Abraham's light momentum breaks special relativity?

[sciencewatch]

The Abraham's photon moment p_A=hbar*w/n*c is not Lorentz covariant, but it has been confirmed by several experiments. For example, G. B. Walker and D.G. Lahoz, Nature 253, 339 (1975); W. She, J. Yu, and R. Feng, Phys. Rev. Lett. 101, 243601 (2008).

The special relativity is flawed or the experiments were not correctly observed?

[yoron]

You lose me here?

"An equation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities (confusingly, some use the term invariant here). The key property of such equations is that if they hold in one inertial frame, then they hold in any inertial frame (this follows from the result that if all the components of a tensor vanish in one frame, they vanish in every frame).

This condition is a requirement according to the principle of relativity, i.e. all non-gravitational laws must make the same predictions for identical experiments taking place at the same spacetime event in two different inertial frames of reference."

Are you saying that the Abraham effect, in where the photon is seen to lose momentum entering a medium is inconsistent? It's been tested and seems to be correct, as far as I know? If you are referring to the way, if seen as a wave, the 'momentum' increase, as the wavelength is found to decrease, then that is correct too. The problem only exist if you want radiation to be only' one', or the other.

Or, is it something else you mean?

[DaleSpam]

Here is a good review article on the topic.
http://arxiv.org/abs/0710.0461

[sciencewatch]

You lose me here?....Or, is it something else you mean?
Let me re-state my question.

For a plane wave in an isotropic, homogeneous, non-conducting medium, the wave vector k and the frequency w constitute a wave 4-vector (k,w/c) which is Lorentz covariant, where |k|=n*w/c with n the refractive index. Sine the Planck constant hbar is assumed to be a Lorentz invariant. Thus hbar*(k,w/c) is a Lorentz covariant momentum-energy 4-vector. The Minkowski's photon momentum is defined as p_M=n*hbar*w/c = hbar*|k|, and we say the Minkowski's momentum hbar*k is Lorentz covariant, as the space component of hbar*(k,w/c).

However, the Abraham's momentum p_A=hbar*w/(n*c) does not have such property, that is, it is not Lorentz covariant, unless in free space. But some experiments strongly support Abraham's formulation. Is the special relativity flawed? or the experiments were not correctly observed?

[sciencewatch]

Here is a good review article on the topic.
http://arxiv.org/abs/0710.0461

This is a good review paper.

It is mainly talking about various EM and material tensors which are used to obtain various momentum and energy conservation equations.

In principle, Maxwell equations support various momentum conservation equations; however, this is an indeterminacy. It is the indeterminacy that results in the question of light momentum in a medium.

[DaleSpam]

It is the indeterminacy that results in the question of light momentum in a medium.Yes, and the answer doesn't really matter. What matters is that the total energy and momentum is conserved and covariant. You can break that total momentum up into parts which are not covariant, but that does not challenge SR in any way.

[sciencewatch]

Yes, and the answer doesn't really matter. What matters is that the total energy and momentum is conserved and covariant. You can break that total momentum up into parts which are not covariant, but that does not challenge SR in any way.

"You can break that total momentum up into parts which are not covariant, but that does not challenge SR in any way."

Do you have any theoretical grounds that support "partial momentum" is not Lorentz covariant?

[DaleSpam]

Do you have any theoretical grounds that support "partial momentum" is not Lorentz covariant?No, I was just going by your claim in the OP that it is not covariant. Do you have reason to doubt your own claim? I do not.

[sciencewatch]

No, I was just going by your claim in the OP that it is not covariant. Do you have reason to doubt your own claim? I do not.

1. "by your claim in the OP that it is not covariant" --- What does it mean for "OP"?

2. My reason is:

For a plane wave in an isotropic, homogeneous, non-conducting medium, the wave vector k and the frequency w constitute a wave 4-vector (k,w/c) which is Lorentz covariant, where |k|=n*w/c with n the refractive index.

Sine the Planck constant hbar is assumed to be a Lorentz invariant. Thus hbar*(k,w/c) is a Lorentz covariant momentum-energy 4-vector. Because hbar*w/c is the photon's energy, hbar*k must be the photon's momentum according to the relativity covariance. Thus only the Minkowski's photon momentum is consistent with the relativity, while the Abraham's momentum is not.

[DaleSpam]

1. "by your claim in the OP that it is not covariant" --- What does it mean for "OP"?OP = Original Post or sometimes Original Poster

2. My reason is:

For a plane wave in an isotropic, homogeneous, non-conducting medium, the wave vector k and the frequency w constitute a wave 4-vector (k,w/c) which is Lorentz covariant, where |k|=n*w/c with n the refractive index.

Sine the Planck constant hbar is assumed to be a Lorentz invariant. Thus hbar*(k,w/c) is a Lorentz covariant momentum-energy 4-vector. Because hbar*w/c is the photon's energy, hbar*k must be the photon's momentum according to the relativity covariance. Thus only the Minkowski's photon momentum is consistent with the relativity, while the Abraham's momentum is not.Yes. And since the choice between them is arbitrary I would recommend using Minkowski's momentum if you are doing relativistic problems.

[sciencewatch]

OP = Original Post or sometimes Original Poster

Yes. And since the choice between them is arbitrary I would recommend using Minkowski's momentum if you are doing relativistic problems.

However some experts of relativistic electrodynamics insist that the wave 4-vector be Lorentz covariant, but the light momentum may take Abraham's momentum. Does that mean the special relativity has some flaw? For example, see: T. Ramos, G. F. Rubilar, and Y. N. Obukhov, Phys. Lett. A 375, 1703 (2011), http://arxiv.org/abs/1103.1654 .

[DaleSpam]

However some experts of relativistic electrodynamics insist that the wave 4-vector be Lorentz covariant, but the light momentum may take Abraham's momentum. Does that mean the special relativity has some flaw?Not at all. A similar thing happens with gauges. There are many different possible choices for gauges. For example Coulomb or Lorentz. Both are equally valid but the Coulomb gauge is not covariant. No big deal.

[sunroof]

The Abraham's photon moment p_A=hbar*w/n*c is not Lorentz covariant, but it has been confirmed by several experiments. For example, G. B. Walker and D.G. Lahoz, Nature 253, 339 (1975); W. She, J. Yu, and R. Feng, Phys. Rev. Lett. 101, 243601 (2008).

The special relativity is flawed or the experiments were not correctly observed?

There also have experiments with a high credibility to support Minkowski momentum,e.g.

Campbell, G.K., Leanhardt, A.E., Mun, J., et al, "Photon Recoil Momentum in Dispersive Media", Physical Review Letters. Vol94, issue 17, 2005, pp.170403

Wang Zhong-Yue, Wang Pin-Yu, Xu Yan-Rong (2011). "Crucial experiment to resolve Abraham-Minkowski Controversy". Optik 122 (22): 1994–1996.

[sciencewatch]

Not at all. A similar thing happens with gauges. There are many different possible choices for gauges. For example Coulomb or Lorentz. Both are equally valid but the Coulomb gauge is not covariant. No big deal.

Choice of gauges and choice of light momentum formulations are different things.
Gauge is a kind of math tool, while light momentum is a physical reality.

Without using Lorentz gauge or Coulomb gauge, one still can solve EM problems. The solutions to Maxwell equations do not deppend on the choice of gauges.
Without Lorentz gauge, covariant EM-field strength tensors also can be set up.

Light momentum is a measuable physical quantity; theoretically there should be a correct formula to calculate, in my opinion. If both Abraham's and Minkowski's formulas are correct, then n=1 must hold.

[sciencewatch]

There also have experiments with a high credibility to support Minkowski momentum,e.g.

Campbell, G.K., Leanhardt, A.E., Mun, J., et al, "Photon Recoil Momentum in Dispersive Media", Physical Review Letters. Vol94, issue 17, 2005, pp.170403

Wang Zhong-Yue, Wang Pin-Yu, Xu Yan-Rong (2011). "Crucial experiment to resolve Abraham-Minkowski Controversy". Optik 122 (22): 1994–1996.

Minkowski's momentum is Lorentz covariant, and it is supported by the Fizeau running experiment.

[John232]

Sometimes, I wonder if special relativity is even compatible with itself. If you take d'/t', you don't get v. They are inversely related to the lorentz, so you would then get a different velocity than the original that determined the amount of spacetime dialation in the first place. I vote for a misassigned t' variable.

[pervect]

In special relativity (or rather in the MInkowski space-time of Special relativity), v always equals dx/dt, so I don't know what your problem is. Offhand, I'd guess you were, in fact, using a missagned 't' variable from the wrong frame, not realizing or having some sort of mental block about 't' being frame dependent.

Note that this remark doesn't apply to GR, because in GR coordinates are general and don't necessarily directly represent distances (or times). This is somewhat similar to the way that lattitude and longitude on the Earth's surface are coordinates, and don't represent distances until you apply the metric.

[John232]

If you look at a geometrical view of SR, there is no reason why velocity shouldn't equal d'/t', since it would equal c. You can pythagreom theorom the equation for t' and d', but then you can't get the original value back that you tried to solve to correct getting the constant value c. d'/t' doesn't give you back c like it should. It would be similair to checking your answer that c is indead the same, the goal of assigining d' and t' in the first place.

[John232]

If t'=t sqr(1-v^2/c^2), and L' = L sqr(1-v^2/c^2), then the lorentz portion would cancel and then L'/t' = c. The difference between the time dialation equation is exchanging the time variables, t and t'. The way it is L'/t' does not equal c.

[John232]

SR has only been around for a hundred years, geometry and algebra was tried and tested for thousands...

[DaleSpam]

Choice of gauges and choice of light momentum formulations are different things.
Gauge is a kind of math tool, while light momentum is a physical reality.Why would you think that? Did you not read the article I referenced earlier? The light momentum is not a physical reality, only the total momentum is. How you partition that into light and matter momentum is arbitrary, not physical.


Light momentum is a measuable physical quantity; theoretically there should be a correct formula to calculate, in my opinion.I can give a long list of quantities that can be measured which depend on some arbitrary choice.
Position
Velocity
Energy
Momentum
Time
Direction
Potential
Length
Duration
Net force
Etc.

[sciencewatch]

Why would you think that? Did you not read the article I referenced earlier? The light momentum is not a physical reality, only the total momentum is. How you partition that into light and matter momentum is arbitrary, not physical.

Abraham's and Minkowski's photon momentums all mean single photon's momentum, instead of the total momentum: light plus material .

I read that paper, which is talking about how to construct various total EM stress-energy tensors based on field- and material-tensors. In principle, one can construct infinite kinds of such tensors, resulting in infinite momentum-conservation equations, just like the Poynting power density vector S=ExH: actually adding an arbitrary vector A with div(A)=0 to ExH will not violate Poynting theorem, namely div (ExH+A)=div (ExH)= ... That is why I say Maxwell equations support variuos light momentum conservation equations.

[sciencewatch]

I can give a long list of quantities that can be measured which depend on some arbitrary choice.
Position
Velocity
Energy
Momentum
Time
Direction
Potential
Length
Duration
Net force
Etc.

I think you got misunderstanding of what I mean. Those quantities you mentioned can be described by Newton's law in classical mechanics.

[DaleSpam]

In principle, one can construct infinite kinds of such tensors, resulting in infinite momentum-conservation equationsExactly. The choice between them being arbitrary.

[yoron]

It's interesting.

A photon, or a wave? (http://physicsworld.com/cws/article/news/41873)

[sunroof]

Minkowski's momentum is Lorentz covariant, and it is supported by the Fizeau running experiment.

Yes. So I think Minkowski momentum is reasonable and Abraham is incorrect.

[sciencewatch]

It's interesting.

A photon, or a wave? (http://physicsworld.com/cws/article/news/41873)

"A century has now passed since the origins of the Abraham-Minkowski controversy pertaining to the correct form of optical momentum in media. Since, the debate has been recast in terms of the wave-particle duality of a photon..."

See: B. A. Kemp, J. Appl. Phys. 109, 111101 (2011).

[sciencewatch]

Exactly. The choice between them being arbitrary.

Then there is a pool of light momentum formulations; take one that can fit your own experiment...

[sciencewatch]

Yes. So I think Minkowski momentum is reasonable and Abraham is incorrect.

if the special relativity holds for light momentum.

[sciencewatch]

The Abraham's photon moment p_A=hbar*w/n*c is not Lorentz covariant, but it has been confirmed by several experiments. For example, G. B. Walker and D.G. Lahoz, Nature 253, 339 (1975); W. She, J. Yu, and R. Feng, Phys. Rev. Lett. 101, 243601 (2008).

The special relativity is flawed or the experiments were not correctly observed?

In the photon-medium block argument for Abraham's light momentum, the photon's mass is taken to be hbar*w/c**2, and the photon's speed is taken to be c/n; thus from Newton's law, momentum=mass*veclocity ----> p_A=(hbar*w/c**2)*(c/n)=hbar*w/n*c.
See: U. Leonhardt, Nature 444, 823 (2006).
http://lib.semi.ac.cn:8080/tsh/dzzy/wsqk/Nature/vol444/444-823.pdf

For the photon, mass-energy equivalence: mass=energy/c**2=hbar*w/c**2 really has nothing open to question?

[DaleSpam]

Then there is a pool of light momentum formulations; take one that can fit your own experiment...All of the formulations fit every possible experiment. That is what it means that the choice is arbitrary.

[sciencewatch]

All of the formulations fit every possible experiment. That is what it means that the choice is arbitrary.

Are you serious? or just kidding?

[Phrak]

"An equation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities (confusingly, some use the term invariant here).

good vectors are invariant. This means they don't depend on any coordinate system in use.

the elements of vectors are contravariant quantities, whereas the the bases of vectors are covariant. Together, the entire vector is invariant. The idea in play is that physics is independent of how we impose human coordanate systems on spacetime. With this point of view, vectors should not dendend on our choice of coordinate system, but be invariant or independent of them.

[DaleSpam]

Are you serious? or just kidding?100% serious, that is the whole point of the paper.

[sciencewatch]

... vectors should not dendend on our choice of coordinate system, ...

Not depend. A vector can be expressed in terms of both contra-variant basis vectors and co-variant basis vectors: the components on the contra-variant basis vectors are co-variant while the components on the co-variant basis vectors are contra-variant.

Usually, that a vector is said to be co-variant means the components of the vector on the contra-variant basis vectors.

In the special relativity, the basis vectors are often not used, because the Minkowski-metric tensors are defined in advance according the Lorentz time-space transformation. The distance is defined by a quadratic of the metric matrix.

In the linear space, the metric matrix is defined by the inner-products of all basis vectors. In principle, the "inner-product" definitions are arbitrary (of course, by a reversible matrix); not necessarily e1*e1=(e1)**2>0 for example.

[juanrga]

The Abraham's photon moment p_A=hbar*w/n*c is not Lorentz covariant, but it has been confirmed by several experiments. For example, G. B. Walker and D.G. Lahoz, Nature 253, 339 (1975); W. She, J. Yu, and R. Feng, Phys. Rev. Lett. 101, 243601 (2008).

The special relativity is flawed or the experiments were not correctly observed?

Momentum p^i is a three vector, it cannot be 4D covariant. The correct 4D covariant property is the four-momentum (or energy-momentum) p^mu

[yoron]

Interesting Phrak, didn't know that one. Although I did know, I think :) they should be coordinate invariant, but it's very cool to see a good explanation of how the definition looks.

[sciencewatch]

Momentum p^i is a three vector, it cannot be 4D covariant. The correct 4D covariant property is the four-momentum (or energy-momentum) p^mu

Please look at POST #4 .

[Phrak]

Not depend. A vector can be expressed in terms of both contra-variant basis vectors and co-variant basis vectors: the components on the contra-variant basis vectors are co-variant while the components on the co-variant basis vectors are contra-variant.

Usually, that a vector is said to be co-variant means the components of the vector on the contra-variant basis vectors.

Well, a covector, or one-form is not a vector. They don't transform the same, and the units are complimentary. And it really doesn't matter what is 'said to be', if it's wrong, but it is good to know what sloppy language is in common use.

