of reference it has no rest mass so this is possible. There is no contraction in any other perpendicular direction in this three space (this is the asymmetry of special relativity). The wave is now propagating (partially) in another three space in an orthogonal direction (zone 2). As the wave approaches the edge of the light cone the wave goes around that hyper-dimensional corner as well and is now in another three space (zone 3). This process happens again as the wave propagates on the light cone around another internal "corner" and it returns to zone 1 forming a complete standing wave cycle inside a closed 6 dimensional volume. The odd thing is the waveform is "inverted" and this process needs to be repeated again to return the wave to the same spatial phase as well as the same standing wave harmonic phase. This is SU (2) symmetry. In the process of rotation through three complex directions i -> j -> k -> -i -> -j -> -k -> i. The little figure 8's around the outside is supposed to represent this feature.
This causes the particle to spin without disruption in 6 dimensions (three orthogonal planes) and is the isospin (+- 1/2). The surface of the particle exhibit some characteristics of normal planar spin but from the outside no vantage can see this higher dimensional activity that the de Broglie particle is currently involved in. This is executing on the edge of a dimensionally closed light-cone which now falls on the outer surface of the six dimensional spherical aspect of this quantum. In our three dimensions we see only the electric fields, magnetic moment, the spin and the mass as curvature of the basic space-time. This space-time handiness causes time reversal in three dimensions to be impossible through CPT conservation. The interior of the particle is a flat-space where a wave can propagate indefinitely in an internally closed reciprocal space... a Hilbert manifold. This is the complement of the space on the outside of the particle which is largely Minkowskian. The change in geometry from Minkowskian (flat) to Hilbert (reciprocal) is effectively a "lens" that behaves like a resonant cavity to suitably energetic photons having the right resonant frequency. At the same time converting the temporal soliton impulse particle to a wave of frequencies centered about the tuned frequency of the cavity and "snipped" to cavity dimensions by the particle "mask". Quantum emission is the reverse process.
This is a fermion, there is an associated boson, a T-Dual. Of course this is the simplest spherical harmonic structure.
Cheers
I wanted to show you what I think happens schematically with the branes of particles undergoing relativistic spin on the edge of the light cone for the particle. This is a 2D drawing of what I think is happening in 6 dimensions. Some concessions were made to draw this.
The drawing represents a standing wave in the interior of a particle. The particle itself is spinning in the six extra-dimensions of space. The closure of the space around the particle which leads to confinement is purely relativistic remembering that photons always travel at the speed of light. I have drawn the radius vector equal to 1/R
(slight typo on figure) since this is in reciprocal space of a Fourier transform frequency and time and space with reciprocal space have been swapped. Seen from our "side" this is viewing the frequency domain from our perspective of the time domain of the particle. A "particle" has entered the brane with the right boundary conditions and is resonant. A photon or electron is now trapped (possibly some other rare exotic particles too). As 1/R -> 0 then R -> infinity. This means in this Hilbert Space the center of the particle is as big as you like and all processes there are asymptotically "free". For example the brane of the universe has R = 10 billion light years , maybe more. The brane of the universe spins once in 50 Billion years so the angular velocity of the "rim" of this sized particle barely rotates at all for the periphery to be traveling at the speed of light. Let this particle's angular frequency increase, the radius R falls dramatically but proportionally to E = hf and the brane has an angular frequency related to its de Broglie wavelength. We see the spin of the initial brane was initially related (in 6 dimensions) to the brane of our universe and has now shrunk in higher dimensions until the same angular momentum is resident in a particle the same size as the brane. This means the initial impulse is scaled by the frequency of the de Broglie particle. This is the energy.This intrinsic spin on the brane wall is shown in the diagram in 2D diagrammatically as a interior wave and three zones. These actually map to nearly the same space but I have split them into 1, 2, 3. In zone one the string wave on the edge of the brane is undergoing relativistic length contraction "in the direction of motion". Actually what "really" happens is the wave is undergoing a "rotation" through an angle of arc sin (V/C). The closer to the edge of the light-cone the waves approaches the more it rotates relativistically. This appears as a rotation of the wave into another direction perpendicular to the three space the wave is currently propagating in (into zone 2). Since the particle is simply a photon in this frame of reference it has no rest mass so this is possible. There is no contraction in any other perpendicular direction in this three space (this is the asymmetry of special relativity). The wave is now propagating (partially) in another three space in an orthogonal direction (zone 2). As the wave approaches the edge of the light cone the wave goes around that hyper-dimensional corner as well and is now in another three space (zone 3). This process happens again as the wave propagates on the light cone around another internal "corner" and it returns to zone 1 forming a complete standing wave cycle inside a closed 6 dimensional volume. The odd thing is the waveform is "inverted" and this process needs to be repeated again to return the wave to the same spatial phase as well as the same standing wave harmonic phase. This is SU (2) symmetry. In the process of rotation through three complex directions i -> j -> k -> -i -> -j -> -k -> i. The little figure 8's around the outside is supposed to represent this feature.
