Is there stored energy in a gravitational field?
If E=mc^2
is the energy of the field [non-existent,included,a bonus,something else] ?
A complicated answer suggests itself, but asking that here is liable to get any number of crackpot answers. 
QUOTE (Confused2+Oct 9 2009, 05:43 PM)
Is there stored energy in a gravitational field?
If E=mc^2
is the energy of the field [non-existent,included,a bonus,something else] ?
This really looks like crank-bait to me....
EDIT: But I can't resist.
I'm weak...
EDIT 2: Weak, but thorough...
If E=mc^2
is the energy of the field [non-existent,included,a bonus,something else] ?
This really looks like crank-bait to me....
EDIT: But I can't resist.
I'm weak...
EDIT 2: Weak, but thorough...
QUOTE (Confused2+Oct 9 2009, 10:43 PM)
Is there stored energy in a gravitational field?
If E=mc^2
is the energy of the field [non-existent,included,a bonus,something else] ?
Crackpot answer #1;
We've already grown accustomed to the wave/particle duality job. What if a gravitational field is merely the resultant manifestation of a trans-dimensional wave state, produced from the innumerous particles that constitute a planetoid etc ?
What if energy is exchanged in this higher dimension between waves of differing magnitude? (nature usually trends towards equilibrium) - the universe might be ridiculously small in greater dimensional elevation, with particles/waves cycling @ trillions + times per sec. The universe we 'see' may only be an 'illusion' born of our dimensional confines.
If E=mc^2
is the energy of the field [non-existent,included,a bonus,something else] ?
Crackpot answer #1;
We've already grown accustomed to the wave/particle duality job. What if a gravitational field is merely the resultant manifestation of a trans-dimensional wave state, produced from the innumerous particles that constitute a planetoid etc ?
What if energy is exchanged in this higher dimension between waves of differing magnitude? (nature usually trends towards equilibrium) - the universe might be ridiculously small in greater dimensional elevation, with particles/waves cycling @ trillions + times per sec. The universe we 'see' may only be an 'illusion' born of our dimensional confines.
Hi what do you actually mean by "bonus"?
OK ..I'll reveal the motive..
We know F=ma .. does the force arise because masses just don't like being pushed - or is there something more sinister going on?
Posible sinister things:-
Possibility 1. To accelerate a particle you have to push it up its own gravitational field.
Possibility 2. Give in.
If work is done (Force x distance) then it must go somewhere .. possibly just overcoming the cussedness of mass .. or it goes into the gravitational field (where else could it go?) .. so the gravitational field (in motion) would store energy - hence the question.
We know F=ma .. does the force arise because masses just don't like being pushed - or is there something more sinister going on?
Posible sinister things:-
Possibility 1. To accelerate a particle you have to push it up its own gravitational field.
Possibility 2. Give in.
If work is done (Force x distance) then it must go somewhere .. possibly just overcoming the cussedness of mass .. or it goes into the gravitational field (where else could it go?) .. so the gravitational field (in motion) would store energy - hence the question.
QUOTE (Confused2+Oct 10 2009, 12:39 PM)
We know F=ma .. does the force arise because masses just don't like being pushed - or is there something more sinister going on?
Posible sinister things:-
Possibility 1. To accelerate a particle you have to push it up its own gravitational field.
Possibility 2. Give in.
If work is done (Force x distance) then it must go somewhere .. possibly just overcoming the cussedness of mass .. or it goes into the gravitational field (where else could it go?) .. so the gravitational field (in motion) would store energy - hence the question.
Repeat after me:
IN-ER-TIA
Posible sinister things:-
Possibility 1. To accelerate a particle you have to push it up its own gravitational field.
Possibility 2. Give in.
If work is done (Force x distance) then it must go somewhere .. possibly just overcoming the cussedness of mass .. or it goes into the gravitational field (where else could it go?) .. so the gravitational field (in motion) would store energy - hence the question.
Repeat after me:
IN-ER-TIA
Yes, else gravitational waves wouldn't be able to move things. Look up the Bondi mass.
QUOTE (Confused2+Oct 10 2009, 04:39 PM)
Posible sinister things:-
Possibility 1. To accelerate a particle you have to push it up its own gravitational field.
Crackpot answer #2:
No. To accelerate a particle, you simply induce energy in such a way its wavestate geometry becomes increasingly irregular, thus 'forcing' the corresponding particle condensate to relocate spatially in order to sustain its harmonic integrity - don't you know anything?
Possibility 1. To accelerate a particle you have to push it up its own gravitational field.
Crackpot answer #2:
No. To accelerate a particle, you simply induce energy in such a way its wavestate geometry becomes increasingly irregular, thus 'forcing' the corresponding particle condensate to relocate spatially in order to sustain its harmonic integrity - don't you know anything?
On reflection I conclude that any self-gravitational effects of (say) a billiard ball are many orders of magnitude too small to explain the observed F=ma (or IN-ER-TIA as Flyingbuttressman puts it).
-C2.
-C2.
Hi All,
This is an interesting but controversial subject...
There are only two forms of energy in the Universe ... Kinetic energy which is energy of motion and potential energy which is energy which is stored by virtue solely of it's physical place relative to other parts of it's system and therefore lies latent in respect to it's own internal frame of reference. As an example of latent energy "binding energy" might actually be "kinetic energy" inside a nucleus however we think of it as "potential energy" since the specifics of any of this motion are entirely hidden. The release of binding energy is always in the form of kinetic energy which can be used to heat fluids or change the state of motion of the system... sometimes explosively.
Mass is generally composed of hidden energy. A lack of specific knowledge of the composition and internal structure of mass in detail is the reason why we are unable to unlock the "rest mass" energy of mC^2. Some of this "hidden" energy may be released such as the "binding energy" previously mentioned. The loss of some of this energy will change the rest mass of a particle (or it's components) but this release of formerly "hidden energy" is not normally affected by external linear motion.
We know that all the internal energy, both kinetic and potential, may be released under some kind of "unraveling symmetry operations" when particle and antiparticle are allowed to meet... or in the case of "sparking the vacuum" where two dissimilar high energy photons are mutually scattered into particle and antiparticle. In theory this "internal symmetry" of energy releasing or storing processes might be controllable somehow.
The energy stored in gravitating systems is also a mixture of kinetic and potential energy. Some kinetic energy of an orbiting body might be released if it was to be struck by another freely falling body (a projectile for instance). The potential energy of a body in free fall is released when the body "falls to earth". These are both sort of equivalent energy conversions the first is usually termed "kinetic energy" like playing celestial billiards the other might be interpreted as losing potential energy in the event of "rocks falling from the sky"... In both cases what was latent (hidden) energy becomes heat or can potentially do work. In that sense gravity stores energy which ultimately could be considered as motion when measured from a system in relative motion. This energy is usually never visible from the inertial frame of a single object. So it is often thought that this "latent energy" must be some substance that might be tapped off... this is not the case. Energy is no "substance" stored in things... it is the relationship between objects that causes energy because energy is proportional to the work that a system can do. You cant calculate the "energy" of a particle in isolation. It must always be in relation to an another particle on which some work can be done. Some portion of "intrinsic energy" like nuclear energy may be released in relationship to the other portions of the nuclei of an atom as "heat" (... or light or other radiations). To do that it is necessary that it do work on a "system". I do not personally accept that light or radiation is "intrinsic energy" but light can do work such as in moving electrons in photocells for instance. Light has energy by virtue of it's state of motion.
According to Lev Okun, JA Wheeler, A Einstein and many other respected authorities on the interpretation of Special Relativity and "mass"... there is no such thing as relativistic mass... it is not able to be "defined" or "measured" directly so should not be called a "mass" of any kind. There is only relativistic energy. Mass is definable in only one way... In a rest frame... any rest frame.
The theory of relativity and the Pythagorean theorem - Authors: L. B. Okun (Submitted on 15 Sep 2008)
In any and every rest frame a particular bit of intrinsic mass has the same value where mass can be measured using a spring and a test mass in the 'time honored way". Whenever a mass is discussed it must be a truly phenomenological property that can only be understood in this "special frame". "Mass in relativistic motion" has no specific way of being defined... It is not a measurable of a system but the intrinsic mass can be measured and it is the same in all inertial frames at any relative velocity where it might be "potentially" measured. Of course a particle does have relativistic energy and some people convert this to a "mass" by dividing this relativistic mass by a C^2 factor which is a derived quantity. It might give the correct answer in some problems but the actual "increase in mass" has no physical significance in it's own rest frame. What is actually noted in the external observer frame is time dilation.
As a matter of interest the energy of a system can be seen as an infinite Taylor Series expansion where the first two terms are the intrinsic mass and the kinetic energy at low velocities with other terms which become more and more significant as V -> C.
Wikipedia: Mass-energy equivalence
"Relativistic mass" is not real mass since it has no influence on the processes happening within the rest frame of the observer or the observed... People misunderstand time dilation for the fictitious effects of "mass increase" or in the case of the Wikipedia article on Special Relativity suggesting that the "reluctance" or inertia of a body is due to it's momentum becoming infinitely large as V approaches C... which is a technical absurdity because all uniform velocity is relative and the "speed" of a particle is not an issue at all. The particle in relative motion is undergoing relative time dilation and a system undergoing extreme time dilation "virtually" arrests all temporal processes (relative to external observers) in which energy transfer can occur such that events proceeding in the moving frame are nearly "frozen" in time. The transfer of a photon from one observing system to the relativistically moving system that photon "appears" to the moving system to be red shifted and this carries less energy (apparently) and can do less work. Of course this effect is due only to relative motion since the photon is the same always just that it's internal energy appears shifted spectrally when viewed from within the moving system or the packets of energy transferred from internal clocks in the source to the realm of the sink are running respectively slower. Acceleration due to the transfer of photons from an observer Lab frame to the motion of the accelerated particle is energetically "inefficient". Time dilation ultimately defeats the energy transfer process involved when the effective wavelength becomes much longer than the object required to be scattered by this interaction. I am ignoring the issue of the electromagnetic interaction but there are similar processes involved with charged particles.
Inside the relatively moving frame time is internally perfectly consistent and normal and all internal relativistic processes are "unseen" in it's own inertial frame while impressed external relativistic processes are affected by the relative motion. External processes are seen to run "slower or faster" depending on the rate of "recession or approach" to sources... as an example of this in an extreme case check on the "apparently superluminal Jet" from M86... the "apparent" speed of the approach of the Jet to earth is "about" 6 times the speed of light... a fictitious velocity. As an example of a down to earth example... People are not becoming infinitely heavy on a relativistically receding planet or rocket or they are not becoming more ponderable as time proceeds and they are not more obese or their "weight" is not magically increasing.
An example that would demonstrate this is if a rocket which had some "magical way to accelerate" at "1 Gee" acceleration forever had a test mass attached to a "thin string" in the ceiling of the cabin ... the tension of this string does not increase without limit as T -> infinity eventually breaking the string. In actual fact ... "one Gee" remains the same acceleration always as it would be on earth as it would also be in the spaceship. The laws of Physics are the same everywhere. Of course looking outside of the spaceship at the "background".. things would eventually become very weird indeed after a few short years. Naturally if a particle is charged then a relative velocity may induce electromagnetic consequences in other objects but that is entirely another question... not going there for now. Otherwise "Relativistic mass" cannot be measured and is a derived quantity. No known instrument can measure "relativistic mass" and is therefore not a system measurable.
For instance otherwise "empty space" might have energy content but will exhibit no actual mass and energy content of some specified volume of space cannot have any form of mass regardless of the frame it is measured "in" or "from". No frame of motion relative to a space devoid of matter containing "energy"... lets say light for instance... can be considered as having mass as seen from any other moving frame. I urge the adoption of Lev B Okun's notions to make sense of all these matters (check out the paper above). The next point is energy is always relative to some "virtually arbitrary" integration constant of a system and is unable to be defined in "isolation" to a measuring system. It is therefore best to refer to energy in relation to the system it is to do work on and in which measurements are made. Two particles have a relative "zero point of energy" relative to each other. But to the existence of some absolute value of some zero point in energy for the entire Universe suggests that there is a universal frame of reference and I seriously doubt that on strong experimental grounds.
In all calculations of Special Relativity this internal energy usually remains where it currently is and is not affected by any processes external to the particle though it is possible to see that thermal energy would increase the energy content of a pellet of matter and increase the stored kinetic energy in all the contained particles and through some as yet unknown process increase the overall "rest mass" temporarily.