[sciencewatch]

100% serious, that is the whole point of the paper.

Well, the options for light momentums are significantly reduced by the recent work by S. M. Barnett, Phys. Rev. Lett. 104, 070401 (2010).

[DaleSpam]

I can't find it on arxiv. Perhaps you can explain why you think that, the abstract certainly doesn't seem to indicate that.

[sciencewatch]

I can't find it on arxiv. Perhaps you can explain why you think that, the abstract certainly doesn't seem to indicate that.

We conclude by noting that a number of further momenta
have been proposed, with the aim of resolving the
Abraham-Minkowski dilemma [2]. By demonstrating the
need for two ‘‘correct’’ momenta and associating these,
unambiguously, with the Abraham and Minkowski forms,
we may hope that we have also removed the need for
further rival forms. By S. M. Barnett, Phys. Rev. Lett. 104, 070401 (2010).

[yoron]

He means this one I think.

The enigma of optical momentum in a medium (http://strathprints.strath.ac.uk/27285/1/AbMinkPhil.pdf)

[DaleSpam]

we have also removed the need for
further rival formsI am not sure that is intended to imply that further forms are incorrect, but again, it is hard to tell without the full paper.

In any case, from the abstract and the quote this paper doesn't seem to claim that SR is in any way challenged by Abraham's momentum.

[sciencewatch]

In any case, from the abstract and the quote this paper doesn't seem to claim that SR is in any way challenged by Abraham's momentum.

This paper implicitly challenges the special relativity by claiming that Abraham's photon's momentum is correct. Because P_A=hbar*w/n*c and E_A=hbar*w, which cannot constitute Lorentz covariant 4-vector, but the wave 4-vector is Lorentz covariant and the Planck constant hbar is a Lorentz invariant.

I think the paper just wants to explain experimental results, by neglecting the self-consistence of theory.

Well, now we have the superluminant neutrino-exp which cannot be explained by SR.
Actually, the linear Sagnac experiments also challenge the principle of relativity [RuyongWang, Yi Zheng, and Aiping Yao, "Generalized Sagnac Effect", Phys. Rev. Lett. 94, 143901 (2004); R.Wang, Y. Zheng, A. Yao, and D. Langley, Phys. Lett. A 312, 7 (2003)]. But who cares?

[DaleSpam]

This paper implicitly challenges the special relativity by claiming that Abraham's photon's momentum is correct. We have already established through the review article I posted that Abrahams is correct (as well as Minkowski) and that is no contraindication to SR. This new article says the same. Evidence in favor of Abrahams is not evidence against SR, for the reasons given above.

We are going around in circles. If you have something new to say then I will be glad to discuss it, otherwise you are welcome to repeat your same invalid argument once more so as to get the last word and end the thread.

[sunroof]

OP is correct that Abraham–Minkowski controversy is not on technical matters. In fact, it is helpful to extend the theory of relativity,e.g.

Ravndal, F., Electromagnetism and photons in continuous media, arXiv:0810.1872

Crenshaw, M.E., Electrodynamics in a Filled Minkowski Spacetime with Application to Classical Continuum Electrodynamics, arXiv:0812.3348v2

Wang, Z.Y., Graphene, neutrino mass and oscillation, arXiv:0909.1856v2

These authors think the light speed c in vacuum can be changed to other constant velocities such as c/n in media, Fermi velocity of condensed matter physics(graphene),sonic speed and that of a neutrino. Recently, a modified Fizeau's experiment was carried out and the result was in favor of the hypothesis( Crucial experiment to resolve Abraham-Minkowski Controversy, Optik, vol122, p1994-1996,2011). An exhaustive study is necessary.

[sciencewatch]

We have already established through the review article I posted that Abrahams is correct (as well as Minkowski) and that is no contraindication to SR. This new article says the same.

Indeed, “Abrahams is correct” is the conclusion made by the review article you posted and the new article I posted:

1. Rev.Mod.Phys.79:1197-1216 (2007); http://arxiv.org/abs/0710.0461 : “On these grounds, all choices for the electromagnetic energy-momentum tensor are equally valid and will produce the same predicted physical results…”

2. Phys. Rev. Lett. 104, 070401 (2010); http://prl.aps.org/abstract/PRL/v104/i7/e070401 : “We show that both the Abraham and Minkowski forms of the momentum density are correct, …”

and also is the conclusion made by the recent study in a standard tensor form of relativistic electrodynamics:

3. Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654 : “the Abraham choice of the ‘correct’ momentum of a light pulse is only one possibility, simple and useful for the description of isotropic media, but not at all an unique one.”

However, “that is no contraindication to SR” is purely your conclusion, because I cannot find that the above papers have shown that, Abraham’s photon momentum and energy can constitute a Lorentz covariant momentum-energy 4-vector, and I cannot find that they have a statement such as Abraham’s momentum “is no contraindication to SR”, or something like that. If you find, please kindly show me.

[DaleSpam]

I cannot find that they have a statement such as Abrahams momentum is no contraindication to SRDo you find a statement in any of those that there is a contradiction with SR?

[sciencewatch]

Do you find a statement in any of those that there is a contradiction with SR?

No. That is why I say "This paper implicitly challenges the special relativity by claiming that Abraham's photon's momentum is correct." (see Post #45) My argument is given below:

1. The wave 4-vector is assumed to be Lorentz covariant; see: the Gordon-metric dispersion equation Eq. (A7) and the wave 4-vector definition Eq. (A8), of Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654

2. The Planck constant is a universal constant, namely a Lorentz invariant; see: http://physics.nist.gov/cuu/Constants/

3. The Abraham's photon energy in a medium is given by E_A=hbar*w, the same as in free space; see: U. Leonhardt, Nature 444, 823 (2006). Interestingly, in the three papers [1 Rev.Mod.Phys.79:1197-1216 (2007); http://arxiv.org/abs/0710.0461; 2 Phys. Rev. Lett. 104, 070401 (2010); http://prl.aps.org/abstract/PRL/v104/i7/e070401 ; 3 Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654 ], no one of them clearly mentioned what the photon’s energy in a medium is.

Based above, Abraham’s photon momentum and energy cannot constitute Lorentz covariant 4-vector. Where am I wrong? Please kindly indicate.

[DaleSpam]

No. That is why I say "This paper implicitly challenges the special relativity by claiming that Abraham's photon's momentum is correct." (see Post #45)I find it interesting that you see an implicit challenge where there is none and yet look for an explicit confirmation. That seems to indicate an anti-mainstream science bias.

My argument is given below:

1. The wave 4-vector is assumed to be Lorentz covariant; see: the Gordon-metric dispersion equation Eq. (A7) and the wave 4-vector definition Eq. (A8), of Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654

2. The Planck constant is a universal constant, namely a Lorentz invariant; see: http://physics.nist.gov/cuu/Constants/

3. The Abraham's photon energy in a medium is given by E_A=hbar*w, the same as in free space; see: U. Leonhardt, Nature 444, 823 (2006). Interestingly, in the three papers [1 Rev.Mod.Phys.79:1197-1216 (2007); http://arxiv.org/abs/0710.0461; 2 Phys. Rev. Lett. 104, 070401 (2010); http://prl.aps.org/abstract/PRL/v104/i7/e070401 ; 3 Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654 ], no one of them clearly mentioned what the photon’s energy in a medium is.

Based above, Abraham’s photon momentum and energy cannot constitute Lorentz covariant 4-vector. Where am I wrong? Please kindly indicate.You are correct in the above. Abraham's momentum is not covariant. If you want a covariant momentum then use Minkowski.

Where you are incorrect is in thinking that challenges SR in any way.

[sciencewatch]

Abraham's momentum is not covariant.

Although Abraham's momentum is not compatible with the special relativity, it is supported by a recent experimental observation, Phys. Rev. Lett. 101, 243601 (2008), where a silica filament fiber "recoiled" as a laser pulse exited.

Interestingly, however, this "recoil" can be also explained as being caused by a transverse radiation force when there is an azimuthal asymmetry present in the fiber such that one side has a slightly different refractive index than the other. See: Phys. Rev. A 81, 011806(R) (2010); http://pra.aps.org/abstract/PRA/v81/i1/e011806.

[DaleSpam]

it is supported by a recent experimental observation, Phys. Rev. Lett. 101, 243601 (2008), where a silica filament fiber "recoiled" as a laser pulse exited. As is every other momentum tensor. The evidence supports Abraham, but it also supports Minkowski. The choice is arbitrary.

You seem to not understand this point despite my repeating it for four pages now.

[sciencewatch]

The choice is arbitrary.

The choice of light momentum formulations is arbitrary no matter whether it is compatible with the special relativity or not. --- Is that what you means for "The choice is arbitrary"?

[DaleSpam]

Yes. You can choose an incompatible (with SR) momentum just as you can choose an incompatible gauge.

[sciencewatch]

Yes. You can choose an incompatible (with SR) momentum just as you can choose an incompatible gauge.


1. Is the light momentum a measurable physical quantity?
2. If it is, then the measured light momentum depends on the choice of light momentum formulations you take. Is that what you mean?

[DaleSpam]

1. Is the light momentum a measurable physical quantity?Yes.

2. If it is, then the measured light momentum depends on the choice of light momentum formulations you take. Is that what you mean?Yes.

Similar things happen e.g. when you measure potential, where the measured value depends on where you set your ground, or length where the measured value depends on what simultaneity convention you adopt.

[sciencewatch]

Yes.

You yes that the measured light momentum depends on the choice of light momentum formulations.

In some experiments, the light momentum behaves as a visual physical phenomenon; for example, the fiber-recoiling experiment, Phys. Rev. Lett. 101, 243601 (2008); http://physics.aps.org/story/v22/st20 ; http://www.youtube.com/watch?v=8wBDmRaqe8I . Do you think the fiber-recoiling depends on the choice of light-momentum formulations you take?

[DaleSpam]

Do you think the fiber-recoiling depends on the choice of light-momentum formulations you take? No, fiber recoiling obviously depends on the total momentum, which is the same for Abraham and Minkowski.

How you partition that total momentum into light momentum and matter momentum is arbitrary and depends on your choice of formulations. But that partitioning won't change the result of measurements which depend on the total momentum.

[sciencewatch]

No, fiber recoiling obviously depends on the total momentum, which is the same for Abraham and Minkowski.

How you partition that total momentum into light momentum and matter momentum is arbitrary and depends on your choice of formulations. But that partitioning won't change the result of measurements which depend on the total momentum.

You claim that
(1) Total momentum = light momentum + matter momentum;
(2) The total momentum is the same (unique), no matter whether the light momentum is described by Abraham’s or Minkowski’s formulation (or even how to partition the total momentum into light momentum and matter momentum is arbitrary);
(3) The result of measurements or fiber recoiling only depends on the total momentum.

From your arguments it follows that:
Theoretically the Abraham’s and Minkowski’s light-momentum formulations have equal rights, and no one takes advantage.
----
My question is: Why the fiber-recoiling experiment [Phys. Rev. Lett. 101, 243601 (2008); http://physics.aps.org/story/v22/st20 ; http://www.youtube.com/watch?v=8wBDmRaqe8I ] cannot be explained by the Minkowski’s formulation since the Minkowski's and Abraham's formulations have equal rights?

[DaleSpam]

Why the fiber-recoiling experiment [Phys. Rev. Lett. 101, 243601 (2008); http://physics.aps.org/story/v22/st20 ; http://www.youtube.com/watch?v=8wBDmRaqe8I ] cannot be explained by the Minkowski’s formulation since the Minkowski's and Abraham's formulations have equal rights?Simply because the authors of the study did not perform such an analysis does not mean that it cannot be done. Again, an experimental confirmation of Abraham is not an experimental contradiction of Minkowski.

In fact, to me it seems obvious that the fiber will be pushed regardless of the formulation. We know the momentum of the light as it exits, so by conservation of momentum we know the total momentum in the fiber is a net push. How you partition that into light and matter momentum is arbitrary.

[sciencewatch]

Simply because the authors of the study did not perform such an analysis does not mean that it cannot be done.

The arguments you provide:
(1) Total momentum = light momentum + matter momentum;
(2) The total momentum is the same (unique), no matter whether the light momentum is described by Abraham’s or Minkowski’s formulation (or even how to partition the total momentum into light momentum and matter momentum is arbitrary);
(3) The result of measurements or fiber recoiling only depends on the total momentum.
require the Abraham’s and the Minkowski’s formulations to have equal rights, which means that, a specific experiment, which can be explained by Abraham’s formulation, also can be explained by Minkowski’s formulation. However, all reported experimental observations (http://physics.aps.org/story/v22/st20, for example) have already broken the property of equal rights that your arguments assign. I hate to but I have to say that, your arguments have some basic logical problem.

[sciencewatch]

Again, an experimental confirmation of Abraham is not an experimental contradiction of Minkowski.

I don't know what this sentense exactly mean. But to my best knowledge, any reported light-momentum-in-medium experiments cannot be explained by both Abraham’s and Minkowski’s formulations at the same time.

[DaleSpam]

However, all reported experimental observations (http://physics.aps.org/story/v22/st20, for example) have already broken the property of equal rights that your arguments assign. No, it didn't. I already rebutted the assertion in this story in post 61.

[DaleSpam]

But to my best knowledge, any reported light-momentum-in-medium experiments cannot be explained by both Abraham’s and Minkowski’s formulations at the same time.Then please re-read the review article I posted at the beginning of this discussion in post 3, you clearly did not understand it.

[sciencewatch]

Then please re-read the review article I posted at the beginning of this discussion in post 3, you clearly did not understand it.

Following your suggestion, I have re-read the review article [Rev. Mod. Phys.79:1197-1216 (2007); http://arxiv.org/abs/0710.0461 ]. The main conclusions in the article are copied below:

1(In I. INTRODUCTION). We therefore hope this paper will increase awareness that the controversy has been resolved, and that predictions regarding measurable behaviors will always be independent of the electromagnetic energy-momentum tensor chosen, provided the accompanying material tensor is also taken into account.

2(In XI. CONCLUSION). The original Abraham-Minkowski controversy, over the preferred form of the electromagnetic energy-momentum tensor in a dielectric medium, has been resolved by the recognition that division of the total energy-momentum tensor into electromagnetic and material components is arbitrary. Hence the Minkowski electromagnetic energy-momentum tensor, like the Abraham tensor, has a material counterpart, and the sum of these components yields the same total energy-momentum tensor as in the Abraham approach.

3(In XI. CONCLUSION). On these grounds, all choices for the electromagnetic energy-momentum tensor are equally valid and will produce the same predicted physical results, as has been demonstrated for a wide range of specific examples...

4(In XI. CONCLUSION)… We have discussed the realization that any electromagnetic energy-momentum tensor must always be accompanied by a counterpart material energy-momentum tensor, and that the division of the total energy-momentum tensor into these two components is entirely arbitrary.
-------
I think, the arguments you provide:
(1) Total momentum = light momentum + matter momentum;
(2) The total momentum is the same (unique), no matter whether the light momentum is described by Abraham’s or Minkowski’s formulation (or even how to partition the total momentum into light momentum and matter momentum is arbitrary);
(3) The result of measurements or fiber recoiling only depends on the total momentum.

have well outlined the conclusions given in the review article.

Your arguments require both the Abraham’s and the Minkowski’s formulations to have equal rights, which means that, a specific experiment, which can be explained by Abraham’s formulation, also can be explained by Minkowski’s formulation. However, all reported experimental observations (http://physics.aps.org/story/v22/st20, for example) have already broken the property of equal rights that your arguments assign. Therefore, your arguments have a serious logical problem.

You suggest me to re-read the review article, because I “clearly did not understand it”. I guess, you mean I did not understand the following article’s statement:

“On these grounds, all choices for the electromagnetic energy-momentum tensor are equally valid and will produce the same predicted physical results, as has been demonstrated for a wide range of specific examples...”

Indeed, I did not understand what this statement exactly means. In my understanding, Abraham’s and Minkowki’s formulations are apparently not compatible, except for in free space, and the same experimental observation cannot be explained by both two formulations. If you know some experiment do can be explained by the both formulations at the same time, please kindly give specific information.

