QUOTE (jal+Jul 21 2006, 03:48 AM)
C2.....with respect to uncertainty....how it was arrived at...."In a wave, a cycle is defined by the return from a certain position to the same position such as from the top of one crest to the next crest. This actually is equivalent to a circle of 360 degrees"
"or it can be written as h/(4π)"
Does that remind you of my SPOT and the four positions?
A structure which could explain or could be the cause of "uncertainty"????
jal
Jal,
My idea's have crest to crest Hz as 720 degree's, a positive & negative cycle via autodynamic trans-dimensional prop'.
Hi fivedoughnut
Well considering that "uncertainty" was worked out on "area" then if we use a structure, as I have, which is responsible for that uncertainty, then when we move to 3D, the structure would move through 720 degree's as you stated.
jal
Well considering that "uncertainty" was worked out on "area" then if we use a structure, as I have, which is responsible for that uncertainty, then when we move to 3D, the structure would move through 720 degree's as you stated.
jal
Hi jal, Why_Not?,5D,
I'm not really very happy with my analagy (the box) .. I just felt it was time to breath some life into the model.
We have entered the zone of C2 speculation here.
It seems this uncertainty is in everything (including empty space). It would probably have been be better to consider each of the oranges as having the uncertainty but the orange jumping out result might not have been so obvious.
However, Heisenberg found that when the position and momentum were multiplied together in that respective order or in the reverse order, there was a difference between the two calculated intensities of h/(2p).
Warning .. serious challenge to accepted theory and probable incorrect conclusion.
I don't like hidden variables very much but I'm going to introduce one here.. I'll call it K.. please bear in mind that at this stage K has no physical significance whatsoever, we just need some parameter we can vary otherwise we'd (obviously) get the same result every time. If you measure the momentum at K you get a probability distribution around p and a position distribution around x.
Repeating at K' you get p' and x'. The HUP result speaks of p and x' OR (equivalently) p' and x .
One of the more popular equations is E = hf. You can add in the de Broglie hypothesis for additional evidence if you wish ( http://en.wikipedia.org/wiki/De_Broglie_hypothesis ).
We also have d2x/dt^2 = -kx sooooo classical .. sooo tempting... sooo nice ...
Put all this into a pot in 1925 and stir and beyond reasonable doubt you get the result that my hidden variable K and time are one and the same thing. Observe C2 sellotaped to a chair being forced to listen to rap music and STILL claiming K is NOT time and K has no physical significance as a hidden variable or anything else.
Heisenberg had to make his result seem plausible .. I don't.
The point of all this was to establish that in the C2 universe it is sufficient for E to propagate without having to worry about frequencies and all that stuff. No rotations, neither 360 nor 720. Uncertainty = Uncertainty = Uncertainty. I suggest photons, neutrinos etc. are all just E propagating because that's what it does and how it does it.
Comments welcome .. preferably no rap music though.
-C2.
I'm not really very happy with my analagy (the box) .. I just felt it was time to breath some life into the model.
We have entered the zone of C2 speculation here.
It seems this uncertainty is in everything (including empty space). It would probably have been be better to consider each of the oranges as having the uncertainty but the orange jumping out result might not have been so obvious.
QUOTE
However, Heisenberg found that when the position and momentum were multiplied together in that respective order or in the reverse order, there was a difference between the two calculated intensities of h/(2p).
Warning .. serious challenge to accepted theory and probable incorrect conclusion.
I don't like hidden variables very much but I'm going to introduce one here.. I'll call it K.. please bear in mind that at this stage K has no physical significance whatsoever, we just need some parameter we can vary otherwise we'd (obviously) get the same result every time. If you measure the momentum at K you get a probability distribution around p and a position distribution around x.
Repeating at K' you get p' and x'. The HUP result speaks of p and x' OR (equivalently) p' and x .
One of the more popular equations is E = hf. You can add in the de Broglie hypothesis for additional evidence if you wish ( http://en.wikipedia.org/wiki/De_Broglie_hypothesis ).
We also have d2x/dt^2 = -kx sooooo classical .. sooo tempting... sooo nice ...
Put all this into a pot in 1925 and stir and beyond reasonable doubt you get the result that my hidden variable K and time are one and the same thing. Observe C2 sellotaped to a chair being forced to listen to rap music and STILL claiming K is NOT time and K has no physical significance as a hidden variable or anything else.
Heisenberg had to make his result seem plausible .. I don't.
The point of all this was to establish that in the C2 universe it is sufficient for E to propagate without having to worry about frequencies and all that stuff. No rotations, neither 360 nor 720. Uncertainty = Uncertainty = Uncertainty. I suggest photons, neutrinos etc. are all just E propagating because that's what it does and how it does it.
Comments welcome .. preferably no rap music though.
-C2.
Hey Confused2, jal, and fivedoughnut,
C2,
Also, I can't see why you have an aversion to k = t. Care to elaborate?
Finally,
C2,
QUOTE
It seems this uncertainty is in everything (including empty space).
... Are you defining "empty space" as space in n dimensions that is devoid of ALL mass, ALL energy, and ALL fields? Also, I can't see why you have an aversion to k = t. Care to elaborate?
Finally,
QUOTE (->
| QUOTE |
| It seems this uncertainty is in everything (including empty space). |
... Are you defining "empty space" as space in n dimensions that is devoid of ALL mass, ALL energy, and ALL fields?
Also, I can't see why you have an aversion to k = t. Care to elaborate?
Finally, Uncertainty = Uncertainty = Uncertainty
Also, I can't see why you have an aversion to k = t. Care to elaborate?
Finally, Uncertainty = Uncertainty = Uncertainty
to what?
Now I'm confused...
jal,
I have been re-reading the last few pages of this thread and I have another question about temperature (better yet, potential energy in your model) and 10^-17. Do all particles and energies have freedom of movement is all dimensions within your model?
Now I'm confused...
jal,
I have been re-reading the last few pages of this thread and I have another question about temperature (better yet, potential energy in your model) and 10^-17. Do all particles and energies have freedom of movement is all dimensions within your model?
Why_Not? jal, and fivedoughnut,
Are you defining [uncertainty in..] "empty space" as space in n dimensions that is devoid of ALL mass, ALL energy, and ALL fields?
http://en.wikipedia.org/wiki/Vacuum_energy
Vacuum energy is an underlying background energy that exists in space even when devoid of matter
I am indeed suggesting there is uncertainty in "empty space" as in space with n dimensions that might otherwise be considered to be devoid of ALL mass, ALL energy, and ALL fields.
I can't see why you have an aversion to k = t. Care to elaborate?
Difficult. Once you try to impose a periodic structure on 'uncertainty' you have to abandon the meaning of uncertainty. The uncertainty is either genuine or false .. I vote for a real uncertainty that simply 'exists' and produces the observed results which can be wilfully misinterpreted as periodic to match historically derived concepts.
-C2.
So the uncertainty of very empty space is the mechanism of the uncertainty principle in space time?
I'm operating outside my zone of competence here. I'd suggest the uncertainty principle is the mechanism of uncertainty in everything, wherever, whatever, and however, it's always there.
By subtracting time from the equation you remove the uncertainty?
This is a dreadful analagy but the best I can think of. Imagine we know there are (say) ten thousand spiders in every square metre. Imagine there is always a standard deviation of 10% when you count spiders. When you do it doesn't matter.
( http://en.wikipedia.org/wiki/Standard_deviation )
The error is totally random .. some spiders you miss , some you count twice and so on. If you count the spiders (say) 10 times this reduces your error to (about) 1%. ( http://en.wikipedia.org/wiki/Confidence_interval ) My 1% is a complete guess because I'm too lazy to read the wiki thing and do the job properly .. but it doesn't affect the principle.
We could count spiders in an area to work out the area enclosed (not very efficiently) .. even if we get a count of zero spiders we can't assume the area is zero and if we find ten spiders we can't assume the area is 1 cm^2 .. we only get a 'probable' answer. Even with zero area we still get the odd spider
turning up.
Spiders, area, momentum, position.. I don't think that subtracting time from the equation will reduce the uncertainty.
That nice E = hf equation .. when you actually try to measure frequency the uncertainty principle appears again and will defeat your best observations
, I think the uncertainty is in everything, not just time .
-C2.
QUOTE (Why_Not?+)
Are you defining [uncertainty in..] "empty space" as space in n dimensions that is devoid of ALL mass, ALL energy, and ALL fields?
http://en.wikipedia.org/wiki/Vacuum_energy
QUOTE (the above URL+)
Vacuum energy is an underlying background energy that exists in space even when devoid of matter
I am indeed suggesting there is uncertainty in "empty space" as in space with n dimensions that might otherwise be considered to be devoid of ALL mass, ALL energy, and ALL fields.
QUOTE (Why_Not?+)
I can't see why you have an aversion to k = t. Care to elaborate?
Difficult. Once you try to impose a periodic structure on 'uncertainty' you have to abandon the meaning of uncertainty. The uncertainty is either genuine or false .. I vote for a real uncertainty that simply 'exists' and produces the observed results which can be wilfully misinterpreted as periodic to match historically derived concepts.
-C2.
Hey Confused2, jal and fivedoughnut,
C2,
So devoid of vacuum energy/fields, lets call it very empty space. So the uncertainty of very empty space is the mechanism of the uncertainty principle in space time? By subtracting time from the equation you remove the uncertainty?
still confused, by trying....
C2,
So devoid of vacuum energy/fields, lets call it very empty space. So the uncertainty of very empty space is the mechanism of the uncertainty principle in space time? By subtracting time from the equation you remove the uncertainty?
still confused, by trying....
QUOTE (Why_Not?+)
So the uncertainty of very empty space is the mechanism of the uncertainty principle in space time?
I'm operating outside my zone of competence here. I'd suggest the uncertainty principle is the mechanism of uncertainty in everything, wherever, whatever, and however, it's always there.
QUOTE (Why_Not?+)
By subtracting time from the equation you remove the uncertainty?
This is a dreadful analagy but the best I can think of. Imagine we know there are (say) ten thousand spiders in every square metre. Imagine there is always a standard deviation of 10% when you count spiders. When you do it doesn't matter.
( http://en.wikipedia.org/wiki/Standard_deviation )
The error is totally random .. some spiders you miss , some you count twice and so on. If you count the spiders (say) 10 times this reduces your error to (about) 1%. ( http://en.wikipedia.org/wiki/Confidence_interval ) My 1% is a complete guess because I'm too lazy to read the wiki thing and do the job properly .. but it doesn't affect the principle.
We could count spiders in an area to work out the area enclosed (not very efficiently) .. even if we get a count of zero spiders we can't assume the area is zero and if we find ten spiders we can't assume the area is 1 cm^2 .. we only get a 'probable' answer. Even with zero area we still get the odd spider
turning up.Spiders, area, momentum, position.. I don't think that subtracting time from the equation will reduce the uncertainty.
That nice E = hf equation .. when you actually try to measure frequency the uncertainty principle appears again and will defeat your best observations
, I think the uncertainty is in everything, not just time .-C2.
Why Not?
hehehee.... How many dimensions do you presume my model to have?
Do you want to use the T-duality concept....many vs few....
My point of view is that the Membrane is 2d ....the units of the membranes (k-k particles) are 10^-17.... they are in constant motion in a complex spherical pattern (12 units)
The actual locations of these units is giving us the "uncertainty principle".
C2....We certainly see things from different poles.
jal
(I'm sure that there will be improvements to my model)
QUOTE
Do all particles and energies have freedom of movement is all dimensions within your model?
hehehee.... How many dimensions do you presume my model to have?
Do you want to use the T-duality concept....many vs few....
My point of view is that the Membrane is 2d ....the units of the membranes (k-k particles) are 10^-17.... they are in constant motion in a complex spherical pattern (12 units)
The actual locations of these units is giving us the "uncertainty principle".
C2....We certainly see things from different poles.
jal
(I'm sure that there will be improvements to my model)
Hey jal, Confused2, et al.
C2,
I agree. But just for arguments sake... If we consider wave function collapse occurring at the moment of interaction, instead of at the moment of observation... I am certain that the moon, sun and stars are still in the sky even though I am not currently observing them. Schrodinger's Cat is definitely dead or alive (but not both) even though information regarding the cat's state is not transmitted until the observation is made. Since uncertainty vanishes at the moment of interaction (or observation, if you prefer) then removing time, removes uncertainty. The probabilities could be inherent in whether the interaction occurs at a specific moment or a different significant moment later (or earlier). Without including time, we can't make sense out of E=hf.
jal,
Ummmm, 6 spatial? That is three large dimension each composed of a 2-brane? If each dimension provide two degrees of freedom, you need 6 to provide 12 degrees of freedom. Or am I way off base with understanding your model?
Earlier, you showed how entropy increases and potential energy decreases as a result of adding dimensions. That's all fine and good. But, if this holds for all energy, as opposed to just gravitational energy, then we should have already witnessed variations in the inverse square law as it applies to the EM interaction if the 2-brane is 10^-17 since our current resolution is down to 10^-18 and 1/R^2 still applies.
C2,
QUOTE
I don't think that subtracting time from the equation will reduce the uncertainty.
I agree. But just for arguments sake... If we consider wave function collapse occurring at the moment of interaction, instead of at the moment of observation... I am certain that the moon, sun and stars are still in the sky even though I am not currently observing them. Schrodinger's Cat is definitely dead or alive (but not both) even though information regarding the cat's state is not transmitted until the observation is made. Since uncertainty vanishes at the moment of interaction (or observation, if you prefer) then removing time, removes uncertainty. The probabilities could be inherent in whether the interaction occurs at a specific moment or a different significant moment later (or earlier). Without including time, we can't make sense out of E=hf.
jal,
Ummmm, 6 spatial? That is three large dimension each composed of a 2-brane? If each dimension provide two degrees of freedom, you need 6 to provide 12 degrees of freedom. Or am I way off base with understanding your model?
Earlier, you showed how entropy increases and potential energy decreases as a result of adding dimensions. That's all fine and good. But, if this holds for all energy, as opposed to just gravitational energy, then we should have already witnessed variations in the inverse square law as it applies to the EM interaction if the 2-brane is 10^-17 since our current resolution is down to 10^-18 and 1/R^2 still applies.
Why Not?
How can I possibly come up with any good guess of how the universe is made if I cannot get any good information?
"garbage in ...garbage out...."
Before I start changing my presentation.... coould you give me the links that makes you say that ...."10^-18 and 1/R^2 still applies".
jal
QUOTE
since our current resolution is down to 10^-18 and 1/R^2 still applies.
How can I possibly come up with any good guess
of how the universe is made if I cannot get any good information?"garbage in ...garbage out...."
Before I start changing my presentation.... coould you give me the links that makes you say that ...."10^-18 and 1/R^2 still applies".
jal
Hey jal,
I think your model is far form garbage, else it would have faded away long ago.
"10^-18" came from one of the links you have provided on this thread (if I am remembering correctly - or maybe it was one of yq's...). The reference did not specifically state that 1/R^2 held at 10^-18 but it did say that our current resolution was down to 10^-18 and that the Standard Model predictions held. Since there is apparently no change in 1/R^2 at this resolution (for EM), I inferred that 1/R^2 should hold (for EM) - if it changed to 1/R^x (where x > 2) that would provide clear indication of extra dimesnions. I need to run, but when I return, I will sift though the links and find the one that I am referring to.
In the meantime, if I read and understood the link correctly, it would mean that EM either does not propagate in extra dimensions, regardless of the size of the extra dimensions. Or, if EM does propagate in extra dimensions, those dimensions would need to be smaller than 10^-18. That does not imply that gravity cannot propagate in more than 3 spatial dimensions and that those dimensions could be as large as ~mm since that it the current experimental resolution for gravity (info again from one of your links).
I think your model is far form garbage, else it would have faded away long ago.
"10^-18" came from one of the links you have provided on this thread (if I am remembering correctly - or maybe it was one of yq's...). The reference did not specifically state that 1/R^2 held at 10^-18 but it did say that our current resolution was down to 10^-18 and that the Standard Model predictions held. Since there is apparently no change in 1/R^2 at this resolution (for EM), I inferred that 1/R^2 should hold (for EM) - if it changed to 1/R^x (where x > 2) that would provide clear indication of extra dimesnions. I need to run, but when I return, I will sift though the links and find the one that I am referring to.
In the meantime, if I read and understood the link correctly, it would mean that EM either does not propagate in extra dimensions, regardless of the size of the extra dimensions. Or, if EM does propagate in extra dimensions, those dimensions would need to be smaller than 10^-18. That does not imply that gravity cannot propagate in more than 3 spatial dimensions and that those dimensions could be as large as ~mm since that it the current experimental resolution for gravity (info again from one of your links).
Hey jal,
It was from the link you posted on yq's thread (April 29),
Test of Inverse square law by E.G. Adelberger. Page 5 in reference to Coulomb's Law.
It was from the link you posted on yq's thread (April 29),
Test of Inverse square law by E.G. Adelberger. Page 5 in reference to Coulomb's Law.
Why Not?
I'm on the road, when I get back we could go into details. This article also explain how they decided to use more dimensions to undertstand the universe.
If you play basket ball..... the hoop has got to be bigger than the ball.
jal
QUOTE
Test of Inverse square law by E.G. Adelberger. Page 5 in reference to Coulomb's Law.
I'm on the road, when I get back we could go into details. This article also explain how they decided to use more dimensions to undertstand the universe.
If you play basket ball..... the hoop has got to be bigger than the ball.
jal
Hi jal,
I'm just dumping these here because this is the only place I can think of for them. Posted by rpenner on another thread .. not my area of competence so I can't assess the relevence. Ought to be able to though.. I'll do my best. Your comments welcome.
The red line is not at D=6, but D=7.2569464048605767801...
http://mathworld.wolfram.com/Hypersphere.html
Kepler's conjecture was for spheres, not hyperspheres, and has lots of counter examples in high dimensions, especially at D=12 and D=24
http://mathworld.wolfram.com/KeplerConjecture.html
http://mathworld.wolfram.com/Coxeter-ToddLattice.html
http://mathworld.wolfram.com/KissingNumber.html
http://mathworld.wolfram.com/LeechLattice.html
http://en.wikipedia.org/wiki/Sphere_packing
Hope all well with you,
Best wishes,
-C2.
Edit
We can't edit for long now.. I've had a quick look .. ??? I know nothing .. perhaps you can help me on this when you return. C2 .. still.
I'm just dumping these here because this is the only place I can think of for them. Posted by rpenner on another thread .. not my area of competence so I can't assess the relevence. Ought to be able to though.. I'll do my best. Your comments welcome.
The red line is not at D=6, but D=7.2569464048605767801...
http://mathworld.wolfram.com/Hypersphere.html
Kepler's conjecture was for spheres, not hyperspheres, and has lots of counter examples in high dimensions, especially at D=12 and D=24
http://mathworld.wolfram.com/KeplerConjecture.html
http://mathworld.wolfram.com/Coxeter-ToddLattice.html
http://mathworld.wolfram.com/KissingNumber.html
http://mathworld.wolfram.com/LeechLattice.html
http://en.wikipedia.org/wiki/Sphere_packing
Hope all well with you,
Best wishes,
-C2.
Edit
We can't edit for long now.. I've had a quick look .. ??? I know nothing .. perhaps you can help me on this when you return. C2 .. still.
Good Day everyone! It’s nice to be back.
Thanks, C2 for posting the links!
I hate making long post and unfortunately, this one will be long. I hope that everyone will be able to swallow all the information in this one gulp.
I found a nice discussion and I would like to make some comments with more links. Hopefully, it will demonstrate the advantages of my approach.
---------------------------------------------------------
Interesting discussion….. now … for my 2 cents….
I think that we use extra dimensions because of
E = hf
It’s the source of the solution and the source of the problems.
See http://www.phys.unsw.edu.au/einsteinlight/...ule6_Planck.htm
---------------------------------------------------------
Interesting discussion….. now … for my 2 cents….
I think that we use extra dimensions because of
E = hf
It’s the source of the solution and the source of the problems.
See http://www.phys.unsw.edu.au/einsteinlight/...ule6_Planck.htm
The Planck length LP is defined by taking the constants of nature and combining them in such a way that their units combine to give a length. Planck's constant, h, has units of Joule seconds. Cavendish's constant G (the constant of gravitation) has units of N.m2kg2. And the speed of light c has units of m.s1. The combination that works is:
LP = (hG/2c3)1/2 .
The Planck length is 1.6 x 1035 metres.
Divide the minuscule Planck length by the speed of light (which is pretty big) and you get a really tiny unit of time, the Planck time, tP, which is:
tP = (hG/2c5)1/2 .
The Planck time is 5.4 x 1044 seconds.
(There is also a Planck mass, which is (ch/2G)1/2 = 22 g. This doesn't sound very much, until you think of a fundamental particle with that mass. Or until you convert it into energy by multiplying by c2 to get 2.0 1012 joules or 1.2 x 1031 eV.)
and http://www.phys.unsw.edu.au/einsteinlight/...y_chemistry.htm
http://www.physicsforums.com/
Another Physics forum…..good discussions
http://www.physicsforums.com/showthread.php?t=54167&page=7
Introduction To Loop Quantum Gravity with lots of links
http://www.physicsforums.com/
Another Physics forum…..good discussions
http://www.physicsforums.com/showthread.php?t=54167&page=7
Introduction To Loop Quantum Gravity with lots of links
Why exactly them loops ?
Well, let’s steal some ideas from particle physics... In QFT we have fermionic matter-fields and bosonic force-fields. The quanta of these force-fields or the so called force-carrier-particles that mediate forces between matter-particles. Sometimes force-carriers can also interact with eachother, like strong-force-mediating gluons for example. These force carriers also have wavelike properties and in this view they are looked as excitations of the bosonic-forcefields. For example some line in a field can start to vibrate (think of a guitar-string) and in QFT one then says that this vibration is a particle. This may sound strange but what is really meant is that the vibration has the properties of some particle with energy, speed, and so on, corresponding to that of the vibration. These lines are also known as Faraday’s lines of force. Photons are "generated" this way in QFT, where they are excitations of the EM-field. Normally these lines go from one matter-particle to another and in the absence of particles or charges they form closed lines, aka loops. Loop Quantum Gravity is the mathematical description of quantum gravity in terms of loops on a manifold. We have already shown how we can work with loops on a manifold and still be assured of background-independence and gauge-invariance for QFT. So we want to quantize the gravitational field by expressing it in terms of loops. These loops are quantum excitations of the Faraday-lines that live in the field and who represent the gravitational force. Gravitons or closed loops that arise as low-energy-excitations of the gravitational field and these particles mediate the gravitational force between objects.
It is important to realize that these loops do not live on some space-time-continuum, they are space-time !!! The loops arise as excitations of the gravitational field, which on itself constitutes “space”. Now the problem is how to incorporate the concept of space or to put it more accurately : “how do we define all these different geometries in order to be able to work with a wave function ?”
The Wheeler-DeWitt equation has solutions describing excitations of the gravitational field in terms of loops. A great step was taken when Abhay Ashtekar rewrote the General Theory of Relativity in a similar form as the Yang-Mills-Theory of QFT. The main gauge-field was not the gravitational field. No, the gravitational field was replaced by the so called connection-field that will then be used to work with different metrics. In this model space must be regarded as some kind of fabric weaved together by loops. This fabric contains finite small space-parts that reflect the quantization of space. It is easy to see that there are no infinite small space regions, thus no space-continuum. Quantum mechanics teaches us that in order to look at very small distance-scales, an very big amount of energy is needed. But since we also work in General Relativity we must take into account the fact that great amounts of energy concentrated at a very small scale gives rise to black holes that make the space-region disappear. By making the Schwardzschildradius equal to the Comptonradius we can get a number expressing the minimum size of such a space-region. The result is a number that is in the order of the Planck Length. (In my approach, I do not go to the Planck Scale)
Now how is space constructed in LQG ? Well, the above mentioned minimal space-regions are denoted by spheres called the nodes. Nodes are connected to eachother by lines called the links.
By quantizing a physical theory, operators that calculate physical quantities will acquire a certain set of possible outcomes or values. It can be proven that in our case the area of the surface between two nodes is quantized and the corresponding quantum numbers can be denoted along a link. These surfaces I am referring are drawn as purple triangles. In this way a three-dimensional space can be constructed.
One can also assign a quantumnumber which each node, that corresponds to the volume of the grain. Finally, a physical state is now represented as a superposition of such spin-networks.
REFERENCE : maestro Carlo Rovelli “Loop Quantum Gravity”
Physics World, November 2003
The challenge for string theorists and LQG theorists is to explain why the vacuum energy exists at 10^120 J/m^3 ( there is no reason to think there is anything wrong with the QM calculation) but does not curve space-time.How can
quantum gravity be proved if gravity is not understood on its own yet?
BTW just to have a basis for comparision, the astronomers' dark energy estimate is currently around 0.6 x 10-9 joule per cubic meter.
(There is also a Planck mass, which is (ch/2G)1/2 = 22 g. This doesn't sound very much, until you think of a fundamental particle with that mass. Or until you convert it into energy by multiplying by c2 to get 2.0 1012 joules or 1.2 x 1031 eV.)
http://arxiv.org/PS_cache/math/pdf/0306/0306440.pdf
http://www.physicsforums.com/showthread.php?t=119294
Randall-Sundrum; Observable particles at LHC?
http://www.physicsforums.com/showthread.php?t=119294
Randall-Sundrum; Observable particles at LHC?
Warped Phenomenology
http://lanl.arxiv.org/abs/hep-ph/9909255
Authors: H. Davoudiasl, J.L. Hewett, T.G. Rizzo
Journal-ref: Phys.Rev.Lett. 84 (2000) 2080
We explore the phenomenology associated with the recently proposed localized gravity model of Randall and Sundrum where gravity propagates in a 5-dimensional non-factorizable geometry and generates the 4-dimensional weak-Planck scale hierarchy by an exponential function of the compactification radius, called a warp factor. The Kaluza-Klein tower of gravitons which emerge in this scenario have strikingly different properties than in the factorizable case with large extra dimensions. We derive the form of the graviton tower interactions with the Standard Model fields and examine their direct production in Drell-Yan and dijet events at the Tevatron and LHC as well as the KK spectrum line-shape at high-energy linear \epem colliders. In the case where the first KK excitation is observed, we outline the procedure to uniquely determine the parameters of this scenario. We also investigate the effect of KK tower exchanges in contact interaction searches. We find that present experiments can place meaningful constraints on the parameters of this model.
Now in particular note the graviton. Each graviton in the five dimensional bulk will have a five-momentum, and some of them will have five-momenta that have zero component orthogonal to the fifth dimension. The wave function of such a particle will have four-components in the Weakbrane that will have zero three-momentum and will therefore appear there as mass. So an interacting particle with mass about the TEV scale of Weakbrane physics is predicted to be detectable at the LHC. But there's more. The momentum of the graviton can have a quantized spactrum coming from vibration modes of the closed string as wound some number of times around the topology of the compacted manifolds. So these LHC particles will have a very characteristic mass spectrum of TEV, 2TEV, 3TEV, and so on. She can also calculate that unlike the free graviton, these particles are not as suppressed by the curved geometry; their interaction probability is 16 orders of magnitude higher than the free graviton (p. 408).
Is it possible that helical strings as [complex] harmonic oscillators could accommodate both the Randall 'large' and Arkani-Hamed 'small' concepts of curled-up, unseen dimensions?
A helix is certainly coiled and applies to QM via the 3D Schroedinger wave equation and a 'space double helix' [likely EM related] was imaged near the galactic core.
Helices [or helicoids] may as [complex] harmonic oscillators may even satisfy the search for the fifth dimension or the helical properties attributed to the 11th dimension of U-duality in M-theory.
A cylindrical space-time [or because of eccentricity an ellipto-cylndrical] complex 5D space may even satisfy the t'Hooft epislon concept of nD as (n-1).99999D.
Helices [with virtual volumes] as [complex] harmonic oscillators may even have gauge-corresponding loops [with virtual areas] of the same period.
Is it possible that helical strings as [complex] harmonic oscillators could accommodate both the Randall 'large' and Arkani-Hamed 'small' concepts of curled-up, unseen dimensions?
The answer is yes.
It could also accommodate a 2d SPOT AT 10^-17 and avoid all the problems associated by going to Planck Scale.
Therefore, MORE DIMENSIONS ARE NOT NEEDED.
jal
Thanks, C2 for posting the links!
I hate making long post and unfortunately, this one will be long. I hope that everyone will be able to swallow all the information in this one gulp.
I found a nice discussion and I would like to make some comments with more links. Hopefully, it will demonstrate the advantages of my approach.
QUOTE
Confused2
First point .. what problem is it that we are trying to solve by invoking extra dimensions?
Why Not?
In particular, and as relevant to this thread, the answer is in an attempt to answers yq's question. Kaluza-Klein Theory, in adding a 5th dimensions to GR, "unifies" Maxwell's equations with GR. My take on it is that if we can get away with adding one extra compact spatial dimension to incorporate EM with GR, why not add more to incorporate the particle masses and properties? Since these properties can be expressed as degrees of freedom, you need the extra dimensions to provide a place for these degrees of freedom to "exist".