The actual energy content of a system is usually shown to be the result of a series expansion of the first several terms... the first term is the rest energy (where m is the intrinsic mass) of a system of mC^2 followed by the kinetic energy of the system which is 1/2 mV^2 plus an infinite series of terms which are more significant the more closely V approaches C. Clearly the energy content of a particle relative to a measuring apparatus has significant extra energy when V gets very close to C than just the simple sum of potential mass energy content plus kinetic energy content. In all cases this V is relative to some system in which actual measurements are being made and the value is critically dependent on only the relative velocity which is the Principle of Special Relativity.
Here is an example of incorrectly using relativistic mass concepts leading to the physically unrealistic states above but as shown in many common and popular text books...
Wikipedia: Relativistic Momentum
Mathematically the answers are still correct but the phenomenological sense is lost as I have noted above. It will never be "put right" until science attempts to understand this process fundamentally and seriously look at these issues.
So the answer to the question "Is energy being stored in a Gravitational field?" is technically true being the intrinsic mass is a measure of hidden energy content. It is possible to harness some of the internal energy of particles of mass as shown by the release of nuclear energy. The trajectory of bodies in free fall are a source of energy. The gravitational attraction between bodies may be used as a source of energy. Regarding relativity... The question of relativistic energy being the same as relativistic mass is a "very sore point" and it will not be possible to convince many that as particles approach the relative speed of light their mass approaches infinity and as a result the particle cannot exceed the speed of light. I would answer this last point by saying that we should not use the term relativistic mass and refer them all to Lev B Okun's many authoritative papers on this subject. While this issue remains unresolved many questions such as "dark matter" and "dark energy" will remain "mysterious" and unnecessary money will be spent on such researches aimed at finding these "Snarks of Physics" rather than properly addressing the educational issues involved. There may be a real issue to be resolved there but until we get our understanding correct it will appear to be an unresolved issue while various factions fight over the interpretations as is happening right now...
I hope this helps...
Cheers
This is an interesting but controversial subject...
There are only two forms of energy in the Universe ... Kinetic energy which is energy of motion and potential energy which is energy which is stored by virtue solely of it's physical place relative to other parts of it's system and therefore lies latent in respect to it's own internal frame of reference. As an example of latent energy "binding energy" might actually be "kinetic energy" inside a nucleus however we think of it as "potential energy" since the specifics of any of this motion are entirely hidden. The release of binding energy is always in the form of kinetic energy which can be used to heat fluids or change the state of motion of the system... sometimes explosively.
Mass is generally composed of hidden energy. A lack of specific knowledge of the composition and internal structure of mass in detail is the reason why we are unable to unlock the "rest mass" energy of mC^2. Some of this "hidden" energy may be released such as the "binding energy" previously mentioned. The loss of some of this energy will change the rest mass of a particle (or it's components) but this release of formerly "hidden energy" is not normally affected by external linear motion.
We know that all the internal energy, both kinetic and potential, may be released under some kind of "unraveling symmetry operations" when particle and antiparticle are allowed to meet... or in the case of "sparking the vacuum" where two dissimilar high energy photons are mutually scattered into particle and antiparticle. In theory this "internal symmetry" of energy releasing or storing processes might be controllable somehow.
The energy stored in gravitating systems is also a mixture of kinetic and potential energy. Some kinetic energy of an orbiting body might be released if it was to be struck by another freely falling body (a projectile for instance). The potential energy of a body in free fall is released when the body "falls to earth". These are both sort of equivalent energy conversions the first is usually termed "kinetic energy" like playing celestial billiards the other might be interpreted as losing potential energy in the event of "rocks falling from the sky"... In both cases what was latent (hidden) energy becomes heat or can potentially do work. In that sense gravity stores energy which ultimately could be considered as motion when measured from a system in relative motion. This energy is usually never visible from the inertial frame of a single object. So it is often thought that this "latent energy" must be some substance that might be tapped off... this is not the case. Energy is no "substance" stored in things... it is the relationship between objects that causes energy because energy is proportional to the work that a system can do. You cant calculate the "energy" of a particle in isolation. It must always be in relation to an another particle on which some work can be done. Some portion of "intrinsic energy" like nuclear energy may be released in relationship to the other portions of the nuclei of an atom as "heat" (... or light or other radiations). To do that it is necessary that it do work on a "system". I do not personally accept that light or radiation is "intrinsic energy" but light can do work such as in moving electrons in photocells for instance. Light has energy by virtue of it's state of motion.
According to Lev Okun, JA Wheeler, A Einstein and many other respected authorities on the interpretation of Special Relativity and "mass"... there is no such thing as relativistic mass... it is not able to be "defined" or "measured" directly so should not be called a "mass" of any kind. There is only relativistic energy. Mass is definable in only one way... In a rest frame... any rest frame.
The theory of relativity and the Pythagorean theorem - Authors: L. B. Okun (Submitted on 15 Sep 2008)
In any and every rest frame a particular bit of intrinsic mass has the same value where mass can be measured using a spring and a test mass in the 'time honored way". Whenever a mass is discussed it must be a truly phenomenological property that can only be understood in this "special frame". "Mass in relativistic motion" has no specific way of being defined... It is not a measurable of a system but the intrinsic mass can be measured and it is the same in all inertial frames at any relative velocity where it might be "potentially" measured. Of course a particle does have relativistic energy and some people convert this to a "mass" by dividing this relativistic mass by a C^2 factor which is a derived quantity. It might give the correct answer in some problems but the actual "increase in mass" has no physical significance in it's own rest frame. What is actually noted in the external observer frame is time dilation.
As a matter of interest the energy of a system can be seen as an infinite Taylor Series expansion where the first two terms are the intrinsic mass and the kinetic energy at low velocities with other terms which become more and more significant as V -> C.
Wikipedia: Mass-energy equivalence
"Relativistic mass" is not real mass since it has no influence on the processes happening within the rest frame of the observer or the observed... People misunderstand time dilation for the fictitious effects of "mass increase" or in the case of the Wikipedia article on Special Relativity suggesting that the "reluctance" or inertia of a body is due to it's momentum becoming infinitely large as V approaches C... which is a technical absurdity because all uniform velocity is relative and the "speed" of a particle is not an issue at all. The particle in relative motion is undergoing relative time dilation and a system undergoing extreme time dilation "virtually" arrests all temporal processes (relative to external observers) in which energy transfer can occur such that events proceeding in the moving frame are nearly "frozen" in time. The transfer of a photon from one observing system to the relativistically moving system that photon "appears" to the moving system to be red shifted and this carries less energy (apparently) and can do less work. Of course this effect is due only to relative motion since the photon is the same always just that it's internal energy appears shifted spectrally when viewed from within the moving system or the packets of energy transferred from internal clocks in the source to the realm of the sink are running respectively slower. Acceleration due to the transfer of photons from an observer Lab frame to the motion of the accelerated particle is energetically "inefficient". Time dilation ultimately defeats the energy transfer process involved when the effective wavelength becomes much longer than the object required to be scattered by this interaction. I am ignoring the issue of the electromagnetic interaction but there are similar processes involved with charged particles.
Inside the relatively moving frame time is internally perfectly consistent and normal and all internal relativistic processes are "unseen" in it's own inertial frame while impressed external relativistic processes are affected by the relative motion. External processes are seen to run "slower or faster" depending on the rate of "recession or approach" to sources... as an example of this in an extreme case check on the "apparently superluminal Jet" from M86... the "apparent" speed of the approach of the Jet to earth is "about" 6 times the speed of light... a fictitious velocity. As an example of a down to earth example... People are not becoming infinitely heavy on a relativistically receding planet or rocket or they are not becoming more ponderable as time proceeds and they are not more obese or their "weight" is not magically increasing.
An example that would demonstrate this is if a rocket which had some "magical way to accelerate" at "1 Gee" acceleration forever had a test mass attached to a "thin string" in the ceiling of the cabin ... the tension of this string does not increase without limit as T -> infinity eventually breaking the string. In actual fact ... "one Gee" remains the same acceleration always as it would be on earth as it would also be in the spaceship. The laws of Physics are the same everywhere. Of course looking outside of the spaceship at the "background".. things would eventually become very weird indeed after a few short years. Naturally if a particle is charged then a relative velocity may induce electromagnetic consequences in other objects but that is entirely another question... not going there for now. Otherwise "Relativistic mass" cannot be measured and is a derived quantity. No known instrument can measure "relativistic mass" and is therefore not a system measurable.
For instance otherwise "empty space" might have energy content but will exhibit no actual mass and energy content of some specified volume of space cannot have any form of mass regardless of the frame it is measured "in" or "from". No frame of motion relative to a space devoid of matter containing "energy"... lets say light for instance... can be considered as having mass as seen from any other moving frame. I urge the adoption of Lev B Okun's notions to make sense of all these matters (check out the paper above). The next point is energy is always relative to some "virtually arbitrary" integration constant of a system and is unable to be defined in "isolation" to a measuring system. It is therefore best to refer to energy in relation to the system it is to do work on and in which measurements are made. Two particles have a relative "zero point of energy" relative to each other. But to the existence of some absolute value of some zero point in energy for the entire Universe suggests that there is a universal frame of reference and I seriously doubt that on strong experimental grounds.
In all calculations of Special Relativity this internal energy usually remains where it currently is and is not affected by any processes external to the particle though it is possible to see that thermal energy would increase the energy content of a pellet of matter and increase the stored kinetic energy in all the contained particles and through some as yet unknown process increase the overall "rest mass" temporarily.
The actual energy content of a system is usually shown to be the result of a series expansion of the first several terms... the first term is the rest energy (where m is the intrinsic mass) of a system of mC^2 followed by the kinetic energy of the system which is 1/2 mV^2 plus an infinite series of terms which are more significant the more closely V approaches C. Clearly the energy content of a particle relative to a measuring apparatus has significant extra energy when V gets very close to C than just the simple sum of potential mass energy content plus kinetic energy content. In all cases this V is relative to some system in which actual measurements are being made and the value is critically dependent on only the relative velocity which is the Principle of Special Relativity.
Here is an example of incorrectly using relativistic mass concepts leading to the physically unrealistic states above but as shown in many common and popular text books...
Wikipedia: Relativistic Momentum
Mathematically the answers are still correct but the phenomenological sense is lost as I have noted above. It will never be "put right" until science attempts to understand this process fundamentally and seriously look at these issues.
So the answer to the question "Is energy being stored in a Gravitational field?" is technically true being the intrinsic mass is a measure of hidden energy content. It is possible to harness some of the internal energy of particles of mass as shown by the release of nuclear energy. The trajectory of bodies in free fall are a source of energy. The gravitational attraction between bodies may be used as a source of energy. Regarding relativity... The question of relativistic energy being the same as relativistic mass is a "very sore point" and it will not be possible to convince many that as particles approach the relative speed of light their mass approaches infinity and as a result the particle cannot exceed the speed of light. I would answer this last point by saying that we should not use the term relativistic mass and refer them all to Lev B Okun's many authoritative papers on this subject. While this issue remains unresolved many questions such as "dark matter" and "dark energy" will remain "mysterious" and unnecessary money will be spent on such researches aimed at finding these "Snarks of Physics" rather than properly addressing the educational issues involved. There may be a real issue to be resolved there but until we get our understanding correct it will appear to be an unresolved issue while various factions fight over the interpretations as is happening right now...
QUOTE
"It is not good to introduce the concept of the mass M = m/√(1 - V^2/C^2) of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ’rest mass’ m. Instead of introducing M [ed: M is relativistic mass] it is better to mention the expression for the momentum and energy of a body in motion."
– Albert Einstein in letter to Lincoln Barnett, 19 June 1948 (quote from L. B. Okun, “The Concept of Mass,” Phys. Today 42, 31, June 1989.)
– Albert Einstein in letter to Lincoln Barnett, 19 June 1948 (quote from L. B. Okun, “The Concept of Mass,” Phys. Today 42, 31, June 1989.)
I hope this helps...
Cheers
QUOTE
"It is not good to introduce the concept of the mass M = m/√(1 - V^2/C^2) of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ’rest mass’ m. Instead of introducing M [ed: M is relativistic mass] it is better to mention the expression for the momentum and energy of a body in motion."