As I have indicated, your arguments have two problems:

(1) The Abraham’s momentum is not compatible with the principle of relativity;
(2) The property of equal rights assigned by your arguments is apparently broken by experimental facts [ http://physics.aps.org/story/v22/st20, Phys. Rev. Lett. 101, 243601 (2008) for example], and such arguments are not self-consistent logically.

In view of above, I would say that, it is premature to conclude “the controversy has been resolved”.

[rpfeifer]

Hello. I'm going to reply to this thread in a few parts. First of all, I will address the original question (Is p_A=hbar*w/n*c consistent with special relativity?), then I'll comment on the fibre experiment of She, Yu, and Feng, respond to a few other points raised in this thread, and finally I'll reply to post #66, which is about the review paper Rev. Mod. Phys.79:1197-1216 (2007), henceforth RMP79.

To begin with the original question (I will use units in which hbar=c=1, for convenience):
If k is the momentum in vacuum and p is the momentum in a medium, people often call
p=nk
the Minkowski formulation, and
p=k/n
the Abraham formulation. This is a gross oversimplification. To understand the flow of energy and momentum in a material, you cannot work with p alone. You need to use the energy-momentum tensor, made up of p (momentum), u (energy density), sigma (stress tensor) and S (Poynting vector). When dealing with electromagnetism, it is customary to further divide each of these into p_EM and p_matter, u_EM and u_matter, etc.

When you put these together in the correct way (as described in RMP79 Eq. (7)), and add together the EM and matter components, you get the total energy momentum tensor, T. Unless you're working on black holes or something, where general relativity will be required, then conservation of energy and conservation of momentum ABSOLUTELY REQUIRE that T is consistent with special relativity. However, they say nothing about individual quantities such as p_EM.

You can also put together a 4-vector (u_EM+u_matter, p_EM+p_matter)T which also behaves correctly under special relativity. However, what about the p in p=k/n and p=nk?

You have probably figured out by now that these are just p_EM. You can make any change you like to p_EM and still be consistent with special relativity, so long as p_EM+p_matter remains the same.

Historically, a lot of people did what the original poster did, and asked questions like
"Is p_EM(Abraham)=k/n consistent with special relativity?" (Answer: NO)
"Is p_EM(Minkowski)=nk consistent with conservation of angular momentum?" (Answer: NO)
"Can p_EM(Abraham) explain this experiment?" (Answer: Yes for some, no for others)
"Can p_EM(Minkowski) explain this experiment?" (Answer: Yes for some, no for others)

The sensible question to ask is:
"Can T explain this experiment?"
Once you specify the properties of your materials, there is only one choice for T. I would like to say that again: There is only one choice for T. There is no T(Minkowski) or T(Abraham). It is uniquely fixed by conservation laws, and by special relativity.
Fortunately, the answer to the sensible question is: YES.

Hopefully things make more sense to you now.

By the way, if you're wondering where the Abraham and Minkowski formulations come into it, if T is fixed, well:
We can write down something we'll call T(EM, Minkowski) (for example). It looks like
( u_EM(Minkowski) S_EM(Minkowski) )
( p_EM(Minkowski) -σ_EM(Minkowski) )
but then T is given by T(EM,Minkowski)+T(matter,Minkowski):
( u_EM(Minkowski) S_EM(Minkowski) ) + ( u_matter(Minkowski) S_matter(Minkowski) )
( p_EM(Minkowski) -σ_EM(Minkowski) ) ( p_matter(Minkowski) -σ_matter(Minkowski) ).
Given that T is fixed, you can work out what the matter terms are. You can do exactly the same for T(EM,Abraham). Same T (it has to be, according to conservation of energy, conservation of momentum, and special relativity), and that means same behaviour.

Incidentally, you might be wondering if we can measure, say, p_EM directly and tell if it is the Abraham or Minkowski version. The short answer is: No, the mathematics of the energy-momentum tensor tells us this is impossible. Any experiment will only measure the total p, p_EM+p_matter, which is the same for Abraham and Minkowski (it has to be, as it is a part of T).

[rpfeifer]

Next, I will quickly comment on how this applies to the experiment of She, Yu, and Feng (Phys. Rev. Lett. 101, 243601 (2008)).

Although these authors do not publish their calculation, I suspect it went something like this:
For Minkowski, p=nk. A photon leaving a medium loses momentum, and the medium gains it, so the medium moves in the same direction as the photon.
For Abraham, p=k/n. A photon leaving a medium gains momentum, and the medium loses it, so the medium recoils.
She, Yu, and Feng observed a recoil, and concluded this meant the Abraham momentum was correct.

Let me show you why this is a problem: Read about the experiment of Ashkin and Dziedzic (Phys. Rev. Lett. 30, 139 (1973), summarised in Sec. IV.B of RMP79). As before, we say:
For Minkowski, p=nk. A photon leaving a medium loses momentum, and the medium gains it, so the medium moves in the same direction as the photon.
For Abraham, p=k/n. A photon leaving a medium gains momentum, and the medium loses it, so the medium recoils.
Ashkin and Dziedzic observed the medium moving in the same direction as the photons. Surely that means the Minkowski momentum is correct? We have reached a contradiction!

(In other words, this approach is internally inconsistent :) )

This isn't really surprising - the behaviour of the system is really described by T, and if we insist on splitting this into EM and matter parts, that's 32 separate parameters! (16 if we don't split it.) The momenta we have been using, p=nk and/or p=k/n, are only three of these 32 parameters (specifically p_EM). We've been ignoring over 90% of the physics! No wonder our results were inconsistent.

Gordon analysed the situation studied by Ashkin and Dziedzic in more detail in Phys. Rev. A 8, 14 (1973), and showed that both the Abraham and Minkowski formulations give the same result. It's quite a complicated calculation (and he uses Gaussian units, not SI, which makes things more difficult to follow for the younger generation of physicists), but the main point is this: There is NO WAY to get the correct result just from p=nk and p=k/n. I suspect She, Yu, and Feng fell into the same trap (though, unless they provide their calculation, there is no way to know for sure). A full analysis of their experiment in the Minkowski formulation would be a good exercise for a postgraduate classical field theory class.

However, we don't need to do this to know that their conclusion is wrong. Why do I say that? Because physics depends only on T, and there is only one choice for T (for a given dielectric material). I'll put a bit more historical context on this in my next post, and also respond to #66.

[rpfeifer]

Before I respond to #66, here are a few brief responses to some of the other posts:

Note - In my posts, to keep things clear I will only use EM to mean "Electromagnetic", never "Energy-Momentum".

Answer to #7:
Yes: In relativistic electrodynamics, there are no equations which depend explicitly on p_EM or p_matter (only on p_total, in T). Therefore, p_EM can be whatever it likes, even if it is not relativistically covariant. T is what matters; p_EM is a fiction. Sometimes it is a convenient fiction, and sometimes it is one which leads us astray. I have tried to provide some guidelines on this in Phys. Rev. A 79, 023813 (2009) (arXiv:0902.2605v2).

Comment on #14:
"Light momentum is a measuable physical quantity; theoretically there should be a correct formula to calculate, in my opinion. If both Abraham's and Minkowski's formulas are correct, then n=1 must hold."
No - momentum transfer is a measurable physical quantity. However, you have no way of ensuring that only the light transfers momentum (except by doing your experiment in vacuum, without any dielectric materials present, in which case it is indeed true that n must be exactly 1).

Answer to #30:
"For the photon, mass-energy equivalence: mass=energy/c**2=hbar*w/c**2 really has nothing open to question?"
In a medium, you have both photons and excitons (corresponding to the EM and material portions of the energy-momentum tensor).

Comment relating to #48:
In an explicitly SR formulation of EM, p_EM does not appear (except in the combination p_EM+p_matter). Thus p_EM can tell us nothing about the validity or otherwise of SR. Thus, 'Abraham’s momentum “is no contraindication to SR”'.

Comment on #57:
Some clarification is required here. You can measure "p_total while some light is passing through". This is not the same as measuring p_EM. DaleSpam may have meant the former, but many readers may have mistaken this for the latter.

[rpfeifer]

Response to #66:

As one of the authors of Rev. Mod. Phys.79:1197-1216 (2007), henceforth RMP79, I would like to point out that there are three very good examples of experiments which can be explained by both formulations at the same time, and which are reviewed in this very paper.
1) The experiment of Jones and Richards (later improved on by Jones and Leslie) in Proc. R. Soc. London, Ser. A 221, 480 (1954), Proc. R. Soc. London, Ser. A 360, 347 (1978), and Sec. IV.A of RMP79. In this experiment a photon reflects off a pivoting mirror suspended in a dielectric fluid. On first inspection the experiment appears to support the Minkowski formulation, but (as pointed out by Jones and Richards in the above citation, and again by Jones in Proc. R. Soc. London, Ser. A 360, 365 (1978), it is equally well explained by the Abraham formulation with appropriate accompanying material momentum tensor. This is also explained in Sec. VIII.C.1 of RMP79.
2) The experiment of Ashkin and Dziedzic (Phys. Rev. Lett. 30, 139 (1973), and Sec. IV.B of RMP79) in which a laser beam exiting a fluid causes the surface of this fluid to bulge outwards. A detailed treatment is provided by Gordon in Phys. Rev. A 8, 14 (1973) (note - he uses Gaussian units, which may cause confusion in readers accustomed to SI units).
3) The experiment of Walker, Lahoz, and Walker Can. J. Phys. 53, 2577 (1975), also Sec. IV.C of RMP79, in which angular momentum is transferred to a rotary pendulum. This experiment initially appears to support the Abraham formulation, but is also correctly described by the Minkowski formulation when the appropriate material momentum tensor is included.

In fact, the main thrust of Sec. VIII of RMP79 is that once the material properties of the dielectric are specified, the total momentum tensor is uniquely determined by
(i) consistency with special relativity, and
(ii) conservation of linear and angular momentum.
This leads to two important conclusions:
(a) No valid combination of EM and material energy-momentum tensors can break special relativity. If you are using a combination of tensors which appears to break this, then your choice of tensors is incorrect (usually, the material tensor is incorrect or missing). Note that I have never yet seen a fully relativistic formulation of the material counterpart tensors written down anywhere in the literature - even those given in RMP79 are valid only for media moving at v<<c, though the full expressions could be obtained from Eqs. (33)-(34).
(b) As the _total_ energy-momentum tensor is uniquely fixed by (i) and (ii) above, any division into components necessarily yields the same total tensor, and thus the same physical behaviours. That is, Abraham and Minkowski correspond to the same T, and thus the same physics.

In your post you stated "such arguments are not self-consistent logically", but there is nothing in your post which supports this statement (you have not presented any internal contradictions in the formulation presented in RMP79). Perhaps you meant "If Phys. Rev. Lett. 101, 243601 (2008) can only be explained by the Abraham momentum, then RMP79 is incorrect"? If so, then please carefully consider points (i), (ii), (a), and (b) above, and also post #67, as these demonstrate why _any_ experiment can be explained in terms of either the Abraham or the Minkowski formulation. If you meant something else, perhaps you can clarify?

I would just like to point out that all the examples I have provided were in RMP79, which you claim to have read. May I suggest that instead of reading superficially through the text, you work through the paper instead, making sure you understand the origin of each equation? You will probably need at the very least:
(i) A copy of Jackson's Classical Electrodynamics (1999)
(ii) Access to journals through a good university library, national library, or equivalent.
If you do this, I can more or less guarantee that all your questions will be answered.

Regards,
Robert Pfeifer
(Many thanks to DaleSpam for doing a great job, and already answering most of these questions elsewhere in the thread - it's great to see that my review paper has been read and appreciated! Hopefully by putting everything in one place like this, we can bring this thread to a close. Sciencewatch, I hope this answers your questions.)

[rpfeifer]

SR has only been around for a hundred years, geometry and algebra was tried and tested for thousands...

Oh, and finally, a comment for John232:
SR is geometry. That's all it is (and it's very nice, too). Specifically, it is the geometry of Lie Group SO(3,1) (X) R4, also known as the Poincare' group. That's why you won't be able to use SR to falsify SR: It's a self-contained, self-consistent mathematical structure. There's always the possibility that SR is only an _approximate_ description of the universe in the absence of significant gravitational effects, but the experimental constraints on this are very strong (and getting stronger - there are research groups which make careers out of testing this).

If you want to learn more about that, you'll need a good background in multidimensional calculus (grad, div, curl, Stokes' theorem, stuff like that) and tensor calculus/notation, and then I'd recommend courses in Riemannian geometry and Differential geometry, or spending a few months working through a book like Frankel's "The Geometry of Physics" (a very nice book, but watch out for the errata!).

[sciencewatch]

Response to #66:
...
In fact, the main thrust of Sec. VIII of RMP79 is that once the material properties of the dielectric are specified, the total momentum tensor is uniquely determined by
(i) consistency with special relativity, and
(ii) conservation of linear and angular momentum.
This leads to two important conclusions:
(a) No valid combination of EM and material energy-momentum tensors can break special relativity. If you are using a combination of tensors which appears to break this, then your choice of tensors is incorrect (usually, the material tensor is incorrect or missing). Note that I have never yet seen a fully relativistic formulation of the material counterpart tensors written down anywhere in the literature - even those given in RMP79 are valid only for media moving at v<<c, though the full expressions could be obtained from Eqs. (33)-(34).
(b) As the _total_ energy-momentum tensor is uniquely fixed by (i) and (ii) above, any division into components necessarily yields the same total tensor, and thus the same physical behaviours. That is, Abraham and Minkowski correspond to the same T, and thus the same physics.
...


Why is the Abraham’s momentum not compatible with the relativity for plane waves in a medium?

To support the compatibility of Abraham’s momentum with the relativity, your strong argument is that the total tensor is Lorentz covariant. However, this is not enough.

The total tensor is constructed from electromagnetic (EM) field–strength tensors in a covariant form. The Lorentz covariance of EM field–strength tensors is a sufficient condition to keep Maxwell equations invariant in form, but it is not a sufficient condition to keep the covariance of momentum-energy 4-vector. For plane waves in a uniform medium, the wave vector and frequency constitute a Lorentz covariant 4-vector [Phys. Lett. A 375, 1703 (2011), Eq. (A7); http://arxiv.org/abs/1103.1654 ], and according to the special relativity, the photon momentum and energy must constitute a covariant 4-vector. However, the Abraham’s momentum and the photon energy cannot constitute a covariant 4-vector. That is why I say the “Abraham’s light momentum breaks the special relativity”.

[sciencewatch]

Response to #66:

... there are three very good examples of experiments which can be explained by both formulations at the same time, and which are reviewed in this very paper.

1) The experiment of Jones and Richards (later improved on by Jones and Leslie) in Proc. R. Soc. London, Ser. A 221, 480 (1954), Proc. R. Soc. London, Ser. A 360, 347 (1978), and Sec. IV.A of RMP79. In this experiment a photon reflects off a pivoting mirror suspended in a dielectric fluid. On first inspection the experiment appears to support the Minkowski formulation, but (as pointed out by Jones and Richards in the above citation, and again by Jones in Proc. R. Soc. London, Ser. A 360, 365 (1978), it is equally well explained by the Abraham formulation with appropriate accompanying material momentum tensor. This is also explained in Sec. VIII.C.1 of RMP79.

2) The experiment of Ashkin and Dziedzic (Phys. Rev. Lett. 30, 139 (1973), and Sec. IV.B of RMP79) in which a laser beam exiting a fluid causes the surface of this fluid to bulge outwards. A detailed treatment is provided by Gordon in Phys. Rev. A 8, 14 (1973) (note - he uses Gaussian units, which may cause confusion in readers accustomed to SI units).

3) The experiment of Walker, Lahoz, and Walker Can. J. Phys. 53, 2577 (1975), also Sec. IV.C of RMP79, in which angular momentum is transferred to a rotary pendulum. This experiment initially appears to support the Abraham formulation, but is also correctly described by the Minkowski formulation when the appropriate material momentum tensor is included.
...


Please support the property of equal rights assigned by your arguments.