As far as I am concerned, they [curled up dimensions] can be considered mathematical constructs that exist in the equations that describe reality instead of reality itself (just like the wave function or i).
Confused2
You hit a few raw nerves there .. we may agree that extra dimensions are OK if they help .. not if they don't.
First point .. what problem is it that we are trying to solve by invoking extra dimensions?
Why Not?
In particular, and as relevant to this thread, the answer is in an attempt to answers yq's question. Kaluza-Klein Theory, in adding a 5th dimensions to GR, "unifies" Maxwell's equations with GR. My take on it is that if we can get away with adding one extra compact spatial dimension to incorporate EM with GR, why not add more to incorporate the particle masses and properties? Since these properties can be expressed as degrees of freedom, you need the extra dimensions to provide a place for these degrees of freedom to "exist".
As far as I am concerned, they [curled up dimensions] can be considered mathematical constructs that exist in the equations that describe reality instead of reality itself (just like the wave function or i).
Confused2
You hit a few raw nerves there .. we may agree that extra dimensions are OK if they help .. not if they don't.
---------------------------------------------------------
Interesting discussion….. now … for my 2 cents….
I think that we use extra dimensions because of
E = hf
It’s the source of the solution and the source of the problems.
See http://www.phys.unsw.edu.au/einsteinlight/...ule6_Planck.htm
QUOTE (->
| QUOTE |
| Confused2 First point .. what problem is it that we are trying to solve by invoking extra dimensions? Why Not? In particular, and as relevant to this thread, the answer is in an attempt to answers yq's question. Kaluza-Klein Theory, in adding a 5th dimensions to GR, "unifies" Maxwell's equations with GR. My take on it is that if we can get away with adding one extra compact spatial dimension to incorporate EM with GR, why not add more to incorporate the particle masses and properties? Since these properties can be expressed as degrees of freedom, you need the extra dimensions to provide a place for these degrees of freedom to "exist". As far as I am concerned, they [curled up dimensions] can be considered mathematical constructs that exist in the equations that describe reality instead of reality itself (just like the wave function or i). Confused2 You hit a few raw nerves there .. we may agree that extra dimensions are OK if they help .. not if they don't. |
---------------------------------------------------------
Interesting discussion….. now … for my 2 cents….
I think that we use extra dimensions because of
E = hf
It’s the source of the solution and the source of the problems.
See http://www.phys.unsw.edu.au/einsteinlight/...ule6_Planck.htm
The Planck length LP is defined by taking the constants of nature and combining them in such a way that their units combine to give a length. Planck's constant, h, has units of Joule seconds. Cavendish's constant G (the constant of gravitation) has units of N.m2kg2. And the speed of light c has units of m.s1. The combination that works is:
LP = (hG/2c3)1/2 .
The Planck length is 1.6 x 1035 metres.
Divide the minuscule Planck length by the speed of light (which is pretty big) and you get a really tiny unit of time, the Planck time, tP, which is:
tP = (hG/2c5)1/2 .
The Planck time is 5.4 x 1044 seconds.
(There is also a Planck mass, which is (ch/2G)1/2 = 22 g. This doesn't sound very much, until you think of a fundamental particle with that mass. Or until you convert it into energy by multiplying by c2 to get 2.0 1012 joules or 1.2 x 1031 eV.)
and http://www.phys.unsw.edu.au/einsteinlight/...y_chemistry.htm
QUOTE
Energy transmitted by light of a certain colour is not continuous, but comes in lumps with energy
E = hf
where f is the frequency of the electromagnetic wave, and h is a constant, called Planck's constant, after Max Planck. The 'packets' of light are now called photons…..Well, h is small. In our ordinary units it is 6.63 x 1034 Js
Planck's constant, , was proposed in reference to the problem of black-body radiation. The underlying assumption to Planck's law of black body radiation was that the electromagnetic radiation emitted by a black body could be modeled as a set of harmonic oscillators with quantized energy.
E = hf
where f is the frequency of the electromagnetic wave, and h is a constant, called Planck's constant, after Max Planck. The 'packets' of light are now called photons…..Well, h is small. In our ordinary units it is 6.63 x 1034 Js
Planck's constant, , was proposed in reference to the problem of black-body radiation. The underlying assumption to Planck's law of black body radiation was that the electromagnetic radiation emitted by a black body could be modeled as a set of harmonic oscillators with quantized energy.
http://www.physicsforums.com/
Another Physics forum…..good discussions
http://www.physicsforums.com/showthread.php?t=54167&page=7
Introduction To Loop Quantum Gravity with lots of links
QUOTE (->
| QUOTE |
| Energy transmitted by light of a certain colour is not continuous, but comes in lumps with energy E = hf where f is the frequency of the electromagnetic wave, and h is a constant, called Planck's constant, after Max Planck. The 'packets' of light are now called photons…..Well, h is small. In our ordinary units it is 6.63 x 1034 Js Planck's constant, , was proposed in reference to the problem of black-body radiation. The underlying assumption to Planck's law of black body radiation was that the electromagnetic radiation emitted by a black body could be modeled as a set of harmonic oscillators with quantized energy. |
http://www.physicsforums.com/
Another Physics forum…..good discussions
http://www.physicsforums.com/showthread.php?t=54167&page=7
Introduction To Loop Quantum Gravity with lots of links
Why exactly them loops ?
Well, let’s steal some ideas from particle physics... In QFT we have fermionic matter-fields and bosonic force-fields. The quanta of these force-fields or the so called force-carrier-particles that mediate forces between matter-particles. Sometimes force-carriers can also interact with eachother, like strong-force-mediating gluons for example. These force carriers also have wavelike properties and in this view they are looked as excitations of the bosonic-forcefields. For example some line in a field can start to vibrate (think of a guitar-string) and in QFT one then says that this vibration is a particle. This may sound strange but what is really meant is that the vibration has the properties of some particle with energy, speed, and so on, corresponding to that of the vibration. These lines are also known as Faraday’s lines of force. Photons are "generated" this way in QFT, where they are excitations of the EM-field. Normally these lines go from one matter-particle to another and in the absence of particles or charges they form closed lines, aka loops. Loop Quantum Gravity is the mathematical description of quantum gravity in terms of loops on a manifold. We have already shown how we can work with loops on a manifold and still be assured of background-independence and gauge-invariance for QFT. So we want to quantize the gravitational field by expressing it in terms of loops. These loops are quantum excitations of the Faraday-lines that live in the field and who represent the gravitational force. Gravitons or closed loops that arise as low-energy-excitations of the gravitational field and these particles mediate the gravitational force between objects.
It is important to realize that these loops do not live on some space-time-continuum, they are space-time !!! The loops arise as excitations of the gravitational field, which on itself constitutes “space”. Now the problem is how to incorporate the concept of space or to put it more accurately : “how do we define all these different geometries in order to be able to work with a wave function ?”
The Wheeler-DeWitt equation has solutions describing excitations of the gravitational field in terms of loops. A great step was taken when Abhay Ashtekar rewrote the General Theory of Relativity in a similar form as the Yang-Mills-Theory of QFT. The main gauge-field was not the gravitational field. No, the gravitational field was replaced by the so called connection-field that will then be used to work with different metrics. In this model space must be regarded as some kind of fabric weaved together by loops. This fabric contains finite small space-parts that reflect the quantization of space. It is easy to see that there are no infinite small space regions, thus no space-continuum. Quantum mechanics teaches us that in order to look at very small distance-scales, an very big amount of energy is needed. But since we also work in General Relativity we must take into account the fact that great amounts of energy concentrated at a very small scale gives rise to black holes that make the space-region disappear. By making the Schwardzschildradius equal to the Comptonradius we can get a number expressing the minimum size of such a space-region. The result is a number that is in the order of the Planck Length. (In my approach, I do not go to the Planck Scale)
Now how is space constructed in LQG ? Well, the above mentioned minimal space-regions are denoted by spheres called the nodes. Nodes are connected to eachother by lines called the links.
By quantizing a physical theory, operators that calculate physical quantities will acquire a certain set of possible outcomes or values. It can be proven that in our case the area of the surface between two nodes is quantized and the corresponding quantum numbers can be denoted along a link. These surfaces I am referring are drawn as purple triangles. In this way a three-dimensional space can be constructed.
One can also assign a quantumnumber which each node, that corresponds to the volume of the grain. Finally, a physical state is now represented as a superposition of such spin-networks.
REFERENCE : maestro Carlo Rovelli “Loop Quantum Gravity”
Physics World, November 2003
The challenge for string theorists and LQG theorists is to explain why the vacuum energy exists at 10^120 J/m^3 ( there is no reason to think there is anything wrong with the QM calculation) but does not curve space-time.How can
quantum gravity be proved if gravity is not understood on its own yet?
BTW just to have a basis for comparision, the astronomers' dark energy estimate is currently around 0.6 x 10-9 joule per cubic meter.
(There is also a Planck mass, which is (ch/2G)1/2 = 22 g. This doesn't sound very much, until you think of a fundamental particle with that mass. Or until you convert it into energy by multiplying by c2 to get 2.0 1012 joules or 1.2 x 1031 eV.)
http://arxiv.org/PS_cache/math/pdf/0306/0306440.pdf
QUOTE
The application of the new structure to quantum geometry has not been
worked out yet, but looks promising. The fibered spaces in the objects we put
on parts of triangulations have natural interpretations as staged quantizations
of geometrical variables. Problems of regularization remain to be considered, as
do the appropriate constraints for quantum gravity.
We have focused on the Poincar´e 2-group for reasons of physical interest. In
fact, our construction has an analog for any choice of a semisimple Lie group and
a representation of it [7]. This means that a whole new chapter of representation
theory is opened up, closely allied to a new family of quantum geometries.
worked out yet, but looks promising. The fibered spaces in the objects we put
on parts of triangulations have natural interpretations as staged quantizations
of geometrical variables. Problems of regularization remain to be considered, as
do the appropriate constraints for quantum gravity.
We have focused on the Poincar´e 2-group for reasons of physical interest. In
fact, our construction has an analog for any choice of a semisimple Lie group and
a representation of it [7]. This means that a whole new chapter of representation
theory is opened up, closely allied to a new family of quantum geometries.
http://www.physicsforums.com/showthread.php?t=119294
Randall-Sundrum; Observable particles at LHC?
QUOTE (->
| QUOTE |
| The application of the new structure to quantum geometry has not been worked out yet, but looks promising. The fibered spaces in the objects we put on parts of triangulations have natural interpretations as staged quantizations of geometrical variables. Problems of regularization remain to be considered, as do the appropriate constraints for quantum gravity. We have focused on the Poincar´e 2-group for reasons of physical interest. In fact, our construction has an analog for any choice of a semisimple Lie group and a representation of it [7]. This means that a whole new chapter of representation theory is opened up, closely allied to a new family of quantum geometries. |
http://www.physicsforums.com/showthread.php?t=119294
Randall-Sundrum; Observable particles at LHC?
Warped Phenomenology
http://lanl.arxiv.org/abs/hep-ph/9909255
Authors: H. Davoudiasl, J.L. Hewett, T.G. Rizzo
Journal-ref: Phys.Rev.Lett. 84 (2000) 2080
We explore the phenomenology associated with the recently proposed localized gravity model of Randall and Sundrum where gravity propagates in a 5-dimensional non-factorizable geometry and generates the 4-dimensional weak-Planck scale hierarchy by an exponential function of the compactification radius, called a warp factor. The Kaluza-Klein tower of gravitons which emerge in this scenario have strikingly different properties than in the factorizable case with large extra dimensions. We derive the form of the graviton tower interactions with the Standard Model fields and examine their direct production in Drell-Yan and dijet events at the Tevatron and LHC as well as the KK spectrum line-shape at high-energy linear \epem colliders. In the case where the first KK excitation is observed, we outline the procedure to uniquely determine the parameters of this scenario. We also investigate the effect of KK tower exchanges in contact interaction searches. We find that present experiments can place meaningful constraints on the parameters of this model.
Now in particular note the graviton. Each graviton in the five dimensional bulk will have a five-momentum, and some of them will have five-momenta that have zero component orthogonal to the fifth dimension. The wave function of such a particle will have four-components in the Weakbrane that will have zero three-momentum and will therefore appear there as mass. So an interacting particle with mass about the TEV scale of Weakbrane physics is predicted to be detectable at the LHC. But there's more. The momentum of the graviton can have a quantized spactrum coming from vibration modes of the closed string as wound some number of times around the topology of the compacted manifolds. So these LHC particles will have a very characteristic mass spectrum of TEV, 2TEV, 3TEV, and so on. She can also calculate that unlike the free graviton, these particles are not as suppressed by the curved geometry; their interaction probability is 16 orders of magnitude higher than the free graviton (p. 408).
Is it possible that helical strings as [complex] harmonic oscillators could accommodate both the Randall 'large' and Arkani-Hamed 'small' concepts of curled-up, unseen dimensions?
A helix is certainly coiled and applies to QM via the 3D Schroedinger wave equation and a 'space double helix' [likely EM related] was imaged near the galactic core.
Helices [or helicoids] may as [complex] harmonic oscillators may even satisfy the search for the fifth dimension or the helical properties attributed to the 11th dimension of U-duality in M-theory.
A cylindrical space-time [or because of eccentricity an ellipto-cylndrical] complex 5D space may even satisfy the t'Hooft epislon concept of nD as (n-1).99999D.
Helices [with virtual volumes] as [complex] harmonic oscillators may even have gauge-corresponding loops [with virtual areas] of the same period.
Is it possible that helical strings as [complex] harmonic oscillators could accommodate both the Randall 'large' and Arkani-Hamed 'small' concepts of curled-up, unseen dimensions?
The answer is yes.
It could also accommodate a 2d SPOT AT 10^-17 and avoid all the problems associated by going to Planck Scale.
Therefore, MORE DIMENSIONS ARE NOT NEEDED.
jal
Hi jal,
I'm glad you're back. I just wish I understood this thread a bit better and could post more constructively.
Don't quote me on this .. but I reckon that E=hf thing is the work of the devil.. a single photon can't (doesn't) have a frequency .. it's just the probability of detecting the thing at particular time .. works wonderfully for lots of photons but for one it's just BS.
As far as I know the whole Uncertainty-Plancky thing is just based on a Gaussian distribution and Planck's constant is chosen to 'work' within one standard deviation .. doesn't mean it (the photon) has to stay within any limits whatsoever. Always works with lots of them .. but not one.
This is a diagram coming up..
---------O-----------
Kinda looks like the 'O' has a size .. but I think it's a fuzzy little beast really.
-C2.
I'm glad you're back. I just wish I understood this thread a bit better and could post more constructively.
Don't quote me on this .. but I reckon that E=hf thing is the work of the devil.. a single photon can't (doesn't) have a frequency .. it's just the probability of detecting the thing at particular time .. works wonderfully for lots of photons but for one it's just BS.
As far as I know the whole Uncertainty-Plancky thing is just based on a Gaussian distribution and Planck's constant is chosen to 'work' within one standard deviation .. doesn't mean it (the photon) has to stay within any limits whatsoever. Always works with lots of them .. but not one.
This is a diagram coming up..
---------O-----------
Kinda looks like the 'O' has a size .. but I think it's a fuzzy little beast really.
-C2.
Hi! Confused2!
LOL
I wish some of our expert lurkers would enlighten me with some sound reason why we have to project down to the Planck scale and show what evidence that they have for their opinions.
I think that the evidence stops at 10^-18.
I wish some of our expert lurkers would enlighten me with some sound reason why we have to project down to the Planck scale and show what evidence that they have for their opinions.
I think that the evidence stops at 10^-18.
Helices [with virtual volumes] as [complex] harmonic oscillators may even have gauge-corresponding loops [with virtual areas] of the same period.
The dynamics vs a snap shot has yet to be worked out.
It's too bad that nobody can produce the math of "pretty pictures". That is where enlightenment and the "new physics" will come.
I'll use T duallity (less dimensions) and let the rest of the world stumble and get lost in more dimensions.
jal
LOL
QUOTE
Don't quote me on this .. but I reckon that E=hf thing is the work of the devil
I wish some of our expert lurkers would enlighten me with some sound reason why we have to project down to the Planck scale and show what evidence that they have for their opinions.
I think that the evidence stops at 10^-18.
QUOTE (->
| QUOTE |
| Don't quote me on this .. but I reckon that E=hf thing is the work of the devil |
I wish some of our expert lurkers would enlighten me with some sound reason why we have to project down to the Planck scale and show what evidence that they have for their opinions.
I think that the evidence stops at 10^-18.
Helices [with virtual volumes] as [complex] harmonic oscillators may even have gauge-corresponding loops [with virtual areas] of the same period.
QUOTE
---------O-----------
The dynamics vs a snap shot has yet to be worked out.
It's too bad that nobody can produce the math of "pretty pictures". That is where enlightenment and the "new physics" will come.
I'll use T duallity (less dimensions) and let the rest of the world stumble and get lost in more dimensions.
jal
Hi Confused2
I guess that there are no takers?
Confused2, I'm also working at the limit of my knowledge and abilities.
I guess that there are no takers?
Confused2, I'm also working at the limit of my knowledge and abilities.
a single photon can't (doesn't) have a frequency .. it's just the probability of detecting the thing at particular time .. works wonderfully for lots of photons but for one it's just BS.
Don't forget that my SPOT is only ONE SINGLE WAVE in one single spot at one instant of time.
I have found a possible approach that might work on making my SPOT dynamic/move.
It's a totally new/outofthebox approach. Yet.... it's old...old....old.
I'm studying it now to see if it has pomises.
Stay tuned..... I'll need help with this one ..... you can replace yq
jal
Explain to me why there is not a 6X problem in your model.
Without looking at the picture .
Bit of a guess without the picture
.
If you forced me into it I'd probably (eventually) start talking about constructive and destructive interference. At a 'sufficient' distance your three sources would start to look like a point source. Are we QM or EM or 'other' here?
Near field . ????? mutter .
-C2.
"THAT [bad things] IS EXACTLY WHAT 1/R^2 DOES when you project OBSERVED 3D energy to the Plack scale."
Yes, I see what you mean. This calls for some heavy thinking. At what point would reality start blowing holes in itself?.. very interesting. The Schwarzschild_radius ( http://en.wikipedia.org/wiki/Schwarzschild_radius ) might come into it somewhere but somehow there needs to be a built in self-defence mechanism rather than a point where one can predict catastrophic failure. Thinking and writing at the same time (usually unwise) .. it looks like planck's constant could be tied in with the solution. The hoop is always smaller than the ball.
I look forward to your thoughts.
-C2.
QUOTE
I wish some of our expert lurkers would enlighten me with some sound reason why we have to project down to the Planck scale and show what evidence that they have for their opinions.
I think that the evidence stops at 10^-18.
I think that the evidence stops at 10^-18.
I guess that there are no takers?
Confused2, I'm also working at the limit of my knowledge and abilities.
QUOTE (->
| QUOTE |
| I wish some of our expert lurkers would enlighten me with some sound reason why we have to project down to the Planck scale and show what evidence that they have for their opinions. I think that the evidence stops at 10^-18. |
I guess that there are no takers?
Confused2, I'm also working at the limit of my knowledge and abilities.
a single photon can't (doesn't) have a frequency .. it's just the probability of detecting the thing at particular time .. works wonderfully for lots of photons but for one it's just BS.
Don't forget that my SPOT is only ONE SINGLE WAVE in one single spot at one instant of time.
QUOTE
The dynamics vs a snap shot has yet to be worked out.
I have found a possible approach that might work on making my SPOT dynamic/move.
It's a totally new/outofthebox approach. Yet.... it's old...old....old.
I'm studying it now to see if it has pomises.
Stay tuned..... I'll need help with this one ..... you can replace yq
jal
jal,
It goes without saying that only yq can replace yq
. One does ones best . I look forward to your next post .
-C2.
It goes without saying that only yq can replace yq
. One does ones best . I look forward to your next post .-C2.
Hi!
So you accept that everything is made from a wave and that they start at PLANCK SIZE.
I HAVE DRAWN 3 WAVES COMING FROM PLANCK SIZE.
AS YOU CAN SEES THEY INTERACT AT ?
ADD ANOTHER 3 WAVES AND SHOW ME HOW I AM WRONG?
THE WAVES OBEY THE INVERSE SQUARE LAW.
HOW WOULD THE STRENGTH OF THE WAVE BE REDUCED BY 4 AT 2R?
The strength of one wave would be reduced by 4. However, there are 6 waves coming from planck size, next to each other.
Explain to me why there is not a 6X problem in your model.
JAL
So you accept that everything is made from a wave and that they start at PLANCK SIZE.
QUOTE
I wish some of our expert lurkers would enlighten me with some sound reason why we have to project down to the Planck scale and show what evidence that they have for their opinions.
I think that the evidence stops at 10^-18.
I think that the evidence stops at 10^-18.
I HAVE DRAWN 3 WAVES COMING FROM PLANCK SIZE.
AS YOU CAN SEES THEY INTERACT AT ?
ADD ANOTHER 3 WAVES AND SHOW ME HOW I AM WRONG?
THE WAVES OBEY THE INVERSE SQUARE LAW.
HOW WOULD THE STRENGTH OF THE WAVE BE REDUCED BY 4 AT 2R?
The strength of one wave would be reduced by 4. However, there are 6 waves coming from planck size, next to each other.
Explain to me why there is not a 6X problem in your model.
JAL
Hi jal,
Hmm. You seem to have drawn a directional 'beam' of waves... that's cheating. Unless you let 'em escape in 3D you can't expect an inverse square. I must admit this has something to do with my problem with any sort of structure in space .. the existence of preferred orientations and grain boundaries and so on. At least with nothing all you have to do is explain the properties of nothing.
I've been thinking a bit about this Plank length environment in a thinky-drinky sort of way.
-C2.
Hmm. You seem to have drawn a directional 'beam' of waves... that's cheating. Unless you let 'em escape in 3D you can't expect an inverse square. I must admit this has something to do with my problem with any sort of structure in space .. the existence of preferred orientations and grain boundaries and so on. At least with nothing all you have to do is explain the properties of nothing.
I've been thinking a bit about this Plank length environment in a thinky-drinky sort of way.
-C2.
Confused2
Ahhhh! the problems with communications.
The bottom circles are spheres at Planck (1/2 colored)
The full colored, is an instant later, where they have expanded to 2R.
Since they are energy waves, I show that they are now no longer solitons and are interfering with each other. Now, we need to use the wave function to figure out what is happening.
I say that it will not make a model of OUR universe.
I'll eagerly await your analysis ....
jal
Ahhhh! the problems with communications.
QUOTE
Hmm. You seem to have drawn a directional 'beam' of waves...
The bottom circles are spheres at Planck (1/2 colored)
The full colored, is an instant later, where they have expanded to 2R.
Since they are energy waves, I show that they are now no longer solitons and are interfering with each other. Now, we need to use the wave function to figure out what is happening.
I say that it will not make a model of OUR universe.
I'll eagerly await your analysis ....
jal
Sorry jal, I still think you're cheating. Imagine an infinite flat plane .. waves coming off that would fall off as .. well they wouldn't would they?. Your three sources are trending in that direction .. if you see what I mean. (give or take a few infinities).
-C2.
-C2.
Confused2
Well.... I certainly don't want to be cheating.....
If the picture is wrong.... are the words right?
jal
Well.... I certainly don't want to be cheating.....
If the picture is wrong.... are the words right?
jal
QUOTE (jal+)
Explain to me why there is not a 6X problem in your model.
Without looking at the picture
.Bit of a guess without the picture
.If you forced me into it I'd probably (eventually) start talking about constructive and destructive interference. At a 'sufficient' distance your three sources would start to look like a point source. Are we QM or EM or 'other' here?
Near field
. ????? mutter .-C2.
Confused2
The only distance is size.... 10^-33 to 10^(experimentally verified)
I made a presumption.... there are multiple Planck size positions generating energy.
Does it change things if there is only ONE plack size position generating ALL of the existing 3D positions in our universe?
jal
QUOTE
...'sufficient' distance...
The only distance is size.... 10^-33 to 10^(experimentally verified)
I made a presumption.... there are multiple Planck size positions generating energy.
Does it change things if there is only ONE plack size position generating ALL of the existing 3D positions in our universe?
jal
From my drinking and thinking phase it does seem that anything happening at that scale would be mega high energy .. impossibly high. If nothing can happen at that scale it follows that nothing can happen at any higher scale .. so.. so.. there it is. It would be nice to be able to justify any assumptions about where reality might kick in at the lower end of things. 10^-?
-C2.
-C2.
Sorry I added without checking for a post.. ignore mine..
"Does it change things if there is only ONE plack size position generating ALL of the existing 3D positions in our universe?"
Could you try to make that a bit clearer please? Just assume that I'm not very bright and you won't go far wrong .
C2
"Does it change things if there is only ONE plack size position generating ALL of the existing 3D positions in our universe?"
Could you try to make that a bit clearer please? Just assume that I'm not very bright and you won't go far wrong
.C2
Confused2
What we are doing is discussing the CONCEPT of HAVING ENERGY BEING GENERATED FROM A PLANCK SIZE STRUCTURE/POSITION.
It has not been discussed enough, in my opinion, for it to be included into any theory and further more when it is incorporated into ANY model, it makes the MODEL CRASH.
THAT IS EXACTLY WHAT 1/R^2 DOES when you project OBSERVED 3D energy to the Planck scale.
jal
What we are doing is discussing the CONCEPT of HAVING ENERGY BEING GENERATED FROM A PLANCK SIZE STRUCTURE/POSITION.
It has not been discussed enough, in my opinion, for it to be included into any theory and further more when it is incorporated into ANY model, it makes the MODEL CRASH.
QUOTE
would be mega high energy .. impossibly high
THAT IS EXACTLY WHAT 1/R^2 DOES when you project OBSERVED 3D energy to the Planck scale.
jal
"THAT [bad things] IS EXACTLY WHAT 1/R^2 DOES when you project OBSERVED 3D energy to the Plack scale."
Yes, I see what you mean. This calls for some heavy thinking. At what point would reality start blowing holes in itself?.. very interesting. The Schwarzschild_radius ( http://en.wikipedia.org/wiki/Schwarzschild_radius ) might come into it somewhere but somehow there needs to be a built in self-defence mechanism rather than a point where one can predict catastrophic failure. Thinking and writing at the same time (usually unwise) .. it looks like planck's constant could be tied in with the solution. The hoop is always smaller than the ball.
I look forward to your thoughts.
-C2.
Confused2
So far.... the wave funtion has been working down to 10^-18 (by plugging in some 19 or so numbers), and by assuming that the energy starts at the Planck scale and that it has expanded and diluted itself (1/R2) by the time it has expanded to where we have measured it.
However, if we look closer and try to see how that energy is STRUCTURED at the Planck scale..... BOOM.....
That is my question...... what structure does all that energy have so that we get our universe?
If you have multiple points/positions from which the energy comes from then there must be a structure.
The structure must be able to re-produce our observed universe.
One point or multiple points? One point cause us to make up toooooo many explanations.
I chose multiple points. Therefore, a structure.
Let's not talk about The Schwarzschild_radius because it will divert the discussions to black holes.
We can use gravity waves that started at the Planck size.
Refer to my poor diagram, As you can see, you cannot have the gravity waves interacting with each other as they grow in size. They would not dilute. We would not observe gravity to be (G= 9.81 m/s² or 32.2 ft/s²) what it is.
The first option, is to have the planck size gravity force (spherical solitons) so far apart that the waves cannot interact. They must have room to expand from 10^-33 to (approx.) the size of a hair.
(The only experimental number that we have.)
The other option, which might be equivalent, is to say that space is filled with spherical structures that have increasing G as you get closer to the center.
I chose an other option. VVVVVV (my presentation)
jal
So far.... the wave funtion has been working down to 10^-18 (by plugging in some 19 or so numbers), and by assuming that the energy starts at the Planck scale and that it has expanded and diluted itself (1/R2) by the time it has expanded to where we have measured it.
However, if we look closer and try to see how that energy is STRUCTURED at the Planck scale..... BOOM.....
That is my question...... what structure does all that energy have so that we get our universe?
If you have multiple points/positions from which the energy comes from then there must be a structure.
The structure must be able to re-produce our observed universe.
One point or multiple points? One point cause us to make up toooooo many explanations.
I chose multiple points. Therefore, a structure.
Let's not talk about The Schwarzschild_radius because it will divert the discussions to black holes.
We can use gravity waves that started at the Planck size.
Refer to my poor diagram, As you can see, you cannot have the gravity waves interacting with each other as they grow in size. They would not dilute. We would not observe gravity to be (G= 9.81 m/s² or 32.2 ft/s²) what it is.
The first option, is to have the planck size gravity force (spherical solitons) so far apart that the waves cannot interact. They must have room to expand from 10^-33 to (approx.) the size of a hair.