– Albert Einstein in letter to Lincoln Barnett, 19 June 1948 (quote from L. B. Okun, “The Concept of Mass,” Phys. Today 42, 31, June 1989.)
– Albert Einstein in letter to Lincoln Barnett, 19 June 1948 (quote from L. B. Okun, “The Concept of Mass,” Phys. Today 42, 31, June 1989.)
It is strange that the person that gave us the answer did not recognize it.
Mass is a storage system of energy. When a mass is increased in velocity, the mass increases. There is only one type of mass. It makes no difference if the mass is a result of rest mass (this may be considered the result of the action of spin as can be recognized in string theory) or the actual transition through space.
Mass effect is over an infinite distance and if you wish to consider this a gravity field then the energy is stored in the gravitational field. Although I do not think this is the best way of thinking of the problem.
Hi tlocity,
Good questions...
Good questions...
QUOTE (tlocity+)
Mass is a storage system of energy. When a mass is increased in velocity, the mass increases.
I do not want to become embroiled in a "point of order" here. If you want to talk in terms of "relativistic mass" then you are free to do so (numerically the answers will not be wrong). What you can't do is measure that mass and it has no "physical" status as a "mass". Energy is something else... it is simply a capacity to perform work and moving bodies have relativistic energy.
Sure... you can store energy in a system through relative motion (an example would be a flywheel). If the flywheel was spinning fast enough then it acquires relativistic energy over an above just the value of it's kinetic energy. In any case the intrinsic mass is invariant if measured in it's own inertial frame of reference (in a flywheel it must be considered "piecemeal" over a very short angular distance where the displacement in an arc and is indistinguishable numerically from that of pure unaccelerated linear motion (see a 'good" dissertation on the Ehrenfest Paradox ). The definition of mass is always in it's own rest frame and is the only "place" where this "notion" makes any sense. Mass must be measured "in place" and from rest (meaning instantaneously unaccelerated). The rotating rim is split for the sake of the problem artificially into a number of infinitesimal straight line segments. This is despite the fact that we can argue along the lines of relativistic mass but we will lose the understanding of the underlying nature of the process that we are discussing physically. To me, at least, this is of utmost importance.
Time dilation in Relativity is what is really causing all the fuss since time dilation will occur in the accelerated system (the clocks run relatively slow altering the relationships and magnitudes of all the forces involved). Once again it is not an effect we "see" within our own frame... People do not start to speak with a more and more greatly exaggerated drawl as they near the speed of light (in the same way as they do not get more and more "obese" or heavier as the observed frame approaches a relative velocity near the speed of light)... the effect is noticed only "between" frames not "in" frames since all inertial frames are identical and equivalent at any relative "speed" so the speed you have referred to is not a "measure" of energy content because it is only in relation to another frame that relativistic effects are seen
Clearly relativistic energy is a very important concept but to be "picky" it must be defined as simply the "storing" of energy in a latent fashion as potential energy or the release of some latent energy as kinetic energy (there are really no other forms)... Heat, for instance, is not "latent (hidden) energy" in relativity (or should not be) since it may be readily measured using a calorimeter. Of course heat is released in many reactions and collisions so then it is no longer "hidden away" such as in binding energy. The classical spin of an object has energy but it too is not latent energy. Relativity bundles all latent energy (internal potential and kinetic) stored in mass as E/C^2. This is invariant mass. Other readily discerned energy is the sort of thing you are describing here is very conventional energy that contributes to "motion" in general relative to internal frames such as contributing to the energy stored in the degrees of freedom of particles as mechanical systems. As a general "rule of thumb" if you can directly measure the energy in the inertial frame then it is no longer "latent" in the relativistic sense.
Energy is when we do work on a system and is not something that has a "constitution" like water where you store water in a tank and you can withdraw that water from the tank. Energy is like light but is not actually light and it's photon bears a strong similarity to sound quanta (phonons). When you sing a song the sounds are not "in you" to start with they are created on the fly by your vocal cords. While light carries energy it is not actually energy itself. Light is a form of wavelet particle which can be dissipated in the same way sound is dissipated... however make no mistake that is actually an "ad hoc" particle according to the way we define them.
Protons and electrons cannot be usually "dissipated" and they are also "particles" but they have conservation rules of CPT that prevent the particle from being "dissipated" and to do work. In that sense the mass remains unable to be accessed as energy (usually). Before a photon of light is emitted from a block of matter there is no photon particle already in matter, it is created on the fly by doing work (an electron is "jiggled around" forming the photon in the process), so it does not actually "store" energy in that fashion. The energy to do that "jiggling" comes from the potential energy stored in where the electron is sitting in the atom and how far it "falls" to a lower energy level.. the electron and the atom "do work" on each other like a rock falling from a high cliff "does work" when it strikes the ground.
Mechanical energy can be stored as relativistic energy and it is hidden except when in reference to an external frame of reference on which one system can do work on the other. Photons are quantized and can only lose energy in whole steps of whole quanta... that is the trick here. There are no half or two thirds quanta even if the quantum numbers themselves can come in fractional quantities. Subtle point actually.
Sure... you can store energy in a system through relative motion (an example would be a flywheel). If the flywheel was spinning fast enough then it acquires relativistic energy over an above just the value of it's kinetic energy. In any case the intrinsic mass is invariant if measured in it's own inertial frame of reference (in a flywheel it must be considered "piecemeal" over a very short angular distance where the displacement in an arc and is indistinguishable numerically from that of pure unaccelerated linear motion (see a 'good" dissertation on the Ehrenfest Paradox ). The definition of mass is always in it's own rest frame and is the only "place" where this "notion" makes any sense. Mass must be measured "in place" and from rest (meaning instantaneously unaccelerated). The rotating rim is split for the sake of the problem artificially into a number of infinitesimal straight line segments. This is despite the fact that we can argue along the lines of relativistic mass but we will lose the understanding of the underlying nature of the process that we are discussing physically. To me, at least, this is of utmost importance.
Time dilation in Relativity is what is really causing all the fuss since time dilation will occur in the accelerated system (the clocks run relatively slow altering the relationships and magnitudes of all the forces involved). Once again it is not an effect we "see" within our own frame... People do not start to speak with a more and more greatly exaggerated drawl as they near the speed of light (in the same way as they do not get more and more "obese" or heavier as the observed frame approaches a relative velocity near the speed of light)... the effect is noticed only "between" frames not "in" frames since all inertial frames are identical and equivalent at any relative "speed" so the speed you have referred to is not a "measure" of energy content because it is only in relation to another frame that relativistic effects are seen
Clearly relativistic energy is a very important concept but to be "picky" it must be defined as simply the "storing" of energy in a latent fashion as potential energy or the release of some latent energy as kinetic energy (there are really no other forms)... Heat, for instance, is not "latent (hidden) energy" in relativity (or should not be) since it may be readily measured using a calorimeter. Of course heat is released in many reactions and collisions so then it is no longer "hidden away" such as in binding energy. The classical spin of an object has energy but it too is not latent energy. Relativity bundles all latent energy (internal potential and kinetic) stored in mass as E/C^2. This is invariant mass. Other readily discerned energy is the sort of thing you are describing here is very conventional energy that contributes to "motion" in general relative to internal frames such as contributing to the energy stored in the degrees of freedom of particles as mechanical systems. As a general "rule of thumb" if you can directly measure the energy in the inertial frame then it is no longer "latent" in the relativistic sense.
Energy is when we do work on a system and is not something that has a "constitution" like water where you store water in a tank and you can withdraw that water from the tank. Energy is like light but is not actually light and it's photon bears a strong similarity to sound quanta (phonons). When you sing a song the sounds are not "in you" to start with they are created on the fly by your vocal cords. While light carries energy it is not actually energy itself. Light is a form of wavelet particle which can be dissipated in the same way sound is dissipated... however make no mistake that is actually an "ad hoc" particle according to the way we define them.
Protons and electrons cannot be usually "dissipated" and they are also "particles" but they have conservation rules of CPT that prevent the particle from being "dissipated" and to do work. In that sense the mass remains unable to be accessed as energy (usually). Before a photon of light is emitted from a block of matter there is no photon particle already in matter, it is created on the fly by doing work (an electron is "jiggled around" forming the photon in the process), so it does not actually "store" energy in that fashion. The energy to do that "jiggling" comes from the potential energy stored in where the electron is sitting in the atom and how far it "falls" to a lower energy level.. the electron and the atom "do work" on each other like a rock falling from a high cliff "does work" when it strikes the ground.
Mechanical energy can be stored as relativistic energy and it is hidden except when in reference to an external frame of reference on which one system can do work on the other. Photons are quantized and can only lose energy in whole steps of whole quanta... that is the trick here. There are no half or two thirds quanta even if the quantum numbers themselves can come in fractional quantities. Subtle point actually.
QUOTE (tlocity+)
It makes no difference if the mass is a result of rest mass (this may be considered the result of the action of spin as can be recognized in string theory) or the actual transition through space.
Nobody has a really well scientifically understood POV regarding "quantum spin". It conveys an idea that is "something like" the spin of a top but is is most certainly not that kind of spin. The addition of linear or rotational speed to a particle does not necessarily increase it's quantized spin. The amount of "rotational spin" would be sufficient to change some particles into other particles (bosons into fermions?) and no matter how hard we try we do not see this "physics" happening... there are very strict rules of CPT that hold everything together and do not allow arbitrary increases in the speed of the "atomic flywheels". Of course there are many kinds of spin that can be changed in a system such as the orbital angular momentum but that is a collective property. These other "spins" are in addition to other quantized phenomena. The "quantized energy" is quantized so it can only lose or gain "energy" in whole quanta. Regarding String Theory... I do not think String Theory is a credible theory "yet"... "For me" it need an unequivocal experiment to prove that it is true.
Anyway it is not going to be settled here and now because of the complexity of the underlying processes. I am simply suggesting that this interpretation is critical in "understanding" Physics as opposed to simply having to do the calculations.... You have made some good points though!
Cheers
Anyway it is not going to be settled here and now because of the complexity of the underlying processes. I am simply suggesting that this interpretation is critical in "understanding" Physics as opposed to simply having to do the calculations.... You have made some good points though!
Cheers
Hi Good Elf.
I realize the desire to separate rest mass from the mass that is created and measured due to velocity. The primary reason for this is to try to rationalize relativity. There is however no valid reason to deny observation and experimental results.
When any mass object is subjected to velocity, the measured mass increases. There is no difference observed or indicated that the effects of mass increase due to velocity is any different then rest mass. In fact, the increase in mass energy is the same as the increase in energy applied from the change in velocity. The mass is the energy.
It is seen when an electron fall into the atom the total mass of the resulting atom is less then the mass of the electron by it self added to the atom before the electron entered the atom. We see a loss of energy of the system. The observed loss is usually seen as light. We see mass converted to light.
This same process occurs in all chemical reactions. As atoms approach each other they lose mass and convert that mass into other forms of energy. In chemical process the energy that results allow for a breaking of the current stable bonding and a reformulation to a total lower energy. In the reverse manner, if energy is applied, the lower energy state can be moved to a higher energy state.
This can also be seen in a simple compression of a gas. As pressure is increased, the molecules are forced closer together. Again the mass of the molecules is decreased and is seen as an increase in heat.
The same function works with larger objects such as planets and stars. This is the basic mechanism of gravity. It must be remembered that the effect of mass is over an infinite distance and any mass object has an effect on any other mass object. In this manner, there is no need for curved space or gravitons to affect the path of objects.
When two mass objects move closer their mass is converted into other forms of energy. In the case of large mass objects, any change in distance results in an increase in velocity, orbital velocity. It is therefore self correcting.
I realize the desire to separate rest mass from the mass that is created and measured due to velocity. The primary reason for this is to try to rationalize relativity. There is however no valid reason to deny observation and experimental results.
When any mass object is subjected to velocity, the measured mass increases. There is no difference observed or indicated that the effects of mass increase due to velocity is any different then rest mass. In fact, the increase in mass energy is the same as the increase in energy applied from the change in velocity. The mass is the energy.
It is seen when an electron fall into the atom the total mass of the resulting atom is less then the mass of the electron by it self added to the atom before the electron entered the atom. We see a loss of energy of the system. The observed loss is usually seen as light. We see mass converted to light.