This causes the particle to spin without disruption in 6 dimensions (three orthogonal planes) and is the isospin (+- 1/2). The surface of the particle exhibit some characteristics of normal planar spin but from the outside no vantage can see this higher dimensional activity that the de Broglie particle is currently involved in. This is executing on the edge of a dimensionally closed light-cone which now falls on the outer surface of the six dimensional spherical aspect of this quantum. In our three dimensions we see only the electric fields, magnetic moment, the spin and the mass as curvature of the basic space-time. This space-time handiness causes time reversal in three dimensions to be impossible through CPT conservation. The interior of the particle is a flat-space where a wave can propagate indefinitely in an internally closed reciprocal space... a Hilbert manifold. This is the complement of the space on the outside of the particle which is largely Minkowskian. The change in geometry from Minkowskian (flat) to Hilbert (reciprocal) is effectively a "lens" that behaves like a resonant cavity to suitably energetic photons having the right resonant frequency. At the same time converting the temporal soliton impulse particle to a wave of frequencies centered about the tuned frequency of the cavity and "snipped" to cavity dimensions by the particle "mask". Quantum emission is the reverse process.
This is a fermion, there is an associated boson, a T-Dual. Of course this is the simplest spherical harmonic structure.
Cheers
Hi Good_Elf et al,
Love the drawing.. too much to deal with after only a few days.
Sorry about the deviation here but it seems important (to me)
Imagine we have an L-C circuit with some energy in it.. it is oscillating happily at its resonant frequency.. (f) .. would the energy be quantised .. like E = n h f where n is an integer?
-C2.
Love the drawing.. too much to deal with after only a few days.
Sorry about the deviation here but it seems important (to me)
Imagine we have an L-C circuit with some energy in it.. it is oscillating happily at its resonant frequency.. (f) .. would the energy be quantised .. like E = n h f where n is an integer?
-C2.
Hi Confused2,
There is a resonant structure containing the oscillation so it is n wavelengths. This is not sufficient to be actually "quantized". The existence of quanta you need a mechanism that "snips" out that quanta. With atoms the "cavity" resonates to a particular "Impulse" like a bell. The bell striker is the impulse which is finite in time and application causes the bell to execute the harmonic oscillation. Impulse produces waves and (in theory) the reverse is also possible. It should be capable of "emitting" an Impulse instantly silencing the bell. Bells are not specifically designed for this of course. That would be a "quanta".
Cheers
There is a resonant structure containing the oscillation so it is n wavelengths. This is not sufficient to be actually "quantized". The existence of quanta you need a mechanism that "snips" out that quanta. With atoms the "cavity" resonates to a particular "Impulse" like a bell. The bell striker is the impulse which is finite in time and application causes the bell to execute the harmonic oscillation. Impulse produces waves and (in theory) the reverse is also possible. It should be capable of "emitting" an Impulse instantly silencing the bell. Bells are not specifically designed for this of course. That would be a "quanta".