The interpretations for these experiments you enumerated are not easy to understand; even the authors themselves, who did the experiments, cannot easily understand them, with minds often changed. How to convince ordinary readers?

The fiber-recoiling experiment [Phys. Rev. Lett. 101, 243601 (2008); http://physics.aps.org/story/v22/st20 ; http://www.youtube.com/watch?v=8wBDmRaqe8I ] is widely recognized as a very clear visual experiment. The authors of the experiment insist that it should support the Abraham’s formulation. In my understanding, the Abraham’s and Minkowski’s formulations are not compatible, and this experiment cannot be explained by the Minkowski’s. According to your arguments, however, this experiment also can be explained by Minkowski’s formulation. So, please give your explanation to support the property of equal rights assigned by your arguments.

[DaleSpam]

Your arguments require both the Abraham’s and the Minkowski’s formulations to have equal rights, which means that, a specific experiment, which can be explained by Abraham’s formulation, also can be explained by Minkowski’s formulation. However, all reported experimental observations (http://physics.aps.org/story/v22/st20, for example) have already broken the property of equal rights that your arguments assign. Therefore, your arguments have a serious logical problem.I already answered this in posts 59 and 61. This experiment does not break the "equal rights" in any way, as I have already told you multiple times.

In order to break the "equal rights" you would have to demonstrate:
1) That the result is explained by Abraham's momentum
2) That the result is not explained by the total momentum

The authors did 1) but did not even attempt 2) including never calculating the total momentum tensor. Personally, I think it is patently obvious that 2) is false. This experiment does not break the "equal rights" argument, as I have already explained several times. Please come up with something new, this is getting repetitive.

the same experimental observation cannot be explained by both two formulations. If you know some experiment do can be explained by the both formulations at the same time, please kindly give specific information.This is false. Specific examples are given in the review article showing how several different experiments can be explained by both.

[DaleSpam]

(Many thanks to DaleSpam for doing a great job, and already answering most of these questions elsewhere in the thread - it's great to see that my review paper has been read and appreciated!)Welcome to PF with a particularly good string of posts! I hope you will stick around for conversations on other topics as well.

[sciencewatch]

I already answered this in posts 59 and 61. This experiment does not break the "equal rights" in any way, as I have already told you multiple times.

In order to break the "equal rights" you would have to demonstrate:
1) That the result is explained by Abraham's momentum
2) That the result is not explained by the total momentum

The authors did 1) but did not even attempt 2) including never calculating the total momentum tensor. Personally, I think it is patently obvious that 2) is false. This experiment does not break the "equal rights" argument, as I have already explained several times. Please come up with something new, this is getting repetitive.


Your Post-59 answer is “fiber recoiling obviously depends on the total momentum, which is the same for Abraham and Minkowski.”

According to your answer, the fiber recoiling can be explained by both Abraham’s and Minkowski’s formulations at the same time. However, the authors of the experiment, She, Yu, and Feng clearly claim:

“From the experiments described above, we believe that the phenomenon observed is due to the force exerted by the outgoing light. The nature of SF movement cannot be explained by Minkowski momentum. Minkowski momentum predicts a pull force, which pulls the whole SF to one side for asymmetric refraction [see Fig. 2(j)] or pulls it straight for direct transmission.” “In conclusion, our experiment and analysis suggest that Abraham momentum is correct.” [See: Phys. Rev. Lett. 101, 243601 (2008); http://physics.aps.org/story/v22/st20 ; http://www.youtube.com/watch?v=8wBDmRaqe8I ]

Obviously, your arguments are not consistent with the above authors’ claim, and you did not give any explanations why the above authors’ claim is wrong. Accordingly, your conclusion “This experiment does not break the ‘equal rights’ in any way” is not well grounded.

--------
Your post-61 answer is “Simply because the authors of the study did not perform such an analysis does not mean that it cannot be done. Again, an experimental confirmation of Abraham is not an experimental contradiction of Minkowski.” ----- Sorry, I don’t understand what you exactly mean.

[rpfeifer]

Response to #72:

The brief answer to your question "Why is the Abraham’s momentum not compatible with the relativity for plane waves in a medium?" is because there is absolutely no reason for it to be compatible on its own (without a material counterpart). This is explained in RMP79.

To expand at greater length:

"Abraham's momentum" has nothing to do with special relativity. Let me distinguish clearly between:
(i) The Abraham-style EM and material energy-momentum tensors
and
(ii) The Abraham momentum.
Using the Abraham momentum to perform a calculation is not the same as using the Abraham-style tensors.

Abraham's momentum (n/k) is not compatible with special relativity on its own, as you have pointed out. This says absolutely nothing about whether the Abraham-style EM and material tensor pair are compatible with special relativity.

I do not assert the compatibility of "Abraham's momentum" with SR, only the compatibility of the Abraham-style tensor pair. You need to appreciate this distinction, as your objections all arise from confusing these two.

Physics is written in terms of the Abraham-style tensor pair ((i), above) or the Minkowski-style tensor pair (the equations are the same - I know; I've written them out; you should too). Using the "Abraham (or Minkowski) momentum" ((i) above) in a calculation is never anything more than a shorthand (and it is frequently a faulty one, as demonstrated in post #68, above).

Once you understand this, you will see that arguing about the lack of Lorentz covariance of the Abraham momentum is pointless: Yes, it is not covariant. No, this does not indicate a problem with SR, or with the Abraham momentum. It is simply irrelevant.

[rpfeifer]

Response to #73:

Supporting the properties of equal rights:
(1) See Proc. R. Soc. London, Ser. A 221, 480 (1954) and Proc. R. Soc. London, Ser. A 360, 365 (1978) (both cited in RMP79).
(2) See Phys. Rev. A 8, 14 (1973), as cited in RMP79.
(3) See Israel, Phys. Lett. B 67, 125 (1977) and Obukov & Hehl in Phys. Lett. A 311, 277 (2003). Both are cited when discussing this experiment in RMP79. Off the top of my head I think the tensors in O&H might differ slightly to the ones given in RMP79, but as I recall, this does not affect the proof.

You will note that all of these papers were clearly cited in RMP79 as providing the demonstrations you were looking for. When asking questions about matters discussed in the review paper RMP79, please have the courtesy to first check RMP79 to see if your questions are already answered in there.

Of course, all three experiments also follow from the general demonstration given in RMP79 (which, in turn, is based on arguments presented in these, and other, papers). That's the point of giving a general demonstration. Once it's done, you don't need to bother proving every individual case any more. Unfortunately, you don't seem to have understood the general demonstration, and I'm not going to go through every experiment ever done, to explain how it works.

Regarding the fibre recoil experiment, you are asking me to repeat myself. Specifically:
(i) The method apparently used to show this experiment was incompatible with the Minkowski momentum is flawed, and leads to a logical contradiction (see post #68). Thus you have no reason to claim that the experiment is incompatible with the Minkowski momentum (unless you have performed a better calculation than the one described there, in which case please post your calculations so we can discuss them).
(ii) The universal demonstration of equivalence presented in RMP79 applies to this experiment.

In summary, you have no reason to state that the Minkowski momentum does not work in this experiment (the only argument I am aware of which leads to this conclusion is trivially shown to be flawed, as described in #68) and a very good reason to believe that it does work (the general demonstration of equivalence in RMP79, in which you have not yet successfully found a fault - your objections, including the question in #72, seem to be based on a misunderstanding, which I have addressed in #77).

Now we have cleared up that misunderstanding, you may find that the evidence leans towards equivalence of the two formulations. Also note that my post #77 above is a direct answer to your original question :smile: .

[rpfeifer]

Response to #76:
I have answered the physics questions in this post in my response to #73.

Regarding your comment "Sorry, I don’t understand what you exactly mean" in response to DaleSpam, may I suggest the following:
Re-read the sentence carefully. Work it out clause by clause if you have to. It makes sense. If you're reading too quickly to understand what this sentence means, you're probably reading too quickly to be thinking about our responses.

[rpfeifer]

In #73 you asked: "The interpretations for these experiments you enumerated are not easy to understand; even the authors themselves, who did the experiments, cannot easily understand them, with minds often changed. How to convince ordinary readers?"

This is a good question. Regrettably, sometimes the answer is:
Explain to that ordinary reader that if they want to understand, they need to take a course in tensor calculus, a postgraduate course in electromagnetism, learn about Gaussian units, read Jackson's book pretty much from cover to cover, and then read and work through all the calculations in my paper, also reading as many of the citations as they need to in order to achieve this.
If you want it easier than that, well, I'm afraid that's the easy way. (Easier than working it out using only papers published before 2007, I think! :smile: )

People often want an explanation in words. That's fine, but when you argue with the words, the answer is usually "The words are an incomplete description. Here is the maths." That seems to be what is happening here - but you keep on ignoring the maths and going back to the words.


Oh, by the way, since you said "even the authors themselves, who did the experiments, cannot easily understand them", I'll just comment on that - my experience is that active theory experts in this field do now seem to agree on this matter (recent examples: S. Barnett, Phys. Rev. Lett. 104, 070401(2010), and C. Baxter and R. Loudon, J. Modern Optics, 57, 830 (2010)). It used to be that the information was scattered. Now that it's all collected together, it no longer seems to be under debate among theorists - though there have been a few lovely papers coming out tying up loose ends. In time, hopefully, experimentalists such as She et al. (the fibre team) will become aware of this, and will stop making misleading statements suggesting that it is still Abraham vs. Minkowski rather than, as we now know, Abraham <3s ("hearts") Minkowski. :smile:

(footnote: The agreement of experts doesn't make something true - but you would be well advised to make sure you understand the consensus opinion before trying to prove it wrong!)

[rpfeifer]

Sciencewatch: In light of the above, time to put your money where your mouth is (metaphorically speaking).

Instead of just claiming that other peoples' work is wrong, please show us some proof. That is, please demonstrate (i.e. using formulae) a mathematical contradiction, or give a mathematical calculation predicting a behaviour which disagrees with experiment, arising as a consequence of these alleged errors.

Here are two of your claims I would like to see mathematical evidence for:

A)
You have asserted that the fibre experiment distinguishes between the Abraham and Minkowski momenta (the Abraham momentum explains it and the Minkowski one doesn't). I am not aware of any valid argument which shows this. Please demonstrate.

(Note: In #68 I presented an invalid argument, then shot it down. As far as I know, this is the only argument which produces that claim, and it is incorrect. If you can provide a better argument, I would welcome it.)

B)
You have also claimed that "Abraham momentum breaks SR", meaning the following:
(1) The Abraham EM momentum is not covariant.
(2) If the Abraham EM momentum is valid, then this means SR is wrong.
I agree with (1). I do not agree with (2).

In RMP79 I provide a framework which allows both the Abraham and Minkowski momenta to be valid at the same time, and which is consistent with SR. This is a constructive disproof of (2) (i.e. I not only show that (2) is wrong, I also explicitly demonstrate the opposite).

Your objections to RMP79 all indicate that you do not understand the mathematics involved (or possibly, the physics).

If you wish to disprove the framework given in RMP79, please do so by either (i) demonstrating a theory-destroying intrinsic mathematical flaw in RMP79, or (ii) demonstrating that RMP79 makes a prediction (i.e. a specific, calculated result) which disagrees with an experiment.

(Also see S. Barnett, Phys. Rev. Lett. 104, 070401(2010), and C. Baxter and R. Loudon, J. Modern Optics, 57, 830 (2010), among others.)

C)
If you have a third option, please feel free to pursue that instead. I look forward to seeing your maths. Not just words.


Why am I asking you to do this? Because this thread is starting to sound increasingly like
S: "You're wrong!"
D&R: "No we're not, and we have maths! Here it is."
S: "Yes you are!"
D&R: "No we're not, and we still have maths! Here it is again."
etc.

The balance is easily redressed: You just need to provide some maths in favour of your argument. (Note that proving the Abraham EM vector is not independently covariant doesn't count: I already agree with that. You would have to show that there cannot exist any material four-vector which makes the total vector covariant (a ridiculous claim), or you would have to show that the Abraham EM vector MUST be independently covariant. Note that SR does NOT require this, as explained in RMP79.)

[sciencewatch]

Sciencewatch: ...
Instead of just claiming that other peoples' work is wrong, please show us some proof. That is, please demonstrate (i.e. using formulae) a mathematical contradiction, or give a mathematical calculation predicting a behaviour which disagrees with experiment, arising as a consequence of these alleged errors.
...
In RMP79 I provide a framework which allows both the Abraham and Minkowski momenta to be valid at the same time, and which is consistent with SR. This is a constructive disproof of (2) (i.e. I not only show that (2) is wrong, I also explicitly demonstrate the opposite).

Your objections to RMP79 all indicate that you do not understand the mathematics involved (or possibly, the physics).

If you wish to disprove the framework given in RMP79, please do so by either (i) demonstrating a theory-destroying intrinsic mathematical flaw in RMP79, or (ii) demonstrating that RMP79 makes a prediction (i.e. a specific, calculated result) which disagrees with an experiment.

(Also see S. Barnett, Phys. Rev. Lett. 104, 070401(2010), and C. Baxter and R. Loudon, J. Modern Optics, 57, 830 (2010), among others.)
...


In fact, there is no need to do math calculations for identifying basic concepts.
Now let me check some of your arguments starting with the principle of relativity.

In your review paper, you repeatedly claim:

“… division of the total energy-momentum tensor into electromagnetic and material components is arbitrary.”
“… the division of the total energy-momentum tensor into these two components is entirely arbitrary.”
[See: Rev. Mod. Phys.79:1197-1216 (2007); http://arxiv.org/abs/0710.0461 ]

My questions are:

1. According to the principle of relativity, the propagation direction of light momentum (electromagnetic field momentum) should be parallel to the wave vector for a plane wave, observed in any inertial frames. In your division of the total energy-momentum tensor, is this principle of relativity taken into account?

2. Since the division is arbitrary, there must be a division that makes the electromagnetic field momentum perpendicular to the direction of the wave vector. Do you think it is physical for the electromagnetic field momentum of a plane wave to be perpendicular to the wave vector?
--------
Can I say your arbitrary division is “a mathematical contradiction” or “intrinsic mathematical flaw”, or at least something related?

[rpfeifer]

1. No. As you would see from the maths, according to the principle of relativity the propagation direction of total momentum should be parallel to the wave vector for a plane wave observed in any inertial frame. This only holds for the EM component on it own when in vacuum. Consequently:
"In your division of the total energy-momentum tensor, is this principle of relativity taken into account?"
Yes.

2. What I (or you) "think" based on gut feeling is irrelevant. The mathematics tells us that this is
(i) permissible
(ii) irrelevant
and
(iii) not in conflict with the principle of relativity.

You have just proven my point: You need to stop arguing with words and start arguing with maths. Better yet, you need to stop thinking with words and start thinking with maths. Then you will understand the situation. Until then, you will keep tying yourself in knots.

You conclude: 'Can I say your arbitrary division is “a mathematical contradiction” or “intrinsic mathematical flaw”, or at least something related?'
Answer: Clearly not.

Hint: To do so, you would need to start by writing some maths... (perhaps you do not understand the meaning of the phrases "a mathematical contradiction" and an "intrinsic mathematical flaw"? These are things which can only be shown using mathematics. Sometimes words can be used to indicate the presence of such a flaw, but these words always translate directly into mathematics. The words which you have been using do not translate into mathematics consistent with physics as we know it. That is why I have asked you to start expressing yourself in maths. If you do so, it will stop you from making careless mistakes like you did just now. Right now you're just showing that you do not understand the physics because you do not understand the maths. That is why your word-based intuitions keep leading you astray.

If you don't start producing some maths, you are wasting my time. I have explained why your word-based arguments are nonsense, but you don't accept that. Unless you start doing physics (hint: physics is done using maths), I see no point in engaging in further armchair philosophy.

(Note: I'm sure philosophers recognise the annoying nature of "armchair philosophers" as well - people who have just read Cliff's Notes on Wittgenstein and suddenly think they know everything about philosophy from Kant to Aristotle...)