This same process occurs in all chemical reactions. As atoms approach each other they lose mass and convert that mass into other forms of energy. In chemical process the energy that results allow for a breaking of the current stable bonding and a reformulation to a total lower energy. In the reverse manner, if energy is applied, the lower energy state can be moved to a higher energy state.
This can also be seen in a simple compression of a gas. As pressure is increased, the molecules are forced closer together. Again the mass of the molecules is decreased and is seen as an increase in heat.
The same function works with larger objects such as planets and stars. This is the basic mechanism of gravity. It must be remembered that the effect of mass is over an infinite distance and any mass object has an effect on any other mass object. In this manner, there is no need for curved space or gravitons to affect the path of objects.
When two mass objects move closer their mass is converted into other forms of energy. In the case of large mass objects, any change in distance results in an increase in velocity, orbital velocity. It is therefore self correcting.
Hi tlocity et al,
QUOTE (tlocity+)
I realize the desire to separate rest mass from the mass that is created and measured due to velocity. The primary reason for this is to try to rationalize relativity. There is however no valid reason to deny observation and experimental results.
When any mass object is subjected to velocity, the measured mass increases. There is no difference observed or indicated that the effects of mass increase due to velocity is any different then rest mass. In fact, the increase in mass energy is the same as the increase in energy applied from the change in velocity. The mass is the energy.
Excellent question... You have made some very important points there that need to be addressed. It is not "my" desire but I agree strongly with the sentiment stated by Lev B. Okun (former head of the High Energy Physics Lab in Moscow) I take your point about exchange of electrons and so forth but the important issue to consider is the exchange of photons which are massless "objects" involving "energy" and how we deal with energy as if it were "ponderable" mass. Nobody is "denying experimental results" but in which experiment were you able to measure the relativistic mass and what instrument did you use to do that? Mass is a fundamental property but what is relativistic mass but a derived quantity? What I am saying is you used a derived figure which came from energy measurements and this "pseudo-property" had no direct comparison to the a mass-like property that might be defined in any fixed way (in fact I indicate a reference below where you need an infinite series of terms to define it while still being "derived"). In Okun's concept if we deal with this invarient mass we result in a simple relationship according to his many papers one of which is shown here...
The theory of relativity and the Pythagorean theorem - Authors: L. B. Okun (Submitted on 15 Sep 2008)
... This idea is very simple and easy to grasp (Pythagoras' Theorem) of "energy" written in mass units (for convenience)... m = √(e² - p²) where m is the intrinsic mass and e is the total energy and p is the momentum.... provided some ground rules are strictly obeyed. Calculation-wise it leads to the same results as calculations using "relativistic mass" but with the provision of some important "epistemological concepts". However you would have used a "rest mass" in these calculations which must be given some kind of significance since the mass of an object is of phenomenological importance. If a particle has internal "binding energy"... it is understood that a part of this energy may be released as kinetic energy with a very well understood small loss of mass from the overall subsequent fermionic constituants. If this energy is lost solely as photons (for the sake of the argument) which are massless particles... then this system is changing the value of the intrinsic mass and Okun's argument does not directly apply. In systems in which intrinsic mass may be defined as 'fixed" (at least temporarily)... additions or losses of energy in the form of photons does not modify this intrinsic quantity of mass because the quantity is defined in it's own "rest frame" (read inertial frame... or the state of motion which has not undergone accelerations)... so there is conservation of "intrinsic mass". To measure this "rest mass" the particles must be "returned to a rest frame" in which the mass will be measured. According to Okun this would be any equivalent rest frame in which we measure the same amount of intrinsic mass. This might mean "cooling down the atoms" to get an accurate measure.
Another more familiar example is if you had a gyroscope and before an experiment it's mass was measured "at rest" in it's own inertial frame (in free fall)... subsequently the gyroscope was "spun up" and now has both kinetic energy and additional angular momentum (and usually a small almost imperceptible additional relativistic energy)... a measure of the mass in a rest frame (relative to an external observer) would show that it's mass had very subtly increased.
However this energy is not entirely "latent" but is clearly due to the additional motion of the gyroscope. You could put the gyroscope in a sealed box and you could (in principle) still say that the internal system is not equivalent to the former system because of a small increase in it's mass). Remember that arguments of this sort were used by Bohr to depose Einstein's Skepticism about certain interpretations of quantum theory (though it never really did). The outcome of this Gedanken Experiment hung on the "weight" of a single transferred "photon" in a box shifting the overall position of the box in a gravity field just the right amount to account for the effect of it's increased mass through the "uncertainty".
Discussions with Einstein on Epistemological Problems in Atomic Physics - N Bohr
So what is the weight of the box if the photon is still in a state where it has no mass?... The box's intrinsic mass would remain unchanged. If the photon is absorbed by the box as additional kinetic energy the box would increase in mass due to the additional energy content of the box plus absorbed kinetic energy but it would be possible to measure the mass increase and suggest that this is a new intrinsic mass. Regarding this Gyroscope... It is important to define which of these two measurements is the "true" intrinsic mass.... the "before" measurement or the "after" measurement? The addition of a photon to the box could be considered as "spinning up" an atomic gyroscope thereby changing the internal frame of reference and altering the intrinsic mass. The lack of commitment to a definition of mass has led to an "uncertainty" in measurements of the actual measurables in Relativity of position and momentum... or alternatively energy and time (Heisenberg's Uncertainty Relationship). Formerly this relationship was dealt with entirely statistically using Heisenberg's Uncertainty Relationship. Currently there are questions regarding the fundamental nature of this relationship of inner products in states where there is not yet a defining measurement. We have learned to make "several partial measurements" of systems as described by Yakir Aharonov resolving some former contradictions (see arguments surrounding Hardy's Paradox). The arguments of particle locality becomes an important issue and this relates back to the Fermi Wavelength (de Broglie Wavelength at the Fermi edge).
A more rigorous application of this principle would have shown that until the energy was absorbed and subsequently the "mass" increased... the system measurement could not be made to show a change in the intrinsic mass. Alternatively... To return this object to it's "intrinsic mass" would need to be brought back to "rest" where another measurement would show that the "gyroscope" had returned to it's former "intrinsic mass" when the kinetic energy was removed. Most importantly the fundamental Principle of Relativity is still to be retained... If these experiments were carried out in a rocket in free fall it is not prevented from undergoing an external acceleration and subsequently returned to an inertial frame by cutting the engines... this latter inertial frame is entirely equivalent to the former inertial frame and will measure the same "intrinsic mass" for the gyroscope (returned to it's former state). Relativity does not discriminate between the two frames... a very important consideration in Okun's argument.
The addition of photons to an atom would effectively cause a "spin up" in the system which is mostly hidden and is possible to be considered as latent or not latent dependent on how we want to measure the system. Photons are not conserved in systems except where matter-antimatter selection rules apply then the photons are conserved... otherwise not! We really cannot speak of an atom plus a photon as having an intrinsic mass greater than the atom without the photon because the photon has no mass. However the atom plus the kinetic energy of a photon (stored as resonance) does have an additional mass. What we must not do is ignore these inputs and outputs of energy. If we want to measure the intrinsic mass of a system "accurately" we must wait for the system to now "spin down" and emit the photon or radiate the infra red energy to measure the same intrinsic mass at an equivalent temperature.
By considerations of this "subtle rest frame" when considering this non-latent energy it is only important to make such considerations when this thermal energy is of significance or other internal systems which store and forward energy or momentum. This "agitation" exciting the degrees of internal freedom is known but small as a proportion of mass. Most calculations ignore these internal modes of motion no matter what they might be or their relative magnitude. They are most assuredly kinetic energy or even potential energy when measured but this would be very difficult to measure given the motion of the overall thermally excited state of the atom. Just because something may be "difficult" does not mean we can dispense with it... this is what this analysis shows.
An example would be a flywheel which is potential energy even though the energy is assuredly kinetic in origin. We can easily see that while we are discussing the difference in mass of an atom near absolute zero Kelvin and room temperature this component of mass is relatively insignificant and I don't know anyone who does calculations of this kind incorporating this small component adding in the even smaller relativistic energy. It is also clearly obvious from a study of condensed matter physics that the The Fermi wavelength λ_F = 2π/k_F which is the de Broglie wavelength of the constituent particles at the Fermi edge... will result in a decrease in the matter wavelength simply due to this thermal motion. There is a connection between de Broglie wavelength and Special Relativity, even at low velocity, since matter waves obey the de Broglie-Einstein relationship...
Wikipedia: Matter wave - The de Broglie relations
In particular we see a relationship which is momentum related all the way down to zero velocity where this effect is greatest...
λ = h/mv √(1 - v²/C²)
If you do not measure this mass in the rest frame then the "state of the agitated condition of the constituents" must add a small but significant amount to the overall mass which must be accounted for... temporary as this change might be. As an example a "hot" atom of beryllium would be ever so slightly heavier than a very cold atom of beryllium due to a tiny component of relativistic internal motion of "components" (and their mass-energy equivalence) within the nucleus and in the electron shells. However if we "cool" a beryllium atom (in a special way) such that it splits into two equal portions releasing the "hot" energy of binding... the mass of these two "cool" component helium atoms, as a combination, will also be slightly reduced relative to the original beryllium atom's components. I realize I am using this idea to emphasize the similarity of kinetic energy and binding energy. Energy is the capacity to perform work and ultimately is not some "fluid" filling space but is the way systems do actual work on each other. Intrinsic matter acquires or loses additional "matter" by some process involving work not on the transfer of some "fluidic energy". The creation of matter and the destruction of matter through antiparticles suggests that relativistic intrinsic mass is entirely stored as energy in some as yet unknown way. The intrinsic mass when considering such fission (or fusion) transmutations (and similar transformations) must be related to this latter "cooler" state of helium atoms and the absorption of this "lets say" massless photonic binding energy that causes the lighter atoms to have a different intrinsic mass. This makes a lot of sense if the binding energy is "similar" in some respect to simply heating the atom through some external process... that is if binding energy and thermal energy which are both underlying kinetic energy are the root origin of this mass change or the fundamental process from which energy is released.
All particles we know about in nature have defined masses (fermions) or they are massless (bosons). It makes sense to consider the mass being different when measured in different states of motion. This intrinsic mass is only a meaningful quantity if the kinetic energy content is not a significant contributor to the mass or it's variable contribution is made the same when a measure of the mass is made rendering internal sources of energy latent (one way to do this would be to measure the "intrinsic mass" at the same temperature all the time). When dealing with the thermal motion of a common heat source it is often the case this mass might be ignored... but when using "ultra-relativistic" sources of energy it cannot be ignored when significantly more energy and mass is involved. We need to separate the mass which must be measured as intrinsic mass from the energy which cannot be normally measured as mass because it may be rendered under certain circumstances as "massless" as photons (which have no rest mass).
There is no reasonable lower cut-off to relativity. The reason I emphasize this point is the fact that as the velocity of a particle approaches it's "lowest possible energy" (zero point energy?) the mass of the particle approaches it's limiting measurable intrinsic mass but at the same time the wavelength is lengthening in an inverse proportion to the momentum exchanged when confined (lets say in a crystal for instance). This is the reason why the intrinsic mass is so important because it also defines a wavelength for a particular particle in a confined or free state. The intrinsic mass also defines other sources of internal energy unaccounted for in our calculations.
In the Wikipedia article on Special Relativity the equations are written to emphasize the fact that total energy minus the rest mass energy, which is the "intrinsic mass", equals the kinetic energy plus other terms of the Taylor Expansion. This "intrinsic mass term" should be placed back where it belongs on the right hand side of this equation which shows clearly that Energy (in all forms) equals "intrinsic mass" plus kinetic energy plus an infinite series of relativistic terms whose importance depends on the proximity to the speed of light the particles are measured... these later terms are entirely relativistic in origin and show how Energy of a particle is not simply the sum of the rest mass energy plus it's straight kinetic energy which is a most important consideration.
Special Relativity - Classical Limit
... note the "classical limit" hides the fact that relativity involves these higher order terms which increase rapidly... that is what some call relativistic mass but it is not "ponderable mass" which is measurable as our "intrinsic mass".