(The only experimental number that we have.)
The other option, which might be equivalent, is to say that space is filled with spherical structures that have increasing G as you get closer to the center.
I chose an other option. VVVVVV (my presentation)
jal
Good Elf!
Here is a more complete discussion on Black Body Radiation. (I know you don't need it. It's for everyone else who does.)
Look under the heading ....Justifying Planck's Formula
http://galileo.phys.virginia.edu/classes/2..._radiation.html
edit: inserted
Which now brings us to the problem of energy at Planck Scale.
jal
Here is a more complete discussion on Black Body Radiation. (I know you don't need it. It's for everyone else who does.)
Look under the heading ....Justifying Planck's Formula
http://galileo.phys.virginia.edu/classes/2..._radiation.html
edit: inserted
QUOTE
Good Elf
The problem is if you have not totally mapped the function and want to know the next step in understanding ... models will not take you there since you can only extrapolate to the known end points of the curve..
The problem is if you have not totally mapped the function and want to know the next step in understanding ... models will not take you there since you can only extrapolate to the known end points of the curve..
Which now brings us to the problem of energy at Planck Scale.
jal
QUOTE (jal+Aug 18 2006, 02:15 PM)
Hi!
So you accept that everything is made from a wave and that they start at PLANCK SIZE.
I HAVE DRAWN 3 WAVES COMING FROM PLANCK SIZE.
AS YOU CAN SEES THEY INTERACT AT ?
ADD ANOTHER 3 WAVES AND SHOW ME HOW I AM WRONG?
THE WAVES OBEY THE INVERSE SQUARE LAW.
HOW WOULD THE STRENGTH OF THE WAVE BE REDUCED BY 4 AT 2R?
The strength of one wave would be reduced by 4. However, there are 6 waves coming from planck size, next to each other.
Explain to me why there is not a 6X problem in your model.
JAL
Consider that if 6 times as many forces are interacting at a location, then locally, time is seen as running 6 times as fast as well and at least for local observations, the relative acceleration over time does not change. Most forces carry information that creates events detectable as time, so time can scale along with force density for many things. The important issue is the average strength of a force communicated and/or alternately the ratio of forces that don't carry an associated piece of information for time, versus the ones that do.
Also, if time creates an appearance of an additional dimension, using a 2-D plane should allow for creating a 3-D universe once it's operated over time. The thickness of the 3rd time dimension may be very small.
In that case forces diffuse as 1/d on large 2-D scales where the time is largely redundant and small, instead of 1/d^2, but you have a mismatch between distance measurements when you're using Euclidean approximations of the spread of fine random events as Brownian motion (because we can't accurately see the 3-D small details) and the average velocities are only proportional to the square root of time. So we use the square of distances on large scales and see 1/d^2 instead of 1/d.
So you accept that everything is made from a wave and that they start at PLANCK SIZE.
I HAVE DRAWN 3 WAVES COMING FROM PLANCK SIZE.
AS YOU CAN SEES THEY INTERACT AT ?
ADD ANOTHER 3 WAVES AND SHOW ME HOW I AM WRONG?
THE WAVES OBEY THE INVERSE SQUARE LAW.
HOW WOULD THE STRENGTH OF THE WAVE BE REDUCED BY 4 AT 2R?
The strength of one wave would be reduced by 4. However, there are 6 waves coming from planck size, next to each other.
Explain to me why there is not a 6X problem in your model.
JAL
Consider that if 6 times as many forces are interacting at a location, then locally, time is seen as running 6 times as fast as well and at least for local observations, the relative acceleration over time does not change. Most forces carry information that creates events detectable as time, so time can scale along with force density for many things. The important issue is the average strength of a force communicated and/or alternately the ratio of forces that don't carry an associated piece of information for time, versus the ones that do.
Also, if time creates an appearance of an additional dimension, using a 2-D plane should allow for creating a 3-D universe once it's operated over time. The thickness of the 3rd time dimension may be very small.
In that case forces diffuse as 1/d on large 2-D scales where the time is largely redundant and small, instead of 1/d^2, but you have a mismatch between distance measurements when you're using Euclidean approximations of the spread of fine random events as Brownian motion (because we can't accurately see the 3-D small details) and the average velocities are only proportional to the square root of time. So we use the square of distances on large scales and see 1/d^2 instead of 1/d.
http://en.wikipedia.org/wiki/Classical_electron_radius
In fact, modern particle physics experiments indicate that the electron is a point particle i.e. it has no size and its radius is zero
This is real scary talk. Your comments invited.
Quantum mechanics has worked happily for many years (even won Nobel prizes) with almost this very same infinity right in the middle of it. As I understand the QM situation .. even though you can get closer and closer to the infinity the result starts to converge on the same number. The QM trick is to say that the number we converge on as we get closer to the infinity will carry us through the infinity... the same number.. soooooo we get away crap mathematics .... and no infinity.
-C2.
QUOTE (wiki+)
In fact, modern particle physics experiments indicate that the electron is a point particle i.e. it has no size and its radius is zero
This is real scary talk. Your comments invited.
Quantum mechanics has worked happily for many years (even won Nobel prizes) with almost this very same infinity right in the middle of it. As I understand the QM situation .. even though you can get closer and closer to the infinity the result starts to converge on the same number. The QM trick is to say that the number we converge on as we get closer to the infinity will carry us through the infinity... the same number.. soooooo we get away crap mathematics .... and no infinity.
-C2.
Hi StevenA!
I would put your statement in the category of concept. After that there should be a theory then a model.
In order to get around "1/d^2" the prefered theory is to use a 5th dimension concept or a curled up dimension concept.
So,.... do you think that there is huge amount of energy at a Planck size position?
Can you give me your version of your structure of that energy?
The 5th dimension concept or a curled up dimension concept do not have a structure.
Confused2 "This is real scary talk. Your comments invited."
I see that I'm not alone in questioning some concepts. Like you said, it helps make QM work. Maybe that's why nobody wants to investigate the structure of Planck scale energy.
From your reference link
I would put your statement in the category of concept. After that there should be a theory then a model.
In order to get around "1/d^2" the prefered theory is to use a 5th dimension concept or a curled up dimension concept.
So,.... do you think that there is huge amount of energy at a Planck size position?
Can you give me your version of your structure of that energy?
The 5th dimension concept or a curled up dimension concept do not have a structure.
Confused2 "This is real scary talk. Your comments invited."
I see that I'm not alone in questioning some concepts. Like you said, it helps make QM work. Maybe that's why nobody wants to investigate the structure of Planck scale energy.
From your reference link
Also, the classical electron radius is roughly the length scale at which renormalization becomes important in quantum electrodynamics.
The classical electron radius is one of a trio of related units of length, the other two being the Bohr radius a0 and the Compton wavelength of the electron λe. The classical electron radius is built from the electron mass me, the speed of light c and the electron charge e. The Bohr radius is built from me, e and Planck's constant h. The Compton wavelength is built from me, h and c. Any one of these three lengths can be written in terms of any other using the fine structure constant α:
I'm reminded of a little song, heheheh..."A wheel within a wheel a rolling...."
jal
Do I need to explain that when energy expands/comes from a point source that all of the energy is concentrated at the wave front?
Do I need to explain that there is no energy behind the wave front?
If anything is a point then maybe everything is a point (maybe even a string?).
If the experimental evidence shows that you can pack a lot of 'properties' into something that looks like a point and it doesn't go 'black hole' .. then you either ignore the evidence or say .. (maybe) .. it's all 'pointlike'.
IMHO there are far too many types of particles. I can see a reason for some but (for example) muons .. aren't they just pure fun?
It's late and I'm tired .. probably shouldn't post this but I will anyway. I hope that's OK.
-C2.
QUOTE
.... forces diffuse as 1/d on large scales instead of 1/d^2 ...
I would put your statement in the category of concept. After that there should be a theory then a model.
In order to get around "1/d^2" the prefered theory is to use a 5th dimension concept or a curled up dimension concept.
So,.... do you think that there is huge amount of energy at a Planck size position?
Can you give me your version of your structure of that energy?
The 5th dimension concept or a curled up dimension concept do not have a structure.
Confused2 "This is real scary talk. Your comments invited."
I see that I'm not alone in questioning some concepts. Like you said, it helps make QM work. Maybe that's why nobody wants to investigate the structure of Planck scale energy.
From your reference link
QUOTE (->
| QUOTE |
| .... forces diffuse as 1/d on large scales instead of 1/d^2 ... |
I would put your statement in the category of concept. After that there should be a theory then a model.
In order to get around "1/d^2" the prefered theory is to use a 5th dimension concept or a curled up dimension concept.
So,.... do you think that there is huge amount of energy at a Planck size position?
Can you give me your version of your structure of that energy?
The 5th dimension concept or a curled up dimension concept do not have a structure.
Confused2 "This is real scary talk. Your comments invited."
I see that I'm not alone in questioning some concepts. Like you said, it helps make QM work. Maybe that's why nobody wants to investigate the structure of Planck scale energy.
From your reference link
Also, the classical electron radius is roughly the length scale at which renormalization becomes important in quantum electrodynamics.
The classical electron radius is one of a trio of related units of length, the other two being the Bohr radius a0 and the Compton wavelength of the electron λe. The classical electron radius is built from the electron mass me, the speed of light c and the electron charge e. The Bohr radius is built from me, e and Planck's constant h. The Compton wavelength is built from me, h and c. Any one of these three lengths can be written in terms of any other using the fine structure constant α:
I'm reminded of a little song, heheheh..."A wheel within a wheel a rolling...."
jal
Regarding my previous comment about a thin depth to the 3rd dimension of time (the other two dimensions might have some similar ratio of length between them), I was wondering whether or not planck units could be derived from a specific thickness to the "time" dimension and read this link:
http://en.wikipedia.org/wiki/Planck_units
Here's an interesting quote:
"[An] important lesson we learn from the way that pure numbers like α define the world is what it really means for worlds to be different. The pure number we call the fine structure constant and denote by α is a combination of the electron charge, e, the speed of light, c, and Planck's constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h, and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our world. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value [including the Planck mass mP] you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged." (Barrow 2002)
Now consider that a single number, with enough precision could contain almost an infinite amount of information ... you just interprete each digit as some unit of information and potentially a single number could be interpreted as describing the universe.
What if the fine structure constant was such a number (possibly indicating the ratio of the sizes of two physical dimensions)? It could be that the specifics of the universe are determined by a single ratio that might be close to an irrational number or at least with enough real digits to describe the real states of the universe ...
For example, if you approximate pi, one close value would be 22/7, but there would be an error. You might be able to use such a rather finite approximation to describe a second dimension (maybe that's not a good analogy, instead imagine you see a 1-D string of information that contains some rather regularly spaced events. You can 'fold' this 1-D string into a 2-D plane by extracting this information as markers for each frame and placing the 1-D frames next to each other to make a 2-D space. You can then reexamine streams of 2-D images to find correlations between similar frames and construct a 3-D approximation etc.) In this case space, motion, velocities and mass etc. are determined by what correlations found and how you fold space in order to predict these recurrances, though likely we wrap things cyclically and use toroidal or spherical forms of data compression instead to map things to angles in order to extract the patterns and examine the remaining errors.
I don't know. I'm just thinking ... take what you want and toss the rest away and no hard feelings (unless I'm being too distracting ) but it seems possible that revereberations within some uniform 2-D that's only critical feature is the ratio of the sizes of two dimensions might be able to describe much with an observer simply 'pinging' the space and listening for echoes. In this case the exact ratio couldn't be determined immediately if discrete impulses were used, because a reflection directly along one dimension or the other would only seem able to give you a chronological order of pulses and the axises would be interchangeable and it would be just like listening to a sound and trying to triangulate positions using sonar. Ultimately we only have local observations available. Even motion or second hand information is only understood once that information results in local detection by an 'observer' (whether it be simply a particle or even a conscious observer trying to understand the space in which it's always locally interacting ... we see the moon but only because of locally detected photons carrying information about it).
BTW, I don't know if forces actually exist that don't carry events we can detect as time (for example, gravity seems to fall into this category). These could be illusionary forces that appear to create a motion, but might be a result of an internally warped understanding of space instead - so when we try to predict the location of an object, when there's an error we simply envision some force moving it, whereas no physical force might have been experienced and instead it could be the result of an incorrect understanding of space that lead to inaccurate assumption about positions, that created a need for these not directly detectable forces to provide an explanation. I tend to think once we have a firm understanding of how we/humans observe and understand large averages of small scale interactions, gravity will pop out of this as a natural illusion resulting from our macroscale approximations.
http://en.wikipedia.org/wiki/Planck_units
Here's an interesting quote:
"[An] important lesson we learn from the way that pure numbers like α define the world is what it really means for worlds to be different. The pure number we call the fine structure constant and denote by α is a combination of the electron charge, e, the speed of light, c, and Planck's constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h, and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our world. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value [including the Planck mass mP] you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged." (Barrow 2002)
Now consider that a single number, with enough precision could contain almost an infinite amount of information ... you just interprete each digit as some unit of information and potentially a single number could be interpreted as describing the universe.
What if the fine structure constant was such a number (possibly indicating the ratio of the sizes of two physical dimensions)? It could be that the specifics of the universe are determined by a single ratio that might be close to an irrational number or at least with enough real digits to describe the real states of the universe ...
For example, if you approximate pi, one close value would be 22/7, but there would be an error. You might be able to use such a rather finite approximation to describe a second dimension (maybe that's not a good analogy, instead imagine you see a 1-D string of information that contains some rather regularly spaced events. You can 'fold' this 1-D string into a 2-D plane by extracting this information as markers for each frame and placing the 1-D frames next to each other to make a 2-D space. You can then reexamine streams of 2-D images to find correlations between similar frames and construct a 3-D approximation etc.) In this case space, motion, velocities and mass etc. are determined by what correlations found and how you fold space in order to predict these recurrances, though likely we wrap things cyclically and use toroidal or spherical forms of data compression instead to map things to angles in order to extract the patterns and examine the remaining errors.
I don't know. I'm just thinking ... take what you want and toss the rest away and no hard feelings
(unless I'm being too distracting ) but it seems possible that revereberations within some uniform 2-D that's only critical feature is the ratio of the sizes of two dimensions might be able to describe much with an observer simply 'pinging' the space and listening for echoes. In this case the exact ratio couldn't be determined immediately if discrete impulses were used, because a reflection directly along one dimension or the other would only seem able to give you a chronological order of pulses and the axises would be interchangeable and it would be just like listening to a sound and trying to triangulate positions using sonar. Ultimately we only have local observations available. Even motion or second hand information is only understood once that information results in local detection by an 'observer' (whether it be simply a particle or even a conscious observer trying to understand the space in which it's always locally interacting ... we see the moon but only because of locally detected photons carrying information about it).BTW, I don't know if forces actually exist that don't carry events we can detect as time (for example, gravity seems to fall into this category). These could be illusionary forces that appear to create a motion, but might be a result of an internally warped understanding of space instead - so when we try to predict the location of an object, when there's an error we simply envision some force moving it, whereas no physical force might have been experienced and instead it could be the result of an incorrect understanding of space that lead to inaccurate assumption about positions, that created a need for these not directly detectable forces to provide an explanation. I tend to think once we have a firm understanding of how we/humans observe and understand large averages of small scale interactions, gravity will pop out of this as a natural illusion resulting from our macroscale approximations.
StevenA
Nice post.
It adds background information.
So,.... do you think that there is huge amount of energy at a Planck size position?
Can you give me your version of your structure of that energy?
The 5th dimension concept or a curled up dimension concept do not have a structure.
jal
Nice post.
It adds background information.
So,.... do you think that there is huge amount of energy at a Planck size position?
Can you give me your version of your structure of that energy?
The 5th dimension concept or a curled up dimension concept do not have a structure.
jal
Hi jal, StevenA,
Sorry Steven I replied without checking for other posts .. please kinda leaprog over this as you please.
jal! Virtual photons! Not forces! Just looking at electron/photon interactions .. I have huge difficulty believing in virtual photons. Given the opportunity I'd look at them as a sort of energy added to space as a result of whatever it is you're doing.. this aside .. we have one point-like particle (electron) interacting with a (point-like?) photon. The chances of point A meeting up with point B are like infinitely small. From memory (QED) the chances of a photon interacting with an electron are 1/137 .. how close do they have to be to start with .. I know nothing. Do you have any insight into this?
-C2.
Sorry Steven I replied without checking for other posts .. please kinda leaprog over this as you please.
jal! Virtual photons! Not forces! Just looking at electron/photon interactions .. I have huge difficulty believing in virtual photons. Given the opportunity I'd look at them as a sort of energy added to space as a result of whatever it is you're doing.. this aside .. we have one point-like particle (electron) interacting with a (point-like?) photon. The chances of point A meeting up with point B are like infinitely small. From memory (QED) the chances of a photon interacting with an electron are 1/137 .. how close do they have to be to start with .. I know nothing. Do you have any insight into this?
-C2.
Hi!
Do I need to explain that when energy expands/comes from a point source that all of the energy is concentrated at the wave front?
Do I need to explain that there is no energy behind the wave front?
Do I need to explain that multiple waves can only come from multiple BIG BANGS?
Do I need to explain that even with multiple BIG BANGS our universe does not have stripes of energy?
DO YOU WANT TO EXPLAIN HOW THE MULTIPLE WAVES CAN BECOME COMPLEX WAVES? (THEY CAN ONLY TRAVEL AT THE SPEED OF LIGHT AND CANNOT CATCH UP TO EACH OTHER)
Confused2 http://electrogravity.blogspot.com/2006/02...iggs-field.html from yq gives a bit of info
Does this mean that packing is not considered? I don't know.
jal
Do I need to explain that when energy expands/comes from a point source that all of the energy is concentrated at the wave front?
Do I need to explain that there is no energy behind the wave front?
Do I need to explain that multiple waves can only come from multiple BIG BANGS?
Do I need to explain that even with multiple BIG BANGS our universe does not have stripes of energy?
DO YOU WANT TO EXPLAIN HOW THE MULTIPLE WAVES CAN BECOME COMPLEX WAVES? (THEY CAN ONLY TRAVEL AT THE SPEED OF LIGHT AND CANNOT CATCH UP TO EACH OTHER)
Confused2 http://electrogravity.blogspot.com/2006/02...iggs-field.html from yq gives a bit of info
QUOTE
'For example, it can be shown that starting with the parameters e and m for a bare Dirac particle, the effect of the 'crowded' vacuum is to change these to new constants e' and m', which must be identified with the observed charge and mass. ... If these contributions were cut off in any reasonable manner, m' - m and e' - e would be of order alpha ~ 1/137. No rigorous justification for such a cut-off has yet been proposed.
'All this means that the present theory of electrons and fields is not complete. ... The particles ... are treated as 'bare' particles.
'All this means that the present theory of electrons and fields is not complete. ... The particles ... are treated as 'bare' particles.
Does this mean that packing is not considered? I don't know.
jal
QUOTE (jal+)
Do I need to explain that when energy expands/comes from a point source that all of the energy is concentrated at the wave front?
Do I need to explain that there is no energy behind the wave front?
If anything is a point then maybe everything is a point (maybe even a string?).
If the experimental evidence shows that you can pack a lot of 'properties' into something that looks like a point and it doesn't go 'black hole' .. then you either ignore the evidence or say .. (maybe) .. it's all 'pointlike'.
IMHO there are far too many types of particles. I can see a reason for some but (for example) muons .. aren't they just pure fun?
It's late and I'm tired .. probably shouldn't post this but I will anyway. I hope that's OK.
-C2.
Hi!
I want to get this finished and then go to the paper that Why Not?found.
http://arxiv.org/PS_cache/hep-th/pdf/0406/0406007.pdf
EXPERIMENTAL CONSEQUENCES OF THE HYPOTHESIS
ABOUT A FUNDAMENTAL MASS IN HIGH - ENERGY
PHYSICS
SPHERES
Area = 4pi r^2
Volume= 4/3(pi r^3)
r=1 V=4.1888 A=12.566
r=2 V=33.51 A=50.265
r=4 V=268.08 A=201.06
r=8 V=2,144.661 A=804.2477
r=16 V=17,157.2847 A=3,216.990
If r=1, All of the energy is contained in V=4.1888.
Therefore, the energy is spread out and contained within the volume of two spheres.
The original smallest sphere had a radius of approx. zero and the largest sphere had a radius of one.
V^0=0, V^1= 4.1888 (V= r^1 –r^0 = 4.1888). All of the energy would be within the difference between the radius of two spheres .
It’s a simple math problem.
As the radius doubles, (need to confirm that the inverse square law works ) at the speed of light, all of the points within the sphere of r=1 which contain an energy pattern, must expand at the speed of light from the origin. If you make the spheres expand to 2r then the energy will only be near the 2r. The energy will still be contained within a volume of 4.1888.
At what size of sphere will there not be enough points (4.1888) to make a new sphere?
To put in another way, at what size will the difference of the two expanding sphere be approx. zero?
To put it another way, at what size will the sphere collapse/burst?
To what size can a sphere (at Planck size 10^-33) expand before bursting?
If the wave/bubble breaks then the wave cannot reach what we have measured, which is the size of a hair.
jal
I want to get this finished and then go to the paper that Why Not?found.
http://arxiv.org/PS_cache/hep-th/pdf/0406/0406007.pdf
EXPERIMENTAL CONSEQUENCES OF THE HYPOTHESIS
ABOUT A FUNDAMENTAL MASS IN HIGH - ENERGY
PHYSICS
QUOTE
From a theoretical point of view the fundamental mass M
and corresponding to it the fundamental length ℓ = ¯h/Mc are supposed to play a major role such as Planck’s constant ¯h, the speed of light c or Newton’s gravitational constant κ.
and corresponding to it the fundamental length ℓ = ¯h/Mc are supposed to play a major role such as Planck’s constant ¯h, the speed of light c or Newton’s gravitational constant κ.
SPHERES
Area = 4pi r^2
Volume= 4/3(pi r^3)
r=1 V=4.1888 A=12.566
r=2 V=33.51 A=50.265
r=4 V=268.08 A=201.06
r=8 V=2,144.661 A=804.2477
r=16 V=17,157.2847 A=3,216.990
If r=1, All of the energy is contained in V=4.1888.
Therefore, the energy is spread out and contained within the volume of two spheres.
The original smallest sphere had a radius of approx. zero and the largest sphere had a radius of one.
V^0=0, V^1= 4.1888 (V= r^1 –r^0 = 4.1888). All of the energy would be within the difference between the radius of two spheres .
It’s a simple math problem.
As the radius doubles, (need to confirm that the inverse square law works
) at the speed of light, all of the points within the sphere of r=1 which contain an energy pattern, must expand at the speed of light from the origin. If you make the spheres expand to 2r then the energy will only be near the 2r. The energy will still be contained within a volume of 4.1888.At what size of sphere will there not be enough points (4.1888) to make a new sphere?
To put in another way, at what size will the difference of the two expanding sphere be approx. zero?
To put it another way, at what size will the sphere collapse/burst?
To what size can a sphere (at Planck size 10^-33) expand before bursting?
If the wave/bubble breaks then the wave cannot reach what we have measured, which is the size of a hair.
jal
Hey jal, et al.
Maybe in reverse to your question, but have you considered The Holographic Principle? Thinking of energy = information...
QUOTE
At what size of sphere will there not be enough points (4.1888) to make a new sphere?
Maybe in reverse to your question, but have you considered The Holographic Principle? Thinking of energy = information...
Why Not?
Loved that link in yq's thread. Thanks.
http://en.wikipedia.org/wiki/Holographic_principle
However, my approach is different. Instead of the region collapses into a black hole., I say it "collapses" to two dimension.
However, my approach is different. Instead of the region collapses into a black hole., I say it "collapses" to two dimension.
Entropy, if considered as information (see information entropy).The total quantity of bits is related to the total degrees of freedom of matter/energy.
Therefore, there is less degree of freedom in a 2D structure (6) than in a 3D structure (12). Therefore, there is less entropy in a 2D structure than in a 3D structure.
Sorry, my approach, has a cycle. ENTROPY AND POTENTIAL ENERGY. (Work was involved in creating the universe)
BACK TO THE SUBJECT, THAT NOBODY WANTS TO DISCUSS. PLANCK SIZE ENERGY.
JAL
edit: inserted
E = hf
It’s the source of the solution and the source of the problems.
Black holes uses Planck scale energy. If you do not have a Planck scale bubble then there has to be another explanation to "black holes".
A wheel within a wheel....
Loved that link in yq's thread. Thanks.
http://en.wikipedia.org/wiki/Holographic_principle
QUOTE
Given any finite, compact region of space (e.g. a sphere), this region will contain matter and energy within it. If this energy surpasses a critical density then the region collapses into a black hole.
A black hole is known theoretically to have an entropy [1] which is directly proportional to the surface area of its event horizon. Black holes are maximal entropy objects [2], so the entropy contained in a given region of space cannot be larger than the entropy of the largest black hole which can fit in that volume.
A black hole is known theoretically to have an entropy [1] which is directly proportional to the surface area of its event horizon. Black holes are maximal entropy objects [2], so the entropy contained in a given region of space cannot be larger than the entropy of the largest black hole which can fit in that volume.
However, my approach is different. Instead of the region collapses into a black hole., I say it "collapses" to two dimension.
QUOTE (->
| QUOTE |
| Given any finite, compact region of space (e.g. a sphere), this region will contain matter and energy within it. If this energy surpasses a critical density then the region collapses into a black hole. A black hole is known theoretically to have an entropy [1] which is directly proportional to the surface area of its event horizon. Black holes are maximal entropy objects [2], so the entropy contained in a given region of space cannot be larger than the entropy of the largest black hole which can fit in that volume. |
However, my approach is different. Instead of the region collapses into a black hole., I say it "collapses" to two dimension.
Entropy, if considered as information (see information entropy).The total quantity of bits is related to the total degrees of freedom of matter/energy.
Therefore, there is less degree of freedom in a 2D structure (6) than in a 3D structure (12). Therefore, there is less entropy in a 2D structure than in a 3D structure.
Sorry, my approach, has a cycle. ENTROPY AND POTENTIAL ENERGY. (Work was involved in creating the universe)
BACK TO THE SUBJECT, THAT NOBODY WANTS TO DISCUSS. PLANCK SIZE ENERGY.
JAL
edit: inserted
E = hf
It’s the source of the solution and the source of the problems.
Black holes uses Planck scale energy. If you do not have a Planck scale bubble then there has to be another explanation to "black holes".
A wheel within a wheel....
Hey jal,
I wasn't really meaning the "black hole" part specifically.
I was thinking more on the lines of 2d being spherical area and 3d being spherical volume and the relationship of the two in regard to energy as expressed within the principle (expanding instead of contracting).
And you're welcome for the link, but I make no testament to its validity of veracity. When I read it, I thought it was an interesting possibility as a solution to you're Planck scale energy question...
I wasn't really meaning the "black hole" part specifically.
QUOTE
I say it "collapses" to two dimension.
I was thinking more on the lines of 2d being spherical area and 3d being spherical volume and the relationship of the two in regard to energy as expressed within the principle (expanding instead of contracting).
And you're welcome for the link, but I make no testament to its validity of veracity.
When I read it, I thought it was an interesting possibility as a solution to you're Planck scale energy question...
copied from yq's thread for discussion
Thanks yquantum
I had to do a little bit of work to make the right link work....here it is
http://www.hep.caltech.edu/~ajw/ph199/ph199_Planck.pdf
I had to do a little bit of work to make the right link work....here it is
http://www.hep.caltech.edu/~ajw/ph199/ph199_Planck.pdf
But is the Planck scale really that high?
• Maybe the Planck mass scale is much lower (eg, the weak scale ~ 1
TeV), and the Planck length much bigger, because G is much larger
• This can happen if gravity actually lives in more than 3 spatial
directions.• In string theory, open strings (which can represent all the SM particles,
including photons, fermions, gauge bosons, Higgs…) must remain
attached to a three-spatial-dimension hyperplane on the boundary of a
d-dimensional (d>3) “bulk” space. Since gravity is curved space, it sees,
and acts in, the bulk, while the SM particles live only on the
hypersurface and don’t see the bulk.
• So the possibility exists that gravity lives
in d (>3) dimensions, making the
“shortest” distance and “highest” energy
much closer to the weak scale.
This can happen if gravity actually lives in more than 3 spatial
directions.
The standard explanation is "more" I achieve the same thing by saying "less".
JUST A DIFFERENT FRAME OF REFERENCE
jal
Thanks yquantum
QUOTE
jal, this will also answer your question you asked all of us to comment on!, et al,
I had to do a little bit of work to make the right link work....here it is
http://www.hep.caltech.edu/~ajw/ph199/ph199_Planck.pdf
QUOTE (->
| QUOTE |
| jal, this will also answer your question you asked all of us to comment on!, et al, |
I had to do a little bit of work to make the right link work....here it is
http://www.hep.caltech.edu/~ajw/ph199/ph199_Planck.pdf
But is the Planck scale really that high?