[DaleSpam]

According to your answer, the fiber recoiling can be explained by both Abraham’s and Minkowski’s formulations at the same time. However, the authors of the experiment, She, Yu, and Feng clearly claim:

“From the experiments described above, we believe that the phenomenon observed is due to the force exerted by the outgoing light. The nature of SF movement cannot be explained by Minkowski momentum. Minkowski momentum predicts a pull force, which pulls the whole SF to one side for asymmetric refraction [see Fig. 2(j)] or pulls it straight for direct transmission.” “In conclusion, our experiment and analysis suggest that Abraham momentum is correct.” [See: Phys. Rev. Lett. 101, 243601 (2008); http://physics.aps.org/story/v22/st20 ; http://www.youtube.com/watch?v=8wBDmRaqe8I ]

Obviously, your arguments are not consistent with the above authors’ claim, and you did not give any explanations why the above authors’ claim is wrong. Accordingly, your conclusion “This experiment does not break the ‘equal rights’ in any way” is not well grounded. The author's claim is unsubstantiated. In their entire article they never once calculated the total momentum tensor. Therefore, they make the claim without any correct justification.

As I mentioned above, in order to disprove the Minkowski momentum they need to do more than just demonstrate Abraham's momentum, they need to demonstrate that their results are consistent with the Abraham's momentum and also that the result does not depend on the total momentum. As the review article shows, any phenomenon which depends on the total momentum can be explained by both. They did not examine that so they cannot make their claim.

Consider a system or free-body diagram consisting of the tip of the fiber. On one side there is a momentum flux of the EM wave in free space, on the other side there is a momentum flus of the EM wave in the fiber as well as the material momentum tensor. Those two terms together are the total momentum. In steady state, the conservation of momentum requires that momentum flux of the light be equal and opposite of the total momentum flux, and therefore the bending of the fiber depends on the total momentum.

Therefore, while this experiment does show that Abraham's momentum is correct, it does not show that Minkowski's momentum is incorrect. I think it is very obvious that this experiment depends on the total momentum.

Your post-61 answer is “Simply because the authors of the study did not perform such an analysis does not mean that it cannot be done. Again, an experimental confirmation of Abraham is not an experimental contradiction of Minkowski.” ----- Sorry, I don’t understand what you exactly mean.I am sorry you don't understand. I have explained several times in the clearest manner I know how. Both Minkowski and Abraham can be true, they do not contradict each other. I hope that is clear enough.

[sciencewatch]

...
If you don't start producing some maths, you are wasting my time. I have explained why your word-based arguments are nonsense, but you don't accept that. Unless you start doing physics (hint: physics is done using maths), I see no point in engaging in further armchair philosophy.
...


Please tell me: What is the total momentum for a uniform plane wave in the medium-rest frame? According to the Eqs. (40)-(43) of your review article [Rev. Mod. Phys.79:1197-1216 (2007), http://arxiv.org/abs/0710.0461 ], the total momentum is ExH/c**2 (=Abraham’s momentum density vector) in such a case; am I right?

[rpfeifer]

No. It is ExH/c**2 + ρv.
You cannot ignore the material medium. It is carrying some of the momentum flux.
(Actually, this is a momentum density. You have to integrate this over the whole of the (infinite) plane wave to get the momentum.)

[sciencewatch]

The author's claim is unsubstantiated. In their entire article they never once calculated the total momentum tensor. Therefore, they make the claim without any correct justification.

As I mentioned above, in order to disprove the Minkowski momentum they need to do more than just demonstrate Abraham's momentum, they need to demonstrate that their results are consistent with the Abraham's momentum and also that the result does not depend on the total momentum. As the review article shows, any phenomenon which depends on the total momentum can be explained by both. They did not examine that so they cannot make their claim.
...


I think, She, Yu, and Feng, the authors of the experiment [Phys. Rev. Lett. 101, 243601 (2008)] have the best position to answer your challenge: “The author's claim is unsubstantiated. In their entire article they never once calculated the total momentum tensor. Therefore, they make the claim without any correct justification.”

I am sorry Physical Review Letters published such unsubstantiated claim.

[sciencewatch]

No. It is ExH/c**2 + ρv.
You cannot ignore the material medium. It is carrying some of the momentum flux.

In an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium, ρv=0, right? Then the total momentum is ExH/c**2=Abraham's momentum density vector. Right?

[rpfeifer]

Such a medium necessarily has a refractive index of 1.

[sciencewatch]

No. It is ExH/c**2 + ρv.
You cannot ignore the material medium. It is carrying some of the momentum flux.
(Actually, this is a momentum density. You have to integrate this over the whole of the (infinite) plane wave to get the momentum.)

ρ is what in Maxwell equations?

[sciencewatch]

Such a medium necessarily has a refractive index of 1.

How come?
The model with an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium but refrative index > 1 is widely used in physics literature.

[rpfeifer]

Under some circumstances it may be possible to approximate a medium as having all physical properties identical to the vacuum except for refractive index (and, by implication, the speed of light in the medium). This is not one of those circumstances.

You have to ask how the medium can have a refractive index other than 1, and this necessarily implies other properties which are relevant to the problem at hand (e.g. construction from EM dipoles, which will break homogeneity and which couple to the electromagnetic fields).

It is often possible to say a lot about a material just from these sorts of self-consistency conditions (a good example is the Kramers-Kronig relationship for dispersion in optics, which relates the absorption of a medium to how the real component of refractive index varies as a function of wavelength.)


ρ is not from Maxwell's equations - it is the density of the material medium, and v is its velocity. These become highly relevant when you involve the dipole structure of the medium. Their origin is from the continuity equations imposing conservation of mass/energy and momentum.

[sciencewatch]

No. It is ExH/c**2 + ρv.
You cannot ignore the material medium. It is carrying some of the momentum flux.
(Actually, this is a momentum density. You have to integrate this over the whole of the (infinite) plane wave to get the momentum.)

The model with an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium but refrative index > 1 is widely used in physics literature. For example,

Tomás Ramos, Guillermo F. Rubilar, Yuri N. Obukhov, Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654 ;

STEPHEN M. BARNETT, AND RODNEY LOUDON, "The enigma of optical momentum in a medium," Phil. Trans. R. Soc. A (2010) 368, 927–939;

M. Mansuripur, Phys. Rev. E 79, 026608 (2009).



Are they all doing wrong things?

[sciencewatch]

Under some circumstances it may be possible to approximate a medium as having all physical properties identical to the vacuum except for refractive index (and, by implication, the speed of light in the medium). This is not one of those circumstances.

You have to ask how the medium can have a refractive index other than 1, and this necessarily implies other properties which are relevant to the problem at hand (e.g. construction from EM dipoles, which will break homogeneity and which couple to the electromagnetic fields).

It is often possible to say a lot about a material just from these sorts of self-consistency conditions (a good example is the Kramers-Kronig relationship for dispersion in optics, which relates the absorption of a medium to how the real component of refractive index varies as a function of wavelength.)


ρ is not from Maxwell's equations - it is the density of the material medium, and v is its velocity. These become highly relevant when you involve the dipole structure of the medium. Their origin is from the continuity equations imposing conservation of mass/energy and momentum.

In the total momentum ExH/c**2 + ρv, with ρ the density of the material medium, v the medium local velocity. I can suppose the medium is in the "frozen" state so that ρv=0. Theoretically such a medium is existent and such a model is widely used in the literature, including your colleagues. Obviously, this total mometum is breaking the principle of relativity. To defend your arguments, you have to deny this widely-used physical model.

[vgv]

Dear collegues!

I hope following referencies will be interesting for you.

Sincerely

V.G.Veselago

Veselago V G “Energy, linear momentum, and mass transfer by an electromagnetic wave in a negative-refraction medium” Phys. Usp. 52 649–654 (2009)
http://ufn.ru/en/articles/2009/6/i/


Veselago V G, Shchavlev V V "On the relativistic invariance of the Minkowski and Abraham energy-momentum tensors" Phys. Usp. 53 317–318 (2010)
http://ufn.ru/en/articles/2010/3/j/

[rpfeifer]

"Are they all doing wrong things?"

No. All of these are good papers. When they talk about an "isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium" they mean one made up of dipoles. When light enters such a medium, the medium inevitably acquires momentum (ρv\not =0).

You specified that ρv=0, which I took to imply that your medium was "homogeneous" to the extent that it was not made up of dipoles, and hence did not couple to the light. In retrospect, you probably just made a mistake.

(Think about this: If ρv=0, the material has no momentum. Conservation of momentum then says that the EM wave still has the same momentum as in vacuum. As the total momentum tensor now only reads ExH, momentum conservation tells us that n=1.)

Also please consider that you are being very rude. All your responses are in the form of attacks. Physics is not a personal battle about whose theory is correct - it is about trying to understand how nature works. If something I say doesn't make sense to you, ask me to explain. Better yet, try to work it out for yourself. All your responses have been of the form "YOU ARE WRONG BECAUSE", rather than "Please explain this". If I have made a mistake, it will be obvious when I can't explain something, or when I arrive at a contradiction. Also, I will gladly admit it (because if we found something wrong, that would be interesting and I could probably write a new paper about it). (Note: This has not happened yet during our conversation.)

Example: You could have said "I do not understand why you say this means n=1, when this model is used in papers such as <xxx> with n>1. Please can you explain?"
You said "To defend your arguments, you have to deny this widely-used physical model."
No I don't, I just need to explain what the difference is between the model that you seemed to be talking about, and the model they are using. And please stop trying to turn this into a fight between me and the rest of the world. It isn't.

On that matter, please take a closer look at the first paper you cited: Tomás Ramos, Guillermo F. Rubilar, Yuri N. Obukhov, Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654
This is an excellent example of how to use the total energy-momentum tensor formalism I am talking about, to show equivalence of Abraham and Minkowski approaches for an Einstein Box.


My advice to you is this: Go to university and learn how to solve your own problems. I have just about run out of patience with you. You don't seem to want to learn - you just seem to want a fight.

[rpfeifer]

Dear collegues!

I hope following referencies will be interesting for you.

Sincerely

V.G.Veselago


Dear Prof. Veselago,

Thank you for your relevant citations (the consideration of media with negative refractive indices is a particularly interesting subject).

I note that you consider only the electromagnetic portion of the Abraham tensor pair, neglecting the associated material momentum (which propagates along with the wave packet).

Thus, what you say is true and the Abraham EM momentum does not transform as a relativistically covariant object. However, this has no bearing on the usefulness of the Abraham tensor _pair_, as the total momentum p_EM+p_mat does transform as a relativistically covariant object.

Indeed, the main thrust of the current discussion is to try and explain this distinction to one of the posters here, which is why I felt it necessary to post to clarify this point.

Best wishes,
Robert Pfeifer

[sciencewatch]

...
You specified that ρv=0, which I took to imply that your medium was "homogeneous" to the extent that it was not made up of dipoles, and hence did not couple to the light. In retrospect, you probably just made a mistake.

(Think about this: If ρv=0, the material has no momentum. Conservation of momentum then says that the EM wave still has the same momentum as in vacuum. As the total momentum tensor now only reads ExH, momentum conservation tells us that n=1.)
...


Suppose that there is a plane wave propagating in an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium. Observed in the medium-rest frame, the medium material momentum should be zero and the refractive index can be assumed to be >1. Please kindly indicate: Where is there a problem with this model?

In your arguments, in such case you think the field momentum = ExH/c**2, the same as in vacuum because the material momentum is zero, resulting in refractive index n=1. However, there is a mistake in your reasoning:

Because of energy-conservation law, the EM energy density with a medium is the same as that without a medium (vacuum). Thus the ExH/c**2 in a medium must be different from the ExH/c**2 in vacuum:

|ExH/c**2 in a medium| / |ExH/c**2 in vacuum| =1/n (refractive index)

Why n =1 must hold?

[sciencewatch]

...
Also please consider that you are being very rude. All your responses are in the form of attacks. ..

Example: You could have said "I do not understand why you say this means n=1, when this model is used in papers such as <xxx> with n>1. Please can you explain?"
You said "To defend your arguments, you have to deny this widely-used physical model."
No I don't, I just need to explain what the difference is between the model that you seemed to be talking about, and the model they are using. And please stop trying to turn this into a fight between me and the rest of the world. It isn't.
...


Probably you misunderstood something. I just got surprised that you refuse to accept a widely-used physical model. But I think, my words "To defend your arguments, you have to deny this widely-used physical model." is a real thing you have to do; otherwise the total momentum is not Lorentz covariant. I apologize to you if my words make you uncomfortable.
----------
In pots #85, I asked you:

“Please tell me: What is the total momentum for a uniform plane wave in the medium-rest frame? According to the Eqs. (40)-(43) of your review article [Rev. Mod. Phys.79:1197-1216 (2007), http://arxiv.org/abs/0710.0461 ], the total momentum is ExH/c**2 (=Abraham’s momentum density vector) in such a case; am I right?”

You answered:

“No. It is ExH/c**2 + ρv.
You cannot ignore the material medium. It is carrying some of the momentum flux.
(Actually, this is a momentum density. You have to integrate this over the whole of the (infinite) plane wave to get the momentum.)”
“Such a medium necessarily has a refractive index of 1.”

You said a lot for why ρv not =0 for my observed "in the medium-rest frame”. I had thought you intentionally misled me. Sorry.

[rpfeifer]

#98:
Good start, much more polite, but then: "there is a mistake in your reasoning" - You're back to trying to turn this into a fight again. Oh well, it was nice while it lasted.

"|ExH/c**2 in a medium| / |ExH/c**2 in vacuum| =1/n (refractive index)"

Think about this. You just said the density goes down by a factor of n. At the same time, the wave packet slows down by a factor of n, so the total momentum of the wave packet as described by ExH/c**2 goes down by a factor of n^2. Conservation of momentum says this has to go somewhere. That is, the material is placed in motion with total momentum
∫ |ExH/c**2 in vacuum| x (1-1/n**2) dV
unless the refractive index is equal to 1.
As you can see, you were mistaken in saying I had made a mistake.

You might want to bear in mind that I already spent a long time thinking about these problems when I wrote the review paper - it wasn't just a matter of scrawling down the first thing that came into my head. This is why I keep suggesting: Instead of saying I've made a mistake, ask me to explain to you. As well as being more polite, you'll look a lot less sloppy and/or possibly foolish.

#99:
"I apologize to you if my words make you uncomfortable."
You don't "make me uncomfortable". You just insult me. Important difference.
Now it seems to me that you are using a false apology to imply that
(i) your arguments are effective, and
(ii) I am taking them personally, and hence am worried.
Neither of these is true, but I am taking your insulting manner personally (of which this is another example) and I would appreciate an apology for that. Actually, never mind, I'm getting a bit arrogant here myself. Just try not to be so confrontational in future, OK?

"in the medium rest frame"
The rest frame before or after a light pulse enters the dielectric?
Typically, this refers to the rest frame before the light enters the dielectric. In this frame the dielectric is then placed in motion.

[rpfeifer]

I'll just expand on my last comment a bit.

"I may have misunderstood you there: You may have wanted to discuss a system where the dielectric is initially in motion, then stops when the light pulse enters it."
Total momentum is also conserved in this instance, as the momentum transferred from the light to the block is sufficient to stop its initial motion. Again, however, you cannot consider the Abraham EM density in isolation, as you have to also consider how the momentum which is transferred to the block propagates. The Maxwell stress tensor tells us that it is not instantaneously spread over the entire block: It has to propagate as some sort of matter wave. Thus, in that frame the momentum of the block behaves like this:

Before the pulse enters it:
Total momentum: Nonzero. Locally: Uniformly ρv\not=0.

Once the pulse has entered it:
Total momentum: Zero. Locally: Takes the form of a matter wave, i.e. <ρv(x)>=0 but ρv(x)\not=0 for most x.
Here, v(x) represents the velocity of the medium at point x (where x is a point within the medium).
Note that for a bounded wave packet propagation of the associated matter wave is made more complicated as you must take into account ongoing interactions as the edges of the packet propagate through the material. Yet another explanation as to why you cannot consider the EM and material portions of the momentum density separately, and thus why it doesn't matter that the Abraham EM density (in isolation) doesn't transform covariantly: You never encounter it in isolation.