A "free particle" unconfined in a space would have no definable wavelength (λ = ∞ if v =0) unless it was measured with respect to a system such as the observer system which may choose to be as close to this velocity as is possible using a confining "box" in order to limit it's motion and make the measurement. The particle and the observer and his instrument form a simple system and it is more or less assumed they are considered to be measuring the particle's intrinsic mass or assemblies of component intrinsic masses (such as fragments of the nucleus). The quanta are fixed masses as assemblies differing in having a lower than average mass when combined than when completely separated into particles such as electrons, protons and neutrons. It is arguably true that any particle of mass could be (in theory) reduced to a photon of equivalent energy which would not have any mass at all (consider the process of "sparking he vacuum" and particle annihilation being ways of reducing any complementary symmetry particles to a "very energetic" photon).
Given these restraints we can therefore understand what is meant by this "intrinsic mass" being an invariant mass within the realm of a system under measurement but needs some care when we choose to measure it. A state in which a measurement may be made involves the observer frame of which there may be many and the value of the kinetic energy term and subsequent relativistic energy terms is dependent on the specific observer frame chosen. In the case of relativistic mass this is a state which cannot be measured since measurements of mass must relate to the inertial frame. We might be able to determine energy relative to some system but this energy is variable and depends on the system it is measured from. However the invariant or intrinsic mass is a property that we can measure, and it has the same significance in all inertial frames.
Cheers
PS: Love the questions!!
When any mass object is subjected to velocity, the measured mass increases. There is no difference observed or indicated that the effects of mass increase due to velocity is any different then rest mass. In fact, the increase in mass energy is the same as the increase in energy applied from the change in velocity. The mass is the energy.
Excellent question... You have made some very important points there that need to be addressed. It is not "my" desire but I agree strongly with the sentiment stated by Lev B. Okun (former head of the High Energy Physics Lab in Moscow) I take your point about exchange of electrons and so forth but the important issue to consider is the exchange of photons which are massless "objects" involving "energy" and how we deal with energy as if it were "ponderable" mass. Nobody is "denying experimental results" but in which experiment were you able to measure the relativistic mass and what instrument did you use to do that? Mass is a fundamental property but what is relativistic mass but a derived quantity? What I am saying is you used a derived figure which came from energy measurements and this "pseudo-property" had no direct comparison to the a mass-like property that might be defined in any fixed way (in fact I indicate a reference below where you need an infinite series of terms to define it while still being "derived"). In Okun's concept if we deal with this invarient mass we result in a simple relationship according to his many papers one of which is shown here...
The theory of relativity and the Pythagorean theorem - Authors: L. B. Okun (Submitted on 15 Sep 2008)
... This idea is very simple and easy to grasp (Pythagoras' Theorem) of "energy" written in mass units (for convenience)... m = √(e² - p²) where m is the intrinsic mass and e is the total energy and p is the momentum.... provided some ground rules are strictly obeyed. Calculation-wise it leads to the same results as calculations using "relativistic mass" but with the provision of some important "epistemological concepts". However you would have used a "rest mass" in these calculations which must be given some kind of significance since the mass of an object is of phenomenological importance. If a particle has internal "binding energy"... it is understood that a part of this energy may be released as kinetic energy with a very well understood small loss of mass from the overall subsequent fermionic constituants. If this energy is lost solely as photons (for the sake of the argument) which are massless particles... then this system is changing the value of the intrinsic mass and Okun's argument does not directly apply. In systems in which intrinsic mass may be defined as 'fixed" (at least temporarily)... additions or losses of energy in the form of photons does not modify this intrinsic quantity of mass because the quantity is defined in it's own "rest frame" (read inertial frame... or the state of motion which has not undergone accelerations)... so there is conservation of "intrinsic mass". To measure this "rest mass" the particles must be "returned to a rest frame" in which the mass will be measured. According to Okun this would be any equivalent rest frame in which we measure the same amount of intrinsic mass. This might mean "cooling down the atoms" to get an accurate measure.
Another more familiar example is if you had a gyroscope and before an experiment it's mass was measured "at rest" in it's own inertial frame (in free fall)... subsequently the gyroscope was "spun up" and now has both kinetic energy and additional angular momentum (and usually a small almost imperceptible additional relativistic energy)... a measure of the mass in a rest frame (relative to an external observer) would show that it's mass had very subtly increased.
However this energy is not entirely "latent" but is clearly due to the additional motion of the gyroscope. You could put the gyroscope in a sealed box and you could (in principle) still say that the internal system is not equivalent to the former system because of a small increase in it's mass). Remember that arguments of this sort were used by Bohr to depose Einstein's Skepticism about certain interpretations of quantum theory (though it never really did). The outcome of this Gedanken Experiment hung on the "weight" of a single transferred "photon" in a box shifting the overall position of the box in a gravity field just the right amount to account for the effect of it's increased mass through the "uncertainty".
Discussions with Einstein on Epistemological Problems in Atomic Physics - N Bohr
So what is the weight of the box if the photon is still in a state where it has no mass?... The box's intrinsic mass would remain unchanged. If the photon is absorbed by the box as additional kinetic energy the box would increase in mass due to the additional energy content of the box plus absorbed kinetic energy but it would be possible to measure the mass increase and suggest that this is a new intrinsic mass. Regarding this Gyroscope... It is important to define which of these two measurements is the "true" intrinsic mass.... the "before" measurement or the "after" measurement? The addition of a photon to the box could be considered as "spinning up" an atomic gyroscope thereby changing the internal frame of reference and altering the intrinsic mass. The lack of commitment to a definition of mass has led to an "uncertainty" in measurements of the actual measurables in Relativity of position and momentum... or alternatively energy and time (Heisenberg's Uncertainty Relationship). Formerly this relationship was dealt with entirely statistically using Heisenberg's Uncertainty Relationship. Currently there are questions regarding the fundamental nature of this relationship of inner products in states where there is not yet a defining measurement. We have learned to make "several partial measurements" of systems as described by Yakir Aharonov resolving some former contradictions (see arguments surrounding Hardy's Paradox). The arguments of particle locality becomes an important issue and this relates back to the Fermi Wavelength (de Broglie Wavelength at the Fermi edge).
A more rigorous application of this principle would have shown that until the energy was absorbed and subsequently the "mass" increased... the system measurement could not be made to show a change in the intrinsic mass. Alternatively... To return this object to it's "intrinsic mass" would need to be brought back to "rest" where another measurement would show that the "gyroscope" had returned to it's former "intrinsic mass" when the kinetic energy was removed. Most importantly the fundamental Principle of Relativity is still to be retained... If these experiments were carried out in a rocket in free fall it is not prevented from undergoing an external acceleration and subsequently returned to an inertial frame by cutting the engines... this latter inertial frame is entirely equivalent to the former inertial frame and will measure the same "intrinsic mass" for the gyroscope (returned to it's former state). Relativity does not discriminate between the two frames... a very important consideration in Okun's argument.
The addition of photons to an atom would effectively cause a "spin up" in the system which is mostly hidden and is possible to be considered as latent or not latent dependent on how we want to measure the system. Photons are not conserved in systems except where matter-antimatter selection rules apply then the photons are conserved... otherwise not! We really cannot speak of an atom plus a photon as having an intrinsic mass greater than the atom without the photon because the photon has no mass. However the atom plus the kinetic energy of a photon (stored as resonance) does have an additional mass. What we must not do is ignore these inputs and outputs of energy. If we want to measure the intrinsic mass of a system "accurately" we must wait for the system to now "spin down" and emit the photon or radiate the infra red energy to measure the same intrinsic mass at an equivalent temperature.
By considerations of this "subtle rest frame" when considering this non-latent energy it is only important to make such considerations when this thermal energy is of significance or other internal systems which store and forward energy or momentum. This "agitation" exciting the degrees of internal freedom is known but small as a proportion of mass. Most calculations ignore these internal modes of motion no matter what they might be or their relative magnitude. They are most assuredly kinetic energy or even potential energy when measured but this would be very difficult to measure given the motion of the overall thermally excited state of the atom. Just because something may be "difficult" does not mean we can dispense with it... this is what this analysis shows.
An example would be a flywheel which is potential energy even though the energy is assuredly kinetic in origin. We can easily see that while we are discussing the difference in mass of an atom near absolute zero Kelvin and room temperature this component of mass is relatively insignificant and I don't know anyone who does calculations of this kind incorporating this small component adding in the even smaller relativistic energy. It is also clearly obvious from a study of condensed matter physics that the The Fermi wavelength λ_F = 2π/k_F which is the de Broglie wavelength of the constituent particles at the Fermi edge... will result in a decrease in the matter wavelength simply due to this thermal motion. There is a connection between de Broglie wavelength and Special Relativity, even at low velocity, since matter waves obey the de Broglie-Einstein relationship...
Wikipedia: Matter wave - The de Broglie relations
In particular we see a relationship which is momentum related all the way down to zero velocity where this effect is greatest...
λ = h/mv √(1 - v²/C²)
If you do not measure this mass in the rest frame then the "state of the agitated condition of the constituents" must add a small but significant amount to the overall mass which must be accounted for... temporary as this change might be. As an example a "hot" atom of beryllium would be ever so slightly heavier than a very cold atom of beryllium due to a tiny component of relativistic internal motion of "components" (and their mass-energy equivalence) within the nucleus and in the electron shells. However if we "cool" a beryllium atom (in a special way) such that it splits into two equal portions releasing the "hot" energy of binding... the mass of these two "cool" component helium atoms, as a combination, will also be slightly reduced relative to the original beryllium atom's components. I realize I am using this idea to emphasize the similarity of kinetic energy and binding energy. Energy is the capacity to perform work and ultimately is not some "fluid" filling space but is the way systems do actual work on each other. Intrinsic matter acquires or loses additional "matter" by some process involving work not on the transfer of some "fluidic energy". The creation of matter and the destruction of matter through antiparticles suggests that relativistic intrinsic mass is entirely stored as energy in some as yet unknown way. The intrinsic mass when considering such fission (or fusion) transmutations (and similar transformations) must be related to this latter "cooler" state of helium atoms and the absorption of this "lets say" massless photonic binding energy that causes the lighter atoms to have a different intrinsic mass. This makes a lot of sense if the binding energy is "similar" in some respect to simply heating the atom through some external process... that is if binding energy and thermal energy which are both underlying kinetic energy are the root origin of this mass change or the fundamental process from which energy is released.
All particles we know about in nature have defined masses (fermions) or they are massless (bosons). It makes sense to consider the mass being different when measured in different states of motion. This intrinsic mass is only a meaningful quantity if the kinetic energy content is not a significant contributor to the mass or it's variable contribution is made the same when a measure of the mass is made rendering internal sources of energy latent (one way to do this would be to measure the "intrinsic mass" at the same temperature all the time). When dealing with the thermal motion of a common heat source it is often the case this mass might be ignored... but when using "ultra-relativistic" sources of energy it cannot be ignored when significantly more energy and mass is involved. We need to separate the mass which must be measured as intrinsic mass from the energy which cannot be normally measured as mass because it may be rendered under certain circumstances as "massless" as photons (which have no rest mass).
There is no reasonable lower cut-off to relativity. The reason I emphasize this point is the fact that as the velocity of a particle approaches it's "lowest possible energy" (zero point energy?) the mass of the particle approaches it's limiting measurable intrinsic mass but at the same time the wavelength is lengthening in an inverse proportion to the momentum exchanged when confined (lets say in a crystal for instance). This is the reason why the intrinsic mass is so important because it also defines a wavelength for a particular particle in a confined or free state. The intrinsic mass also defines other sources of internal energy unaccounted for in our calculations.
In the Wikipedia article on Special Relativity the equations are written to emphasize the fact that total energy minus the rest mass energy, which is the "intrinsic mass", equals the kinetic energy plus other terms of the Taylor Expansion. This "intrinsic mass term" should be placed back where it belongs on the right hand side of this equation which shows clearly that Energy (in all forms) equals "intrinsic mass" plus kinetic energy plus an infinite series of relativistic terms whose importance depends on the proximity to the speed of light the particles are measured... these later terms are entirely relativistic in origin and show how Energy of a particle is not simply the sum of the rest mass energy plus it's straight kinetic energy which is a most important consideration.
Special Relativity - Classical Limit
... note the "classical limit" hides the fact that relativity involves these higher order terms which increase rapidly... that is what some call relativistic mass but it is not "ponderable mass" which is measurable as our "intrinsic mass".