• Maybe the Planck mass scale is much lower (eg, the weak scale ~ 1
TeV), and the Planck length much bigger, because G is much larger
• This can happen if gravity actually lives in more than 3 spatial
directions.• In string theory, open strings (which can represent all the SM particles,
including photons, fermions, gauge bosons, Higgs…) must remain
attached to a three-spatial-dimension hyperplane on the boundary of a
d-dimensional (d>3) “bulk” space. Since gravity is curved space, it sees,
and acts in, the bulk, while the SM particles live only on the
hypersurface and don’t see the bulk.
• So the possibility exists that gravity lives
in d (>3) dimensions, making the
“shortest” distance and “highest” energy
much closer to the weak scale.
This can happen if gravity actually lives in more than 3 spatial
directions.
The standard explanation is "more" I achieve the same thing by saying "less".
JUST A DIFFERENT FRAME OF REFERENCE
jal
Good day All!
From http://www.hep.caltech.edu/~ajw/ph199/ph199_Planck.pdf
The model that is the easiest to fix and get rid of the 6X problem is the one on your right, the RS model.
It uses an exp. curve.
Go to it to see it better. It's on page 15
jal
From http://www.hep.caltech.edu/~ajw/ph199/ph199_Planck.pdf
The model that is the easiest to fix and get rid of the 6X problem is the one on your right, the RS model.
It uses an exp. curve.
Go to it to see it better. It's on page 15
jal
Hi all!
Everyone is still too shy
From http://cpht.polytechnique.fr/exp0408/research.html
Everyone is still too shy
From http://cpht.polytechnique.fr/exp0408/research.html
In a different direction, it was realized that for string ground-states containing D-branes (open string vacua, orientifolds, etc), the size of strings (the string scale) is allowed to be very low compared to the Planck scale. The reason is that the Standard Model gauge group can arise from gauge fields living on D-branes.
Such a situation opens new possibilities for the physics beyond standard model, and provides an alternative view to old problems related to supersymmetry breaking, the hierarchy problem etc. In particular, gravity is descending from ten dimensions via the Kaluza-Klein idea whereas the standard model gauge fields can be four-dimensional without Kaluza-Klein excitations. It is compatible with present day data that gravity becomes effectively higher-dimensional already at such a large length scale as a few micrometers.
New realizations for four-dimensional gravity have been proposed, inspired by the concept of D-branes and the AdS/CFT correspondence. The Randall-Sundrum branes provide an alternative to standard compactification. Brane induced gravity provides a localisation mechanism for gravitons in the UV unlike compactification with the potential to alter the short distance nature of gravity on branes and consequently, early cosmological evolution.
Why Not? Your question on Holography
For more in depth
http://arxiv.org/abs/hep-th/0504219 Holography and Brane-bulk Energy Exchange
Jal
QUOTE
gauge hierarchy problem/Planck scale energy
Everyone is still too shy
From http://cpht.polytechnique.fr/exp0408/research.html
QUOTE (->
| QUOTE |
| gauge hierarchy problem/Planck scale energy |
Everyone is still too shy
From http://cpht.polytechnique.fr/exp0408/research.html
In a different direction, it was realized that for string ground-states containing D-branes (open string vacua, orientifolds, etc), the size of strings (the string scale) is allowed to be very low compared to the Planck scale. The reason is that the Standard Model gauge group can arise from gauge fields living on D-branes.
Such a situation opens new possibilities for the physics beyond standard model, and provides an alternative view to old problems related to supersymmetry breaking, the hierarchy problem etc. In particular, gravity is descending from ten dimensions via the Kaluza-Klein idea whereas the standard model gauge fields can be four-dimensional without Kaluza-Klein excitations. It is compatible with present day data that gravity becomes effectively higher-dimensional already at such a large length scale as a few micrometers.
New realizations for four-dimensional gravity have been proposed, inspired by the concept of D-branes and the AdS/CFT correspondence. The Randall-Sundrum branes provide an alternative to standard compactification. Brane induced gravity provides a localisation mechanism for gravitons in the UV unlike compactification with the potential to alter the short distance nature of gravity on branes and consequently, early cosmological evolution.
Why Not? Your question on Holography
For more in depth
http://arxiv.org/abs/hep-th/0504219 Holography and Brane-bulk Energy Exchange
Jal
Hey jal,
Excellent link.
I am trying to take a stab at the "gauge hierarchy problem/Planck scale energy", and to help as well...
AdS/CFT correspondence, in Randall-Sundrum models, is "holographic", which is why I asked earlier if you had considered the Holographic Principle within your model.
Maybe I still do not understand what your model is trying to say ( ), but I think it has potential ( )... It seems to me that the surface area of the 2D spheres in your structured space provide 3D extended space with a reduction of energy/increase of entropy dictated by maximal sphere packing. If so, then the maximal energy contained "within" each 2D sphere should follow the Bekenstein Bound, ( for reference, http://en.wikipedia.org/wiki/Bekenstein_bound), which, should in turn provide an avenue to address the Planck scale energy problem.
Excellent link.
I am trying to take a stab at the "gauge hierarchy problem/Planck scale energy", and to help as well...
AdS/CFT correspondence, in Randall-Sundrum models, is "holographic", which is why I asked earlier if you had considered the Holographic Principle within your model.
Maybe I still do not understand what your model is trying to say (
), but I think it has potential ( )... It seems to me that the surface area of the 2D spheres in your structured space provide 3D extended space with a reduction of energy/increase of entropy dictated by maximal sphere packing. If so, then the maximal energy contained "within" each 2D sphere should follow the Bekenstein Bound, ( for reference, http://en.wikipedia.org/wiki/Bekenstein_bound), which, should in turn provide an avenue to address the Planck scale energy problem.
Hi Why Not?
I was in the process of reflecting.... should I find an other forum??? I was wondering if this forum was self destructing.
http://en.wikipedia.org/wiki/Bekenstein_bound
Can someone help dig deeper......
There appears to be a presumption..... a want to make everything nice and tidy
by presumming the first part of the quote (by including Planck size energy).
Can someone help dig deeper......
There appears to be a presumption..... a want to make everything nice and tidy
by presumming the first part of the quote (by including Planck size energy).
"gauge hierarchy problem/Planck scale energy",
It does not work.... ( if you "the readers" think it does, you have not given me your explanations)
What does work is
When taking the Randall-Sundrum models and doing an imbedding (packing) of the Bulk, which will be the 2D surfaces, into OUR universe, you will only get what I have been showing.
If you do not "pack" you get the RS model and you get the 6X problem.
See my explanation of the problems with all models earlier in this thread.
jal
edit: inserted
Find this and the explanation follows
I was in the process of reflecting.... should I find an other forum??? I was wondering if this forum was self destructing.
http://en.wikipedia.org/wiki/Bekenstein_bound
QUOTE
In physics, the Bekenstein bound imposes a limit on the information that can be contained within a three-dimensional region of a given surface area:
S<A/4 where S is the entropy and A is the two-dimensional area in units of the Planck area, .
(The bound was originally found by Jacob Bekenstein in the form S<2piEL, where L is the linear size of the region, and E is the energy of the contained matter as measured when the matter is moved to an infinite distance, i.e., accounting for binding force potential energies. Gerard t' Hooft later generalized it to the form involving A/4.)
S<A/4 where S is the entropy and A is the two-dimensional area in units of the Planck area, .
(The bound was originally found by Jacob Bekenstein in the form S<2piEL, where L is the linear size of the region, and E is the energy of the contained matter as measured when the matter is moved to an infinite distance, i.e., accounting for binding force potential energies. Gerard t' Hooft later generalized it to the form involving A/4.)
Can someone help dig deeper......
There appears to be a presumption..... a want to make everything nice and tidy
by presumming the first part of the quote (by including Planck size energy).
QUOTE (->
| QUOTE |
| In physics, the Bekenstein bound imposes a limit on the information that can be contained within a three-dimensional region of a given surface area: S<A/4 where S is the entropy and A is the two-dimensional area in units of the Planck area, . (The bound was originally found by Jacob Bekenstein in the form S<2piEL, where L is the linear size of the region, and E is the energy of the contained matter as measured when the matter is moved to an infinite distance, i.e., accounting for binding force potential energies. Gerard t' Hooft later generalized it to the form involving A/4.) |
Can someone help dig deeper......
There appears to be a presumption..... a want to make everything nice and tidy
by presumming the first part of the quote (by including Planck size energy).
"gauge hierarchy problem/Planck scale energy",
It does not work.... ( if you "the readers"
think it does, you have not given me your explanations)What does work is
When taking the Randall-Sundrum models and doing an imbedding (packing) of the Bulk, which will be the 2D surfaces, into OUR universe, you will only get what I have been showing.
If you do not "pack" you get the RS model and you get the 6X problem.
See my explanation of the problems with all models earlier in this thread.
jal
edit: inserted
Find this and the explanation follows
Hey jal,
Me thinks you may presume too much.
I offered the Bekenstein bound (S < or = 2piEL) and the paper at the top of this page to (possibly) provide some math and references that could be applied to your model. I have no particular desire to see the Planck length or energy included one way or another. You can make "L" whatever you like, as long as it does not contradict empirical evidence.
Me thinks you may presume too much.
QUOTE
There appears to be a presumption..... a want to make everything nice and tidy
by presumming the first part of the quote (by including Planck size energy)
by presumming the first part of the quote (by including Planck size energy)
I offered the Bekenstein bound (S < or = 2piEL) and the paper at the top of this page to (possibly) provide some math and references that could be applied to your model. I have no particular desire to see the Planck length or energy included one way or another. You can make "L" whatever you like, as long as it does not contradict empirical evidence.
Why Not?
I agree.
Maybe an approach has already been found by Good Elf?
http://forum.physorg.com/index.php?showtop...15&#entry119085
I agree.
Maybe an approach has already been found by Good Elf?
http://forum.physorg.com/index.php?showtop...15&#entry119085
Together we are able to derive an easy equation for frequency independent of h but dependent on R, the radius of the particle.
From your reference....
http://www.ag-physics.org/rmass/ The Origin of Mass
If you follow the idea that mass energy equivalence is just a consequence of the set up of an elementary particle then this has a remarkable further consequence: As a reverse conclusion the mass energy equivalence cannot be valid below the level of an elementary particle.
jal
QUOTE
can make "L" whatever you like, as long as it does not contradict empirical evidence
I agree.
Maybe an approach has already been found by Good Elf?
http://forum.physorg.com/index.php?showtop...15&#entry119085
QUOTE (->
| QUOTE |
| can make "L" whatever you like, as long as it does not contradict empirical evidence |
I agree.
Maybe an approach has already been found by Good Elf?
http://forum.physorg.com/index.php?showtop...15&#entry119085
Together we are able to derive an easy equation for frequency independent of h but dependent on R, the radius of the particle.
From your reference....
http://www.ag-physics.org/rmass/ The Origin of Mass
QUOTE
If you follow the idea that mass energy equivalence is just a consequence of the set up of an elementary particle then this has a remarkable further consequence: As a reverse conclusion the mass energy equivalence cannot be valid below the level of an elementary particle.
jal
Hey jal,
I will be watching to see what Good Elf has up his sleeve as well... "m=h-bar/Rc" sounds interesting but gives an electron radius ~ 100 times larger than the classical radius.
Can wait to see what he's up too.
I will be watching to see what Good Elf has up his sleeve as well... "m=h-bar/Rc" sounds interesting but gives an electron radius ~ 100 times larger than the classical radius.
Can wait to see what he's up too.
Hi Why Not?
Just like strings were proposed for a different initial problem .....
I'm looking at it from my prospective, "basic particles = Spot"
I'm seeing people trying different approaches to get out of the "Planck size box."
I have no objection to admitting that many people could be finding parts of the answer.
...where the basic constituents have no mass.
Which would qualify them as being the 2d spot.
Just like strings were proposed for a different initial problem .....
I'm looking at it from my prospective, "basic particles = Spot"
I'm seeing people trying different approaches to get out of the "Planck size box."
I have no objection to admitting that many people could be finding parts of the answer.
QUOTE
In the case considered here only the alternative is usable because our goal is to explain the existence of mass in a configuration where the basic constituents have no mass.
.....
Please note that r is the distance between the basic particles in the configuration. So, for an elementary particle built by 2 constituents it is the diameter of the particle.
This result has the following remarkable aspects:
It yields the fact that the quotient of force and acceleration is constant at non relativistic velocities. Therefore this is a deduction of Newton’s law of motion. For Newton, this law had the property of an axiom.
The result shows that the mass is inversely proportional to the size of an elementary particle r.
is usable because our goal is to explain the existence of mass in a configuration where the basic constituents have no mass......
Please note that r is the distance between the basic particles in the configuration. So, for an elementary particle built by 2 constituents it is the diameter of the particle.
This result has the following remarkable aspects:
It yields the fact that the quotient of force and acceleration is constant at non relativistic velocities. Therefore this is a deduction of Newton’s law of motion. For Newton, this law had the property of an axiom.
The result shows that the mass is inversely proportional to the size of an elementary particle r.
...where the basic constituents have no mass.
Which would qualify them as being the 2d spot.
Hi!
doing a search of Albrecht Giese http://www.ag-physics.org/rmass/ The Origin of Mass leads me to http://www.tardyon.de/index.htm LUXON THEORY.
with 20 different approaches. (bottom of page).
"They still need packing"
jal
QUOTE
I'm seeing people trying different approaches to get out of the "Planck size box."
doing a search of Albrecht Giese http://www.ag-physics.org/rmass/ The Origin of Mass leads me to http://www.tardyon.de/index.htm LUXON THEORY.
with 20 different approaches. (bottom of page).
"They still need packing"
jal
Hi Good Elf!
I hope that his math approach has passed "peer review".
Has it been accepted?
I hope that his math approach has passed "peer review".
Has it been accepted?
As it stands it could/would complement some of the proposals of the RS model.
It also adresses the "gauge hierarchy problem/Planck scale energy", .
It opens the way to finding “A DYNAMIC WORKING MODEL OF SPACETIME.”
As I said in Yin_yang of spacetime and matter, finding the shape of space/time
at
http://forum.physorg.com/index.php?showtop...75&#entry116413
Things are definitely converging.
A "zero mass particles"/spot. would certainly be hard to detect in my approach.
jal
QUOTE
Yes Jal, it also leads to "my" spot as well. This all ties in with a reciprocal space interpretation. A quick look at the way Dr. Albrecht Giese resolves this mass problem involves the use of the effects of the near field. He has a particularly "easy going" view of this problem based on "zero mass particles".
I hope that his math approach has passed "peer review".
Has it been accepted?
QUOTE (->
| QUOTE |
| Yes Jal, it also leads to "my" spot as well. This all ties in with a reciprocal space interpretation. A quick look at the way Dr. Albrecht Giese resolves this mass problem involves the use of the effects of the near field. He has a particularly "easy going" view of this problem based on "zero mass particles". |
I hope that his math approach has passed "peer review".
Has it been accepted?
As it stands it could/would complement some of the proposals of the RS model.
It also adresses the "gauge hierarchy problem/Planck scale energy", .
It opens the way to finding “A DYNAMIC WORKING MODEL OF SPACETIME.”
As I said in Yin_yang of spacetime and matter, finding the shape of space/time
at
http://forum.physorg.com/index.php?showtop...75&#entry116413
QUOTE
WOULD THE MAGIC BOX/CUBE/HEX BE A VALID APPROACH TO FINDING HOW A SYMMETRICALLY STRUCTURED SPACETIME IS PUT TOGETHER?
DUE TO IT'S SYMMETRY, WE CANNOT DETECT IT.
DUE TO IT'S SYMMETRY, WE CANNOT DETECT IT.
Things are definitely converging.
A "zero mass particles"/spot. would certainly be hard to detect in my approach.
jal
Hi All!
I was expecting someone to bring forth the following calculation for discussion.
Ref.: http://en.wikipedia.org/wiki/Planck_units
SPHERES
Area = 4pi r^2
Volume= 4/3(pi r^3)
r=1 V=4.1888 A=12.566
r=2 V=33.51 A=50.265
r=3 V= 113.1 A= 113.1
r=4 V=268.08 A=201.06
r=8 V=2,144.661 A=804.2477
r=16 V=17,157.2847 A=3,216.990
What would be the minimum size of a Planck Sphere?
In order to make a sphere there has to be enough Planck areas to cover a hollow sphere
Therefore, when r=3, (3 Planck lengths) V= 113.1, A= 113.1 is the minimum size of a Planck Sphere. But that won't work.
That would be a shell that is too thin. It has to be at least Planck thick.
Therefore, What would be the minimum size of a Planck sphere?
jal
I was expecting someone to bring forth the following calculation for discussion.
Ref.: http://en.wikipedia.org/wiki/Planck_units
SPHERES
Area = 4pi r^2
Volume= 4/3(pi r^3)
r=1 V=4.1888 A=12.566
r=2 V=33.51 A=50.265
r=3 V= 113.1 A= 113.1
r=4 V=268.08 A=201.06
r=8 V=2,144.661 A=804.2477
r=16 V=17,157.2847 A=3,216.990
What would be the minimum size of a Planck Sphere?
In order to make a sphere there has to be enough Planck areas to cover a hollow sphere
Therefore, when r=3, (3 Planck lengths) V= 113.1, A= 113.1 is the minimum size of a Planck Sphere. But that won't work.
That would be a shell that is too thin. It has to be at least Planck thick.
Therefore, What would be the minimum size of a Planck sphere?
jal
Hey jal,
How can a 2D surface area have a "thin" or "think" shell?
I found... http://www.aci.net/kalliste/holographic_universe.pdf#search=%22Planck%20sphere%22 ://http://www.aci.net/kalliste/hologra...ck%20sphere%22 ... I don't know if it has been peer reviewed, and yes, it involves the explicit expression of Planck, but it fairly well sums up what I was trying to get across regarding the "holography" that I see in your model. Hope it helps.
QUOTE
That would be a shell that is too thin.
How can a 2D surface area have a "thin" or "think" shell?
I found... http://www.aci.net/kalliste/holographic_universe.pdf#search=%22Planck%20sphere%22 ://http://www.aci.net/kalliste/hologra...ck%20sphere%22 ... I don't know if it has been peer reviewed, and yes, it involves the explicit expression of Planck, but it fairly well sums up what I was trying to get across regarding the "holography" that I see in your model. Hope it helps.
Hi Why Not?
I'm glad to have you.... for an extra pair of eyes. You are a help.
I'll do a peer review of his paper .... after dealing with this.
A sphere with a radius of one Planck length will not have a surface area that would be suficient to make a sphere.
A Planck Sphere must have a radius of 4 Planck length.
As a result the Planck length is not violated. By definition nothing can be smaller.
A simple wave of a Planck area can therefore orbit around the Planck sphere.
The wave must be contained within the 3 Planck length radius and the 4 Planck length radius.
REASON # 2
The wave must visit each of the 8 Planck length quadrant of the sphere within its allotted time of one Planck time. Other wise .... the wave will colapse.
A sphere with a radius of one Planck length will not have a surface area that would be suficient to make a sphere.
A Planck Sphere must have a radius of 4 Planck length.
As a result the Planck length is not violated. By definition nothing can be smaller.
A simple wave of a Planck area can therefore orbit around the Planck sphere.
The wave must be contained within the 3 Planck length radius and the 4 Planck length radius.
REASON # 2
The wave must visit each of the 8 Planck length quadrant of the sphere within its allotted time of one Planck time. Other wise .... the wave will colapse.
In physics, the Planck time (tP), is the unit of time in the system of natural units known as Planck units. It is the time it would take a photon travelling at the speed of light to cross a distance equal to the Planck length.
Therefore, You must decide.....Is the Planck wave capable of traveling 8 X the speed of light? If it cannot then a Planck size wave is not possible.
Jal
I'm glad to have you.... for an extra pair of eyes. You are a help.
I'll do a peer review of his paper
.... after dealing with this.QUOTE
Therefore, What would be the minimum size of a Planck sphere?
A sphere with a radius of one Planck length will not have a surface area that would be suficient to make a sphere.
A Planck Sphere must have a radius of 4 Planck length.
As a result the Planck length is not violated. By definition nothing can be smaller.
A simple wave of a Planck area can therefore orbit around the Planck sphere.
The wave must be contained within the 3 Planck length radius and the 4 Planck length radius.
REASON # 2
The wave must visit each of the 8 Planck length quadrant of the sphere within its allotted time of one Planck time. Other wise .... the wave will colapse.
QUOTE (->
| QUOTE |
| Therefore, What would be the minimum size of a Planck sphere? |
A sphere with a radius of one Planck length will not have a surface area that would be suficient to make a sphere.
A Planck Sphere must have a radius of 4 Planck length.
As a result the Planck length is not violated. By definition nothing can be smaller.
A simple wave of a Planck area can therefore orbit around the Planck sphere.
The wave must be contained within the 3 Planck length radius and the 4 Planck length radius.
REASON # 2
The wave must visit each of the 8 Planck length quadrant of the sphere within its allotted time of one Planck time. Other wise .... the wave will colapse.
In physics, the Planck time (tP), is the unit of time in the system of natural units known as Planck units. It is the time it would take a photon travelling at the speed of light to cross a distance equal to the Planck length.
Therefore, You must decide.....Is the Planck wave capable of traveling 8 X the speed of light? If it cannot then a Planck size wave is not possible.
Jal
Hi! Why Not?
Do you agree... the minimum thickness is one Planck length?
Do you agree... the minimum thickness is one Planck length?
The wave must be contained within the 3 Planck length radius and the 4 Planck length radius.
There cannot be any energy within the Planck sphere.
Let's cut the sphere open and lay it flat.
If I got a sheet of paper and I cut it so that it can make a sphere..... do I have any paper inside the sphere that I just made? Of course not.
The paper is only one Planck length thick. It cannot be any thinner.
Is there a minimum size of paper that I can fold/make into a sphere?
Yes.... see the presentation in the previous post. It must have a radius of 4 Planck length.
Let's look at the numbers again and look at the area of a circle.
SPHERES
Area = 4pi r^2
Volume= 4/3(pi r^3)
r=1 V=4.1888 A=12.566
r=2 V=33.51 A=50.265
r=3 V= 113.1 A= 113.1
r=4 V=268.08 A=201.06
r=8 V=2,144.661 A=804.2477
r=16 V=17,157.2847 A=3,216.990
CIRCLES
Circumference = 2 pi R
Area = pi R^2
R = 1 C = 6.2832 A = 6.2832
R = 2 C = 12.566 A = 12.566
R = 3 C = 18.85 A = 28.274
R = 4 C = 25.133 A = 50.265 X 4 = 201.06
R = 8 C = 50.265 A = 201.06
R = 16 C = 100.53 A = 804.25
Can a 2D area cover the surface Area of a 3D sphere? Yes, if there are 4 2D units of the same radius as the radius of the sphere.
In physics, the Bekenstein bound imposes a limit on the information that can be contained within a three-dimensional region of a given surface area:
S<A/4 where S is the entropy and A is the two-dimensional area in units of the Planck area, .
(The bound was originally found by Jacob Bekenstein in the form S<2piEL, where L is the linear size of the region, and E is the energy of the contained matter as measured when the matter is moved to an infinite distance, i.e., accounting for binding force potential energies. Gerard t' Hooft later generalized it to the form involving A/4.)
Why Not?.... Does that help to explain..... why the energy/information is in the Area and that there is nothing on the other side of the area just because you have changed it's topology.
Okay... what does the 2D surface look like? 4 circles is what I said... It is what Gerard t' Hooft said.....It looks like what I have been saying all the time.
The 2D surfaces have been inserted/imbeded in/into what we see as 3D.
The chalenge is to have a dynamic model.
jal
jal, WN? et al,
jal, keep plugging in the numbers and information you can find that is the best way to find the answer down the pipe I would wish for you.
Your not alone on this and maybe this will help and then might not?
http://www.cerncourier.com/main/article/42/7/18
You just might be just like a patient clerk we all know about. EH!
ciao_
yquantum
Must get back to work, take care and will try and drop in soon.
Do you post just for the sake of posting?
Sometimes I post just to say 'hi' to people I like .. from your PoV that probably does look like 'just for the sake of posting'.. so 'yes' and 'no' to that question.
It is conceptually (and philosophically) difficult to work at the past-present-future boundary. If my chosen name, my signature at the end of every post or my apology at the end of this particular post 'sorry if this is unhelpful' was not sufficient to alert you to the possibility that I am not claiming access to the ultimate truth .. I can only apologize again.
IMHO the divergence theorEm begins to encapsulate a property of reality where that which is present remains present until it leaves and that which leaves actually leaves, if we add to this the amount that arrives .. then some sort of balance should be established. After following this thread for some time I feel it would be useful to discuss the past-present-future boundary and how each region might communicate with the other if that would shed any light on the points being discussed.
The reference here http://cnx.org/content/m12858/latest/ gives a good graphical starting point for ..? It isn't for me to say.
If we take a (say) a point charge with a past-present-future and another one very similar .. it seems they are interacting in the 'now' zone ... any insight would be most welcome. Please respect the fact that this is an established thread and unless you have anything constructive to offer it might be better to start a new thread of your own.
Best wishes,
C2.
Apologies for typos seem to be 'de rigeour' nowadays .. in addition to my other faults, please also forgive my spelling mistakes.
Do you post just for the sake of posting?
Sometimes I post just to say 'hi' to people I like .. from your PoV that probably does look like 'just for the sake of posting'.. so 'yes' and 'no' to that question.
It is conceptually (and philosophically) difficult to work at the past-present-future boundary. If my chosen name, my signature at the end of every post or my apology at the end of this particular post 'sorry if this is unhelpful' was not sufficient to alert you to the possibility that I am not claiming access to the ultimate truth .. I can only apologize again.
IMHO the divergence theorEm begins to encapsulate a property of reality where that which is present remains present until it leaves and that which leaves actually leaves, if we add to this the amount that arrives .. then some sort of balance should be established. After following this thread for some time I feel it would be useful to discuss the past-present-future boundary and how each region might communicate with the other if that would shed any light on the points being discussed.
The reference here http://cnx.org/content/m12858/latest/ gives a good graphical starting point for ..? It isn't for me to say.
If we take a (say) a point charge with a past-present-future and another one very similar .. it seems they are interacting in the 'now' zone ... any insight would be most welcome. Please respect the fact that this is an established thread and unless you have anything constructive to offer it might be better to start a new thread of your own.
Best wishes,
C2.
Apologies for typos seem to be 'de rigeour' nowadays .. in addition to my other faults, please also forgive my spelling mistakes.
Word salad. The divergence theorem has nothing to do with past-present-future. This is physics, not METAphysics.
QUOTE
How can a 2D surface area have a "thin" or "think" shell?
Do you agree... the minimum thickness is one Planck length?
QUOTE (->
| QUOTE |
| How can a 2D surface area have a "thin" or "think" shell? |
Do you agree... the minimum thickness is one Planck length?
The wave must be contained within the 3 Planck length radius and the 4 Planck length radius.
There cannot be any energy within the Planck sphere.
Let's cut the sphere open and lay it flat.
If I got a sheet of paper and I cut it so that it can make a sphere..... do I have any paper inside the sphere that I just made? Of course not.
The paper is only one Planck length thick. It cannot be any thinner.
Is there a minimum size of paper that I can fold/make into a sphere?
Yes.... see the presentation in the previous post. It must have a radius of 4 Planck length.
Let's look at the numbers again and look at the area of a circle.
SPHERES
Area = 4pi r^2
Volume= 4/3(pi r^3)
r=1 V=4.1888 A=12.566
r=2 V=33.51 A=50.265
r=3 V= 113.1 A= 113.1
r=4 V=268.08 A=201.06
r=8 V=2,144.661 A=804.2477
r=16 V=17,157.2847 A=3,216.990
CIRCLES
Circumference = 2 pi R
Area = pi R^2
R = 1 C = 6.2832 A = 6.2832
R = 2 C = 12.566 A = 12.566
R = 3 C = 18.85 A = 28.274
R = 4 C = 25.133 A = 50.265 X 4 = 201.06
R = 8 C = 50.265 A = 201.06
R = 16 C = 100.53 A = 804.25
Can a 2D area cover the surface Area of a 3D sphere? Yes, if there are 4 2D units of the same radius as the radius of the sphere.
QUOTE
http://en.wikipedia.org/wiki/Bekenstein_bound
QUOTE (->
| QUOTE |
| http://en.wikipedia.org/wiki/Bekenstein_bound |
In physics, the Bekenstein bound imposes a limit on the information that can be contained within a three-dimensional region of a given surface area:
S<A/4 where S is the entropy and A is the two-dimensional area in units of the Planck area, .
(The bound was originally found by Jacob Bekenstein in the form S<2piEL, where L is the linear size of the region, and E is the energy of the contained matter as measured when the matter is moved to an infinite distance, i.e., accounting for binding force potential energies. Gerard t' Hooft later generalized it to the form involving A/4.)