Cheers
Hello Good_Elf,
Re LC circuit not quantised.. I disagree .. I feel it's as much an 'electron in a box problem' as an electron in an actual box .. just easier to solve .. the components are designed for entrapment purposes. No point in proceeding to look at the consequences if the initial premise is rejected though. I think the bell people would mutter about phonons.. but no problem . I've tried this before and failed .. c'est la vie.
Best wishes, C2.
Re LC circuit not quantised.. I disagree .. I feel it's as much an 'electron in a box problem' as an electron in an actual box .. just easier to solve .. the components are designed for entrapment purposes. No point in proceeding to look at the consequences if the initial premise is rejected though. I think the bell people would mutter about phonons.. but no problem
. I've tried this before and failed .. c'est la vie.Best wishes, C2.
Hi Confused2,
Electrons are already "quantized" and does not count. It is a photon in a "box" that "becomes" an electron.
Cheers
Electrons are already "quantized" and does not count. It is a photon in a "box" that "becomes" an electron.
Cheers
Hi Good_Elf,
You're right about the box.. I was thinking of potential wells.
http://www.du.edu/~jcalvert/phys/sqwell.htm
Classically, E can have any value from 0 up to V with the particle confined to the well, but this is not observed. What is found is that only a small number of energies E are possible, sometimes only one or two, and perhaps none at all, so the particle cannot be confined to the well.
My suggestion is that the LC circuit (resonant at f) is a way of making E = N h f the most likely (or only) wave solution for a trapped electron.
As far as I know electrons are not 'quantised'.. they can have any energy, just like a photon (but + mass) .. it's where you try to put them wot quantises them. The LC network only has (I suggest) one solution .. hence E = N hf .
Best wishes, C2.
You're right about the box.. I was thinking of potential wells.
http://www.du.edu/~jcalvert/phys/sqwell.htm
QUOTE
Classically, E can have any value from 0 up to V with the particle confined to the well, but this is not observed. What is found is that only a small number of energies E are possible, sometimes only one or two, and perhaps none at all, so the particle cannot be confined to the well.
My suggestion is that the LC circuit (resonant at f) is a way of making E = N h f the most likely (or only) wave solution for a trapped electron.
As far as I know electrons are not 'quantised'.. they can have any energy, just like a photon (but + mass) .. it's where you try to put them wot quantises them. The LC network only has (I suggest) one solution .. hence E = N hf .
Best wishes, C2.
Hi Confused2,
Well look at the mass of the electron, its dipole moment, its charge, its spin. These are "fixed". I suggest this is "quantization". There is also the possibility of absorption of a photon. The electron has a bosonic dual and that could take photons in a similar way to atomic shells.
There is also the mystery of the electron's two heavy partners the muon and tauon. Some call them "mesons", I prefer to think of them as "heavy electrons", they come from the "dark side". They form a triplet with the electron but the electron is the stable one. All particles come in "triplets" with three orders of particles like the three x three Dimensional spaces = 9 dimensions + Time. The mesons are made of two quarks and if electrons were not so well "embedded" in D6 space I think we would know they would have two "quarks" as well. This is an idea that I am still playing with. It is bound up with the topology... even quarks need to be interpreted as spun, twisted and boosted "photons".
Let me hear what you have to say about that.
The Free Dictionary: Sub-atomic particles
Cheers
QUOTE
As far as I know electrons are not 'quantized'.. they can have any energy, just like a photon (but + mass) ..
Well look at the mass of the electron, its dipole moment, its charge, its spin. These are "fixed". I suggest this is "quantization". There is also the possibility of absorption of a photon. The electron has a bosonic dual and that could take photons in a similar way to atomic shells.