A "free particle" unconfined in a space would have no definable wavelength (λ = ∞ if v =0) unless it was measured with respect to a system such as the observer system which may choose to be as close to this velocity as is possible using a confining "box" in order to limit it's motion and make the measurement. The particle and the observer and his instrument form a simple system and it is more or less assumed they are considered to be measuring the particle's intrinsic mass or assemblies of component intrinsic masses (such as fragments of the nucleus). The quanta are fixed masses as assemblies differing in having a lower than average mass when combined than when completely separated into particles such as electrons, protons and neutrons. It is arguably true that any particle of mass could be (in theory) reduced to a photon of equivalent energy which would not have any mass at all (consider the process of "sparking he vacuum" and particle annihilation being ways of reducing any complementary symmetry particles to a "very energetic" photon).
Given these restraints we can therefore understand what is meant by this "intrinsic mass" being an invariant mass within the realm of a system under measurement but needs some care when we choose to measure it. A state in which a measurement may be made involves the observer frame of which there may be many and the value of the kinetic energy term and subsequent relativistic energy terms is dependent on the specific observer frame chosen. In the case of relativistic mass this is a state which cannot be measured since measurements of mass must relate to the inertial frame. We might be able to determine energy relative to some system but this energy is variable and depends on the system it is measured from. However the invariant or intrinsic mass is a property that we can measure, and it has the same significance in all inertial frames.
Cheers
PS: Love the questions!!
Hello tiocity, GoodElf
One could say that intrinsic mass generates a time gradient about itself while relativistic mass determines at what rate a time gradient starts in relation to the universe as a whole.
The time gradient stays the same but the foot print with respect to the universe increases.
One could say that intrinsic mass generates a time gradient about itself while relativistic mass determines at what rate a time gradient starts in relation to the universe as a whole.
The time gradient stays the same but the foot print with respect to the universe increases.
Hi Montec, tiocity, Confused2, Geoff Mollusc, AlphaNumeric, flyingbuttressman et al,
QUOTE (Montec+)
One could say that intrinsic mass generates a time gradient about itself while relativistic mass determines at what rate a time gradient starts in relation to the universe as a whole.
The time gradient stays the same but the foot print with respect to the universe increases.
The time gradient stays the same but the foot print with respect to the universe increases.
Gee... I see you were smiling when you said that. I think you were saying that there is no relativistic time dilation within the one inertial frame (even if points being compared are "distributed" spatially). Special Relativity and all of it's effects are the result of either time dilation or "length contraction".. and not the result of the fictitious relativistic "mass increase". That bit you said about "the Universe as a whole" makes no sense in Relativity since all inertial frames are equivalent (... though obviously not the same).
In General Relativity the same overall time dilation effect can be noted when "immersed" in a gravitational (or inertial) gradient such as the so called Earth's "field"... then there could be a "time gradient" between the rate of clocks "immersed" more deeply in the Earth's "field" and an observer in an elevated position "at rest" due to Gravitational Red Shift which should be independent of a separable Special Relativistic Effect.
Pound–Rebka experiment
Once again the effect is not down to photons mass changing (photons have no mass) but due to photons losing momentum climbing out of a gravity well. See Okun's paper on this interpretation.
Various similar experiment were performed using a circling aircraft which showed that there are two components to this time dilation effect but in general... accelerated clocks run slow and that is aside from any attendant optical phenomenon. light usually "propagates" between separated points in space except when we consider certain special cases where we are within the evanescent field and the photons are still attached to sources. Note that in the evanescent field of electromagnetic phenomena temporal events are able to proceed (our power lines, alternating fields and magnetic machines have sources that all work in our near field)... just as well because we need our clocks to measure time accurately. On the other hand photons that are propagating in the far field are "frozen in time" due to the most extreme effects of time dilation (photons travel at the speed of light) and will remain intact and unchanged nearly forever or until they are absorbed in a near-field situation. These photons simultaneously undergo the most extreme form of length contraction as well such that the distance between events seen from the frame of reference of the photon is exactly zero... this juxtaposes the source of photons with sinks in the frame of the photon making the spacelike and timelike separation observers see nonexistent to the propagating photon.. Alternatively large spacelike separations may be contrived to be entangled with events that have no timelike separation... in the near field of the gravitational potential.
World's Largest Quantum Bell Test Spans Three Swiss Towns
Physicists Seek Answers to Quantum Correlations
The optical phenomena are not really that important such as Relativistic Stellar Aberration and change in frequency of light when a source is either approaching or receding. These phenomena are similar to fair ground hall of mirror effects... some make you look fat or thin or warped into strange shapes. These effects are independent of Special Relativity but are only seen when we are discussing very high relative velocities near the speed of light. Some people think that it is all about how light behaves and relates to the problem of travel at faster than the speed of light. Relativity is actually about the two main phenomena of time dilation and "length contraction".
An example of "relativistic" optical effects is M87 and it's apparently superluminal Jet (probably due to a "Black Hole")... the Jet is not traveling at the "apparent" absurd speed of six times the speed of light even though it is visibly approaching us across space at this speed... that would be absurd. Matter cannot even travel at the speed of light. What we are seeing is the light from this Jet compressed spatially in our direction and now being seen at six times the frequency it was originally emitted from the moving source which is currently very close to our position. The light that was emitted is now being "fast forwarded" at X6 speed and the events appear to be happening six times as fast as they originally occurred. The effect is purely an optical phenomena due to relative motion and light's ability to find it's own way from sources to sinks. If we were a planet on the far side of this jet and the jet was moving directly away from us it would appear to us to be traveling at only slightly less than half the speed of light and would be deeply red shifted when compared to the original sources... It is all smoke and mirrors and we need to understand that no object can "appear" to recede at a speed greater than half the speed of light. Any object visibly traveling faster than half the speed of light away from us must be being "inertially pulled away". The explanation for this extra "speed" is Hubble Expansion which is due to a continuing spacetime spreading/stretching in every direction as a consequence of the "Big Bang".
Note that the "at rest" comment in a non-inertial field statement above is also in parenthesis because this Pound–Rebka Effect is for non-inertial systems (General Relativity) while Special Relativity is related to inertial systems (free fall) so the application of Special Relativity should use a piecemeal incremental summation approach. I am not aware of any GR Theory that will actually work near the speed of light (and been tested) and the theory is best used to describe lower velocity ponderable masses on a slightly curved spacetime without spin or manifold torsion because the tensor maths used to describe the theory will not work in a highly curved spacetime. The four-momentum description is at odds with Okun's Special Relativity Interpretation (...special relativity is not wrong or even "special"... just deals with the problem in a different way) ... so I have far less confidence about a general interpretation of four-momentum (or even energy-momentum tensor) when considering any massless content of spacetime which consider energy as having a "density".
This relates back to the original question "Is Energy Stored In A Gravitational Field?". Energy is capacity to do work and energy must be applied specifically for it to actually exist at all. As an example a rock on the top of Mount Everest has potential energy to do work on the desk in front of you. You may be able to work out how much work it might do but it is meaningless since that rock cannot be arranged to perform that work and work that the rock may do will more likely be performed on some other system that you have no control over... such as falling down the cliff face locally where the energy it has there will be quite different and do work on an entirely different system. This must be viewed in the context of the energy content of matter which is very high but unable to be directly harnessed. The matter content is undeniable and is the intrinsic mass. Any other energy is 'something else" and the ability to harness the energy depends on the specific process we undertake to "unravel" this bound and system specific energy in matter.
The "energy density" of the space or of spacetime is a very non-physical concept that has not been fully tested except in the Newtonian limit with "real systems". The general notion might seem reasonable to many but to me it appears very hypothetical and not directly related to our world of experimental physics. Yet there are many features that are applicable to the way our universe works such as general covariance and limiting conditions that converge on Newton's Laws. Of course all such theories must do this in order to have a chance of working. Where the test for such theories resides is in regions of large masses and mass densities and also to these masses moving at large velocities and to it's applicability to "mostly empty" space. Under these conditions tensor maths fail because they are involved with only infinitesimal deformations and cannot directly handle sources where densities rise to infinity. This means as it stands presently at the level of a Theory it must fail even when dealing with any single common particle of matter or even worse when dealing with "Black Holes".
These extreme conditions are hard to test on the Earth. On the other hand Special Relativity has a more concrete application and is physically meaningful and scientists can work out many more problems with it with a lot of certainty since we can actually do tests on relativistic particles and the theory holds up pretty well. Special Relativity has made no such "assumptions" and does not necessarily use Tensor Maths so has a more general applicability (assuming Okun is correct). IMHO a lot of problems with dark matter, dark energy, great attractors and our current GR theory may be related to these epistemological problems Okun has mentioned. They must be resolved before we are able to proceed. It is no use simply ignoring these problems and saying it is of no consequence what we do.
Regarding the energy content of space with "Gravitational Fields"... Yes there is energy stored there mainly at the "sources" but matter sources presently cannot be decomposed too far to do additional work except in Fission and Fusion Bombs and other methods such as antimatter-matter reactions. Certainly we are not able to "tap off some energy" anywhere we would like it for the reasons given above (matter sources in free space are not local)... it does not work like "water" and 'flow" as we usually hear about in the so called "healing arts", it is not a substance of any kind at all. We actually need to build machines in order to harness energy by "doing work". Maybe someday we might build a machine that can unravel the energy stored in bulk matter completely... I dunno?... But that would be very useful.
Cheers
In General Relativity the same overall time dilation effect can be noted when "immersed" in a gravitational (or inertial) gradient such as the so called Earth's "field"... then there could be a "time gradient" between the rate of clocks "immersed" more deeply in the Earth's "field" and an observer in an elevated position "at rest" due to Gravitational Red Shift which should be independent of a separable Special Relativistic Effect.
Pound–Rebka experiment
Once again the effect is not down to photons mass changing (photons have no mass) but due to photons losing momentum climbing out of a gravity well. See Okun's paper on this interpretation.
Various similar experiment were performed using a circling aircraft which showed that there are two components to this time dilation effect but in general... accelerated clocks run slow and that is aside from any attendant optical phenomenon. light usually "propagates" between separated points in space except when we consider certain special cases where we are within the evanescent field and the photons are still attached to sources. Note that in the evanescent field of electromagnetic phenomena temporal events are able to proceed (our power lines, alternating fields and magnetic machines have sources that all work in our near field)... just as well because we need our clocks to measure time accurately. On the other hand photons that are propagating in the far field are "frozen in time" due to the most extreme effects of time dilation (photons travel at the speed of light) and will remain intact and unchanged nearly forever or until they are absorbed in a near-field situation. These photons simultaneously undergo the most extreme form of length contraction as well such that the distance between events seen from the frame of reference of the photon is exactly zero... this juxtaposes the source of photons with sinks in the frame of the photon making the spacelike and timelike separation observers see nonexistent to the propagating photon.. Alternatively large spacelike separations may be contrived to be entangled with events that have no timelike separation... in the near field of the gravitational potential.
World's Largest Quantum Bell Test Spans Three Swiss Towns
Physicists Seek Answers to Quantum Correlations
The optical phenomena are not really that important such as Relativistic Stellar Aberration and change in frequency of light when a source is either approaching or receding. These phenomena are similar to fair ground hall of mirror effects... some make you look fat or thin or warped into strange shapes. These effects are independent of Special Relativity but are only seen when we are discussing very high relative velocities near the speed of light. Some people think that it is all about how light behaves and relates to the problem of travel at faster than the speed of light. Relativity is actually about the two main phenomena of time dilation and "length contraction".
An example of "relativistic" optical effects is M87 and it's apparently superluminal Jet (probably due to a "Black Hole")... the Jet is not traveling at the "apparent" absurd speed of six times the speed of light even though it is visibly approaching us across space at this speed... that would be absurd. Matter cannot even travel at the speed of light. What we are seeing is the light from this Jet compressed spatially in our direction and now being seen at six times the frequency it was originally emitted from the moving source which is currently very close to our position. The light that was emitted is now being "fast forwarded" at X6 speed and the events appear to be happening six times as fast as they originally occurred. The effect is purely an optical phenomena due to relative motion and light's ability to find it's own way from sources to sinks. If we were a planet on the far side of this jet and the jet was moving directly away from us it would appear to us to be traveling at only slightly less than half the speed of light and would be deeply red shifted when compared to the original sources... It is all smoke and mirrors and we need to understand that no object can "appear" to recede at a speed greater than half the speed of light. Any object visibly traveling faster than half the speed of light away from us must be being "inertially pulled away". The explanation for this extra "speed" is Hubble Expansion which is due to a continuing spacetime spreading/stretching in every direction as a consequence of the "Big Bang".