Why Not?.... Does that help to explain..... why the energy/information is in the Area and that there is nothing on the other side of the area just because you have changed it's topology.
Okay... what does the 2D surface look like? 4 circles is what I said... It is what Gerard t' Hooft said.....It looks like what I have been saying all the time.
The 2D surfaces have been inserted/imbeded in/into what we see as 3D.
The chalenge is to have a dynamic model.
jal
jal, Why Not?, et al,
jal, I have been reading your post and I am sure it is my lack of understanding what your postulating? So please be patient with me on this.
http://www.virtualsciencefair.org/2004/wup...ic_html/sa.html
This is from the article above tell me what you think? I am just a y on this and I have a question I hope you can help me with.
Best!
ciao_
yquantum
jal, I have been reading your post and I am sure it is my lack of understanding what your postulating?
So please be patient with me on this.http://www.virtualsciencefair.org/2004/wup...ic_html/sa.html
QUOTE
Considering the previous concept of a particle was a dimensionless point, it's not too far a stretch too see how they arrived at strings. A one-dimensional object is a natural extension of a point-particle. These strings have to be incredibly small, 10-33 cm, in order to incorporate gravity. This is because the scale of quantum gravity is at
Planck's length, 10-33 cm (like Planck's constant, another extremely small number that has been very useful for describing our universe). In order to be this small and still produce the larger masses seen in nature, strings must have a gigantic tension. It comes out to approximately 1039 tons. These strings act like really smooth, elastic playdoh. They can bend, vibrate, spin, and even join their ends together. The "super" in "superstrings" comes from the fact that supersymmetry has been incorporated into the theory. Insights from Grand Unification are used as well. String theories are grouped by whether they include fermions in their particle spectrum and whether they have open or closed loops.
Planck's length, 10-33 cm (like Planck's constant, another extremely small number that has been very useful for describing our universe). In order to be this small and still produce the larger masses seen in nature, strings must have a gigantic tension. It comes out to approximately 1039 tons. These strings act like really smooth, elastic playdoh. They can bend, vibrate, spin, and even join their ends together. The "super" in "superstrings" comes from the fact that supersymmetry has been incorporated into the theory. Insights from Grand Unification are used as well. String theories are grouped by whether they include fermions in their particle spectrum and whether they have open or closed loops.
This is from the article above tell me what you think? I am just a y on this and I have a question I hope you can help me with.
Best!
ciao_
yquantum
Hi yquantum!
I'm a nobody..... I'm glad that you have been following what I've been saying.
I'm obviously going to need help.
I've just finished saying that curled up dimensions must have a radius of 4 Planck units and must be one Planck unit thick.
So my math must be wrong.... or somebody invented a way around the Planck Scale.
Maybe!!!..... I've found a way for strings to get into the act.
Yquantum….. I'm sure that your friends, Gerard t' Hooft and Susskind are smarter than me. They must have figured out everything that I've been saying.
If it doesn't work, why did they not publish?
After this I was going to address the link from Why Not? Most of what I was going to say .... I have already said.
"The holographic principle is a simple consequence of the divergence theorem
J. Orlin Grabbe
February 27, 2006"
jal
I'm a nobody.....
I'm glad that you have been following what I've been saying.I'm obviously going to need help.
I've just finished saying that curled up dimensions must have a radius of 4 Planck units and must be one Planck unit thick.
So my math must be wrong.... or somebody invented a way around the Planck Scale.
Maybe!!!..... I've found a way for strings to get into the act.
Yquantum….. I'm sure that your friends, Gerard t' Hooft and Susskind are smarter than me. They must have figured out everything that I've been saying.
If it doesn't work, why did they not publish?
After this I was going to address the link from Why Not? Most of what I was going to say .... I have already said.
QUOTE
I found... http://www.aci.net/kalliste/holographic_un...nck%20sphere%22 ://http://www.aci.net/kalliste/hologra...ck%20sphere%22 ... I don't know if it has been peer reviewed, and yes, it involves the explicit expression of Planck, but it fairly well sums up what I was trying to get across regarding the "holography" that I see in your model. Hope it helps.
"The holographic principle is a simple consequence of the divergence theorem
J. Orlin Grabbe
February 27, 2006"
jal
jal, WN? et al,jal, keep plugging in the numbers and information you can find that is the best way to find the answer down the pipe I would wish for you.
Your not alone on this and maybe this will help and then might not?
http://www.cerncourier.com/main/article/42/7/18
QUOTE
. If this is true for every singular space-time background, it would be a manifestation of the so-called holographic conjecture of 't Hooft and Susskind, according to which any information that enters the horizon of a black hole (a sort of space-time boundary) is encoded on the boundary and no information is lost.
Unfortunately, the situation may not be that simple. Physicists have so far been unable to demonstrate the holographic principle rigorously outside certain restricted classes of stringy black hole backgrounds. Moreover, within the modern context of brane theory there have been theoretical arguments demonstrating that it is impossible to describe the formation of a black hole by collapsing string matter, or the final stage of its evaporation by purely unitary quantum methods.
Unfortunately, the situation may not be that simple. Physicists have so far been unable to demonstrate the holographic principle rigorously outside certain restricted classes of stringy black hole backgrounds. Moreover, within the modern context of brane theory there have been theoretical arguments demonstrating that it is impossible to describe the formation of a black hole by collapsing string matter, or the final stage of its evaporation by purely unitary quantum methods.
You just might be just like a patient clerk we all know about. EH!
ciao_
yquantum
Must get back to work, take care and will try and drop in soon.
Hi All,
I haven't posted for a bit because I've not been able to advance things at all. Just a minor point is that Gauss's Theorum (divergence theorum) works for any enclosed volume of any shape .. including a very flat one. My brain fails on an attempt to apply it at the past present future interface .. but I think it ought to work. Sorry if this is unhelpful.
-C2.
I haven't posted for a bit because I've not been able to advance things at all. Just a minor point is that Gauss's Theorum (divergence theorum) works for any enclosed volume of any shape .. including a very flat one. My brain fails on an attempt to apply it at the past present future interface .. but I think it ought to work. Sorry if this is unhelpful.
-C2.
QUOTE (Confused2+Aug 29 2006, 11:23 PM)
Hi All,
I haven't posted for a bit because I've not been able to advance things at all. Just a minor point is that Gauss's Theorum (divergence theorum) works for any enclosed volume of any shape .. including a very flat one. My brain fails on an attempt to apply it at the past present future interface .. but I think it ought to work. Sorry if this is unhelpful.
-C2.
Do you post just for the sake of posting? Gauss theorEm (not theorUm) applies for a very specific set of conditions:
The region must be closed, bounded by a piecewise smooth orientable surface. The vector function under consideration must be continuous and have continous partial derivatives of first order. Then you can say that:
Triple_Integral (div U) dw=Double_integral <U,n> dS
I haven't posted for a bit because I've not been able to advance things at all. Just a minor point is that Gauss's Theorum (divergence theorum) works for any enclosed volume of any shape .. including a very flat one. My brain fails on an attempt to apply it at the past present future interface .. but I think it ought to work. Sorry if this is unhelpful.
-C2.
Do you post just for the sake of posting? Gauss theorEm (not theorUm) applies for a very specific set of conditions:
The region must be closed, bounded by a piecewise smooth orientable surface. The vector function under consideration must be continuous and have continous partial derivatives of first order. Then you can say that:
Triple_Integral (div U) dw=Double_integral <U,n> dS
QUOTE (Pupamancur+)
Do you post just for the sake of posting?
Sometimes I post just to say 'hi' to people I like .. from your PoV that probably does look like 'just for the sake of posting'.. so 'yes' and 'no' to that question.
It is conceptually (and philosophically) difficult to work at the past-present-future boundary. If my chosen name, my signature at the end of every post or my apology at the end of this particular post 'sorry if this is unhelpful' was not sufficient to alert you to the possibility that I am not claiming access to the ultimate truth .. I can only apologize again.
IMHO the divergence theorEm begins to encapsulate a property of reality where that which is present remains present until it leaves and that which leaves actually leaves, if we add to this the amount that arrives .. then some sort of balance should be established. After following this thread for some time I feel it would be useful to discuss the past-present-future boundary and how each region might communicate with the other if that would shed any light on the points being discussed.
The reference here http://cnx.org/content/m12858/latest/ gives a good graphical starting point for ..? It isn't for me to say.
If we take a (say) a point charge with a past-present-future and another one very similar .. it seems they are interacting in the 'now' zone ... any insight would be most welcome. Please respect the fact that this is an established thread and unless you have anything constructive to offer it might be better to start a new thread of your own.
Best wishes,
C2.
Apologies for typos seem to be 'de rigeour' nowadays .. in addition to my other faults, please also forgive my spelling mistakes.
QUOTE (Confused2+Aug 30 2006, 01:18 AM)
QUOTE (Pupamancur+)
Do you post just for the sake of posting?
Sometimes I post just to say 'hi' to people I like .. from your PoV that probably does look like 'just for the sake of posting'.. so 'yes' and 'no' to that question.
It is conceptually (and philosophically) difficult to work at the past-present-future boundary. If my chosen name, my signature at the end of every post or my apology at the end of this particular post 'sorry if this is unhelpful' was not sufficient to alert you to the possibility that I am not claiming access to the ultimate truth .. I can only apologize again.
IMHO the divergence theorEm begins to encapsulate a property of reality where that which is present remains present until it leaves and that which leaves actually leaves, if we add to this the amount that arrives .. then some sort of balance should be established. After following this thread for some time I feel it would be useful to discuss the past-present-future boundary and how each region might communicate with the other if that would shed any light on the points being discussed.
The reference here http://cnx.org/content/m12858/latest/ gives a good graphical starting point for ..? It isn't for me to say.
If we take a (say) a point charge with a past-present-future and another one very similar .. it seems they are interacting in the 'now' zone ... any insight would be most welcome. Please respect the fact that this is an established thread and unless you have anything constructive to offer it might be better to start a new thread of your own.
Best wishes,
C2.
Apologies for typos seem to be 'de rigeour' nowadays .. in addition to my other faults, please also forgive my spelling mistakes.
Word salad. The divergence theorem has nothing to do with past-present-future. This is physics, not METAphysics.
Hey jal, et al.
jal,
Ummmm, strictly speaking, no. The 2D surface area of a sphere is strictly 2D (longitudinal and latitudinal). To add "thickness" is to add a third dimension. That said, if you consider the "surface" of a 3D sphere to be a shell and if you agree that the minimum physical length is the Planck length, then I suppose the minimum thickness would be zero and the maximum thickness would be one Planck Length (uncertainty dictating the probability of finding the thickness at zero or Planck). But your entire thread is about more with less. If you stick with the 2D portion of you model, I do not see how you can logically justify a "thickness" in a third dimension.
Ummmm, strictly speaking, no. The 2D surface area of a sphere is strictly 2D (longitudinal and latitudinal). To add "thickness" is to add a third dimension. That said, if you consider the "surface" of a 3D sphere to be a shell and if you agree that the minimum physical length is the Planck length, then I suppose the minimum thickness would be zero and the maximum thickness would be one Planck Length (uncertainty dictating the probability of finding the thickness at zero or Planck). But your entire thread is about more with less. If you stick with the 2D portion of you model, I do not see how you can logically justify a "thickness" in a third dimension.
There cannot be any energy within the Planck sphere.
Agreed (I think). The energy/information is contained in the 2D surface area.
I am not trying to be too picky, but if the paper has thickness, then it is 3D not 2D.
I am not trying to be too picky, but if the paper has thickness, then it is 3D not 2D.
Can a 2D area cover the surface Area of a 3D sphere? Yes, if there are 4 2D units of the same radius as the radius of the sphere.
I agree that the ratio is 4/1.
Yes. Which is why a 2D surface area cannot have a "thickness" and why the energy/information is contained on that area (not within the volume).
Yes. Which is why a 2D surface area cannot have a "thickness" and why the energy/information is contained on that area (not within the volume).
Okay... what does the 2D surface look like? 4 circles is what I said... It is what Gerard t' Hooft said.....It looks like what I have been saying all the time.
The 2D surfaces have been inserted/imbeded in/into what we see as 3D.
The chalenge is to have a dynamic model.
Which is why I suggested the Holographic Principle (in principle, not necessarily in the details) in the first place. That is what your model looks like to me - holographic.
Sorry this post is getting so lengthy, but I have one last thing to add.
I think C2 has discovered why I mentioned that I was "struggling" with Gauss on another thread...
From the link posted by "guest"...
Regardless of the applicability of Gauss's Law to various surface areas, since we are talking about spheres, I am sticking with spheres! Anyway, I am trying to figure out if your model can be applied, with the help of Gauss's Law, to determine the minimum radius an electron, derived from it's charge...
jal,
QUOTE
Do you agree... the minimum thickness is one Planck length?
Ummmm, strictly speaking, no.
The 2D surface area of a sphere is strictly 2D (longitudinal and latitudinal). To add "thickness" is to add a third dimension. That said, if you consider the "surface" of a 3D sphere to be a shell and if you agree that the minimum physical length is the Planck length, then I suppose the minimum thickness would be zero and the maximum thickness would be one Planck Length (uncertainty dictating the probability of finding the thickness at zero or Planck). But your entire thread is about more with less. If you stick with the 2D portion of you model, I do not see how you can logically justify a "thickness" in a third dimension. QUOTE (->
| QUOTE |
| Do you agree... the minimum thickness is one Planck length? |
Ummmm, strictly speaking, no.
The 2D surface area of a sphere is strictly 2D (longitudinal and latitudinal). To add "thickness" is to add a third dimension. That said, if you consider the "surface" of a 3D sphere to be a shell and if you agree that the minimum physical length is the Planck length, then I suppose the minimum thickness would be zero and the maximum thickness would be one Planck Length (uncertainty dictating the probability of finding the thickness at zero or Planck). But your entire thread is about more with less. If you stick with the 2D portion of you model, I do not see how you can logically justify a "thickness" in a third dimension. There cannot be any energy within the Planck sphere.
Agreed (I think). The energy/information is contained in the 2D surface area.
QUOTE
The paper is only one Planck length thick. It cannot be any thinner.
I am not trying to be too picky, but if the paper has thickness, then it is 3D not 2D.
QUOTE (->
| QUOTE |
| The paper is only one Planck length thick. It cannot be any thinner. |
I am not trying to be too picky, but if the paper has thickness, then it is 3D not 2D.
Can a 2D area cover the surface Area of a 3D sphere? Yes, if there are 4 2D units of the same radius as the radius of the sphere.
I agree that the ratio is 4/1.
QUOTE
Why Not?.... Does that help to explain..... why the energy/information is in the Area and that there is nothing on the other side of the area just because you have changed it's topology.
Yes. Which is why a 2D surface area cannot have a "thickness" and why the energy/information is contained on that area (not within the volume).
QUOTE (->
| QUOTE |
| Why Not?.... Does that help to explain..... why the energy/information is in the Area and that there is nothing on the other side of the area just because you have changed it's topology. |
Yes. Which is why a 2D surface area cannot have a "thickness" and why the energy/information is contained on that area (not within the volume).
Okay... what does the 2D surface look like? 4 circles is what I said... It is what Gerard t' Hooft said.....It looks like what I have been saying all the time.
The 2D surfaces have been inserted/imbeded in/into what we see as 3D.
The chalenge is to have a dynamic model.
Which is why I suggested the Holographic Principle (in principle, not necessarily in the details) in the first place.
That is what your model looks like to me - holographic.Sorry this post is getting so lengthy, but I have one last thing to add.
I think C2 has discovered why I mentioned that I was "struggling" with Gauss on another thread...
From the link posted by "guest"...
QUOTE
A conducting sphere of radius [r] carries a charge Q on its surface.
- my emphasis added.Regardless of the applicability of Gauss's Law to various surface areas, since we are talking about spheres, I am sticking with spheres! Anyway, I am trying to figure out if your model can be applied, with the help of Gauss's Law, to determine the minimum radius an electron, derived from it's charge...
yquantum
Your comments were unexpected. I'll take you comment as a compliment.
It is obvious that the Planck Scale cannot be broken and my calculation was one that I presume to be so obvious that it is taken for granted.
The holographic conjecture of 't Hooft and Susskind and 2D structure which arise is just as obvious.
I'l keep trying.
Confused2
Your comments were unexpected. I'll take you comment as a compliment.
It is obvious that the Planck Scale cannot be broken and my calculation was one that I presume to be so obvious that it is taken for granted.
The holographic conjecture of 't Hooft and Susskind and 2D structure which arise is just as obvious.
I'l keep trying.
Confused2
QUOTE
Gauss's Theorum
Lead me to look at QUOTE (->
| QUOTE |
| Gauss's Theorum |
Lead me to look at
permittivity of free space
- The permittivity of free space (a vacuum) is a physical constant equal to approximately 8.85 x 10-12 farad per meter (F/m). It is symbolized o. In general, permittivity is symbolized and is a constant of proportionality that exists between electric displacement and electric field intensity in a given medium.
Someone who has read my posts has better explain to me how spacetime could be involved. As far as I can tell spacetime seems to act pretty neutral in this area.
( I'll listen to your input Why Not?)
Pupamancur
I hope that you can put your math skills to helping me make more sense of my struggling efforts.
As I have just been advised,".....keep plugging in the numbers "
Why Not?
Yep....I know.... Then I got to ask how can we get a 2D surface, made of an energy structure when Planck Scale is the limit?
Yep....I know.... Then I got to ask how can we get a 2D surface, made of an energy structure when Planck Scale is the limit?
then I suppose the minimum thickness would be zero and the maximum thickness would be one Planck Length
Noooo.... Re-read. You have made a presumption. You cannot get a sphere if the radius of the sphere is one Planck length. Nor... can you get a soliton.
It bugs the hell out of me too. I would have to find a way to get rid of the Planck scale.
jal
permittivity of free space
- The permittivity of free space (a vacuum) is a physical constant equal to approximately 8.85 x 10-12 farad per meter (F/m). It is symbolized o. In general, permittivity is symbolized and is a constant of proportionality that exists between electric displacement and electric field intensity in a given medium.
Someone who has read my posts has better explain to me how spacetime could be involved. As far as I can tell spacetime seems to act pretty neutral in this area.
( I'll listen to your input Why Not?)
Pupamancur
I hope that you can put your math skills to helping me make more sense of my struggling efforts.
As I have just been advised,".....keep plugging in the numbers "
Why Not?
QUOTE
The 2D surface area of a sphere is strictly 2D (longitudinal and latitudinal). To add "thickness" is to add a third dimension.
Yep....I know.... Then I got to ask how can we get a 2D surface, made of an energy structure when Planck Scale is the limit?
QUOTE (->
| QUOTE |
| The 2D surface area of a sphere is strictly 2D (longitudinal and latitudinal). To add "thickness" is to add a third dimension. |
Yep....I know.... Then I got to ask how can we get a 2D surface, made of an energy structure when Planck Scale is the limit?
then I suppose the minimum thickness would be zero and the maximum thickness would be one Planck Length
Noooo.... Re-read. You have made a presumption. You cannot get a sphere if the radius of the sphere is one Planck length. Nor... can you get a soliton.
QUOTE
If you stick with the 2D portion of you model, I do not see how you can logically justify a "thickness" in a third dimension.
It bugs the hell out of me too. I would have to find a way to get rid of the Planck scale.
jal
Good Day ALL!
Can we have rules in one kind of dimensions and have different rules that govern in a different kind of dimensions?
Can we ignore the rule that are different in these two kinds of dimensions and then join up the two dimensions?
Don't be intimidated by the following "foreign" language. Those are the two points being discussed by J. Baez
(I'm not going to try to reproduce the symbols. If you are interested .... read the article.)
http://math.ucr.edu/home/baez/planck/
Can we have rules in one kind of dimensions and have different rules that govern in a different kind of dimensions?
Can we ignore the rule that are different in these two kinds of dimensions and then join up the two dimensions?
Don't be intimidated by the following "foreign" language. Those are the two points being discussed by J. Baez
(I'm not going to try to reproduce the symbols. If you are interested .... read the article.)
http://math.ucr.edu/home/baez/planck/
The plan of the paper is as follows. In Section 2, I begin by recalling why some physicists expect general relativity and quantum field theory to collide at the Planck length. This is a unit of distance concocted from three fundamental constants: the speed of light , Newton's gravitational constant , and Planck's constant . General relativity idealizes reality by treating Planck's constant as negligible, while quantum field theory idealizes it by treating Newton's gravitational constant as negligible. By analyzing the physics of and , we get a glimpse of the sort of theory that would be needed to deal with situations where these idealizations break down. In particular, I shall argue that we need a background-free quantum theory with local degrees of freedom propagating causally.
... in which -h sets the scale at which the uncertainty principle becomes important.
(insert: If the Planck scale exist, the uncertainty principle cannot apply at the Planck scale. It is 100% certain. As a result my previous post is correct)
The reason is very simple: any calculation that predicts a length using only the constants , and must give the Planck length, possibly multiplied by an unimportant numerical factor like pi .
The `unimportant numerical factor' I mentioned above might actually be very large, or very small. A theory of quantum gravity might make testable predictions of dimensionless quantities like the ratio of the muon and electron masses. For that matter, a theory of quantum gravity might involve physical constants other than , , and . The latter two alternatives are especially plausible if we study quantum gravity as part of a larger theory describing other forces and particles. However, even though we cannot prove that the Planck length is significant for quantum gravity, I think we can glean some wisdom from pondering the constants and -- and more importantly, the physical insights that lead us to regard these constants as important.
In Section 3, I discuss `topological quantum field theories'. These are the first examples of background-free quantum theories. However, they lack local degrees of freedom. In other words, they describe imaginary worlds in which everywhere looks like everywhere else! This might at first seem to condemn them to the status of mathematical curiosities. However, they suggest an important analogy between the mathematics of spacetime and the mathematics of quantum theory. I argue that this is the beginning of a new bridge between general relativity and quantum field theory.
In the second part J. Baez make a case for inventing new rules for other dimensions.
http://math.ucr.edu/home/baez/quantum/quantum.html
An important goal of the enterprise of physics is to describe, not just one physical system at a time, but also how a large complicated system can be built out of smaller simpler ones. The simplest case is a so-called `joint system': a system built out of two separate parts. Our experience with the everyday world leads us to believe that to specify the state of a joint system, it is necessary and sufficient to specify states of its two parts. (Here and in what follows, by `states' we always mean what physicists call `pure states'.) In other words, a state of the joint system is just an ordered pair of states of its parts. So, if the first part has as its set of states, and the second part has as its set of states, the joint system has the cartesian product as its set of states.
One of the more shocking discoveries of the twentieth century is that this is wrong. In both classical and quantum physics, given states of each part we get a state of the joint system. But only in classical physics is every state of the joint system of this form! In quantum physics are also `entangled' states, which can only be described as superpositions of states of this form. The reason is that in quantum theory, the states of a system are no longer described by a set, but by a Hilbert space. Moreover -- and this is really an extra assumption -- the states of a joint system are described not by the cartesian product of Hilbert spaces, but by their tensor product.
In the conclusion, J. Baez, sits on the fence.
SOOOOOO...... Everybody is breaking the rules so that they can dream up all kinds of science fiction scenarios.
They use (uncertainty principle ....`entangled' states) to bypass the Planck Scale. This allow them to make their scenarios work.
Who has the final word......
Can I make a 2D membrane without imposing a Planck Scale of one unit for the thickness?
However, do the Planck Scale rule still apply in our 3D?
jal
QUOTE
I would have to find a way to get rid of the Planck scale.
Can we have rules in one kind of dimensions and have different rules that govern in a different kind of dimensions?
Can we ignore the rule that are different in these two kinds of dimensions and then join up the two dimensions?
Don't be intimidated by the following "foreign" language. Those are the two points being discussed by J. Baez
(I'm not going to try to reproduce the symbols. If you are interested .... read the article.)
http://math.ucr.edu/home/baez/planck/
QUOTE (->
| QUOTE |
| I would have to find a way to get rid of the Planck scale. |
Can we have rules in one kind of dimensions and have different rules that govern in a different kind of dimensions?
Can we ignore the rule that are different in these two kinds of dimensions and then join up the two dimensions?
Don't be intimidated by the following "foreign" language. Those are the two points being discussed by J. Baez
(I'm not going to try to reproduce the symbols. If you are interested .... read the article.)
http://math.ucr.edu/home/baez/planck/
The plan of the paper is as follows. In Section 2, I begin by recalling why some physicists expect general relativity and quantum field theory to collide at the Planck length. This is a unit of distance concocted from three fundamental constants: the speed of light , Newton's gravitational constant , and Planck's constant . General relativity idealizes reality by treating Planck's constant as negligible, while quantum field theory idealizes it by treating Newton's gravitational constant as negligible. By analyzing the physics of and , we get a glimpse of the sort of theory that would be needed to deal with situations where these idealizations break down. In particular, I shall argue that we need a background-free quantum theory with local degrees of freedom propagating causally.
... in which -h sets the scale at which the uncertainty principle becomes important.
(insert: If the Planck scale exist, the uncertainty principle cannot apply at the Planck scale. It is 100% certain. As a result my previous post is correct)
The reason is very simple: any calculation that predicts a length using only the constants , and must give the Planck length, possibly multiplied by an unimportant numerical factor like pi .
The `unimportant numerical factor' I mentioned above might actually be very large, or very small. A theory of quantum gravity might make testable predictions of dimensionless quantities like the ratio of the muon and electron masses. For that matter, a theory of quantum gravity might involve physical constants other than , , and . The latter two alternatives are especially plausible if we study quantum gravity as part of a larger theory describing other forces and particles. However, even though we cannot prove that the Planck length is significant for quantum gravity, I think we can glean some wisdom from pondering the constants and -- and more importantly, the physical insights that lead us to regard these constants as important.
In Section 3, I discuss `topological quantum field theories'. These are the first examples of background-free quantum theories. However, they lack local degrees of freedom. In other words, they describe imaginary worlds in which everywhere looks like everywhere else! This might at first seem to condemn them to the status of mathematical curiosities. However, they suggest an important analogy between the mathematics of spacetime and the mathematics of quantum theory. I argue that this is the beginning of a new bridge between general relativity and quantum field theory.
In the second part J. Baez make a case for inventing new rules for other dimensions.
http://math.ucr.edu/home/baez/quantum/quantum.html
QUOTE
To build a category of this sort of mathematical object, we must also define morphisms between these objects. When the objects are sets equipped with extra structure and properties, the morphisms are typically taken to be functions that preserve the extra structure......
The case of general, possibly infinite-dimensional Hilbert spaces is subtler, but the puzzle persists. The category of all Hilbert spaces and bounded linear operators between them is not equivalent to the category of all complex vector spaces and linear operators. However, it is equivalent to the category of `Hilbertizable' vector spaces -- that is, vector spaces equipped with a topology coming from some Hilbert space structure -- and continuous linear operators between these. So, in defining this category, what matters is not the inner product but merely the topology it gives rise to. The point is that bounded linear operators don't preserve the inner product, just the topology, and a structure that is not preserved might as well be ignored, as far as the category is concerned.
The case of general, possibly infinite-dimensional Hilbert spaces is subtler, but the puzzle persists. The category of all Hilbert spaces and bounded linear operators between them is not equivalent to the category of all complex vector spaces and linear operators. However, it is equivalent to the category of `Hilbertizable' vector spaces -- that is, vector spaces equipped with a topology coming from some Hilbert space structure -- and continuous linear operators between these. So, in defining this category, what matters is not the inner product but merely the topology it gives rise to. The point is that bounded linear operators don't preserve the inner product, just the topology, and a structure that is not preserved might as well be ignored, as far as the category is concerned.
QUOTE (->
| QUOTE |
| To build a category of this sort of mathematical object, we must also define morphisms between these objects. When the objects are sets equipped with extra structure and properties, the morphisms are typically taken to be functions that preserve the extra structure...... The case of general, possibly infinite-dimensional Hilbert spaces is subtler, but the puzzle persists. The category of all Hilbert spaces and bounded linear operators between them is not equivalent to the category of all complex vector spaces and linear operators. However, it is equivalent to the category of `Hilbertizable' vector spaces -- that is, vector spaces equipped with a topology coming from some Hilbert space structure -- and continuous linear operators between these. So, in defining this category, what matters is not the inner product but merely the topology it gives rise to. The point is that bounded linear operators don't preserve the inner product, just the topology, and a structure that is not preserved might as well be ignored, as far as the category is concerned. |
An important goal of the enterprise of physics is to describe, not just one physical system at a time, but also how a large complicated system can be built out of smaller simpler ones. The simplest case is a so-called `joint system': a system built out of two separate parts. Our experience with the everyday world leads us to believe that to specify the state of a joint system, it is necessary and sufficient to specify states of its two parts. (Here and in what follows, by `states' we always mean what physicists call `pure states'.) In other words, a state of the joint system is just an ordered pair of states of its parts. So, if the first part has as its set of states, and the second part has as its set of states, the joint system has the cartesian product as its set of states.