There is also the mystery of the electron's two heavy partners the muon and tauon. Some call them "mesons", I prefer to think of them as "heavy electrons", they come from the "dark side". They form a triplet with the electron but the electron is the stable one. All particles come in "triplets" with three orders of particles like the three x three Dimensional spaces = 9 dimensions + Time. The mesons are made of two quarks and if electrons were not so well "embedded" in D6 space I think we would know they would have two "quarks" as well. This is an idea that I am still playing with. It is bound up with the topology... even quarks need to be interpreted as spun, twisted and boosted "photons".
Let me hear what you have to say about that.
The Free Dictionary: Sub-atomic particles
Cheers
Hello Good_Elf,
I think part of the problem here is the language we are using and partly we're (now) coming at 'electricity' from totally different directions..
I'm sure we're both aware of the de Broglie wavelength for a massive particles in motion.
( http://en.wikipedia.org/wiki/De_Broglie_hypothesis .. for a refresher )
Assuming we accept non-localisation of massive particles..
http://en.wikipedia.org/wiki/Particle_in_a_box gives a box and a solution for free propagation.. this should (and may actually be) the same as the de Broglie wavelength.. life is too short (for me at least) to work out which is what, the principle is sufficient..
The charge on the electron electron prevents it from leaving (say) the LC circuit .. it is trapped just like the particle in a box (potential well). Hence the solutions will be quantised.. we know the resonant frequency from f = 1/(2 pi) sqrt ( 1/(LC)) .. so I make the asumption that this gives an insight into the 'size' of a quanta in the circuit (e = h . f), and in general e = N h f. It might be one of those things that you either see or you don't - I'm no longer qualified to judge.
All this hand waving says nothing about what you will find inside an electron if you caught one .. only about the energy levels on a much larger scale. It's just another level of complexity that we didn't ask for.
In such a way do I justify my suggestion that circuits (LC most obviously) are quantised. This takes one back to Ivor Catt and his assertion that wires don't work like what they say.. despite denying the existence of QM he may actually be observing it in practice - that's what I'm most interested in at the moment.
Best wishes, John.
I think part of the problem here is the language we are using and partly we're (now) coming at 'electricity' from totally different directions..
I'm sure we're both aware of the de Broglie wavelength for a massive particles in motion.
( http://en.wikipedia.org/wiki/De_Broglie_hypothesis .. for a refresher )
Assuming we accept non-localisation of massive particles..
http://en.wikipedia.org/wiki/Particle_in_a_box gives a box and a solution for free propagation.. this should (and may actually be) the same as the de Broglie wavelength.. life is too short (for me at least) to work out which is what, the principle is sufficient..
The charge on the electron electron prevents it from leaving (say) the LC circuit .. it is trapped just like the particle in a box (potential well). Hence the solutions will be quantised.. we know the resonant frequency from f = 1/(2 pi) sqrt ( 1/(LC)) .. so I make the asumption that this gives an insight into the 'size' of a quanta in the circuit (e = h . f), and in general e = N h f. It might be one of those things that you either see or you don't - I'm no longer qualified to judge.
All this hand waving says nothing about what you will find inside an electron if you caught one .. only about the energy levels on a much larger scale. It's just another level of complexity that we didn't ask for.
In such a way do I justify my suggestion that circuits (LC most obviously) are quantised. This takes one back to Ivor Catt and his assertion that wires don't work like what they say.. despite denying the existence of QM he may actually be observing it in practice - that's what I'm most interested in at the moment.
Best wishes, John.
Hi Good Elf and Confused2:
The D6 space of the older string-M-theory based upon the Calabi-Yau Manifold is probably consistent with the more recent complex D3 twistor space and string theory of Penrose, Witten and others that I mentioned in a previous post [Jan 16 2006, 02:37 PM].
A part of the problem is the different ways in which dimensions are used by different mathematicians, physicists and other scientists.