Note that the "at rest" comment in a non-inertial field statement above is also in parenthesis because this Pound–Rebka Effect is for non-inertial systems (General Relativity) while Special Relativity is related to inertial systems (free fall) so the application of Special Relativity should use a piecemeal incremental summation approach. I am not aware of any GR Theory that will actually work near the speed of light (and been tested) and the theory is best used to describe lower velocity ponderable masses on a slightly curved spacetime without spin or manifold torsion because the tensor maths used to describe the theory will not work in a highly curved spacetime. The four-momentum description is at odds with Okun's Special Relativity Interpretation (...special relativity is not wrong or even "special"... just deals with the problem in a different way) ... so I have far less confidence about a general interpretation of four-momentum (or even energy-momentum tensor) when considering any massless content of spacetime which consider energy as having a "density".
This relates back to the original question "Is Energy Stored In A Gravitational Field?". Energy is capacity to do work and energy must be applied specifically for it to actually exist at all. As an example a rock on the top of Mount Everest has potential energy to do work on the desk in front of you. You may be able to work out how much work it might do but it is meaningless since that rock cannot be arranged to perform that work and work that the rock may do will more likely be performed on some other system that you have no control over... such as falling down the cliff face locally where the energy it has there will be quite different and do work on an entirely different system. This must be viewed in the context of the energy content of matter which is very high but unable to be directly harnessed. The matter content is undeniable and is the intrinsic mass. Any other energy is 'something else" and the ability to harness the energy depends on the specific process we undertake to "unravel" this bound and system specific energy in matter.
The "energy density" of the space or of spacetime is a very non-physical concept that has not been fully tested except in the Newtonian limit with "real systems". The general notion might seem reasonable to many but to me it appears very hypothetical and not directly related to our world of experimental physics. Yet there are many features that are applicable to the way our universe works such as general covariance and limiting conditions that converge on Newton's Laws. Of course all such theories must do this in order to have a chance of working. Where the test for such theories resides is in regions of large masses and mass densities and also to these masses moving at large velocities and to it's applicability to "mostly empty" space. Under these conditions tensor maths fail because they are involved with only infinitesimal deformations and cannot directly handle sources where densities rise to infinity. This means as it stands presently at the level of a Theory it must fail even when dealing with any single common particle of matter or even worse when dealing with "Black Holes".
These extreme conditions are hard to test on the Earth. On the other hand Special Relativity has a more concrete application and is physically meaningful and scientists can work out many more problems with it with a lot of certainty since we can actually do tests on relativistic particles and the theory holds up pretty well. Special Relativity has made no such "assumptions" and does not necessarily use Tensor Maths so has a more general applicability (assuming Okun is correct). IMHO a lot of problems with dark matter, dark energy, great attractors and our current GR theory may be related to these epistemological problems Okun has mentioned. They must be resolved before we are able to proceed. It is no use simply ignoring these problems and saying it is of no consequence what we do.
Regarding the energy content of space with "Gravitational Fields"... Yes there is energy stored there mainly at the "sources" but matter sources presently cannot be decomposed too far to do additional work except in Fission and Fusion Bombs and other methods such as antimatter-matter reactions. Certainly we are not able to "tap off some energy" anywhere we would like it for the reasons given above (matter sources in free space are not local)... it does not work like "water" and 'flow" as we usually hear about in the so called "healing arts", it is not a substance of any kind at all. We actually need to build machines in order to harness energy by "doing work". Maybe someday we might build a machine that can unravel the energy stored in bulk matter completely... I dunno?... But that would be very useful.
Cheers
I'm pretty such a shorter answer would be :
"Yes, the Einstein Hilbert action has Lagrangian density sqrt(g) R, where R is the Ricci scalar and so is determined entirely by the curvature of space".
"Yes, the Einstein Hilbert action has Lagrangian density sqrt(g) R, where R is the Ricci scalar and so is determined entirely by the curvature of space".
Hi AlphaNumeric,
Nice to hear from you again... I like what you said there but for me "less is more"...
Nice to hear from you again... I like what you said there but for me "less is more"...
QUOTE (AlphaNumeric+)
I'm pretty such a shorter answer would be :
"Yes, the Einstein Hilbert action has Lagrangian density sqrt(g) R, where R is the Ricci scalar and so is determined entirely by the curvature of space".
"Yes, the Einstein Hilbert action has Lagrangian density sqrt(g) R, where R is the Ricci scalar and so is determined entirely by the curvature of space".
Yep... It is short, it is sweet, it is to the point... and quite technical! However I think I am disagreeing with that "devil in the detail" complaining that you have driven past where I was intending to get off.... The idea of energy for me is not something that ties directly into curvature. The stress-energy momentum tensor describes the "density" and the "flux" of energy..... I can see this energy now in my mind's eye "trickling down a hill". It is so "good" that it can be bottled like spring water. The idea of energy has become merged with some problematic ideas that I do not entirely agree with and as far as I know have not been experimentally tested.
Energy is a "boring" idea that does not lend itself to clean "bookkeeping". Energy is not only "capacity to do work" it must relate to work that is actually done. Work is also performed only at the point of application... an ugly "handle" but how else is it to be defined? This is because there are so many ways in which work might be performed but it cannot be "smeared" through an empty spacetime like peanut butter on a slice of bread if there are no points of application to apply it. I am thinking about massless photons here in superposition between sources and sinks.
Energy must relate to the work it can do since the nature of the energy often defines the kind of work. I have to stay "rambling" on this one since I am disagreeing with the conventional view and I am trying to lead you all with a trail of breadcrumbs to the gingerbread house.
Cheers
Energy is a "boring" idea that does not lend itself to clean "bookkeeping". Energy is not only "capacity to do work" it must relate to work that is actually done. Work is also performed only at the point of application... an ugly "handle" but how else is it to be defined? This is because there are so many ways in which work might be performed but it cannot be "smeared" through an empty spacetime like peanut butter on a slice of bread if there are no points of application to apply it. I am thinking about massless photons here in superposition between sources and sinks.
Energy must relate to the work it can do since the nature of the energy often defines the kind of work. I have to stay "rambling" on this one since I am disagreeing with the conventional view and I am trying to lead you all with a trail of breadcrumbs to the gingerbread house.
Cheers
QUOTE (Good Elf+Oct 19 2009, 03:17 PM)
The idea of energy for me is not something that ties directly into curvature. The stress-energy momentum tensor describes the "density" and the "flux" of energy.....
The definition of the stress-eneetgy tensor is that its proportional (up to factors of sqrt(g) and 4pi) to dS/d(g_ab), where g_ab is the metric and d is the little delta associated with variations. If you have S = int sqrt(g) R then you have
4 pi T_ab = (\/sqrt(g)) (d/dg_ab) int sqrt(g) R
A few basic tensor identities and that R = Tr(R_ab) and you get that the right hand side is (1/2)( R_ab - (1/2) R g_ab ), thus obtaining the Einstein Field Equations (well its almost the reverse, the EFE suggest that action). The Lagrangian isn't equal to energy, that'd be more the Hamiltonian but you can see that even if T_ab = 0 you can get non-trivial Hamiltonians.
(Anti) de Sitter space-times possess non-zero vacuum energies but they are T_ab = 0 solutiions to the EFEs for (dropping factors of pi and stuff)
T_ab = G_ab + L g_ab
where L is Lambda, the cosmological constant. T_ab = 0 but L not 0 implies that some balancing act has been done between the curvature of space-time and the energy intrinsic to the space-time itself. If L=0 then you end up with Minkowski space-time and you can legitimately say there's no energy there but if L is not 0 then surelly some kind of energy (positiive or negative, depending on L) exists iin the curvature of space-time as measured by G_ab.?
The definition of the stress-eneetgy tensor is that its proportional (up to factors of sqrt(g) and 4pi) to dS/d(g_ab), where g_ab is the metric and d is the little delta associated with variations. If you have S = int sqrt(g) R then you have
4 pi T_ab = (\/sqrt(g)) (d/dg_ab) int sqrt(g) R
A few basic tensor identities and that R = Tr(R_ab) and you get that the right hand side is (1/2)( R_ab - (1/2) R g_ab ), thus obtaining the Einstein Field Equations (well its almost the reverse, the EFE suggest that action). The Lagrangian isn't equal to energy, that'd be more the Hamiltonian but you can see that even if T_ab = 0 you can get non-trivial Hamiltonians.
(Anti) de Sitter space-times possess non-zero vacuum energies but they are T_ab = 0 solutiions to the EFEs for (dropping factors of pi and stuff)
T_ab = G_ab + L g_ab
where L is Lambda, the cosmological constant. T_ab = 0 but L not 0 implies that some balancing act has been done between the curvature of space-time and the energy intrinsic to the space-time itself. If L=0 then you end up with Minkowski space-time and you can legitimately say there's no energy there but if L is not 0 then surelly some kind of energy (positiive or negative, depending on L) exists iin the curvature of space-time as measured by G_ab.?
Good Elf you have brought up so many points let me try an go through them one at a time.
The increase in mass with velocity must be considered real mass in every respect. In particle accelerators the increase in mass with velocity behaves the same as rest mass and is indistinct when measured or acted upon. The inertial forces are those for the total mass and the control forces must account for the additional mass due to the increase in velocity.
Time dilation, the slowing of clocks with velocity, can be accounted for by the increase in mass cause by the increase in velocity. This is well stated in Special Relativity. Special Relativity missed the point and attributed the slowing of clock functions to the slowing of time.
I think you miss the point that the increase in mass is absolute with velocity and is not just a difference in observation from frame to frame. A person would become more obese with velocity.
The compression of a gas adds energy to the system with the result of an increase in heat. The heat can be seen as an increase in velocity in the motion of the gas. The obvious question is what produced the heat and the increase in velocity of the molecules. The only function that takes place is the moving closer of the molecules.
The increase of energy in the form of heat must come from the basic structure of the molecules. The only thing that can change is a change in mass. Only charge and mass are energy sources in a molecule. Since mass change is demonstrated in fusion and fission as well as electron and proton, and no change is see in charge with changes in velocity, proximity or gravity the source of energy must be considered the result of a change in mass.
The nature of chemistry becomes clear when viewed as a change of energy resulting from of change of mass proximity. Chemical systems of lower energy have molecules in closer proximity to each other.
After our test gas is compressed and increases in heat we then allow the heated gas to cool. If the pressure is then decreased, we note that the gas becomes cooler. Again the only action that has taken place is a change of proximity of molecules to each other. The only function is that the molecules must absorb energy and the only thing that changes is the mass of the molecule.
You will note that a change in the energy of the molecule takes place even after the velocity of the molecule was allowed to dissipate.
As measured in experiments an atom that has an electron fall toward the nucleus has a decrease in the total mass with the creation of a photon. There need not be a conservation of mass since mass and all other forms of energy are interchangeable. A photon has defined energy with respect to the wavelength. When added together the resulting mass added to the energy in the photons wavelength the result is about equal to the mass of the atom and the electron before the action. I say about because I believe that a very small amount of energy is left over. But that is another subject.
This is all I have time for right now. It is great to find a real discussion. Thanks a lot.
The increase in mass with velocity must be considered real mass in every respect. In particle accelerators the increase in mass with velocity behaves the same as rest mass and is indistinct when measured or acted upon. The inertial forces are those for the total mass and the control forces must account for the additional mass due to the increase in velocity.
Time dilation, the slowing of clocks with velocity, can be accounted for by the increase in mass cause by the increase in velocity. This is well stated in Special Relativity. Special Relativity missed the point and attributed the slowing of clock functions to the slowing of time.
I think you miss the point that the increase in mass is absolute with velocity and is not just a difference in observation from frame to frame. A person would become more obese with velocity.
The compression of a gas adds energy to the system with the result of an increase in heat. The heat can be seen as an increase in velocity in the motion of the gas. The obvious question is what produced the heat and the increase in velocity of the molecules. The only function that takes place is the moving closer of the molecules.