One of the more shocking discoveries of the twentieth century is that this is wrong. In both classical and quantum physics, given states of each part we get a state of the joint system. But only in classical physics is every state of the joint system of this form! In quantum physics are also `entangled' states, which can only be described as superpositions of states of this form. The reason is that in quantum theory, the states of a system are no longer described by a set, but by a Hilbert space. Moreover -- and this is really an extra assumption -- the states of a joint system are described not by the cartesian product of Hilbert spaces, but by their tensor product.
In the conclusion, J. Baez, sits on the fence.
QUOTE
However, as we have seen, the fact that Hilbert spaces are sets equipped with extra structure and properties is almost a distraction when trying to understand , because its morphisms are not functions that preserve this extra structure......
However, the textbook treatments and even most of the research literature on category-theoretic logic focus on categories where the monoidal structure is cartesian. The study of logic within more general monoidal categories is just beginning. More precisely, while generalizations of `algebraic theories' to categories of this sort have been studied for many years in topology and physics [22,25], it is hard to find work that explicitly recognizes the relation of such theories to the traditional concerns of logic, or even of quantum logic.
However, the textbook treatments and even most of the research literature on category-theoretic logic focus on categories where the monoidal structure is cartesian. The study of logic within more general monoidal categories is just beginning. More precisely, while generalizations of `algebraic theories' to categories of this sort have been studied for many years in topology and physics [22,25], it is hard to find work that explicitly recognizes the relation of such theories to the traditional concerns of logic, or even of quantum logic.
SOOOOOO...... Everybody is breaking the rules so that they can dream up all kinds of science fiction scenarios.
They use (uncertainty principle ....`entangled' states) to bypass the Planck Scale. This allow them to make their scenarios work.
Who has the final word......
Can I make a 2D membrane without imposing a Planck Scale of one unit for the thickness?
However, do the Planck Scale rule still apply in our 3D?
jal
Hey jal, et al.
jal, lots to chew on... I will wait to delve further into Gauss until I have a better understanding of your Planck scale logic.
Mathematically, in 3D, you can create a sphere from any real number > zero and determine it's surface area as 4pi r^2. Whether or not the Planck length represents the smallest meaningful distance in the Cosmos is yet to be determined. But mathematically, you can certainly determine the spherical area with a radius of one Planck length.
Mathematically, in 3D, you can create a sphere from any real number > zero and determine it's surface area as 4pi r^2. Whether or not the Planck length represents the smallest meaningful distance in the Cosmos is yet to be determined. But mathematically, you can certainly determine the spherical area with a radius of one Planck length.
Then I got to ask how can we get a 2D surface, made of an energy structure when Planck Scale is the limit?
I am not sure that you can. But I bet you can speculate on the smallest possible energy wavelength... 1/2 that wavelength would determine the smallest possible sphere radius, yes?
I enjoy reading Baez's work. He combines incredible insights in math, physics and logic to "think outside the sphere."
jal, lots to chew on... I will wait to delve further into Gauss until I have a better understanding of your Planck scale logic.
QUOTE
You cannot get a sphere if the radius of the sphere is one Planck length.
Mathematically, in 3D, you can create a sphere from any real number > zero and determine it's surface area as 4pi r^2. Whether or not the Planck length represents the smallest meaningful distance in the Cosmos is yet to be determined. But mathematically, you can certainly determine the spherical area with a radius of one Planck length.
QUOTE (->
| QUOTE |
| You cannot get a sphere if the radius of the sphere is one Planck length. |
Mathematically, in 3D, you can create a sphere from any real number > zero and determine it's surface area as 4pi r^2. Whether or not the Planck length represents the smallest meaningful distance in the Cosmos is yet to be determined. But mathematically, you can certainly determine the spherical area with a radius of one Planck length.
Then I got to ask how can we get a 2D surface, made of an energy structure when Planck Scale is the limit?
I am not sure that you can. But I bet you can speculate on the smallest possible energy wavelength... 1/2 that wavelength would determine the smallest possible sphere radius, yes?
I enjoy reading Baez's work. He combines incredible insights in math, physics and logic to "think outside the sphere."
QUOTE (Baez+)
The point is that bounded linear operators don't preserve the inner product, just the topology, and a structure that is not preserved might as well be ignored, as far as the category is concerned.
Does that not sound like, "what's inside the sphere can be ignored. (which would include the 'thickness' of the 'shell')"? I have some further comments to make on Baez and the link, but I will wait for now...
Yes. As long as you somehow restrict the potential vibrational area to that 2D and as long as any potential vibrational volume in the third dimension is always less than the Plank Length (effectively making the third dimension zero - if, of course the Planck length is indeed the smallest meaningful distance).
Yes. As long as you somehow restrict the potential vibrational area to that 2D and as long as any potential vibrational volume in the third dimension is always less than the Plank Length (effectively making the third dimension zero - if, of course the Planck length is indeed the smallest meaningful distance).
However, do the Planck Scale rule still apply in our 3D?
Isn't that what we are all trying to find out?
QUOTE
Can I make a 2D membrane without imposing a Planck Scale of one unit for the thickness?
Yes. As long as you somehow restrict the potential vibrational area to that 2D and as long as any potential vibrational volume in the third dimension is always less than the Plank Length (effectively making the third dimension zero - if, of course the Planck length is indeed the smallest meaningful distance).
QUOTE (->
| QUOTE |
| Can I make a 2D membrane without imposing a Planck Scale of one unit for the thickness? |
Yes. As long as you somehow restrict the potential vibrational area to that 2D and as long as any potential vibrational volume in the third dimension is always less than the Plank Length (effectively making the third dimension zero - if, of course the Planck length is indeed the smallest meaningful distance).
However, do the Planck Scale rule still apply in our 3D?
Isn't that what we are all trying to find out?
Jal, y, y! , ppm et al,
Tucked away in here ( http://www.answers.com/topic/four-vector#after_ad1 ) is a 'derivation ' of Planck's constant. Once the pretty lights have settled down it seems that (for an EM wave) the ratio of frequency to energy in any inertial frame is fixed.. and Planck got his name attached to the ratio. I'm maybe suggesting that it might be premature to dwell too long on Planck's constant (and length in particular) until the model has settled down a bit. Until you have a mechanism for a 'speed of light' nothing derived from 'c' is going to have much significance in your model. By all means have scale factors ready for tweaking later .. h and c might just appear naturally. By implication I am suggesting you can probably have a mathematical 2D spot without having to worry about the implications in other models.
-C2.
Tucked away in here ( http://www.answers.com/topic/four-vector#after_ad1 ) is a 'derivation ' of Planck's constant. Once the pretty lights have settled down it seems that (for an EM wave) the ratio of frequency to energy in any inertial frame is fixed.. and Planck got his name attached to the ratio. I'm maybe suggesting that it might be premature to dwell too long on Planck's constant (and length in particular) until the model has settled down a bit. Until you have a mechanism for a 'speed of light' nothing derived from 'c' is going to have much significance in your model. By all means have scale factors ready for tweaking later .. h and c might just appear naturally. By implication I am suggesting you can probably have a mathematical 2D spot without having to worry about the implications in other models.
-C2.
Good Day! .... Confused2...Why Not?...All!
Every little bit helps.
Where did reality stop?
Where did pretending start?
Where did pretending get out of hand and become science fiction?
Let’s start with the Compton wavelength for this post.
If there are no problems, I’ll continue with the Schwarzschild radius in the next post.
I will not reproduce the formulas. If you are interested you will look them up on the links supplied.
http://en.wikipedia.org/wiki/Compton_wavelength
http://en.wikipedia.org/wiki/Classical_electron_radius
http://en.wikipedia.org/wiki/Classical_electron_radius
The classical electron radius is built from the electron mass me, the speed of light c and the electron charge e.
The classical electron radius, also known as the Compton radius or the Thomson scattering length is based on a classical (i.e., non-quantum) relativistic model of the electron. Its value is calculated as
(see formula)
where e and m are the electric charge and the mass of the electron, c is the speed of light, and ε0 is the permittivity of free space. Using classical electrostatics, the amount of energy required to assemble a sphere of constant charge density, of radius re and charge e is approximately
(see formula)
.
If this is equated to the relativistic energy of the electron (E = mc2) and solved for re, the above result is obtained.
(Something to discuss with confused2 and Why not?)
In simple terms, the classical electron radius is roughly the size the electron would need to have for its mass to be completely due to its electrostatic potential energy-not taking quantum mechanics into account. We now know that quantum mechanics, indeed quantum field theory, is needed to understand the behavior of electrons at such short distance scales, thus the classical electron radius is no longer regarded as the actual size of an electron. In fact, modern particle physics experiments indicate that the electron is a point particle, i.e. it has no size and its radius is zero
(which means…. Let’s pretend that it is all at the center. THIS IS A MAJOR PRETEND).
Still, the classical electron radius is used in modern classical-limit theories involving the electron, such as non-relativistic Thomson scattering. Also, the classical electron radius is roughly the length scale at which renormalization becomes important in quantum electrodynamics.
(Which means, that if the pretending does not agree to then we will make it agree to the classical electron radius)
The classical electron radius is one of a trio of related units of length, the other two being the Bohr radius a0 and the Compton wavelength of the electron λe. The classical electron radius is built from the electron mass me, the speed of light c and the electron charge e. The Bohr radius is built from me, e and Planck's constant h. The Compton wavelength is built from me, h and c. Any one of these three lengths can be written in terms of any other using the fine structure constant α:
(see formula)
Extrapolating from the initial equation, any mass m0 can be imagined to have an 'electromagnetic radius' similar to the electron's classical radius.
(see formula)
where kC is Coulomb's constant, α is the fine structure constant and is Planck's constant. Such a radius does not exist as a physical entity but it is sometimes useful in theoretical calculations.
(which means…. Let’s pretend. ANOTHER MAJOR PRETEND.)
http://en.wikipedia.org/wiki/Point_particle
http://en.wikipedia.org/wiki/Bohr_radius
http://en.wikipedia.org/wiki/Bohr_radius
the Bohr radius has a value of 5.291772108(18)×10−11 m
While the Bohr model does not correctly describe an atom, the Bohr radius keeps its physical meaning as a characteristic size of the electron cloud in a full quantum-mechanical description
The Bohr radius including the effect of reduced mass can be given by the following equation:
(see formula)
where,
is the Compton wavelength of the proton.
is the Compton wavelength of the electron.
is the fine structure constant.
In the above equation, the effect of the reduced mass is achieved by using the increased Compton wavelength, which is just the Compton wavelengths of the electron and the proton added together.
So fine….You can pretend…. But your pretending has got to be brought back to reality which is the classical electron radius. 2.817940325(28) X 10^-15m
You’ve got to be able to plug in the numbers.
If you want to push and go into science fiction then you got to bring your concepts/theory back to reality which is the classical electron radius. 2.817940325(28) X 10^-15m
That means that you’ve got to be able to plug in the numbers.
Any Comments?
Jal
ps the second half is still to come
Every little bit helps.
Where did reality stop?
Where did pretending start?
Where did pretending get out of hand and become science fiction?
Let’s start with the Compton wavelength for this post.
If there are no problems, I’ll continue with the Schwarzschild radius in the next post.
I will not reproduce the formulas. If you are interested you will look them up on the links supplied.
http://en.wikipedia.org/wiki/Compton_wavelength
QUOTE
Quantum field theory says that associated to any mass there is a length called its Compton wavelength,
The Compton wavelength of the electron is approximately 2.4 × 10-12 meters.
The Compton wavelength is built from the electron mass me, Planck's constant h and the speed of light c.
The Bohr radius is built from me, h and the electron charge e.
The classical electron radius is built from me, c and e.
The Compton wavelength of the electron is approximately 2.4 × 10-12 meters.
The Compton wavelength is built from the electron mass me, Planck's constant h and the speed of light c.
The Bohr radius is built from me, h and the electron charge e.
The classical electron radius is built from me, c and e.
http://en.wikipedia.org/wiki/Classical_electron_radius
QUOTE (->
| QUOTE |
| Quantum field theory says that associated to any mass there is a length called its Compton wavelength, The Compton wavelength of the electron is approximately 2.4 × 10-12 meters. The Compton wavelength is built from the electron mass me, Planck's constant h and the speed of light c. The Bohr radius is built from me, h and the electron charge e. The classical electron radius is built from me, c and e. |
http://en.wikipedia.org/wiki/Classical_electron_radius
The classical electron radius is built from the electron mass me, the speed of light c and the electron charge e.
The classical electron radius, also known as the Compton radius or the Thomson scattering length is based on a classical (i.e., non-quantum) relativistic model of the electron. Its value is calculated as
(see formula)
where e and m are the electric charge and the mass of the electron, c is the speed of light, and ε0 is the permittivity of free space. Using classical electrostatics, the amount of energy required to assemble a sphere of constant charge density, of radius re and charge e is approximately
(see formula)
.
If this is equated to the relativistic energy of the electron (E = mc2) and solved for re, the above result is obtained.
(Something to discuss with confused2 and Why not?)
In simple terms, the classical electron radius is roughly the size the electron would need to have for its mass to be completely due to its electrostatic potential energy-not taking quantum mechanics into account. We now know that quantum mechanics, indeed quantum field theory, is needed to understand the behavior of electrons at such short distance scales, thus the classical electron radius is no longer regarded as the actual size of an electron. In fact, modern particle physics experiments indicate that the electron is a point particle, i.e. it has no size and its radius is zero
(which means…. Let’s pretend that it is all at the center. THIS IS A MAJOR PRETEND).
Still, the classical electron radius is used in modern classical-limit theories involving the electron, such as non-relativistic Thomson scattering. Also, the classical electron radius is roughly the length scale at which renormalization becomes important in quantum electrodynamics.
(Which means, that if the pretending does not agree to then we will make it agree to the classical electron radius)
The classical electron radius is one of a trio of related units of length, the other two being the Bohr radius a0 and the Compton wavelength of the electron λe. The classical electron radius is built from the electron mass me, the speed of light c and the electron charge e. The Bohr radius is built from me, e and Planck's constant h. The Compton wavelength is built from me, h and c. Any one of these three lengths can be written in terms of any other using the fine structure constant α:
(see formula)
Extrapolating from the initial equation, any mass m0 can be imagined to have an 'electromagnetic radius' similar to the electron's classical radius.
(see formula)
where kC is Coulomb's constant, α is the fine structure constant and is Planck's constant. Such a radius does not exist as a physical entity but it is sometimes useful in theoretical calculations.
(which means…. Let’s pretend. ANOTHER MAJOR PRETEND.)
http://en.wikipedia.org/wiki/Point_particle
QUOTE
A point particle is an idealized particle heavily used in physics. Its distinguishing features are that it does not have any volume or surface area; it is zero dimensional. A point particle is often a good approximation of real particles and also more extended bodies. In Newtonian gravitation as well as general relativity and electromagnetism, the respective fields outside of a spherical object are identical to those of a point particle of equal charge/mass located at the center of the sphere.
(which means Let’s pretend, …. As if it was located at the center. THE JUSTIFICATION FOR THE MAJOR PRETENTIONS)
Particle physics suggests that fundamental particles (quarks, electrons and other leptons) may be point particles which can contain mass, charge, spin, and multipole moments without occupying any volume.
(which means Let’s pretend, …. As if it was located at the center. THE JUSTIFICATION FOR THE MAJOR PRETENTIONS)
Particle physics suggests that fundamental particles (quarks, electrons and other leptons) may be point particles which can contain mass, charge, spin, and multipole moments without occupying any volume.
http://en.wikipedia.org/wiki/Bohr_radius
QUOTE (->
| QUOTE |
| A point particle is an idealized particle heavily used in physics. Its distinguishing features are that it does not have any volume or surface area; it is zero dimensional. A point particle is often a good approximation of real particles and also more extended bodies. In Newtonian gravitation as well as general relativity and electromagnetism, the respective fields outside of a spherical object are identical to those of a point particle of equal charge/mass located at the center of the sphere. (which means Let’s pretend, …. As if it was located at the center. THE JUSTIFICATION FOR THE MAJOR PRETENTIONS) Particle physics suggests that fundamental particles (quarks, electrons and other leptons) may be point particles which can contain mass, charge, spin, and multipole moments without occupying any volume. |
http://en.wikipedia.org/wiki/Bohr_radius
the Bohr radius has a value of 5.291772108(18)×10−11 m
While the Bohr model does not correctly describe an atom, the Bohr radius keeps its physical meaning as a characteristic size of the electron cloud in a full quantum-mechanical description
The Bohr radius including the effect of reduced mass can be given by the following equation:
(see formula)
where,
is the Compton wavelength of the proton.
is the Compton wavelength of the electron.
is the fine structure constant.
In the above equation, the effect of the reduced mass is achieved by using the increased Compton wavelength, which is just the Compton wavelengths of the electron and the proton added together.
So fine….You can pretend…. But your pretending has got to be brought back to reality which is the classical electron radius. 2.817940325(28) X 10^-15m
You’ve got to be able to plug in the numbers.
If you want to push and go into science fiction then you got to bring your concepts/theory back to reality which is the classical electron radius. 2.817940325(28) X 10^-15m
That means that you’ve got to be able to plug in the numbers.
Any Comments?
Jal
ps the second half is still to come
Hi jal et al,
Surely you want at least the actual radius of an electron as determined by HEP experiments. I recall many mutterings along the lines of it being much smaller than the classically calculated radius.. but not what it actually is or how it was found to be that. From memory it is 'not larger than' .. ie could potentially be zero.
I'm googling for
electron radius particle accelerator measurement
but not found anything in the first four pages .. ??
Thought I'd better show I'm paying attention.
-C2.
Surely you want at least the actual radius of an electron as determined by HEP experiments. I recall many mutterings along the lines of it being much smaller than the classically calculated radius.. but not what it actually is or how it was found to be that. From memory it is 'not larger than' .. ie could potentially be zero.
I'm googling for
electron radius particle accelerator measurement
but not found anything in the first four pages .. ??
Thought I'd better show I'm paying attention.
-C2.
Hey jal, C2, et al.
In response to jal's argument (which, while excellent, is (IMHO) limiting the strength of the model) and C2's question, I have found this... Hope it helps...
From...
http://www.citebase.org/fulltext?format=ap...ron%20radius%22
jal, I am not trying to discourage, just trying to make sure we are all agree on fact - vs- fiction.
P.s. I googled "hep electron radius".
In response to jal's argument (which, while excellent, is (IMHO) limiting the strength of the model) and C2's question, I have found this... Hope it helps...
QUOTE
From the data of the LEP collaborations at 183 and 189 GeV we extract the following upper limit on the electron radius at 95% confidence level:
re < 2.8 · 10−19 m. (12) This limit is one order of magnitude lower than the limit derived from (g−2)e measurements in the case where the deviations from the SM of the magnetic dipole moment of the electron depend quadratically on its mass. High energy analyses have been performed in interactions involving electrons and quarks, assuming a single form-factor for all fermions. The H1 collaboration at HERA uses deep inelastic scattering and obtains a limit of r < 26 · 10−19 m at 95 % confidence level [23]. The CDF collaboration at the TEVATRON studies the Drell-Yan process to put a limit of r < 5.6 · 10−19 m at 95 % confidence level [24].
re < 2.8 · 10−19 m. (12) This limit is one order of magnitude lower than the limit derived from (g−2)e measurements in the case where the deviations from the SM of the magnetic dipole moment of the electron depend quadratically on its mass. High energy analyses have been performed in interactions involving electrons and quarks, assuming a single form-factor for all fermions. The H1 collaboration at HERA uses deep inelastic scattering and obtains a limit of r < 26 · 10−19 m at 95 % confidence level [23]. The CDF collaboration at the TEVATRON studies the Drell-Yan process to put a limit of r < 5.6 · 10−19 m at 95 % confidence level [24].
From...
http://www.citebase.org/fulltext?format=ap...ron%20radius%22
jal, I am not trying to discourage, just trying to make sure we are all agree on fact - vs- fiction.
P.s. I googled "hep electron radius".
Why Not?
discourage.... not with good new like that ...re < 2.8 · 10−19 m.
http://www.citebase.org/fulltext?format=ap...ron%20radius%22
Search for TeV Strings and New Phenomena
in Bhabha Scattering at LEP2
Dimitri Bourilkov∗
Institute for Particle Physics (IPP), ETH Z¨urich,
CH-8093 Z¨urich, Switzerland
16 Feb 2000
Somebody has been sitting on this info. since 2000
It supports what I have been presenting.
Now..... the hoop is big enough for the electron.
(I hope that you don't find anything to weaken what I've been saying. I'll have to find another job. )
jal
I'll wait for more good inputs before doing the second part.
discourage.... not with good new like that ...re < 2.8 · 10−19 m.
http://www.citebase.org/fulltext?format=ap...ron%20radius%22
Search for TeV Strings and New Phenomena
in Bhabha Scattering at LEP2
Dimitri Bourilkov∗
Institute for Particle Physics (IPP), ETH Z¨urich,
CH-8093 Z¨urich, Switzerland
16 Feb 2000
Somebody has been sitting on this info. since 2000
QUOTE
Abstract
A combined analysis of the data on Bhabha scattering at centre-of-mass energies 183 and 189 GeV from the LEP experiments ALEPH, L3 and OPAL is performed to search for effects of TeV strings in quantum gravity models with large extra dimensions. No statistically significant deviations from the Standard Model expectations are observed and lower limit on the string scale MS = 0.631 TeV at 95 % confidence level is derived.
The data are used to set lower limits on the scale of contact interactions ranging from 4.2 to 16.2 TeV depending on the model. In a complementary analysis we derive an upper limit on the electron size of 2.8 · 10−19 m at 95 % confidence level.
A combined analysis of the data on Bhabha scattering at centre-of-mass energies 183 and 189 GeV from the LEP experiments ALEPH, L3 and OPAL is performed to search for effects of TeV strings in quantum gravity models with large extra dimensions. No statistically significant deviations from the Standard Model expectations are observed and lower limit on the string scale MS = 0.631 TeV at 95 % confidence level is derived.
The data are used to set lower limits on the scale of contact interactions ranging from 4.2 to 16.2 TeV depending on the model. In a complementary analysis we derive an upper limit on the electron size of 2.8 · 10−19 m at 95 % confidence level.
It supports what I have been presenting.
Now..... the hoop is big enough for the electron.
(I hope that you don't find anything to weaken what I've been saying. I'll have to find another job.
)jal
I'll wait for more good inputs before doing the second part.
Hey jal,
Now you've lost me. In you previous post you said,
The results from the link state that the maximum (it could still be smaller) radius of an electron is ~ 10 -19m. Don't want you to find another job, just explain a bit more...
Now you've lost me.
In you previous post you said,QUOTE
So fine….You can pretend…. But your pretending has got to be brought back to reality which is the classical electron radius. 2.817940325(28) X 10^-15m
You’ve got to be able to plug in the numbers.
If you want to push and go into science fiction then you got to bring your concepts/theory back to reality which is the classical electron radius. 2.817940325(28) X 10^-15m
You’ve got to be able to plug in the numbers.
If you want to push and go into science fiction then you got to bring your concepts/theory back to reality which is the classical electron radius. 2.817940325(28) X 10^-15m
The results from the link state that the maximum (it could still be smaller) radius of an electron is ~ 10 -19m. Don't want you to find another job, just explain a bit more...
Hi Why Not?
Yes.... it applies to everyone... even me.
If I proposed a theory that fits only 10^-15m and it cannot fit 10 -19m I would be out of a job
So far..... I don't have much of a theory. It's more of a concept.
I guess that it could get shot down by what we observe our universe to be.
That comes from the particle experiments. I'm using the word particle "loosely" to include the electron as an "energy package" of some kind.
My "spot" could be represented by a large vibrating string as I have said before.
Help me out here....How is the electron size limiting the strength of my model?
You know how it goes......love makes you blind
jal
Yes.... it applies to everyone... even me.
If I proposed a theory that fits only 10^-15m and it cannot fit 10 -19m I would be out of a job
So far..... I don't have much of a theory. It's more of a concept.
I guess that it could get shot down by what we observe our universe to be.
That comes from the particle experiments. I'm using the word particle "loosely" to include the electron as an "energy package" of some kind.
My "spot" could be represented by a large vibrating string as I have said before.
Help me out here....How is the electron size limiting the strength of my model?
You know how it goes......love makes you blind
jal
Hey jal,
The "limiting" part does not specifically have to do with the electron, it has to do with your insistence on 10 -15 as the boundary between science fiction and reality (with the evidence that the electron radius < 10 -19). So I guess I still do not understand what you meant by...
Maybe it would help if you explained your "hoop" once again. I think the first time I saw that expression you were discussing 10 -17??? What is 10 -17? What is the hoop?
Maybe it would help if you explained your "hoop" once again. I think the first time I saw that expression you were discussing 10 -17??? What is 10 -17? What is the hoop?
It supports what I have been presenting.
Now..... the hoop is big enough for the electron.
The "limiting" part does not specifically have to do with the electron, it has to do with your insistence on 10 -15 as the boundary between science fiction and reality (with the evidence that the electron radius < 10 -19). So I guess I still do not understand what you meant by...
QUOTE
So fine….You can pretend…. But your pretending has got to be brought back to reality which is the classical electron radius. 2.817940325(28) X 10^-15m
Maybe it would help if you explained your "hoop" once again. I think the first time I saw that expression you were discussing 10 -17??? What is 10 -17? What is the hoop?
QUOTE (->
| QUOTE |
| So fine….You can pretend…. But your pretending has got to be brought back to reality which is the classical electron radius. 2.817940325(28) X 10^-15m |
Maybe it would help if you explained your "hoop" once again. I think the first time I saw that expression you were discussing 10 -17??? What is 10 -17? What is the hoop?
It supports what I have been presenting.
Now..... the hoop is big enough for the electron.
Good Day Why Not?
I’m the nobody…I’m the outsider….. I’m learning.
Will I read something and get wrong info?…. yes ……. Will I get some info and not understand it and make harsh statements? ……..yes
You, yq and C2 are the only ones that have attempted to help me by actually discussing this subject.
What the following paper does is to show that they are tying their theories into reality. (Sooo.... that's why I made the post about pretending and fiction.)
http://arxiv.org/PS_cache/hep-ph/pdf/0307/0307284.pdf
The size of my “spot” (which I have not tried to do with math) is determined by “coupling to electrons, to u, d, or s quarks”???
Therefore, it must be in that range 10^-17 to -19.
If the maximum electron size gets smaller then it will affect the theories.
The reference to the “hoop” is because I like the idea that there must be room for things to happen without clashing into each other.
I want to get a better understanding of Planck Scale. I could have it all wrong. I’ll only find out by having a discussion.
From the above paper, (which I’m glad to bring back down for reference)
In particular, the radius of new dimensions can fluctuate independently at each
point in our four-dimensional spacetime.
Therefore, we are having a discussion on Planck scale.
What are the limitations imposed by the Planck Scale?
Your “guiding hand” could be more direct. I won’t get offended.
The second part of "pretending" is still to come.
jal
I’m the nobody…I’m the outsider….. I’m learning.
Will I read something and get wrong info?…. yes ……. Will I get some info and not understand it and make harsh statements? ……..yes
You, yq and C2 are the only ones that have attempted to help me by actually discussing this subject.
What the following paper does is to show that they are tying their theories into reality. (Sooo.... that's why I made the post about pretending and fiction.)
http://arxiv.org/PS_cache/hep-ph/pdf/0307/0307284.pdf
QUOTE
INVERSE-SQUARE LAW TESTS
p.57 ISL has been verified down to a distance λ = 200 µm. At length scales between
20 nm and 4 mm, many square decades in Yukawa-parameter space have been
ruled out. These results have eliminated some specific theoretical scenarios, but
many other interesting ideas are still viable because their predicted effects lie
somewhat below the current experimental limits.
p.11 For instance, in theories of gravity, the concept of entropy must be generalized because entropy cannot be an extensive quantity scaling like volume. In fact, strong evidence favors an upper bound on the entropy of any region that scales as the
surface area of the boundary of the region (34, 35, 36).
A further conjecture, the “holographic principle,” suggests that this entropy bound indicates that the fundamental degrees of freedom of a gravitational theory can actually be formulated in a lower-dimensional theory. Reference (37) reviews these ideas and their subsequent development.
Extra dimensions might seem to contradict the holographic assertion that the
fundamental theory is actually lower-dimensional. However, as comprehensively
reviewed in Reference (38), the discovery that string theory on certain spacetimes
with n noncompact dimensions is dual to a nongravitational gauge theory with
n−1 dimensions provides additional theoretical evidence for holography, as well
as for string theory.
p.17 In theories of gravity, the geometry of spacetime is dynamical and can fluctuate.
In particular, the radius of new dimensions can fluctuate independently at each
point in our four-dimensional spacetime.