By the way, do you feel that we have answered your original question yet? I ask because we do now seem to be talking about something only tangentially related (i.e. whether the framework in RMP79 is consistent, rather than whether the Abraham EM expression is inconsistent with SR).

[sciencewatch]

#98:
...
"|ExH/c**2 in a medium| / |ExH/c**2 in vacuum| =1/n (refractive index)"

Think about this. You just said the density goes down by a factor of n. At the same time, the wave packet slows down by a factor of n, so the total momentum of the wave packet as described by ExH/c**2 goes down by a factor of n^2. Conservation of momentum says this has to go somewhere. That is, the material is placed in motion with total momentum
∫ |ExH/c**2 in vacuum| x (1-1/n**2) dV
unless the refractive index is equal to 1.
As you can see, you were mistaken in saying I had made a mistake.
...

Please pay attention to the model: Suppose that there is a plane wave propagating in an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium. Observed in the medium-rest frame, the medium material momentum should be zero and the refractive index can be assumed to be >1. Observed in the medium-rest frame, the dielectric is not moving.

In your arguments, in such case you think the field momentum = ExH/c**2, the same as in vacuum because the material momentum is zero, resulting in refractive index n=1. However, there are two mistakes now in your reasoning:

(1) The field momentum should be DxB (instead of ExH/c**2) in a medium,
(2) Under the energy conservation, the EM energy density with a medium is the same as that without a medium (vacuum). Thus the ExH/c**2 in a medium is different from the ExH/c**2 in vacuum:

|ExH/c**2 in a medium| / |ExH/c**2 in vacuum| =1/n (refractive index) ----- (1)
---
Momentum flus conservation:

With a medium, momentum flux = DxB*(c/n)=n**2 *(ExH)/c**2 *(c/n) = n *(ExH)/c ----(2)
Without a medium (vacuum), momentum flux = ExH/c**2 * c = ExH/c -----(3)

Using Eq. (1), we find Eq. (2) = Eq. (3), the momentum-flux conservation.
----------------------
Why n =1 must hold?

[DaleSpam]

Observed in the medium-rest frame, the dielectric is not moving.The medium rest frame is non-inertial.

[rpfeifer]

"Please pay attention to the model: Suppose that there is a plane wave propagating in an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium. Observed in the medium-rest frame, the medium material momentum should be zero and the refractive index can be assumed to be >1. Observed in the medium-rest frame, the dielectric is not moving."

OK, how did this EM wave get into this dielectric? When it entered, it set up a wave in the dielectric, which is still there. That is, <ρv(x)>=0 but ρv(x)\not=0. And this dipole matter wave couples to the EM field.

If you do not allow for the entry of the wave into the medium at some point in the past, then the situation you describe is unphysical (e.g. infinite dielectric). This even applies to a plane wave (for which it is necessary to assume that the beam is "turned on" gradually at t=-∞, but I will not attempt to explain details of boundary conditions at infinity to you here. If interested, look it up).

"In your arguments, in such case you think the field momentum = ExH/c**2, the same as in vacuum because the material momentum is zero, resulting in refractive index n=1. However, there are two mistakes now in your reasoning:"

*rolls eyes* Here we go again.

(1) You assert the Minkowski momentum. However, for conservation of angular momentum the total momentum multiplied by c must equal the Poynting vector plus the material energy flux, i.e.
c x (p_EM+p_mat) = ExH/c+ρcv.
Note that neither the Poynting vector nor the material energy flux have ever been under debate in the controversy. These are the S terms in T^{\mu\nu}.

If we use the Minkowski momentum, then we have to have a "material" momentum of
ρv+ExH/c^2-DxB.
Do you like having a material momentum density which contains E, H, D, and B? Does this make sense to you? Sure, it might not contribute to momentum transfer, but it doesn't describe the movement of matter any more.

(2) "Under the energy conservation, the EM energy density with a medium is the same as that without a medium (vacuum)."

Don't be ridiculous. The wave packet is packed into a smaller volume, so the energy density goes up. Exactly the same as happened with momentum. If you're thinking about a plane wave, which is infinite, it still has this compression. To see this, remember that a plane wave may be infinite, but it still propagates. Therefore, consider a "chunk" of wave just about to enter the dielectric. Work out what happens. You'll see it gets compressed.

"Using Eq. (1), we find Eq. (2) = Eq. (3), the momentum-flux conservation."

There are mistakes in your working. If you fix them, you might end up with a derivation of the Minkowski momentum density - which then violates conservation of angular momentum.

If you eventually managed to fix that, you would have the material given in RMP79.

You are retracing the steps of hundreds of physicists before you. This is why literature reviews exist: To show what has already been done. Go away and read the literature. Start with all the citations in RMP79. M∅ller is particularly relevant here.

----------------------
"Why n =1 must hold?"

Because the argument I gave above is valid, and the one you gave was based on two mistakes.

[rpfeifer]

The medium rest frame is non-inertial.

Thanks, Dale, very elegant. Yep, you can construct a co-ordinate frame using GR in which space--time as you know it is rippling gently back and forth rather than the atoms of the medium.

That would be very silly, but in a good way. (The physics would be 100% correct, and absolutely no practical use whatsoever!) Nice one! :smile:

Being a GR solution, the maths involved are, of course, way beyond those presented in RMP79 (and would involve a stress-energy tensor for spacetime in the adopted co-ordinate frame, which would (by definition of the frame) couple to the EM tensor).

I doubt that sciencewatch had such a solution in mind.

(Note for junior physicists: The phrase "co-ordinate frame" has a special mathematical meaning. It comes from differential geometry, and refers to a very specific type of mathematical object, which people usually first encounter as the set of objects e^a_\mu(x) in tetrad-formalism GR.)

[rpfeifer]

"Do you like having a material momentum density which contains E, H, D, and B? Does this make sense to you? Sure, it might not contribute to momentum transfer, but it doesn't describe the movement of matter any more."

Just wanted to say - there's nothing wrong with such a formulation, but you do have to be very careful in interpreting it. That is:
Even if DxB contains all the momentum, the medium still moves because its behaviour is governed by ρv, not ρv+ExH/c^2-DxB.

Thus the Minkowski formulation is good for describing momentum transfer to objects in a dielectric, but not so useful for describing the motion of the dielectric itself.

[sciencewatch]

The medium rest frame is non-inertial.

For a plane wave propagating in an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium, the refractive index can be assumed to be >1. Observed in the medium-rest frame, the dielectric is not moving.

For such an ideal model, macro-electromagnetically speaking, there are no reasons to say the medium moves with accelerations. Don’t ask me how to set up the plane wave and how to get such a medium; I don’t know. But I do know there is such a solution to Maxwell equations, and this physical model is widely presented in physics textbooks:

J. D. Jackson, Classical Electrodynamics, (John Wiley & Sons, NJ, 1999), 3rd Edition;
M. Born and E. Wolf, Principles of optics (5th edition) (Oxford, 1975);
J. A. Stratton, Electromagnetic theory, (McGraw-Hill, NY, 1941);
J. A. Kong, Theory of Electromagnetic Waves, (John Wiley & Sons, NY, 1975);
W. R. Smythe, Static and dynamic electricity, (McGraw-Hill, NY, 1968), 3rd edition;
D. J. Griffths, Introduction to Electrodynamics, (Prentice-Hall, NJ, 1999), 3rd edition;

to name a few.

[rpfeifer]

Error: The situation we are discussing is more complex than those addressed in the textbooks. Approximations valid in the problems they address may not be valid here.

[rpfeifer]

If you don't know how to set up a rigorous model of the wave and medium, and then take limits, that's fair enough. It is good to be able to admit your limitations.

This same limitation is why you are struggling with the A-M controversy. You need to learn how to set up this sort of more detailed model before you can understand the explanation.

Regards,
R. Pfeifer

[DaleSpam]

For such an ideal model, macro-electromagnetically speaking, there are no reasons to say the medium moves with accelerations. Conservation of momentum is a pretty good reason to say the medium moves with accelerations. The acceleration can often be neglected, as in the textbooks you cited, except when it cannot be neglected, as in the fiber bending experiment.

[sciencewatch]

Conservation of momentum is a pretty good reason to say the medium moves with accelerations. The acceleration can often be neglected, as in the textbooks you cited, except when it cannot be neglected, as in the fiber bending experiment.
You are talking about media with discontinuities.

Let me restate: For a plane wave propagating in an infinite isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium, the refractive index can be assumed to be >1. Observed in the medium-rest frame, the dielectric is not moving.

For such an ideal model, speaking in macro-electromagnetic theory , there are no reasons to say the medium moves with accelerations. Don’t ask me how to set up the plane wave and how to get such a medium; I don’t know. But I do know there is such a solution to Maxwell equations, and this physical model is widely presented in physics textbooks:

J. D. Jackson, Classical Electrodynamics, (John Wiley & Sons, NJ, 1999), 3rd Edition;
M. Born and E. Wolf, Principles of optics (5th edition) (Oxford, 1975);
J. A. Stratton, Electromagnetic theory, (McGraw-Hill, NY, 1941);
J. A. Kong, Theory of Electromagnetic Waves, (John Wiley & Sons, NY, 1975);
W. R. Smythe, Static and dynamic electricity, (McGraw-Hill, NY, 1968), 3rd edition;
D. J. Griffths, Introduction to Electrodynamics, (Prentice-Hall, NJ, 1999), 3rd edition;

to name a few.
------
If there are any discontinuities in a medium, there is no strict uniform plane-wave solution to Maxwell equations; I think this implication is well-known in the community of electromagetic theory. I am sorry I did not strcitly state it.

[DaleSpam]

a plane wave propagating in an infinite ...Oops, I did miss that. I assume that you mean an infinite wave also, otherwise the rest frame would be non-inertial even for an infinite medium.

You will have to remind me: why are we considering an infinite dielectric? How is it relevant to the problem under consideration? And what is the concern for an infinite dielectric?

EDIT: actually, even for an infinite medium and an infinite plane wave a reference frame where the medium is everywhere at rest will be non-inertial. Parts of the medium accelerate wrt each other as the momentum flux at each location changes. I.e. You can consider conservation of momentum for a differential element of the medium as the fields vary across it.

[sciencewatch]

Oops, I did miss that. I assume that you mean an infinite wave also, otherwise the rest frame would be non-inertial even for an infinite medium.

You will have to remind me: why are we considering an infinite dielectric? How is it relevant to the problem under consideration? And what is the concern for an infinite dielectric?

EDIT: actually, even for an infinite medium and an infinite plane wave a reference frame where the medium is everywhere at rest will be non-inertial. Parts of the medium accelerate wrt each other as the momentum flux at each location changes. I.e. You can consider conservation of momentum for a differential element of the medium as the fields vary across it.

Let me restate: For an infinite uniform plane wave propagating in an infinite isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium, the refractive index can be assumed to be >1. Observed in the medium-rest frame, the dielectric is not moving.

For such an ideal model, speaking in macro-electromagnetic theory , there are no reasons to say the medium moves with accelerations. Don’t ask me how to set up the plane wave and how to get such a medium; I don’t know. But I do know there is such a solution to Maxwell equations, and this physical model is widely presented in physics textbooks:

J. D. Jackson, Classical Electrodynamics, (John Wiley & Sons, NJ, 1999), 3rd Edition;
M. Born and E. Wolf, Principles of optics (5th edition) (Oxford, 1975);
J. A. Stratton, Electromagnetic theory, (McGraw-Hill, NY, 1941);
J. A. Kong, Theory of Electromagnetic Waves, (John Wiley & Sons, NY, 1975);
W. R. Smythe, Static and dynamic electricity, (McGraw-Hill, NY, 1968), 3rd edition;
D. J. Griffths, Introduction to Electrodynamics, (Prentice-Hall, NJ, 1999), 3rd edition;

to name a few.
------
If there are any discontinuities in a medium, there is no strict uniform plane-wave solution to Maxwell equations; this implication is a well-known common sense in the community of electromagetic theory. I apologize again that I did not strcitly state it.

PS:

"speaking in macro-electromagnetic theory..." --- means there is no motion for the medium as a whole because the medium is "rigid", and the total force is zero after taking average over light-wave period and space for all possible micro-forces.

"why are we considering an infinite dielectric?" ---- Thousands of examples cannot validate a theory; however, to negate it, one is enough. For example, when I write down a code for solving differential equations, I don't know if it is correct, and I usually use a simple analytically solvable equation to check first.

I can be sure that you know all these simple things. Since you ask me to say, I have to say.

[DaleSpam]

"why are we considering an infinite dielectric?" ---- Thousands of examples cannot validate a theory; however, to negate it, one is enough. For example, when I write down a code for solving differential equations, I don't know if it is correct, and I usually use a simple analytically solvable equation to check first.OK, so what theory does this example negate and how?

[DaleSpam]

Thanks, Dale, very elegant. Yep, you can construct a co-ordinate frame using GR in which space--time as you know it is rippling gently back and forth rather than the atoms of the medium.It took me a while, but I got what you said here. I wish I could take credit for such a subtle idea. I was thinking of a finite block of dielectric and just the fact that radiation pressure would accelerate it as the wave entered. But your idea applies even for the infinite dielectric.

[sciencewatch]

OK, so what theory does this example negate and how?

Suppose that an infinite uniform plane wave propagates in an infinite isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium with a refractive index >1. Speaking in macro-electromagnetic theory, the medium-rest frame is an inertial frame.

For such an ideal plane-wave model, the medium is assumed to be "rigid", and the total force acting on the whole medium is zero after taking average over time (in one light-wave period) and space (in one wavelength) for all possible micro-scale forces. In other words, there are no accelerations for the medium. Don’t ask me how to set up the plane wave and how to get such a medium; I don’t know. But I do know there is such a solution to Maxwell equations, and this physical model is widely presented in physics textbooks:

J. D. Jackson, Classical Electrodynamics, (John Wiley & Sons, NJ, 1999), 3rd Edition;
M. Born and E. Wolf, Principles of optics (5th edition) (Oxford, 1975);
J. A. Stratton, Electromagnetic theory, (McGraw-Hill, NY, 1941);
J. A. Kong, Theory of Electromagnetic Waves, (John Wiley & Sons, NY, 1975);
W. R. Smythe, Static and dynamic electricity, (McGraw-Hill, NY, 1968), 3rd edition;
D. J. Griffths, Introduction to Electrodynamics, (Prentice-Hall, NJ, 1999), 3rd edition;

to name a few.

************************
“OK, so what theory does this example negate and how?”

The author [Rev. Mod. Phys.79:1197-1216 (2007), http://arxiv.org/abs/0710.0461 ] claims that the total energy-momentum tensor is “uniquely determined by consistency with special relativity”. However, if applying their total-tensor model to the ideal plane wave described above, we obtain the total momentum = ExH/c**2 (=Abraham’s momentum density vector) from their Eqs. (40)-(43), or Eq. (33) by setting the dielectric velocity v = 0, and ExH/c**2 cannot be used to constitute a Lorentz covariant momentum-energy 4-vector. Therefore, the total-tensor model does break the special relativity, unless they have strong arguments to refute the above ideal plane-wave model.

------------------
To the authors [Rev. Mod. Phys.79:1197-1216 (2007)]: Please check the last term of Eq. (33), “+ ExM/c**2”, and make sure if there is a sign typo: – ?. Seems not consistent with Eq. (31) and Eqs. (40)-(43).

************************
PS:

In post #70, the author of Rev. Mod. Phys.79:1197-1216 (2007) (henceforth RMP79) claims:

In fact, the main thrust of Sec. VIII of RMP79 is that once the material properties of the dielectric are specified, the total momentum tensor is uniquely determined by

(i) consistency with special relativity, and
(ii) conservation of linear and angular momentum.

This leads to two important conclusions:

(a) No valid combination of EM and material energy-momentum tensors can break special relativity. If you are using a combination of tensors which appears to break this, then your choice of tensors is incorrect (usually, the material tensor is incorrect or missing). Note that I have never yet seen a fully relativistic formulation of the material counterpart tensors written down anywhere in the literature - even those given in RMP79 are valid only for media moving at v<<c, though the full expressions could be obtained from Eqs. (33)-(34).