The increase of energy in the form of heat must come from the basic structure of the molecules. The only thing that can change is a change in mass. Only charge and mass are energy sources in a molecule. Since mass change is demonstrated in fusion and fission as well as electron and proton, and no change is see in charge with changes in velocity, proximity or gravity the source of energy must be considered the result of a change in mass.
The nature of chemistry becomes clear when viewed as a change of energy resulting from of change of mass proximity. Chemical systems of lower energy have molecules in closer proximity to each other.
After our test gas is compressed and increases in heat we then allow the heated gas to cool. If the pressure is then decreased, we note that the gas becomes cooler. Again the only action that has taken place is a change of proximity of molecules to each other. The only function is that the molecules must absorb energy and the only thing that changes is the mass of the molecule.
You will note that a change in the energy of the molecule takes place even after the velocity of the molecule was allowed to dissipate.
As measured in experiments an atom that has an electron fall toward the nucleus has a decrease in the total mass with the creation of a photon. There need not be a conservation of mass since mass and all other forms of energy are interchangeable. A photon has defined energy with respect to the wavelength. When added together the resulting mass added to the energy in the photons wavelength the result is about equal to the mass of the atom and the electron before the action. I say about because I believe that a very small amount of energy is left over. But that is another subject.
This is all I have time for right now. It is great to find a real discussion. Thanks a lot.
Hi tlocity,
QUOTE (tlocity+)
The increase in mass with velocity must be considered real mass in every respect. In particle accelerators the increase in mass with velocity behaves the same as rest mass and is indistinct when measured or acted upon. The inertial forces are those for the total mass and the control forces must account for the additional mass due to the increase in velocity.
I accept the interpretation Einstein placed on this concept. There really are only two "true" phenomena that have any effect in Special Relativity... Time dilation and length contraction and these are "relative" to some other inertial frame in which measurements are being made. Once again I ask how do you measure "relativistic mass"? An object traveling at close to the speed of light cannot be "weighed" from the observer frame. The definition of mass is all about how a particular mass relates to a test mass in producing proportional reciprocal accelerations on each other. That is the only way mass has ever been defined since the time of Newton.
Einstein's Principle of Special Relativity is that the Laws of Physics are the same within all inertial frames. Relativity is a "phenomenon" that is measured "between frames" not actually within frames. What I mean by "within" is a frame has infinite extent and all points within that frame are at rest relative to all hteother points in it. There are practical limits of course. This means that "speed" of a frame is relative and not absolute. Optical phenomenon not withstanding... If you were in a closed box and had no idea that there were objects outside that box moving at a relative velocity near the speed of light (such as other objects in our Universe always are) you have no "internal" physical indication of motion and the measurements made within it's own rest frame are always the same at any "speed" since the "velocity" you believe is so important is different relative to all other objects in the Universe which are all currently in relative motion in "free fall" and you must choose which frame is the "real" observer frame. Then when you have chosen that frame why don't you consider your observer frame to be the one with the velocity and you should be feeling heavier. The principle says that speed is no indicator of mass. Speed relative to other particles is an indication of relative energy.
Relative velocity does imply for a specific system of a pair of particles where one has a history of acceleration and the other has not such a history a preference for treatment. Einstein dealt with this issue by synchronizing clocks at the beginning of the experiment and then bringing clocks back together again after the experiment to compare times. One clock will have apparently have lost time... it will be the accelerated clock. To measure time dilation it is important to synchronize clocks at the outset and then to later measure the clocks in the same frame of reference to find out if there has been any observable difference. It is also possible to measure the difference in times by measuring the time by a local observation of the fast moving clock from the observation frame and correct back to the time at the origin In either case one clock will have lost "ticks" according to Einstein's famous formula. This measure of time dilation is a scalar and the accelerated clock loses ticks regardless of the direction the clock is moving in. On the other hand there may be some optical effects due to stellar abberation. This effect is different depending on the direction the accelerated particle was moving and acquiring a history of acceleration.
Considering the effect of time dilation... either time dilation is the outcome of having a past history of acceleration or if you ignore time dilation and think of this as "relativistic mass" the figures do balance... I stress these are not two influences but only one influence. The relative slowing of time in a highly accelerated frame provides the impression of lagging behind the impressed force .... some may think of this as "inertia" but it is the real measurable process of a physical time dilation.
Cesium clocks today are so accurate that it is easily possible to record the relative time differential due to gravitational acceleration differences solely due to that change in height above ground for a single floor in a building to record time dilation due to General Relativistic Acceleration. You simply take two atomic clocks and adjust their rate to be the same while side by side and then move one of these two identical clocks to the next floor of a building and if the display is carrying sufficient digits you can watch the time peel away.
This can be set up in a single building to record the net differences in time and you could walk between them and literally see the clock that is more deeply immersed in the earths gravitational field losing small time at a constant rate simply due to that one effect. In a subtle way the effect of Special Relativity time dilation due to "speed" differences between clocks is far more difficult to show but it is still easily shown to occur in the case of circling airplanes. Despite the approach and recession of the plane inducing a Relativistic Doppler Shift due to "speed" a second effect is due to Gravitational Red Shift. These two actually subtract in this case since planes circle at a higher altitude where the clock is faster than an identical ground based clock (more ticks per second) while the speed of the clock due to linear acceleration causes the planes clock to lose additional time relative to the "stay at home clock".
Relativity is "invisible" in the frame of the observer or within the moving frame ... the effects of Relativity is only seen when we compare frames.
Einstein's Principle of Special Relativity is that the Laws of Physics are the same within all inertial frames. Relativity is a "phenomenon" that is measured "between frames" not actually within frames. What I mean by "within" is a frame has infinite extent and all points within that frame are at rest relative to all hteother points in it. There are practical limits of course. This means that "speed" of a frame is relative and not absolute. Optical phenomenon not withstanding... If you were in a closed box and had no idea that there were objects outside that box moving at a relative velocity near the speed of light (such as other objects in our Universe always are) you have no "internal" physical indication of motion and the measurements made within it's own rest frame are always the same at any "speed" since the "velocity" you believe is so important is different relative to all other objects in the Universe which are all currently in relative motion in "free fall" and you must choose which frame is the "real" observer frame. Then when you have chosen that frame why don't you consider your observer frame to be the one with the velocity and you should be feeling heavier. The principle says that speed is no indicator of mass. Speed relative to other particles is an indication of relative energy.
Relative velocity does imply for a specific system of a pair of particles where one has a history of acceleration and the other has not such a history a preference for treatment. Einstein dealt with this issue by synchronizing clocks at the beginning of the experiment and then bringing clocks back together again after the experiment to compare times. One clock will have apparently have lost time... it will be the accelerated clock. To measure time dilation it is important to synchronize clocks at the outset and then to later measure the clocks in the same frame of reference to find out if there has been any observable difference. It is also possible to measure the difference in times by measuring the time by a local observation of the fast moving clock from the observation frame and correct back to the time at the origin In either case one clock will have lost "ticks" according to Einstein's famous formula. This measure of time dilation is a scalar and the accelerated clock loses ticks regardless of the direction the clock is moving in. On the other hand there may be some optical effects due to stellar abberation. This effect is different depending on the direction the accelerated particle was moving and acquiring a history of acceleration.
Considering the effect of time dilation... either time dilation is the outcome of having a past history of acceleration or if you ignore time dilation and think of this as "relativistic mass" the figures do balance... I stress these are not two influences but only one influence. The relative slowing of time in a highly accelerated frame provides the impression of lagging behind the impressed force .... some may think of this as "inertia" but it is the real measurable process of a physical time dilation.
Cesium clocks today are so accurate that it is easily possible to record the relative time differential due to gravitational acceleration differences solely due to that change in height above ground for a single floor in a building to record time dilation due to General Relativistic Acceleration. You simply take two atomic clocks and adjust their rate to be the same while side by side and then move one of these two identical clocks to the next floor of a building and if the display is carrying sufficient digits you can watch the time peel away.
This can be set up in a single building to record the net differences in time and you could walk between them and literally see the clock that is more deeply immersed in the earths gravitational field losing small time at a constant rate simply due to that one effect. In a subtle way the effect of Special Relativity time dilation due to "speed" differences between clocks is far more difficult to show but it is still easily shown to occur in the case of circling airplanes. Despite the approach and recession of the plane inducing a Relativistic Doppler Shift due to "speed" a second effect is due to Gravitational Red Shift. These two actually subtract in this case since planes circle at a higher altitude where the clock is faster than an identical ground based clock (more ticks per second) while the speed of the clock due to linear acceleration causes the planes clock to lose additional time relative to the "stay at home clock".
Relativity is "invisible" in the frame of the observer or within the moving frame ... the effects of Relativity is only seen when we compare frames.
QUOTE (tlocity+)
The compression of a gas adds energy to the system with the result of an increase in heat. The heat can be seen as an increase in velocity in the motion of the gas. The obvious question is what produced the heat and the increase in velocity of the molecules. The only function that takes place is the moving closer of the molecules.
It does. You have done work on the gas... "Heat" is a form of vibrational energy. There is an interesting idea here... "Heat" is usually called infra red light which are photons. In that form as "free photons" it is not actually "heat" per se since the actual heat is vibrational energy and that is in a system of particles where the amplitude and modes of vibration are increased. When these infra red photons are absorbed then it becomes vibrational energy of molecules. An increase in temperature increases the general velocity of the gas molecules.
Almost none of this energy goes in increasing the rest mass of mC² (term 1 of Taylors Expansion) but into the kinetic energy of the particles ½mV² (term 2 of Taylors expansion) but another smaller amount of energy would show up in all infinite number of remaining terms in the expansion (usually termed relativistic energy) which contribute insignificant amounts at low relativistic velocities but contribute a larger and more significant amount to the overall energy as V -> C and eventually dominates the overall energy contribution swamping the second term as V/C -> 1. Is this additional energy a mass? It certainly could be written down in terms of mass units since the units we write our measurables in are irrelevant... but the principle is what is the phenomenon being measured and in this case it is the relative velocity of the particles and the gross energy contributions.
Almost none of this energy goes in increasing the rest mass of mC² (term 1 of Taylors Expansion) but into the kinetic energy of the particles ½mV² (term 2 of Taylors expansion) but another smaller amount of energy would show up in all infinite number of remaining terms in the expansion (usually termed relativistic energy) which contribute insignificant amounts at low relativistic velocities but contribute a larger and more significant amount to the overall energy as V -> C and eventually dominates the overall energy contribution swamping the second term as V/C -> 1. Is this additional energy a mass? It certainly could be written down in terms of mass units since the units we write our measurables in are irrelevant... but the principle is what is the phenomenon being measured and in this case it is the relative velocity of the particles and the gross energy contributions.
QUOTE (tlocity+)
As measured in experiments an atom that has an electron fall toward the nucleus has a decrease in the total mass with the creation of a photon. There need not be a conservation of mass since mass and all other forms of energy are interchangeable.
I am not so sure about that... the electron in an outer shell has more kinetic energy (or potential energy?... you choose!) and that is term two of Taylor's Expansion.... sure there is a small amount of mass lost in this transition but at the velocity at which the electron circulates around the nucleus this relativistic contribution is very small. When it falls to the lower shell it must surrender it's kinetic or potential energy up in the creation of the photon. That process does not significantly change the gross intrinsic mass of the electron. In principle mass and all forms of energy are interchangeable but nobody has yet been able to "unravel" the energy of a single lone atom. It is easy to state what we may believe but experiment is another thing altogether... so while all energy might be equivalent it is not so easy to show term one in Taylor's expansion (intrinsic mass) is simply convertible to another term like term two (Newtonian Kinetic Energy) and all the subsequent "relativistic" terms. "For now" these terms of energy are experimentally distinct. Some small mass of a nucleus may be converted into "photons" if the nucleus is split in a transmutation through the release of some binding energy but compared with all the energy of the nucleus this is "small". However this energy release is fantastically much greater than the pure relativistic mass loss we have spoken of in a electronic transition that this mass is ignored except in our "philosophy" of this process.
Thanks again for your questions however I will be on leave for a couple of weeks and unable to answer these questions soon... I apologize for cutting this short... Watch this space!
Cheers
Thanks again for your questions however I will be on leave for a couple of weeks and unable to answer these questions soon... I apologize for cutting this short... Watch this space!
Cheers
QUOTE (Good Elf+Oct 21 2009, 03:32 PM)
I apologize for cutting this short... Watch this space!
Cheers
Cheers
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