When one tends to restrict dimensions to degrees of freedom, then the three imaginary axes may have no freedom since they are probably always orthogonal to their respective three real axes. Hence although there are six axes, there may be only three dimensions.
If there were really six degrees of freedom, then there probably would be a range of such spaces that would have six real or six imaginary or other combinations of real and imaginary totaling six axes instead of always having three real and three imaginary axes.
Just a thought - but the helicity discussed in twistor string theory appears consistent with phasor equations of Sreinmetz which in turn appear to be related to Grassman algebra and probably consistent with the de Broglie, Dirac, Schroedinger and Heisenberg equations
“If we knew what it was we were doing, it would not be called research, would it?” Einstein
The D6 space of the older string-M-theory based upon the Calabi-Yau Manifold is probably consistent with the more recent complex D3 twistor space and string theory of Penrose, Witten and others that I mentioned in a previous post [Jan 16 2006, 02:37 PM].
A part of the problem is the different ways in which dimensions are used by different mathematicians, physicists and other scientists.
When one tends to restrict dimensions to degrees of freedom, then the three imaginary axes may have no freedom since they are probably always orthogonal to their respective three real axes. Hence although there are six axes, there may be only three dimensions.
If there were really six degrees of freedom, then there probably would be a range of such spaces that would have six real or six imaginary or other combinations of real and imaginary totaling six axes instead of always having three real and three imaginary axes.
Just a thought - but the helicity discussed in twistor string theory appears consistent with phasor equations of Sreinmetz which in turn appear to be related to Grassman algebra and probably consistent with the de Broglie, Dirac, Schroedinger and Heisenberg equations
“If we knew what it was we were doing, it would not be called research, would it?” Einstein
Hi all
Interesting discusions in this thread.
I have tried to search for "speed of magnetic fields" on this forum and in general on the web.
Do anyone know where to find information regarding this, and if there are different speeds depending on material?
Interesting discusions in this thread.
I have tried to search for "speed of magnetic fields" on this forum and in general on the web.
Do anyone know where to find information regarding this, and if there are different speeds depending on material?
Hi Kettricken,
The speed of light is based on the combined ratios of the electric permittivity and the magnetic susceptibility...
A careful inspection of this formula indicates (to me) that it is a kind of "bulk average" of the separate speeds of the electric and magnetic propagations... They are kind of related reciprocally to each other. I believe this is closely related to the Fourier nature of the propagation of electromagnetic waves. Light only means something when it is related to the entire picture of light. In a higher dimension this is a "soliton" executing a "helix". The wave is "spinning" while progressing. It has integer "spin" for photons and half integer spin for fermions. A way to understand fermions is that they are "light" too but they are forced to apparently loop within their own space. A moving fermion exhibits a wave and this is related to that internal spin now being externalized through linear motion... the de Broglie wavelength. Everything is ultimately light, geometry and spin. There is "nothing" else other than these "vibrating strings" of geometry driven by laws of conservation of energy and direct application of the theory of Special and General Relativity.
Cheers
The speed of light is based on the combined ratios of the electric permittivity and the magnetic susceptibility...
A careful inspection of this formula indicates (to me) that it is a kind of "bulk average" of the separate speeds of the electric and magnetic propagations... They are kind of related reciprocally to each other. I believe this is closely related to the Fourier nature of the propagation of electromagnetic waves. Light only means something when it is related to the entire picture of light. In a higher dimension this is a "soliton" executing a "helix". The wave is "spinning" while progressing. It has integer "spin" for photons and half integer spin for fermions. A way to understand fermions is that they are "light" too but they are forced to apparently loop within their own space. A moving fermion exhibits a wave and this is related to that internal spin now being externalized through linear motion... the de Broglie wavelength. Everything is ultimately light, geometry and spin. There is "nothing" else other than these "vibrating strings" of geometry driven by laws of conservation of energy and direct application of the theory of Special and General Relativity.
Cheers
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