Thus, low-energy effective theories of compact extra dimensions inevitably contain spin-0 fields parameterizing the radii of the new dimensions.
p.23 In order for a scalar particle, φ, to exert a coherent force on matter, it must
have a Yukawa coupling to electrons, to u, d, or s quarks, to the square of the
gluon field strength, or to higher-dimension operators such as certain four-quark
operators. The candidates of lowest dimension are
(see formula)
When embedded in the standard model, these all arise from dimension-5 operators,
hence the common factor of 1/f, where f has dimensions of mass.
This scale approximately coincides with the scale at which naturalness of the electroweak-breaking sector demands new physics. A scalar coupled more weakly would correspond to a higher value for _.
p.57 ISL has been verified down to a distance λ = 200 µm. At length scales between
20 nm and 4 mm, many square decades in Yukawa-parameter space have been
ruled out. These results have eliminated some specific theoretical scenarios, but
many other interesting ideas are still viable because their predicted effects lie
somewhat below the current experimental limits.
p.11 For instance, in theories of gravity, the concept of entropy must be generalized because entropy cannot be an extensive quantity scaling like volume. In fact, strong evidence favors an upper bound on the entropy of any region that scales as the
surface area of the boundary of the region (34, 35, 36).
A further conjecture, the “holographic principle,” suggests that this entropy bound indicates that the fundamental degrees of freedom of a gravitational theory can actually be formulated in a lower-dimensional theory. Reference (37) reviews these ideas and their subsequent development.
Extra dimensions might seem to contradict the holographic assertion that the
fundamental theory is actually lower-dimensional. However, as comprehensively
reviewed in Reference (38), the discovery that string theory on certain spacetimes
with n noncompact dimensions is dual to a nongravitational gauge theory with
n−1 dimensions provides additional theoretical evidence for holography, as well
as for string theory.
p.17 In theories of gravity, the geometry of spacetime is dynamical and can fluctuate.
In particular, the radius of new dimensions can fluctuate independently at each
point in our four-dimensional spacetime.
Thus, low-energy effective theories of compact extra dimensions inevitably contain spin-0 fields parameterizing the radii of the new dimensions.
p.23 In order for a scalar particle, φ, to exert a coherent force on matter, it must
have a Yukawa coupling to electrons, to u, d, or s quarks, to the square of the
gluon field strength, or to higher-dimension operators such as certain four-quark
operators. The candidates of lowest dimension are
(see formula)
When embedded in the standard model, these all arise from dimension-5 operators,
hence the common factor of 1/f, where f has dimensions of mass.
This scale approximately coincides with the scale at which naturalness of the electroweak-breaking sector demands new physics. A scalar coupled more weakly would correspond to a higher value for _.
The size of my “spot” (which I have not tried to do with math) is determined by “coupling to electrons, to u, d, or s quarks”???
Therefore, it must be in that range 10^-17 to -19.
If the maximum electron size gets smaller then it will affect the theories.
The reference to the “hoop” is because I like the idea that there must be room for things to happen without clashing into each other.
I want to get a better understanding of Planck Scale. I could have it all wrong. I’ll only find out by having a discussion.
From the above paper, (which I’m glad to bring back down for reference)
In particular, the radius of new dimensions can fluctuate independently at each
point in our four-dimensional spacetime.
Therefore, we are having a discussion on Planck scale.
What are the limitations imposed by the Planck Scale?
Your “guiding hand” could be more direct. I won’t get offended.
The second part of "pretending" is still to come.
jal
I missed the edit deadline
n-1 = My SPOT.
JAL
QUOTE
...is dual to a nongravitational gauge theory with
n−1 dimensions provides additional theoretical evidence for holography, as well
as for string theory.
n−1 dimensions provides additional theoretical evidence for holography, as well
as for string theory.
n-1 = My SPOT.
JAL
Hey jal,
My lack of "direct-ness" is not from an effort to be non-offensive, it is because I am trying to learn and I still do not fully understand what your model is trying to say. However, your last post certainly helped.
The discussion regarding the Planck Scale and it's relation to other length scales that I have found most useful is http://math.ucr.edu/home/baez/lengths.html. Not sure if it will help, but hopefully it will answer some of your questions regarding the limitations (boundaries?) that result from the Planck Scale.
Also, you may find this paper interesting http://arxiv.org/PS_cache/hep-th/pdf/0307/0307174.pdf
My lack of "direct-ness" is not from an effort to be non-offensive, it is because I am trying to learn and I still do not fully understand what your model is trying to say. However, your last post certainly helped.
The discussion regarding the Planck Scale and it's relation to other length scales that I have found most useful is http://math.ucr.edu/home/baez/lengths.html. Not sure if it will help, but hopefully it will answer some of your questions regarding the limitations (boundaries?) that result from the Planck Scale.
Also, you may find this paper interesting http://arxiv.org/PS_cache/hep-th/pdf/0307/0307174.pdf
QUOTE ( from the Abstract+)
We consider Uncertainty Principles which take into account the role of gravity and the possible existence of extra spatial dimensions. Explicit expressions for such Generalized Uncertainty Principles in 4+n dimensions are given and their holographic properties investigated. In particular, we show that the predicted number of degrees of freedom enclosed in a given spatial volume matches the holographic counting only for one of the available generalizations and without extra
dimensions.
And this one as well... http://arxiv.org/PS_cache/gr-qc/pdf/0201/0201030.pdf... Baez as well on Ng and van Dam.
Looking forward to "pretending" part 2.
dimensions.
And this one as well... http://arxiv.org/PS_cache/gr-qc/pdf/0201/0201030.pdf... Baez as well on Ng and van Dam.
Looking forward to "pretending" part 2.
Hey again jal,
I guess I could summarize my previous post by saying that we don't know. What we do know (as verified by experiment) is the value of c, G and h, the reality (within bounds) of QM and SR. Putting those numbers together, with the theories give us the Planck Scale - the "starting point" so to speak. Theoretical work during the past few decades has far outpaced experimentation. So in a sense, we can use the Planck Scale as one extreme and from there try to work out what might be found in the future experimental data between 10 -35m and 10 -15m. I like what your model say (to the level of my understanding anyway). C2 was right. Maybe you should not worry about "size" at the moment except at the extremes. Figure out the minimum and maximum size that is applicable to your model (the bounds) and go from there. And keep in mind, I am just a curious nobody as well!
I guess I could summarize my previous post by saying that we don't know. What we do know (as verified by experiment) is the value of c, G and h, the reality (within bounds) of QM and SR. Putting those numbers together, with the theories give us the Planck Scale - the "starting point" so to speak. Theoretical work during the past few decades has far outpaced experimentation. So in a sense, we can use the Planck Scale as one extreme and from there try to work out what might be found in the future experimental data between 10 -35m and 10 -15m. I like what your model say (to the level of my understanding anyway). C2 was right. Maybe you should not worry about "size" at the moment except at the extremes. Figure out the minimum and maximum size that is applicable to your model (the bounds) and go from there. And keep in mind, I am just a curious nobody as well!
Why Not? and All
heheheh
Since my SPOT is a further development of the "holographic principle" I want to quote one of your links. It's going to come back to haunt you and give you nightmares.
Tomorrow.... I'll post the second part. I'll wait in case someone has a relevant links that should be included at this stage.
Generalized Uncertainty Principle, Extra-dimensions
and Holography
Fabio Scardiglia∗ and Roberto Casadiob†
aInstitute for Theoretical Physics, University of Bern,
Sidlerstrasse 5, 3012 Bern, Switzerland
bDipartimento di Fisica, Universit`a di Bologna and I.N.F.N., Sezione di Bologna,
via Irnerio 46, 40126 Bologna, Italy
May 23, 2006
http://arxiv.org/PS_cache/hep-th/pdf/0307/0307174.pdf
heheheh
Since my SPOT is a further development of the "holographic principle" I want to quote one of your links. It's going to come back to haunt you and give you nightmares.
Tomorrow.... I'll post the second part. I'll wait in case someone has a relevant links that should be included at this stage.
Generalized Uncertainty Principle, Extra-dimensions
and Holography
Fabio Scardiglia∗ and Roberto Casadiob†
aInstitute for Theoretical Physics, University of Bern,
Sidlerstrasse 5, 3012 Bern, Switzerland
bDipartimento di Fisica, Universit`a di Bologna and I.N.F.N., Sezione di Bologna,
via Irnerio 46, 40126 Bologna, Italy
May 23, 2006
http://arxiv.org/PS_cache/hep-th/pdf/0307/0307174.pdf
On the other hand, the holographic principle is claimed to apply to all of the gravitational systems. The existence of GUP’s satisfying the holography in four dimensions (one of the main examples is due to Ng and Van Dam [3]) led us to explore the holographic properties of the GUP’s extended to the brane-world scenarios. The results, at least for the examples we considered, are quite surprising. The expected holographic scaling indeed seems to hold only in four dimensions, and only for the Ng and van Dam’s GUP. When extra spatial dimensions are admitted, the holography
is destroyed. This fact allows two different interpretations: either the holographic principle is not universal and does not apply when extra dimensions are present; or, on the contrary, we take seriously the holographic claim in any number of dimensions, and our results are therefore evidence against the existence of extra dimensions.
A number of general remarks are however in order. First of all, we cannot claim that our list of possible GUP’s is complete and other relations might be derived in different contexts which accommodate for both the holography and extra dimensions. Further, one might find hard to accept that quantum mechanics and general relativity enter the construction of GUP’s on the same footing, since the former is supposed to be a fundamental framework for all theories while the latter can be just regarded as a theory of the gravitational interaction. We might agree on the point of view that GUP’s must be considered as “effective” (phenomenological) bounds valid at low energy (below the Planck scale) rather than “fundamental” relations. This would in fact reconcile our
result that four dimensions are preferred with the fact that string theory (as a consistent theory of quantum gravity) requires more dimensions through the compactification which must occur at low energy, as we mentioned above. Let us also note that general relativity (contrary to usual field theories) determines the space-time including the causality structure, and the latter is an essential ingredient in all actual measurements. It is therefore (at least) equally hard to conceive uncertainty relations which neglect general relativity at all. This conclusion would become even stronger in the presence of extra dimensions, since the fundamental energy scale of gravity is then lowered [1, 2]
(possibly) within the scope of present or near-future experiments and the gravitational radius of matter sources is correspondingly enlarged [7].
A final remark regards cases with less than four dimensions. Since Einstein gravity does not propagate in such space-times and no direct analogue of the Schwarzschild solution exists, one expects a qualitative difference with respect to the cases that we have considered here. For instance, a point-like source in three dimensions would generate a flat space-time with a conical singularity and no horizon 1. Consequently, one does expect that the usual Heisenberg uncertainty relations hold with no corrections for gravity.
If you see that we need some more info....add a link.
jal
Hey jal,
Let the nightmares continue!!!
Just keep in mind the last link, "Baez as well on Ng and van Dam."
QUOTE
C2 was right. Maybe you should not worry about "size" at the moment except at the extremes. Figure out the minimum and maximum size that is applicable to your model (the bounds) and go from there.
heheheh
Since my SPOT is a further development of the "holographic principle" I want to quote one of your links. It's going to come back to haunt you and give you nightmares.
Tomorrow.... I'll post the second part. I'll wait in case someone has a relevant links that should be included at this stage.
Generalized Uncertainty Principle, Extra-dimensions
and Holography
Fabio Scardiglia∗ and Roberto Casadiob†
aInstitute for Theoretical Physics, University of Bern,
Sidlerstrasse 5, 3012 Bern, Switzerland
bDipartimento di Fisica, Universit`a di Bologna and I.N.F.N., Sezione di Bologna,
via Irnerio 46, 40126 Bologna, Italy
May 23, 2006
http://arxiv.org/PS_cache/hep-th/pdf/0307/0307174.pdf
QUOTE (->
| QUOTE |
| C2 was right. Maybe you should not worry about "size" at the moment except at the extremes. Figure out the minimum and maximum size that is applicable to your model (the bounds) and go from there. |
heheheh
Since my SPOT is a further development of the "holographic principle" I want to quote one of your links. It's going to come back to haunt you and give you nightmares.
Tomorrow.... I'll post the second part. I'll wait in case someone has a relevant links that should be included at this stage.
Generalized Uncertainty Principle, Extra-dimensions
and Holography
Fabio Scardiglia∗ and Roberto Casadiob†
aInstitute for Theoretical Physics, University of Bern,
Sidlerstrasse 5, 3012 Bern, Switzerland
bDipartimento di Fisica, Universit`a di Bologna and I.N.F.N., Sezione di Bologna,
via Irnerio 46, 40126 Bologna, Italy
May 23, 2006
http://arxiv.org/PS_cache/hep-th/pdf/0307/0307174.pdf
On the other hand, the holographic principle is claimed to apply to all of the gravitational systems. The existence of GUP’s satisfying the holography in four dimensions (one of the main examples is due to Ng and Van Dam [3]) led us to explore the holographic properties of the GUP’s extended to the brane-world scenarios. The results, at least for the examples we considered, are quite surprising. The expected holographic scaling indeed seems to hold only in four dimensions, and only for the Ng and van Dam’s GUP. When extra spatial dimensions are admitted, the holography
is destroyed. This fact allows two different interpretations: either the holographic principle is not universal and does not apply when extra dimensions are present; or, on the contrary, we take seriously the holographic claim in any number of dimensions, and our results are therefore evidence against the existence of extra dimensions.
A number of general remarks are however in order. First of all, we cannot claim that our list of possible GUP’s is complete and other relations might be derived in different contexts which accommodate for both the holography and extra dimensions. Further, one might find hard to accept that quantum mechanics and general relativity enter the construction of GUP’s on the same footing, since the former is supposed to be a fundamental framework for all theories while the latter can be just regarded as a theory of the gravitational interaction. We might agree on the point of view that GUP’s must be considered as “effective” (phenomenological) bounds valid at low energy (below the Planck scale) rather than “fundamental” relations. This would in fact reconcile our
result that four dimensions are preferred with the fact that string theory (as a consistent theory of quantum gravity) requires more dimensions through the compactification which must occur at low energy, as we mentioned above. Let us also note that general relativity (contrary to usual field theories) determines the space-time including the causality structure, and the latter is an essential ingredient in all actual measurements. It is therefore (at least) equally hard to conceive uncertainty relations which neglect general relativity at all. This conclusion would become even stronger in the presence of extra dimensions, since the fundamental energy scale of gravity is then lowered [1, 2]
(possibly) within the scope of present or near-future experiments and the gravitational radius of matter sources is correspondingly enlarged [7].
A final remark regards cases with less than four dimensions. Since Einstein gravity does not propagate in such space-times and no direct analogue of the Schwarzschild solution exists, one expects a qualitative difference with respect to the cases that we have considered here. For instance, a point-like source in three dimensions would generate a flat space-time with a conical singularity and no horizon 1. Consequently, one does expect that the usual Heisenberg uncertainty relations hold with no corrections for gravity.
If you see that we need some more info....add a link.
jal
Hey jal,QUOTE
Since my SPOT is a further development of the "holographic principle"
Let the nightmares continue!!!
Just keep in mind the last link, "Baez as well on Ng and van Dam."
Holographic principle.
A nightmare shared is a nightmare shared. Yup, it's really scary. I'm not sure whether the idea is that you set up everything 'statically' and when you press the 'go' button it all springs into life and the laws of physics emerge naturally.. or 'something else'.
Essence of here:
http://www.damtp.cam.ac.uk/user/gr/public/holo/
Assertion 1 The first assertion of the Holographic Principle is that all of the information contained in some region of space can be represented as a `Hologram' - a theory which `lives' on the boundary of that region. For example, if the region of space in question is the DAMTP Tearoom, then the holographic principle asserts that all of the physics which takes place in the DAMTP Tearoom can be represented by a theory which is defined on the walls of the Tearoom.
Assertion 2 The second assertion of the Holographic Principle is that the theory on the boundary of the region of space in question should contain at most one degree of freedom per Planck area.
......
In fact, the way in which the Holographic Principle appears in M-theory is much more subtle. In M-theory we are the shadows on the wall. The `room' is some larger, five-dimensional spacetime and our four-dimensional world is just the boundary of this larger space. If we try to move away from the wall, we are moving into an extra dimension of space - a fifth dimension. In fact, people have recently been trying to think of ways in which we might actually experimentally `probe' this fifth dimension.
Wiki's entry is slightly different..
http://en.wikipedia.org/wiki/Holographic_principle
Wiki's entry is slightly different..
http://en.wikipedia.org/wiki/Holographic_principle
The holographic principle also states that at most there is one degree of freedom (or 1 Boltzmann constant k unit of maximum entropy) for every four Planck area in that theory. This can be stated as the Bekenstein bound
This takes us into a 'think of a number' realm for the number of degrees of freedom per Planck area(s).
C2 thoughts ..
Are we using an area to describe the properties of a region 'seen through' that area? I suspect the intention is that the surface contains no information about where the source is .. it just has information or 'not information' in it.
It occurs to me that it's difficult to tile the surface of a sphere with anything so a cube would seem to be the natural way to go. Assume I am inside a cube .. the suggestion seems to be that I could find out everything about my place in the world by considering each of the six faces of the cube. Conversely the universe can find out everything it needs to know about me by considering the six faces of the cube that surround me.
As the cube gets smaller the condition of 'information' or 'not information' at each face makes the situation increasingly uncertain, maybe this is the intention. Unless we are prepared to lose information it seems to me that the information presented at each face will need to change with time to (gradually) build up a perfect picture of what the box contains. If we chose a big cube then we would get a more accurate picture of what was inside it .. but changes at each area with time would start to defeat the accuracy of our observation.
Jals point about hoops applies here .. the thing that gives properties to the smallest closed box must be smaller then the box.
Madness?
-C2.
A nightmare shared is a nightmare shared. Yup, it's really scary. I'm not sure whether the idea is that you set up everything 'statically' and when you press the 'go' button it all springs into life and the laws of physics emerge naturally.. or 'something else'.
Essence of here:
http://www.damtp.cam.ac.uk/user/gr/public/holo/
QUOTE
Assertion 1 The first assertion of the Holographic Principle is that all of the information contained in some region of space can be represented as a `Hologram' - a theory which `lives' on the boundary of that region. For example, if the region of space in question is the DAMTP Tearoom, then the holographic principle asserts that all of the physics which takes place in the DAMTP Tearoom can be represented by a theory which is defined on the walls of the Tearoom.
Assertion 2 The second assertion of the Holographic Principle is that the theory on the boundary of the region of space in question should contain at most one degree of freedom per Planck area.
......
In fact, the way in which the Holographic Principle appears in M-theory is much more subtle. In M-theory we are the shadows on the wall. The `room' is some larger, five-dimensional spacetime and our four-dimensional world is just the boundary of this larger space. If we try to move away from the wall, we are moving into an extra dimension of space - a fifth dimension. In fact, people have recently been trying to think of ways in which we might actually experimentally `probe' this fifth dimension.
Wiki's entry is slightly different..
http://en.wikipedia.org/wiki/Holographic_principle
QUOTE (->
| QUOTE |
Assertion 1 The first assertion of the Holographic Principle is that all of the information contained in some region of space can be represented as a `Hologram' - a theory which `lives' on the boundary of that region. For example, if the region of space in question is the DAMTP Tearoom, then the holographic principle asserts that all of the physics which takes place in the DAMTP Tearoom can be represented by a theory which is defined on the walls of the Tearoom. Assertion 2 The second assertion of the Holographic Principle is that the theory on the boundary of the region of space in question should contain at most one degree of freedom per Planck area. ...... In fact, the way in which the Holographic Principle appears in M-theory is much more subtle. In M-theory we are the shadows on the wall. The `room' is some larger, five-dimensional spacetime and our four-dimensional world is just the boundary of this larger space. If we try to move away from the wall, we are moving into an extra dimension of space - a fifth dimension. In fact, people have recently been trying to think of ways in which we might actually experimentally `probe' this fifth dimension. |
Wiki's entry is slightly different..
http://en.wikipedia.org/wiki/Holographic_principle
The holographic principle also states that at most there is one degree of freedom (or 1 Boltzmann constant k unit of maximum entropy) for every four Planck area in that theory. This can be stated as the Bekenstein bound
This takes us into a 'think of a number' realm for the number of degrees of freedom per Planck area(s).
C2 thoughts ..
Are we using an area to describe the properties of a region 'seen through' that area? I suspect the intention is that the surface contains no information about where the source is .. it just has information or 'not information' in it.
It occurs to me that it's difficult to tile the surface of a sphere with anything so a cube would seem to be the natural way to go. Assume I am inside a cube .. the suggestion seems to be that I could find out everything about my place in the world by considering each of the six faces of the cube. Conversely the universe can find out everything it needs to know about me by considering the six faces of the cube that surround me.
As the cube gets smaller the condition of 'information' or 'not information' at each face makes the situation increasingly uncertain, maybe this is the intention. Unless we are prepared to lose information it seems to me that the information presented at each face will need to change with time to (gradually) build up a perfect picture of what the box contains. If we chose a big cube then we would get a more accurate picture of what was inside it .. but changes at each area with time would start to defeat the accuracy of our observation.
Jals point about hoops applies here .. the thing that gives properties to the smallest closed box must be smaller then the box.
Madness?
-C2.
Good Day! ALL!
Oh! How I wish that I was that good.
Confused2
Geee! thanks ... forgot to put that link about Holographic principle for everyone to see.
Oh! How I wish that I was that good.
Confused2
Geee! thanks ... forgot to put that link about Holographic principle for everyone to see.
It occurs to me that it's difficult to tile the surface of a sphere with anything so a cube would seem to be the natural way to go. Assume I am inside a cube .. the suggestion seems to be that I could find out everything about my place in the world by considering each of the six faces of the cube.
You can consider …..that packing in 2d is 6…..and packing in 3d is 12.
Also…. Do not forget that the surface area of a sphere (3D) is equal to 4 2d areas
We did the math in the previous posts.
Why Not?
I don’t know why, ………………….. but the fine structure is also important.
http://en.wikipedia.org/wiki/Fine_structure_constant
I'm not forgetting J. Baez
http://math.ucr.edu/home/baez/lengths.html
I'm not forgetting J. Baez
http://math.ucr.edu/home/baez/lengths.html
It's worth noting that the classical electron radius is 1/137 as big as the Compton wavelength of the electron - the all-important fine structure constant again! So we have 3 length scales:
• Bohr radius r - about 5 × 10-11 meters
• Compton wavelength LCompton - about 4 × 10-13 meters
• Classical electron radius re - about 3 × 10-15 meters
each of which is 1/137 as big as the previous one. The Bohr radius depends only on hbar, e, and m. The Compton wavelength depends only on hbar, c, and m. The classical electron radius depends only on e, c, and m. Nice set-up, huh? I suppose I should relent and tell you that this mysterious number 1/137, the fine structure constant, is just
e2/hbar c.
It's a dimensionless constant depending only on hbar, e, and c. In this respect it's more fundamental than any of the length scales mentioned, because all the length scales mentioned involve the electron mass, and one could work them out for particles other than the electron, whereas
e2/hbar c
is truly universal, once you remember that the "electron charge" is nothing specific to the electron but is a basic aspect of electromagnetism that applies to all charged particles. (Yes, quarks apparently have charge 1/3, but that doesn't really affect my point.) In other words, the fine structure constant is a dimensionless measure of how strong the electromagnetic force is, and we have seen that it sets the ratio of 3 important length scales.
Things are coming along just fine for part two
jal
QUOTE
I'm not sure whether the idea is that you set up everything 'statically' and when you press the 'go' button it all springs into life and the laws of physics emerge naturally.. or 'something else'.
Oh! How I wish that I was that good. Confused2
Geee! thanks ... forgot to put that link about Holographic principle for everyone to see.
QUOTE (->
| QUOTE |
| I'm not sure whether the idea is that you set up everything 'statically' and when you press the 'go' button it all springs into life and the laws of physics emerge naturally.. or 'something else'. |
Oh! How I wish that I was that good. Confused2
Geee! thanks ... forgot to put that link about Holographic principle for everyone to see.
It occurs to me that it's difficult to tile the surface of a sphere with anything so a cube would seem to be the natural way to go. Assume I am inside a cube .. the suggestion seems to be that I could find out everything about my place in the world by considering each of the six faces of the cube.
You can consider …..that packing in 2d is 6…..and packing in 3d is 12.
Also…. Do not forget that the surface area of a sphere (3D) is equal to 4 2d areas
We did the math in the previous posts.
Why Not?
I don’t know why, ………………….. but the fine structure is also important.
http://en.wikipedia.org/wiki/Fine_structure_constant
QUOTE
Quote
It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it. Richard P. Feynman, QED: The Strange Theory of Light and Matter, Princeton University Press 1985, p. 129
It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it. Richard P. Feynman, QED: The Strange Theory of Light and Matter, Princeton University Press 1985, p. 129
I'm not forgetting J. Baez
http://math.ucr.edu/home/baez/lengths.html
QUOTE (->
| QUOTE |
| Quote It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it. Richard P. Feynman, QED: The Strange Theory of Light and Matter, Princeton University Press 1985, p. 129 |
I'm not forgetting J. Baez
http://math.ucr.edu/home/baez/lengths.html
It's worth noting that the classical electron radius is 1/137 as big as the Compton wavelength of the electron - the all-important fine structure constant again! So we have 3 length scales:
• Bohr radius r - about 5 × 10-11 meters
• Compton wavelength LCompton - about 4 × 10-13 meters
• Classical electron radius re - about 3 × 10-15 meters
each of which is 1/137 as big as the previous one. The Bohr radius depends only on hbar, e, and m. The Compton wavelength depends only on hbar, c, and m. The classical electron radius depends only on e, c, and m. Nice set-up, huh? I suppose I should relent and tell you that this mysterious number 1/137, the fine structure constant, is just
e2/hbar c.
It's a dimensionless constant depending only on hbar, e, and c. In this respect it's more fundamental than any of the length scales mentioned, because all the length scales mentioned involve the electron mass, and one could work them out for particles other than the electron, whereas
e2/hbar c
is truly universal, once you remember that the "electron charge" is nothing specific to the electron but is a basic aspect of electromagnetism that applies to all charged particles. (Yes, quarks apparently have charge 1/3, but that doesn't really affect my point.) In other words, the fine structure constant is a dimensionless measure of how strong the electromagnetic force is, and we have seen that it sets the ratio of 3 important length scales.
Things are coming along just fine for part two
jal
Good Day All!
part #2
However,When dealing with mass at the Plack scale The dimensions of G are important
http://en.wikipedia.org/wiki/Schwarzschild_radius
http://en.wikipedia.org/wiki/Gravitational_constant
http://en.wikipedia.org/wiki/Gravitational_constant
According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them.
(see formula)
YOU CANNOT PRETEND THAT THE PLANCK LENGTH IS A POINT. THAT IS A MAJOR ERROR. THE PLANCK LENGTH IS 100% CERTAIN. The Planck lengths must be conserved. Therefore, you can only use “Uncertainty Principle”, “entangled states”, “Quantum indeterminacy” , where the waves are located and there cannot be any waves less than the Planck length.
http://en.wikipedia.org/wiki/Local_realism
See: http://en.wikipedia.org/wiki/Uncertainty_principle
See: http://en.wikipedia.org/wiki/Uncertainty_principle
Heisenberg did not just use any arbitrary number to describe the minimum standard deviation between position and momentum of a particle. Heisenberg knew that particles behaved like waves and he knew that the energy of any wave is the frequency multiplied by Planck's constant. In a wave, a cycle is defined by the return from a certain position to the same position such as from the top of one crest to the next crest. This actually is equivalent to a circle of 360 degrees, or 2π radians. Therefore, dividing h by 2π describes a constant that when multiplied by the frequency of a wave gives the energy of one radian. Heisenberg took ½ of as his standard deviation. This can be written as over 2 as above or it can be written as h/(4π). Normally one will see over 2 as this is simpler.
(see formula)
http://en.wikipedia.org/wiki/Quantum_entanglement
http://en.wikipedia.org/wiki/Quantum_indeterminacy
http://en.wikipedia.org/wiki/Quantum_indeterminacy
Quantum indeterminacy can be quantitatively characterized by a probability distribution on the set of outcomes of measurements of an observable. The distribution is uniquely determined by the system state, and moreover quantum mechanics provides a recipe for calculating this probability distribution.
An adequate account of quantum indeterminacy requires a theory of measurement. Many theories have been proposed since the beginning of quantum mechanics and quantum measurement continues to be an active research area in both theoretical and experimental physics (Braginski and Khalili 1992.) Possibly the first systematic attempt at a mathematical theory was developed by John von Neumann. The kind of measurements he investigated are now called projective measurements. That theory was based in turn on the theory of projection-valued measures for self-adjoint operators which had been recently developed (by von Neumann and independently by Marshall Stone) and the Hilbert space formulation of quantum mechanics (attributed by von Neumann to Paul Dirac).
http://en.wikipedia.org/wiki/Quantum_measurement
The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications.[b]
The case of a continuous spectrum is more involved, since, physically speaking, the basis has uncountably many eigenstates, but the general concept is the same. In the position representation, for instance, the eigenstates can be represented by the set of delta functions, indexed by all possible positions of the particle. In the experimental setting, the resolution of any given measurement is finite, and therefore the continuous space may be divided into discrete segments. Another solution is to approximate any lab experiments by a "box" potential (which bounds the volume in which the particle can be found, and thus ensures a discrete spectrum).
http://en.wikipedia.org/wiki/Continuous_spectrum
http://en.wikipedia.org/wiki/Discrete_spectrum
http://en.wikipedia.org/wiki/Decomposition...nal_analysis%29
…..ON AND ON AND ON…..