(b) As the _total_ energy-momentum tensor is uniquely fixed by (i) and (ii) above, any division into components necessarily yields the same total tensor, and thus the same physical behaviours. That is, Abraham and Minkowski correspond to the same T, and thus the same physics.

[DaleSpam]

First, you are making a whole bunch of unphysical assumptions, so even if your conclusion is correct, it could serve as a reducto ad absurdum disproof of your assumptions rather than a disproof of the total tensor model. However, I don't think that you have reached that level yet: However, if applying their total-tensor model to the ideal plane wave described above, we obtain the total momentum = ExH/c**2 (=Abraham’s momentum density vector) from their Eqs. (40)-(43), or Eq. (33) by setting the dielectric velocity v = 0, and ExH/c**2 cannot be used to constitute a Lorentz covariant momentum-energy 4-vector.Why not? Can you form this into a proper total momentum tensor and show that boosting it to some other frame v<<c gives the wrong total momentum?

[PhilDSP]

The medium rest frame is non-inertial.

Just to make sure I'm following... The medium rest frame will be non-inertial while a force is being exchanged with any particle in the media, right? For that matter, the media rest frame will also be non-inertial, won't it?

However, once all forces are exchanged (or balanced) both the medium and media frames will be inertial and the relationship between the rest frames gives the classical Fizeau result (medium partially dragged by the media)

[DaleSpam]

The medium rest frame will be non-inertial while a force is being exchanged with any particle in the media, right?Yes.

However, once all forces are exchanged (or balanced) both the medium and media frames will be inertialYes, provided the material is perfectly rigid so that only the 0 total momentum (net force) is important and not the non-zero local momentum flux (internal forces).

[DaleSpam]

But I do know there is such a solution to Maxwell equations, and this physical model is widely presented in physics textbooks:

J. D. Jackson, Classical Electrodynamics, (John Wiley & Sons, NJ, 1999), 3rd Edition;
M. Born and E. Wolf, Principles of optics (5th edition) (Oxford, 1975);
J. A. Stratton, Electromagnetic theory, (McGraw-Hill, NY, 1941);
J. A. Kong, Theory of Electromagnetic Waves, (John Wiley & Sons, NY, 1975);
W. R. Smythe, Static and dynamic electricity, (McGraw-Hill, NY, 1968), 3rd edition;
D. J. Griffths, Introduction to Electrodynamics, (Prentice-Hall, NJ, 1999), 3rd edition;

to name a few.FYI, although it is slightly off-topic, just in case you were unaware I wanted to let you know that ideal gasses are also not physical, although they are even more widely presented in textbooks.

Oh, also, rigid bodies aren't really rigid.

And ideal capacitors, inductors, and batteries don't actually exist.

And there aren't any perfect crystals.

There aren't any classical point particles either.

And Santa Claus and the Easter Bunny and the Tooth Fairy too.

[PeterDonis]

Whaddaya mean all that stuff isn't real? I can buy it on the web, right here:

http://www.lhup.edu/~dsimanek/ideal/ideal.htm

:wink:

[DaleSpam]

Whaddaya mean all that stuff isn't real? I can buy it on the web, right here:

http://www.lhup.edu/~dsimanek/ideal/ideal.htm

:wink::rofl: That is excellent! Thanks.

[jtbell]

But it doesn't list inertial reference frames. :cry:

[PeterDonis]

Yes, I think they need to expand their catalog:

NEW! Taylor-Wheeler ideal clocks! Guaranteed to tick off *exact* proper time regardless of acceleration or your money back! Never worry about the clock postulate again!

Special bundle offer: order a Taylor-Wheeler ideal clock and get a FREE Taylor-Wheeler ideal meter stick as well! Guaranteed to mark off exactly 9,192,631,770 / 299,792,458 cesium-133 hyperfine transition wavelengths!

[sciencewatch]

...please take a closer look at the first paper you cited: Tomás Ramos, Guillermo F. Rubilar, Yuri N. Obukhov, Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654
This is an excellent example of how to use the total energy-momentum tensor formalism I am talking about, to show equivalence of Abraham and Minkowski approaches for an Einstein Box....


In the paper [Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654 ], the total energy-momentum tensor Tmn is given by Eq. (3), which is a Lorentz covariant second-rank 4-tensor.

To my knowledge, a row- or column-vector of a Lorentz covariant second-rank 4-tensor has 4 components, but it is not necessarily a Lorentz covariant 4-vector. Am I right?

But, why does Eq. (5) denote a Lorentz covariant 4-momentum? Tm0 is just a row- or column-vector of the total energy-momentum tensor Tmn. Did I miss something?

To DaleSpam: Help me, please. You are a good expert.

[sciencewatch]

FYI, although it is slightly off-topic, just in case you were unaware I wanted to let you know that ideal gasses are also not physical, although they are even more widely presented in textbooks.

Oh, also, rigid bodies aren't really rigid.
...

I guess the Einstein box [Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654 ] is also assumed to be "rigid", made from isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal dielectric; otherwise the internal energy of Einstein box would change when the light pulse goes through the box, and the refractive index n would be a complex number and a function of frequency. Note: A light pulse occupies a finite-width spectrum of frequency.

[DaleSpam]

To my knowledge, a row- or column-vector of a Lorentz covariant second-rank 4-tensor has 4 components, but it is not necessarily a Lorentz covariant 4-vector. Am I right?

But, why does Eq. (5) denote a Lorentz covariant 4-momentum? Tm0 is just a row- or column-vector of the total energy-momentum tensor Tmn. Did I miss something?I agree, I am not comfortable taking a certain column, it makes the equation no longer manifestly covariant. Particularly under different coordinate systems that may not be orthonormal or inertial.

[sciencewatch]

Suppose that an infinite uniform plane wave propagates in an infinite isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium with a refractive index >1. Speaking in macro-electromagnetic theory, the medium-rest frame is an inertial frame.

For such an ideal plane-wave model, the medium is assumed to be "rigid", and the total force acting on the whole medium is zero after taking average over time (in one light-wave period) and space (in one wavelength) for all possible micro-scale forces. In other words, there are no accelerations for the medium. Don’t ask me how to set up the plane wave and how to get such a medium; I don’t know. But I do know there is such a solution to Maxwell equations, and this physical model is widely presented in physics textbooks:

J. D. Jackson, Classical Electrodynamics, (John Wiley & Sons, NJ, 1999), 3rd Edition;
M. Born and E. Wolf, Principles of optics (5th edition) (Oxford, 1975);
J. A. Stratton, Electromagnetic theory, (McGraw-Hill, NY, 1941);
J. A. Kong, Theory of Electromagnetic Waves, (John Wiley & Sons, NY, 1975);
W. R. Smythe, Static and dynamic electricity, (McGraw-Hill, NY, 1968), 3rd edition;
D. J. Griffths, Introduction to Electrodynamics, (Prentice-Hall, NJ, 1999), 3rd edition;

to name a few.

************************
“OK, so what theory does this example negate and how?”

The author [Rev. Mod. Phys.79:1197-1216 (2007), http://arxiv.org/abs/0710.0461 ] claims that the total energy-momentum tensor is “uniquely determined by consistency with special relativity”. However, if applying their total-tensor model to the ideal plane wave described above, we obtain the total momentum = ExH/c**2 (=Abraham’s momentum density vector) from their Eqs. (40)-(43), or Eq. (33) by setting the dielectric velocity v = 0, and ExH/c**2 cannot be used to constitute a Lorentz covariant momentum-energy 4-vector. Therefore, the total-tensor model does break the special relativity, unless they have strong arguments to refute the above ideal plane-wave model.

------------------
To the authors [Rev. Mod. Phys.79:1197-1216 (2007)]: Please check the last term of Eq. (33), “+ ExM/c**2”, and make sure if there is a sign typo: – ?. Seems not consistent with Eq. (31) and Eqs. (40)-(43).

************************
PS:

In post #70, the author of Rev. Mod. Phys.79:1197-1216 (2007) (henceforth RMP79) claims:

In fact, the main thrust of Sec. VIII of RMP79 is that once the material properties of the dielectric are specified, the total momentum tensor is uniquely determined by

(i) consistency with special relativity, and
(ii) conservation of linear and angular momentum.

This leads to two important conclusions:

(a) No valid combination of EM and material energy-momentum tensors can break special relativity. If you are using a combination of tensors which appears to break this, then your choice of tensors is incorrect (usually, the material tensor is incorrect or missing). Note that I have never yet seen a fully relativistic formulation of the material counterpart tensors written down anywhere in the literature - even those given in RMP79 are valid only for media moving at v<<c, though the full expressions could be obtained from Eqs. (33)-(34).

(b) As the _total_ energy-momentum tensor is uniquely fixed by (i) and (ii) above, any division into components necessarily yields the same total tensor, and thus the same physical behaviours. That is, Abraham and Minkowski correspond to the same T, and thus the same physics.

A misunderstanding of the special principle of relativity?

In the community of special theory of relativity, there is a well-recognized implicit assumption that a physical formulation represented by a Lorentz covariant 4-vector or tensor must be consistent with the principle of relativity. Some scientists even say everything is Lorentz transformation. In fact, this is a delusion. One example, as I indicated, is the total energy-momentum tensor model developed by Rev. Mod. Phys.79:1197-1216 (2007), http://arxiv.org/abs/0710.0461 , and verified by Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654 (confer: Posts #116, #126, #125, #127). The total energy-momentum tensor is Lorentz covariant, indeed; however, its physical implication is breaking the principle of relativity.

There is another simpler example to show this delusion, presented in the thread entitled “Are the principle of relativity and the Lorentz invariance equivalent?” [ http://www.physicsforums.com/showthread.php?t=551544 ], which is copied below:

The fundamental requirements of the special relativity on relativistic electrodynamics are that time-space coordinates and two electromagnetic (EM) field-strength tensors follow Lorentz transformations, resulting in the invariance of Maxwell equations in forms in any inertial frames.

Sometimes a formulation, which follows Lorentz transformation, might breaks the special principle of relativity. A typical example is the formulation for Fizeau running water experiment. Why?

The Fizeau experiment is usually used to illustrate the relativistic velocity addition rule in the textbooks. Observed in a frame which is fixed with a uniform medium with a refractive index of n, the photon's speed is c/n, and the photon's 4-velocity is gp'*(up',c), with |up'|=c/n and gp'=1/sqrt(1-up'**2/c**2). Suppose the medium moves at v, relatively to the lab frame. Observed in the lab frame, the photon 3D-velocity, up, is obtained from the Lorentz transformation of gp'*(up',c). However, the obtained-photon-velocity up is not parallel to the 3D-wave vectror k in the lab frame, unless the medium moves parallel to the wave vector k.

According to the principle of relativity, the photon's velocity must be parallel to the wave vector in any inertial frames. Thus from above analysis, the photon's 3D-velocity in a medium can not be used to constitute a Lorentz covariant 4-velocity. In other words, the photon's 4-velocity in a medium, which follows Lorentz transformation, breaks the special principle of relativity instead.

------

PS:

A slightly different total–momentum model seems to be first presented by Baxter et al. [Phys. Rev. A 47, 1278 (1993), http://pra.aps.org/abstract/PRA/v47/i2/p1278_1 ], and later by Leonhardt at a different angle of view [Phys. Rev. A 73, 032108 (2006), http://pra.aps.org/abstract/PRA/v73/i3/e032108 ]. The model of total momentum = dielectric kinetic momentum + Abraham’s momentum is further analyzed and identified by Barnett [see Eq. (7), Phys. Rev. Lett. 104, 070401 (2010), http://prl.aps.org/abstract/PRL/v104/i7/e070401]. When applying this total-momentum model to the ideal infinite uniform plane wave in an ideal infinite dielectric medium (Confer Post #116), the total momentum is Abraham’s momentum, which is the same as that obtained from the mentioned-above total momentum-energy tensor model [Rev. Mod. Phys.79:1197-1216 (2007), http://arxiv.org/abs/0710.0461].

[rpfeifer]

Hello all!

It looks like a lot of interesting things have been said on this thread since I last checked in. In particular, sciencewatch's model is now much more thoroughly described.

First, though, I'd like to warn about using macroscopic EM theory to attempt to calculate momentum density. This is inappropriate as momentum density is a microscopic property of the system.

Now, on to the interesting question raised by this model:
Why should p be covariant?
In vacuum, this doesn't seem to be open to debate. In a material medium, however, v is essentially a free parameter, so this doesn't seem to be enforced.
I'll address my argument to steady state scenarios (e.g. laser beam passing through glass block), as the situation is more complex when not at steady state.

(1) In a system where the beam enters the medium from vacuum, p is a 4-vector just outside the medium, and conservation of momentum requires that it be a 4-vector inside the medium as well, constraining v accordingly.

(2) In a system where the dielectric is infinite and fills all of space and time, the EM pulse does not enter the system from vacuum. In the absence of external constraints, we may set v arbitrarily, as sciencewatch has done, even where this results in a T^{\mu\nu} which violates special relativity.

However, such a system is "unphysical": Our universe is largely empty space, and is believed to be described by physical models where the density of all fields (including matter fields) drops to zero at spatial infinity. Trace its trajectory back to t=-∞, and no matter how large the dielectric, that photon originally entered from vacuum.

Although the situation is a little more complicated when you consider that the EM wave may have been emitted by decay of an excited electron state in e.g. air rather than vacuum, the emitting matter itself also has a history, and this too must be consistent with the boundary conditions of the universe. To properly treat this goes beyond the limitations of classical EM, but ultimately, the implication is that only situations in which total momentum forms a 4-vector are compatible with the assumption of zero fields (of all sorts; bosons & fermions) at x→∞.

Hence SR is not compatible with situation (2), but situation (2) does not describe a situation compatible with the physical universe.

I guess sciencewatch and I must just rub each other up the wrong way - the sophistication of his arguments seem to have increased the moment I left the thread :smile:

Also:
PS - Thanks for the erratum! Fortunately the error doesn't carry forwards into any subsequent expressions. I'll recheck the explicit expression for T as well, and upload a correction. It just goes to show - you should always check what you read in the papers!

[keji8341]

...

(2) In a system where the dielectric is infinite and fills all of space and time, the EM pulse does not enter the system from vacuum. In the absence of external constraints, we may set v arbitrarily, as sciencewatch has done, even where this results in a T^{\mu\nu} which violates special relativity.

However, such a system is "unphysical": Our universe is largely empty space, and is believed to be described by physical models where the density of all fields (including matter fields) drops to zero at spatial infinity. Trace its trajectory back to t=-∞, and no matter how large the dielectric, that photon originally entered from vacuum.

...

Please note: Einstein used a unifrom plane wave in free space to derive Doppler effect [A. Einstein, Ann. Phys. Lpz. 17, 891 (1905), “On the Electrodynamics of Moving Bodies,” http://www.fourmilab.ch/etexts/einstein/specrel/www/ ].

Is there a real plane wave in practice?
Is there a real free space in practice?

[PeterDonis]

Our universe is largely empty space, and is believed to be described by physical models where the density of all fields (including matter fields) drops to zero at spatial infinity. Trace its trajectory back to t=-∞, and no matter how large the dielectric, that photon originally entered from vacuum.

For models that are just supposed to cover isolated systems, I agree; but for cosmological models, where we are trying to model the entire universe, this is not really true, is it? The universe's average density of mass-energy is nonzero. And if we trace a photon's trajectory back far enough (assuming it's a photon that has been traveling freely through the universe's entire history since "recombination", such as a CMB photon), we end up in a hot, dense plasma, not vacuum.

[rpfeifer]

Keji - regarding your question (which was subsequently deleted) as to whether I had "banned" sciencewatch: I have no moderation powers, and I had assumed sciencewatch had voluntarily unsubscribed from the forum.

I'm not sure if you were trying to insult me with the deleted comment, or whether you were just asking whether I had some sort of unquestioned authority here (I don't). I'll give you the benefit of the doubt on that one.