I have shown you were the waves are located and how they are arranged.
I shown that it is possible to make the link to REALITY.
ONLY IF YOU MAKE THE MEASUREMENTS/CALCULATIONS WHERE THE WAVES ARE LOCATED.
Therefore, can “Uncertainty Principle”, “entangled states”, “Quantum indeterminacy” change those distances?
My simple presentation ONCE AGAIN.
part #2
However,When dealing with mass at the Plack scale The dimensions of G are important
http://en.wikipedia.org/wiki/Schwarzschild_radius
QUOTE
The dimensions assigned to the gravitational constant (length cubed, divided by mass and by time squared) are those needed to make gravitational equations 'come out right'. However, these dimensions have fundamental significance in terms of Planck units: when expressed in SI units, the gravitational constant is dimensionally and numerically equal to the CUBE of the Planck length divided by the Planck mass and by the square of Planck time.
The formula for the Schwarzschild radius can be found by setting the escape velocity to the speed of light, and is
(see formula)
where
rs is the Schwarzschild radius,
G is the gravitational constant,
m is the mass of the gravitating object, and
c is the speed of light.
The proportionality constant, 2G / c2, can be approximated as 1.48 × 10-27 m / kg.
This means that the equation can be approximately written as
(see formula)
with rs in meters and m in kilograms.
Note that although the result is correct, general relativity must be used to properly derive the Schwarzschild radius. Some consider it to be only a coincidence that Newtonian physics produces the same result, yet this may be an indication of a deeper underlining symmetry in Nature.
The formula for the Schwarzschild radius can be found by setting the escape velocity to the speed of light, and is
(see formula)
where
rs is the Schwarzschild radius,
G is the gravitational constant,
m is the mass of the gravitating object, and
c is the speed of light.
The proportionality constant, 2G / c2, can be approximated as 1.48 × 10-27 m / kg.
This means that the equation can be approximately written as
(see formula)
with rs in meters and m in kilograms.
Note that although the result is correct, general relativity must be used to properly derive the Schwarzschild radius. Some consider it to be only a coincidence that Newtonian physics produces the same result, yet this may be an indication of a deeper underlining symmetry in Nature.
http://en.wikipedia.org/wiki/Gravitational_constant
QUOTE (->
| QUOTE |
| The dimensions assigned to the gravitational constant (length cubed, divided by mass and by time squared) are those needed to make gravitational equations 'come out right'. However, these dimensions have fundamental significance in terms of Planck units: when expressed in SI units, the gravitational constant is dimensionally and numerically equal to the CUBE of the Planck length divided by the Planck mass and by the square of Planck time. The formula for the Schwarzschild radius can be found by setting the escape velocity to the speed of light, and is (see formula) where rs is the Schwarzschild radius, G is the gravitational constant, m is the mass of the gravitating object, and c is the speed of light. The proportionality constant, 2G / c2, can be approximated as 1.48 × 10-27 m / kg. This means that the equation can be approximately written as (see formula) with rs in meters and m in kilograms. Note that although the result is correct, general relativity must be used to properly derive the Schwarzschild radius. Some consider it to be only a coincidence that Newtonian physics produces the same result, yet this may be an indication of a deeper underlining symmetry in Nature. |
http://en.wikipedia.org/wiki/Gravitational_constant
According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them.
(see formula)
YOU CANNOT PRETEND THAT THE PLANCK LENGTH IS A POINT. THAT IS A MAJOR ERROR. THE PLANCK LENGTH IS 100% CERTAIN. The Planck lengths must be conserved. Therefore, you can only use “Uncertainty Principle”, “entangled states”, “Quantum indeterminacy” , where the waves are located and there cannot be any waves less than the Planck length.
http://en.wikipedia.org/wiki/Local_realism
QUOTE
Locality is one of the axioms of relativistic quantum field theory, as required for causality. The formalization of locality in this case is as follows: if we have two observables, each localized within two distinct spacetime regions which happen to be at a spacelike separation from each other, the observables must commute. This interpretation of the word "locality" is closely related to the relativistic version of in physics. In physics a solution is local if the underlying equations are either Lorentz invariant or, more generally, generally covariant or locally Lorentz invariant.
See: http://en.wikipedia.org/wiki/Uncertainty_principle
QUOTE (->
| QUOTE |
| Locality is one of the axioms of relativistic quantum field theory, as required for causality. The formalization of locality in this case is as follows: if we have two observables, each localized within two distinct spacetime regions which happen to be at a spacelike separation from each other, the observables must commute. This interpretation of the word "locality" is closely related to the relativistic version of in physics. In physics a solution is local if the underlying equations are either Lorentz invariant or, more generally, generally covariant or locally Lorentz invariant. |
See: http://en.wikipedia.org/wiki/Uncertainty_principle
Heisenberg did not just use any arbitrary number to describe the minimum standard deviation between position and momentum of a particle. Heisenberg knew that particles behaved like waves and he knew that the energy of any wave is the frequency multiplied by Planck's constant. In a wave, a cycle is defined by the return from a certain position to the same position such as from the top of one crest to the next crest. This actually is equivalent to a circle of 360 degrees, or 2π radians. Therefore, dividing h by 2π describes a constant that when multiplied by the frequency of a wave gives the energy of one radian. Heisenberg took ½ of as his standard deviation. This can be written as over 2 as above or it can be written as h/(4π). Normally one will see over 2 as this is simpler.
(see formula)
http://en.wikipedia.org/wiki/Quantum_entanglement
QUOTE
In some formal mathematical settings, it is noted that the correct setting for pure states in quantum mechanics is projective Hilbert space endowed with the Fubini-Study metric. The product of two pure states is then given by the Segre embedding.
http://en.wikipedia.org/wiki/Quantum_indeterminacy
QUOTE (->
| QUOTE |
| In some formal mathematical settings, it is noted that the correct setting for pure states in quantum mechanics is projective Hilbert space endowed with the Fubini-Study metric. The product of two pure states is then given by the Segre embedding. |
http://en.wikipedia.org/wiki/Quantum_indeterminacy
Quantum indeterminacy can be quantitatively characterized by a probability distribution on the set of outcomes of measurements of an observable. The distribution is uniquely determined by the system state, and moreover quantum mechanics provides a recipe for calculating this probability distribution.
An adequate account of quantum indeterminacy requires a theory of measurement. Many theories have been proposed since the beginning of quantum mechanics and quantum measurement continues to be an active research area in both theoretical and experimental physics (Braginski and Khalili 1992.) Possibly the first systematic attempt at a mathematical theory was developed by John von Neumann. The kind of measurements he investigated are now called projective measurements. That theory was based in turn on the theory of projection-valued measures for self-adjoint operators which had been recently developed (by von Neumann and independently by Marshall Stone) and the Hilbert space formulation of quantum mechanics (attributed by von Neumann to Paul Dirac).
http://en.wikipedia.org/wiki/Quantum_measurement
The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications.[b]
The case of a continuous spectrum is more involved, since, physically speaking, the basis has uncountably many eigenstates, but the general concept is the same. In the position representation, for instance, the eigenstates can be represented by the set of delta functions, indexed by all possible positions of the particle. In the experimental setting, the resolution of any given measurement is finite, and therefore the continuous space may be divided into discrete segments. Another solution is to approximate any lab experiments by a "box" potential (which bounds the volume in which the particle can be found, and thus ensures a discrete spectrum).
http://en.wikipedia.org/wiki/Continuous_spectrum
http://en.wikipedia.org/wiki/Discrete_spectrum
http://en.wikipedia.org/wiki/Decomposition...nal_analysis%29
…..ON AND ON AND ON…..
I have shown you were the waves are located and how they are arranged.
I shown that it is possible to make the link to REALITY.
ONLY IF YOU MAKE THE MEASUREMENTS/CALCULATIONS WHERE THE WAVES ARE LOCATED.
Therefore, can “Uncertainty Principle”, “entangled states”, “Quantum indeterminacy” change those distances?
My simple presentation ONCE AGAIN.
QUOTE
Therefore, What would be the minimum size of a Planck sphere?
A sphere with a radius of one Planck length will not have a surface area that would be suficient to make a sphere.
[b]A Planck Sphere must have a radius of 4 Planck length.
As a result the Planck length is not violated. By definition nothing can be smaller.
A simple wave of a Planck area can therefore orbit around the Planck sphere.
The wave must be contained within the 3 Planck length radius and the 4 Planck length radius.
REASON # 2
The wave must visit each of the 8 Planck length quadrant of the sphere within its allotted time of one Planck time. Other wise .... the wave will collapse. (The snake must eats its tail.)
The 2D surfaces are inserted/imbedded/in/into what we see as 3D.
Like J. Baez said, “The ’unimportant numerical factor' I mentioned above (2pi) might actually be very large, or very small.”
The only restriction is that the “SPOT” must be smaller than a hair.
I prefer 10^-18.
And …. Maybe …. It might have a thickness of one Planck length. (Which is probably not a problem with reality.)
Any comments?
jal
A sphere with a radius of one Planck length will not have a surface area that would be suficient to make a sphere.
[b]A Planck Sphere must have a radius of 4 Planck length.
As a result the Planck length is not violated. By definition nothing can be smaller.
A simple wave of a Planck area can therefore orbit around the Planck sphere.
The wave must be contained within the 3 Planck length radius and the 4 Planck length radius.
REASON # 2
The wave must visit each of the 8 Planck length quadrant of the sphere within its allotted time of one Planck time. Other wise .... the wave will collapse. (The snake must eats its tail.)
QUOTE (->
| QUOTE |
| Therefore, What would be the minimum size of a Planck sphere? A sphere with a radius of one Planck length will not have a surface area that would be suficient to make a sphere. [b]A Planck Sphere must have a radius of 4 Planck length. As a result the Planck length is not violated. By definition nothing can be smaller. A simple wave of a Planck area can therefore orbit around the Planck sphere. The wave must be contained within the 3 Planck length radius and the 4 Planck length radius. REASON # 2 The wave must visit each of the 8 Planck length quadrant of the sphere within its allotted time of one Planck time. Other wise .... the wave will collapse. (The snake must eats its tail.) In physics, the Planck time (tP), is the unit of time in the system of natural units known as Planck units. It is the time it would take a photon travelling at the speed of light to cross a distance equal to the Planck length. Therefore, You must decide.....Is the Planck wave capable of traveling 8 X the speed of light? If it cannot then a Planck size wave is not possible inside a sphere. Can a 2D area cover the surface Area of a 3D sphere? When you lay it out flat….voila …. IT’S A 2D MEMBRANE!!!! When you fold it up …….VOILA…. A SPHERE. It is only at this scale that 2D is equal to 3D. There is nothing inside the 3D. It is an empty shell. Okay... what does the 2D membrane look like? 4 circles/spots is what I said... It is what Gerard t' Hooft said.....Therefore, we can easily transfer to a quantized 2D membrane and not violate the speed of light. We automatically get packing in 2D which is a membrane. It looks like what I have been saying all the time. |
The 2D surfaces are inserted/imbedded/in/into what we see as 3D.
Like J. Baez said, “The ’unimportant numerical factor' I mentioned above (2pi) might actually be very large, or very small.”
The only restriction is that the “SPOT” must be smaller than a hair.
I prefer 10^-18.
And …. Maybe …. It might have a thickness of one Planck length. (Which is probably not a problem with reality.)
Any comments?
jal
Jal,
I've been thinking recently in 'wavefronts' mode .....these buggers have no thickness, so plank whatever goes outta the window....wavefronts (waves) in my model eminate from singularities of zero size, merely illusions of transdimensionality and arise from migration from one dimension to another (0 to infinity), you could call them "aspects of a big nothing"
Love your 2-D plastering on 3-D, this is truly significant!....however, as I see things
"the big nothing" is a high dimensional singularity, it's daughter nothings, grand daughters and great-great-great daughter "nothings" atemporally interacting via an event reversal/dimensional propagative process.
Realise a point, a ring, a sphere, a hypersphere can be regarded a singularities; by going from one to the the other respectively is an infinite progression
What I'm really saying that there's no distance, no time or any other humanly perceived thang....just a mishmish of recurring degrading dimensional instants.
I've been thinking recently in 'wavefronts' mode
.....these buggers have no thickness, so plank whatever goes outta the window....wavefronts (waves) in my model eminate from singularities of zero size, merely illusions of transdimensionality and arise from migration from one dimension to another (0 to infinity), you could call them "aspects of a big nothing"Love your 2-D plastering on 3-D, this is truly significant!....however, as I see things
"the big nothing" is a high dimensional singularity, it's daughter nothings, grand daughters and great-great-great daughter "nothings" atemporally interacting via an event reversal/dimensional propagative process.
Realise a point, a ring, a sphere, a hypersphere can be regarded a singularities; by going from one to the the other respectively is an infinite progression
What I'm really saying that there's no distance, no time or any other humanly perceived thang....just a mishmish of recurring degrading dimensional instants.
Hey jal, C2, 5D, et al.
jal,
Great stuff! Now time for some "direct-ness"...
4pi r^2 provides four "2d circles" each of a radius of one Lp (Planck Length) from a sphere where r = 1Lp. Therefore, your statement does not make sense. 2D, by definition, cannot have "thickness" in a third dimension. If your argument is that uncertainty necessitates the possibility of a "thickness" of up to one Lp, then there are potentially an infinite number of extra dimensions, each with a potential maximum extension of 1Lp - and that certainly does not make any sense.
4pi r^2 provides four "2d circles" each of a radius of one Lp (Planck Length) from a sphere where r = 1Lp. Therefore, your statement does not make sense. 2D, by definition, cannot have "thickness" in a third dimension. If your argument is that uncertainty necessitates the possibility of a "thickness" of up to one Lp, then there are potentially an infinite number of extra dimensions, each with a potential maximum extension of 1Lp - and that certainly does not make any sense.
The wave must be contained within the 3 Planck length radius and the 4 Planck length radius.
The wave must visit each of the 8 Planck length quadrant of the sphere within its allotted time of one Planck time.
The wave is contained on the surface of the sphere. (Brief segway to C2- I can't make a sine wave work on the surface of a cube - it is possible?) A wave moving in one of the two possible dimensions on the surface of the sphere would have a wavelength of 2Lp. A wave moving in both of the possible dimensions would have a wavelength of 4Lp (think of the first as a circle around the "equator" of the sphere and the second as a "figure - 8" wrapped around the sphere). The minimum time to cross through the interior of a sphere where r = 1Lp is 2Tp (Planck Time). But since we can't go "through the sphere" the minimum time to circumnavigate the sphere is 2pi Tp. To circumnavigate the sphere twice (once in each dimension) would be 4pi Tp.
Which implies:
1. The maximum "quanta" of energy (assuming that is what the wave is) has a wavelength 2Lp.
2. All possible wavelengths existing on the surface of a Planck sphere must be the product of any natural number times 2Lp.
3. The highest possible EM frequency = c/2pi Lp = ~ 2.98e+42 Hz. A photon at this frequency would have an energy = ~ 1.9e+9 J ~ 1.2e+28 eV. (Just playing with some numbers - someone please check my math.)
Which implies:
1. The maximum "quanta" of energy (assuming that is what the wave is) has a wavelength 2Lp.
2. All possible wavelengths existing on the surface of a Planck sphere must be the product of any natural number times 2Lp.
3. The highest possible EM frequency = c/2pi Lp = ~ 2.98e+42 Hz. A photon at this frequency would have an energy = ~ 1.9e+9 J ~ 1.2e+28 eV. (Just playing with some numbers - someone please check my math.)
Why Not?
I don’t know why, ………………….. but the fine structure is also important.
Agreed. Possible avenue of discussion after fully considering your "Part 2".
jal,
Great stuff! Now time for some "direct-ness"...
QUOTE
A sphere with a radius of one Planck length will not have a surface area that would be sufficient to make a sphere.
A Planck Sphere must have a radius of 4 Planck length.
As a result the Planck length is not violated. By definition nothing can be smaller.
A simple wave of a Planck area can therefore orbit around the Planck sphere.
The wave must be contained within the 3 Planck length radius and the 4 Planck length radius.
A Planck Sphere must have a radius of 4 Planck length.
As a result the Planck length is not violated. By definition nothing can be smaller.
A simple wave of a Planck area can therefore orbit around the Planck sphere.
The wave must be contained within the 3 Planck length radius and the 4 Planck length radius.
4pi r^2 provides four "2d circles" each of a radius of one Lp (Planck Length) from a sphere where r = 1Lp. Therefore, your statement does not make sense. 2D, by definition, cannot have "thickness" in a third dimension. If your argument is that uncertainty necessitates the possibility of a "thickness" of up to one Lp, then there are potentially an infinite number of extra dimensions, each with a potential maximum extension of 1Lp - and that certainly does not make any sense.
QUOTE (->
| QUOTE |
| A sphere with a radius of one Planck length will not have a surface area that would be sufficient to make a sphere. A Planck Sphere must have a radius of 4 Planck length. As a result the Planck length is not violated. By definition nothing can be smaller. A simple wave of a Planck area can therefore orbit around the Planck sphere. The wave must be contained within the 3 Planck length radius and the 4 Planck length radius. |
4pi r^2 provides four "2d circles" each of a radius of one Lp (Planck Length) from a sphere where r = 1Lp. Therefore, your statement does not make sense. 2D, by definition, cannot have "thickness" in a third dimension. If your argument is that uncertainty necessitates the possibility of a "thickness" of up to one Lp, then there are potentially an infinite number of extra dimensions, each with a potential maximum extension of 1Lp - and that certainly does not make any sense.
The wave must be contained within the 3 Planck length radius and the 4 Planck length radius.
The wave must visit each of the 8 Planck length quadrant of the sphere within its allotted time of one Planck time.
The wave is contained on the surface of the sphere. (Brief segway to C2- I can't make a sine wave work on the surface of a cube - it is possible?) A wave moving in one of the two possible dimensions on the surface of the sphere would have a wavelength of 2Lp. A wave moving in both of the possible dimensions would have a wavelength of 4Lp (think of the first as a circle around the "equator" of the sphere and the second as a "figure - 8" wrapped around the sphere). The minimum time to cross through the interior of a sphere where r = 1Lp is 2Tp (Planck Time). But since we can't go "through the sphere" the minimum time to circumnavigate the sphere is 2pi Tp. To circumnavigate the sphere twice (once in each dimension) would be 4pi Tp.
QUOTE
(The snake must eats its tail.)
Which implies:
1. The maximum "quanta" of energy (assuming that is what the wave is) has a wavelength 2Lp.
2. All possible wavelengths existing on the surface of a Planck sphere must be the product of any natural number times 2Lp.
3. The highest possible EM frequency = c/2pi Lp = ~ 2.98e+42 Hz. A photon at this frequency would have an energy = ~ 1.9e+9 J ~ 1.2e+28 eV. (Just playing with some numbers - someone please check my math.)
QUOTE (->
| QUOTE |
| (The snake must eats its tail.) |
Which implies:
1. The maximum "quanta" of energy (assuming that is what the wave is) has a wavelength 2Lp.
2. All possible wavelengths existing on the surface of a Planck sphere must be the product of any natural number times 2Lp.
3. The highest possible EM frequency = c/2pi Lp = ~ 2.98e+42 Hz. A photon at this frequency would have an energy = ~ 1.9e+9 J ~ 1.2e+28 eV. (Just playing with some numbers - someone please check my math.)
Why Not?
I don’t know why, ………………….. but the fine structure is also important.
Agreed. Possible avenue of discussion after fully considering your "Part 2".
Hi Why Not?.. fivedoughnut .... Confused2 and everyone
Great to get you analysis and comments.
Do not forget that at the Planck Scale all length cannot be less than one Planck unit and all times are at Planck scale.
We are blocked from reachind down and reaching up is not fair.
I have two other posts prepared.....I must wait for inputs so that I can incorporate the suggested corrections from all of you.
Jal
and everyoneGreat to get you analysis and comments.
Do not forget that at the Planck Scale all length cannot be less than one Planck unit and all times are at Planck scale.
We are blocked from reachind down and reaching up is not fair. I have two other posts prepared.....I must wait for inputs so that I can incorporate the suggested corrections from all of you.
Jal
Why Not, jal,y, pupa et al,
I fear we have a problem here.
The divergence theorum speaks of what passes through a surface. Unless I am mistaken the main thrust of discussion seems to be about what passes along a surface The power of the divergence theorum is that it works for any surface that encloses a volume of any shape .. a sphere, a banana, or a cube. In a similar way the holographic principle speaks of areas and when a region is totally enclosed then all information about anything inside a closed region can be read by looking through the windows that enclose it. If a cube (6 windows) is not an acceptable enclosure then the holographic principle is shown to be faulty.
Please .. is transmission proposed to be along the 2D surface or through it?
C2.
I fear we have a problem here.
The divergence theorum speaks of what passes through a surface. Unless I am mistaken the main thrust of discussion seems to be about what passes along a surface The power of the divergence theorum is that it works for any surface that encloses a volume of any shape .. a sphere, a banana, or a cube. In a similar way the holographic principle speaks of areas and when a region is totally enclosed then all information about anything inside a closed region can be read by looking through the windows that enclose it. If a cube (6 windows) is not an acceptable enclosure then the holographic principle is shown to be faulty.
Please .. is transmission proposed to be along the 2D surface or through it?
C2.
Confused2
Through or along ...... worth thinking about when trying to create a sphere and everthing cannot be less or more than 1 Planck unit.
If it's more then your not there...yet
If it's less.... it's impossible if we want to keep C etc
jal
Through or along ...... worth thinking about when trying to create a sphere and everthing cannot be less or more than 1 Planck unit.
If it's more then your not there...yet
If it's less.... it's impossible if we want to keep C etc
jal
Hey C2, jal, 5D, et al.
Very good point C2. While divergence theorem works on any shape as long as it is fully enclosed, not only is a sphere easier for me to visualize, it is the shape that encloses the greatest volume with the smallest surface area; so it seems the most natural shape to begin with when considering the "smallest".
If I am understanding jal's model, there is a certain surface area where "through" the surface is equal to "on" the surface. If we assume that a Planck sphere is the smallest possible surface area, I believe that "through" and "on" are the same thing, thus the "2-D plastering on 3-D" in fivedoughnut's words.
If we take a Planck sphere, cut it in half, and open it up, it will look like two circles side by side (like the symbol for infinity ). If we further assume that the smallest possible wavelength is defined by the Lp, our split open Planck sphere will represent two of these wavelengths (sine waves). Therefore, assuming that Lp is the smallest unit of distance, no matter how you slice it, the "energy" (wavelength) "within" a Planck Sphere must also be contained on it's surface.
jal, this is also why I have been taking issue with the shell having a "thickness". Once a "thickness" is established, "in" the sphere and "on" the sphere are no longer the same thing.
If I messed something up here, please let me know.
Very good point C2. While divergence theorem works on any shape as long as it is fully enclosed, not only is a sphere easier for me to visualize, it is the shape that encloses the greatest volume with the smallest surface area; so it seems the most natural shape to begin with when considering the "smallest".
If I am understanding jal's model, there is a certain surface area where "through" the surface is equal to "on" the surface. If we assume that a Planck sphere is the smallest possible surface area, I believe that "through" and "on" are the same thing, thus the "2-D plastering on 3-D" in fivedoughnut's words.
If we take a Planck sphere, cut it in half, and open it up, it will look like two circles side by side (like the symbol for infinity
). If we further assume that the smallest possible wavelength is defined by the Lp, our split open Planck sphere will represent two of these wavelengths (sine waves). Therefore, assuming that Lp is the smallest unit of distance, no matter how you slice it, the "energy" (wavelength) "within" a Planck Sphere must also be contained on it's surface. jal, this is also why I have been taking issue with the shell having a "thickness". Once a "thickness" is established, "in" the sphere and "on" the sphere are no longer the same thing.
If I messed something up here, please let me know.
Why Not? and all
I'm listening, your inputs are helping to make all of us understand a planck size sphere made of energy waves.
Nobody can mess things up.
jal
I'm listening, your inputs are helping to make all of us understand a planck size sphere made of energy waves.
Nobody can mess things up.
jal
QUOTE (jal+Sep 3 2006, 04:03 AM)
Why Not? and all
I'm listening, your inputs are helping to make all of us understand a planck size sphere made of energy waves.
Nobody can mess things up.
jal
Excellent attitude Jal...we're working as a team, hopefully greater than the sum of their parts.
I'm listening, your inputs are helping to make all of us understand a planck size sphere made of energy waves.
Nobody can mess things up.
jal
Excellent attitude Jal...we're working as a team, hopefully greater than the sum of their parts.
Jal etc,
Earlier in the discussion Jal mentioned plank scales in dimensions other than 3; I thought this was of particular interest
.....What would the size of a plank circle or of a plank line?? moreover my model is one where event horizons will form from wave propagation in all dimensional states as these lower dimensional waves would not have the necessary 'mechanism' to perpetuate......photons and hypothetical linearons would simply not exist!
Earlier in the discussion Jal mentioned plank scales in dimensions other than 3; I thought this was of particular interest
.....What would the size of a plank circle or of a plank line?? moreover my model is one where event horizons will form from wave propagation in all dimensional states as these lower dimensional waves would not have the necessary 'mechanism' to perpetuate......photons and hypothetical linearons would simply not exist!
Hi jal,5D,y, Why Not , Pupa et al,
I'm going to propose a method of propagation for everybody to hate. There's a packing problem .. but let's get a primitive mechanism first.
Startiing with a row of cubes where each edge = 1 Planck length. Source in C[0] emits one photon. We only allow 1D propagation. C[1] has a probability to see this photon through it's window .. the photon, momentum etc is now in C[1] .. and so on to C[n]. Wavelength at this stage has no physical interpretation .. hopefully this will emerge naturally as the probability of finding the photon in a particular box at a particular time. We might imagine that a photon with a lot of momentum has a greater probability of being seen by the C[n+1] neighbour rather than the C[n-1]. We might also imagine that the greater the energy of the photon the greater the probabiility of it being seen at any window. This word salad model gives a hand-waving constant velocity.
Packing this sort of thing into 3D is difficult without leaving preferred directions .. even with spheres you end up with an orientation. I don't see a solution to this.
Pupa .. this is undefended territory .. no point in attacking it .. I'm sure we'd all welcome positive input from you.
-C2.
I'm going to propose a method of propagation for everybody to hate. There's a packing problem .. but let's get a primitive mechanism first.
Startiing with a row of cubes where each edge = 1 Planck length. Source in C[0] emits one photon. We only allow 1D propagation. C[1] has a probability to see this photon through it's window .. the photon, momentum etc is now in C[1] .. and so on to C[n]. Wavelength at this stage has no physical interpretation .. hopefully this will emerge naturally as the probability of finding the photon in a particular box at a particular time. We might imagine that a photon with a lot of momentum has a greater probability of being seen by the C[n+1] neighbour rather than the C[n-1]. We might also imagine that the greater the energy of the photon the greater the probabiility of it being seen at any window. This word salad model gives a hand-waving constant velocity.
Packing this sort of thing into 3D is difficult without leaving preferred directions .. even with spheres you end up with an orientation. I don't see a solution to this.
Pupa .. this is undefended territory .. no point in attacking it .. I'm sure we'd all welcome positive input from you.
-C2.
Yeah, come on Pupa'....you've got the knowledge....surprise us all with a little imaginative construction based on that foundation.
5D,y, Why Not , Pupa ....All
I admit defeat.... Planck scale has me doing all kinds of "cheating" which I cannot justify ..... for a minute I thought that I had a solution and wrote up 2 posts....
I have to scrap them....I forgot one of the dimensions
I'm now reflecting on having a vibrating string which can vibrate in six directions.... no success....
Can we find a justifiable "cheating"?
The previous math on 2d area and sphere area seems to be an enticing dead end
I was also hope...ing that we might solve it by using more solitons ??? 6 ??? that would work in a dynamic coordinated dance to create the illusion of a sphere. (cube?)
Pretending and science fiction won't do it on this problem.
jal
I admit defeat.... Planck scale has me doing all kinds of "cheating" which I cannot justify ..... for a minute I thought that I had a solution and wrote up 2 posts....
I have to scrap them....I forgot one of the dimensions
I'm now reflecting on having a vibrating string which can vibrate in six directions.... no success....
Can we find a justifiable "cheating"?
The previous math on 2d area and sphere area seems to be an enticing dead end
I was also hope...ing that we might solve it by using more solitons ??? 6 ??? that would work in a dynamic coordinated dance to create the illusion of a sphere. (cube?)
Pretending and science fiction won't do it on this problem.
jal
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