Regarding plane waves and free space:
(i) Plane waves are generally recognised as a useful basis from which an arbitrary waveform may be constructed; however, in my experience most scientists agree that they can only be at best approximated in a real-world context. Thus: Any waveform may be considered a superposition of a possibly infinte number of plane waves - but you're unlikely to meet one on its own.
(ii) Free space: Good question.

Peter Donis: You also makes some good points regarding this.

One way to refine the argument is as follows:
It is in fact sufficient that the area of interest be enclosed by _any_ boundary B on its past light cone (not necessarily at infinity), provided all fields and their gradients vanish on this boundary, and that this boundary, or a smooth perturbation of it, persists over the duration that we monitor the system of interest. Thus we don't need to go to t=-∞.

I am not sure of the rigorous status of the "fields vanish at infinity" argument, except that it is widely used in quantum field theory. If it isn't proven, then it is at least a useful working assumption. Nor do I know how it is usually reconciled with the early history of the universe. Possibly it's just really hard to find a situation where you need to go that far back to construct a boundary B.

It's a good question, and one you'd need to ask a cosmologist or quantum cosmologist.

[rpfeifer]

One way to refine the argument is as follows:
It is in fact sufficient that the area of interest be enclosed by _any_ boundary B on its past light cone (not necessarily at infinity), provided all fields and their gradients vanish on this boundary, and that this boundary, or a smooth perturbation of it, persists over the duration that we monitor the system of interest. Thus we don't need to go to t=-∞.

Which is really just a paraphrase of Peter Donis' comment that this is fine for isolated systems :)

[PeterDonis]

Which is really just a paraphrase of Peter Donis' comment that this is fine for isolated systems :)

Yes, as long as the average density of mass-energy in the universe as a whole is small enough to ignore when constructing the model of the isolated system, so that you can find a boundary surface B on which the fields can be taken to be zero to within the accuracy desired.

[yoron]

Very nice reading. And I think you've done a very good job explaining your points in words too RP. I will have to read up on those tensors.

[DaleSpam]

In the community of special theory of relativity, there is a well-recognized implicit assumption that a physical formulation represented by a Lorentz covariant 4-vector or tensor must be consistent with the principle of relativity.This is correct. There are two transformations which are consistent with the principle of relativity, the Lorentz transform and the Galilean transform. If a law is covariant wrt arbitrary diffeomorphisms then it is necessarily covariant wrt both the Lorentz transform and the Galilean transform. Therefore any physical law expressed in a tensor form is mathematically guaranteed to be compatible with the principle of relativity.

Some scientists even say everything is Lorentz transformation. In fact, this is a delusion.This language is completely inappropriate for this forum.

One example, as I indicated, is the total energy-momentum tensor model developed by Rev. Mod. Phys.79:1197-1216 (2007), http://arxiv.org/abs/0710.0461 , and verified by Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654 (confer: Posts #116, #126, #125, #127). The total energy-momentum tensor is Lorentz covariant, indeed; however, its physical implication is breaking the principle of relativity.In post 117 I challenged you to justify this claim by showing that boosting the total momentum tensor into a different frame and showing that you get the wrong total momentum, which you did not do. Simply repeating a statement is not a justification.

[DaleSpam]

(2) In a system where the dielectric is infinite and fills all of space and time, the EM pulse does not enter the system from vacuum. In the absence of external constraints, we may set v arbitrarily, as sciencewatch has done, even where this results in a T^{\mu\nu} which violates special relativity.I am not convinced that even in the admittedly unphysical case of an infinite dielectric that special relativity is violated. It seems to me that you should be able to find a frame where the matter tensor corresponding to Abraham's light tensor is 0 (at least the spacelike components). If you boost that total momentum you should get the correct total momentum in any frame. The mere fact that the matter tensor is 0 in some frame doesn't seem to violate anything.

I haven't worked it out myself to verify, but neither did sciencewatch, so I am skeptical about the assertion.

[PhilDSP]

(2) In a system where the dielectric is infinite and fills all of space and time, the EM pulse does not enter the system from vacuum. In the absence of external constraints, we may set v arbitrarily, as sciencewatch has done, even where this results in a T^{\mu\nu} which violates special relativity.

However, such a system is "unphysical": Our universe is largely empty space, and is believed to be described by physical models where the density of all fields (including matter fields) drops to zero at spatial infinity. Trace its trajectory back to t=-∞, and no matter how large the dielectric, that photon originally entered from vacuum.

Although the situation is a little more complicated when you consider that the EM wave may have been emitted by decay of an excited electron state in e.g. air rather than vacuum, the emitting matter itself also has a history, and this too must be consistent with the boundary conditions of the universe. To properly treat this goes beyond the limitations of classical EM, but ultimately, the implication is that only situations in which total momentum forms a 4-vector are compatible with the assumption of zero fields (of all sorts; bosons & fermions) at x→∞.


Shouldn't the atom or molecule from which the EM wave was emitted be considered a micro-dielectric? Certainly \epsilon != \epsilon_0 and \mu != \mu_0 in the atom's near field.

[rpfeifer]

I am not convinced that even in the admittedly unphysical case of an infinite dielectric that special relativity is violated. It seems to me that you should be able to find a frame where the matter tensor corresponding to Abraham's light tensor is 0 (at least the spacelike components). If you boost that total momentum you should get the correct total momentum in any frame. The mere fact that the matter tensor is 0 in some frame doesn't seem to violate anything.

I haven't worked it out myself to verify, but neither did sciencewatch, so I am skeptical about the assertion.

You're right - I was wrong in considering the possibility of SR violation. The value of p has no effect on the transformation properties of p. I got dazzled by the unphysicality of the situation (which really isn't all that relevant to this part of the issue, after all).

Also, it should still be possible to model such a system consistent with the approach in RMP79. Earlier, I assumed (mistakenly) that without constraints from a spatial material boundary, the v field would be arbitrary. However, this is only true for the v you choose as initial conditions, on some initial slice of Minkowski space-time which is isochronous in the rest frame of the dielectric. That slice then acts as initial conditions for subsequent evolution, and even from a starting point with arbitrary v the evolution of the system is going to involve coupling between the EM wave and the dielectric. Two possibilities arise for v=0 on that initial slice:
(i) If the material is only instantaneously at rest, this is not incompatible with the Abraham material component. It just represents one extreme of the wave motion.
(ii) If the material is at rest and its acceleration is zero, this probably just represents an instantaneous superposition of an EM wave, its accompanying material excitation, and another material wave of some sort (pressure, phonons) that just happened to be passing through. Coupling to the EM wave will presumably still occur for any reasonable (i.e. physical) model of a dielectric.

So I'm going to change my position and say that I don't think this situation has the potential to violate SR or to cause problems for RMP79, either.

I think we'd need at least two separate Cauchy surfaces (sets of initial conditions on surfaces in Minkowski space that lie on the past or forward lightcone of everywhere) to create a contradiction with RMP79, and all this would disprove is the physical validity of the initial conditions, not of the model. I don't think it's possible to get conflict with SR at all, which is as it should be, since the mechanism used for time evolution (i.e. RMP79) respects SR.

(An example of such a non-physical set of initial conditions for n\not=1:
Surface 1: Wave present, v everywhere 0, at time t.
Surface 2: Wave present, v everywhere 0, at time t+dt where dt is infinitesimal, implying no coupling between wave and dielectric.)

[rpfeifer]

Shouldn't the atom or molecule from which the EM wave was emitted be considered a micro-dielectric? Certainly \epsilon != \epsilon_0 and \mu != \mu_0 in the atom's near field.

I'm not sure how safe the description of a dielectric in terms of \epsilon and \mu is in this regime. Given that the usual description of the origin of refractive index is in terms of multiple dipole scatterings retarding the propagation of the wavefront, I'd be very careful about using this model on the scale of a single atom.

That's not to say it doesn't work - just that based on the derivation I'm aware of, this situation is running right up against the limits of validity for this particular set of tools. I'd be much more comfortable here considering an ideal wave source rather than a source atom.

After writing this, I had some fun with the idea of an ideal wave source - e.g. put the atom (or a lot of hot atoms) in a box with a shutter, then open the shutter to let out the wave pulse. If you time it right, the wave can potentially completely avoid interacting with the box at all, but we can consider the opening in the box to be the source.

But then, if the wave doesn't interact with the box, we can remove the box entirely to guarantee no interaction... so really, a perfect source is just any bit of vacuum that a photon happens to be travelling through after leaving its matter source, and we can call anything a vacuum so long as the nearest atoms are far enough away...

No point to that bit of musing, really, other than as a reflection on the sorts of abstractions that go into these large-scale descriptions of physical systems.

[rpfeifer]

I haven't worked it out myself to verify, but neither did sciencewatch, so I am skeptical about the assertion.

I haven't formally set up the most general situation, evolved it, and boosted it, either, but I don't particularly feel the need to right now. Given the explicitly SR-invariant construction of the formalism, I believe the burden of proof is now on anyone who wishes to claim they have a situation which uses this formalism to violate SR.

[rpfeifer]

Very nice reading. And I think you've done a very good job explaining your points in words too RP. I will have to read up on those tensors.

Thanks yoron, it's nice to see my efforts (and those of other posters, such as DaleSpam) appreciated. That's why I stuck around in this thread - in case there was someone reading it who would find my explanations useful.

Best of luck with the tensors! They're not as fierce as they look. :smile:

[DaleSpam]

I haven't formally set up the most general situation, evolved it, and boosted it, either, but I don't particularly feel the need to right now. Given the explicitly SR-invariant construction of the formalism, I believe the burden of proof is now on anyone who wishes to claim they have a situation which uses this formalism to violate SR.I agree. Since the formalism is based on tensors and since tensor equations are manifestly covariant it seems impossible for the formalism to violate SR. That is, after all, the whole point of expressing physics in terms of tensors.

[PhilDSP]

I'm not sure how safe the description of a dielectric in terms of \epsilon and \mu is in this regime. Given that the usual description of the origin of refractive index is in terms of multiple dipole scatterings retarding the propagation of the wavefront, I'd be very careful about using this model on the scale of a single atom.

That's not to say it doesn't work - just that based on the derivation I'm aware of, this situation is running right up against the limits of validity for this particular set of tools. I'd be much more comfortable here considering an ideal wave source rather than a source atom.


Okay, thanks for your opinion. I imagine you were thinking of the derivation behind the Ewald-Oseen extinction theory. I agree with the need for care in deriving and using procedures more fundamental than that. I'm thinking that a rigorous derivation of a provisional more basic theory plus one or two or three dependent experimental facts would be enough to warrant some attention.

[yoron]

Well, Dale is also good to read. And uses clear approaches which makes it understandable for us laymen, on the whole this thread is one of the most interesting I've read so far. And there Science watch also have to get credit. After all, without his questions I wouldn't have gotten this far, learning how physics considered it mathematically.

[keji8341]

...any physical law expressed in a tensor form is mathematically guaranteed to be compatible with the principle of relativity.
...

You'd better carefully check your statement: What are your grouds? Mathematically or physically? Sufficiency or/and necessity?

I checked Sciencewatch's simple example copied below; it's true. You'd better check it to see what mistakes Sciencewatch made before refuting him (her).
--------------------
Sometimes a formulation, which follows Lorentz transformation, might breaks the special principle of relativity. A typical example is the formulation for Fizeau running water experiment. Why?

The Fizeau experiment is usually used to illustrate the relativistic velocity addition rule in the textbooks. Observed in a frame which is fixed with a uniform medium with a refractive index of n, the photon's speed is c/n, and the photon's 4-velocity is gp'*(up',c), with |up'|=c/n and gp'=1/sqrt(1-up'**2/c**2). Suppose the medium moves at v, relatively to the lab frame. Observed in the lab frame, the photon 3D-velocity, up, is obtained from the Lorentz transformation of gp'*(up',c). However, the obtained-photon-velocity up is not parallel to the 3D-wave vectror k in the lab frame, unless the medium moves parallel to the wave vector k.

According to the principle of relativity, the photon's velocity must be parallel to the wave vector in any inertial frames. Thus from above analysis, the photon's 3D-velocity in a medium can not be used to constitute a Lorentz covariant 4-velocity. In other words, the photon's 4-velocity in a medium, which follows Lorentz transformation, breaks the special principle of relativity instead.
---------------
Be sure to set the dielectric moving direction NOT parallel to the wave vector. In the dielectric-rest frame, the photon's 3D-velocity is parallel to the wave vector.

[DaleSpam]

Well, Dale is also good to read. And uses clear approaches which makes it understandable for us laymenThanks, I appreciate that. Sometimes encouragement is difficult to come by.

[longlive]

Suppose that an infinite uniform plane wave propagates in an infinite isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium with a refractive index >1. Speaking in macro-electromagnetic theory, the medium-rest frame is an inertial frame.

For such an ideal plane-wave model, the medium is assumed to be "rigid", and the total force acting on the whole medium is zero after taking average over time (in one light-wave period) and space (in one wavelength) for all possible micro-scale forces. In other words, there are no accelerations for the medium. Don’t ask me how to set up the plane wave and how to get such a medium; I don’t know. But I do know there is such a solution to Maxwell equations, and this physical model is widely presented in physics textbooks:

J. D. Jackson, Classical Electrodynamics, (John Wiley & Sons, NJ, 1999), 3rd Edition;
M. Born and E. Wolf, Principles of optics (5th edition) (Oxford, 1975);
J. A. Stratton, Electromagnetic theory, (McGraw-Hill, NY, 1941);
J. A. Kong, Theory of Electromagnetic Waves, (John Wiley & Sons, NY, 1975);
W. R. Smythe, Static and dynamic electricity, (McGraw-Hill, NY, 1968), 3rd edition;
D. J. Griffths, Introduction to Electrodynamics, (Prentice-Hall, NJ, 1999), 3rd edition;

to name a few.

************************
“OK, so what theory does this example negate and how?”

The author [Rev. Mod. Phys.79:1197-1216 (2007), http://arxiv.org/abs/0710.0461 ] claims that the total energy-momentum tensor is “uniquely determined by consistency with special relativity”. However, if applying their total-tensor model to the ideal plane wave described above, we obtain the total momentum = ExH/c**2 (=Abraham’s momentum density vector) from their Eqs. (40)-(43), or Eq. (33) by setting the dielectric velocity v = 0, and ExH/c**2 cannot be used to constitute a Lorentz covariant momentum-energy 4-vector. Therefore, the total-tensor model does break the special relativity, unless they have strong arguments to refute the above ideal plane-wave model.

------------------
To the authors [Rev. Mod. Phys.79:1197-1216 (2007)]: Please check the last term of Eq. (33), “+ ExM/c**2”, and make sure if there is a sign typo: – ?. Seems not consistent with Eq. (31) and Eqs. (40)-(43).

************************
PS:

In post #70, the author of Rev. Mod. Phys.79:1197-1216 (2007) (henceforth RMP79) claims:

In fact, the main thrust of Sec. VIII of RMP79 is that once the material properties of the dielectric are specified, the total momentum tensor is uniquely determined by

(i) consistency with special relativity, and
(ii) conservation of linear and angular momentum.

This leads to two important conclusions:

(a) No valid combination of EM and material energy-momentum tensors can break special relativity. If you are using a combination of tensors which appears to break this, then your choice of tensors is incorrect (usually, the material tensor is incorrect or missing). Note that I have never yet seen a fully relativistic formulation of the material counterpart tensors written down anywhere in the literature - even those given in RMP79 are valid only for media moving at v<<c, though the full expressions could be obtained from Eqs. (33)-(34).

(b) As the _total_ energy-momentum tensor is uniquely fixed by (i) and (ii) above, any division into components necessarily yields the same total tensor, and thus the same physical behaviours. That is, Abraham and Minkowski correspond to the same T, and thus the same physics.

Seems right.

Time-space coordinates and electromagnetic field-strength tensors obey Lorentz transformations, and the Maxwell equations keep the same forms in all inertial frames.

An ideal uniform plane wave is a simplest solution to Maxwell equations, and observed in any inertial frames, it is always a plane wave and satisfies Maxwell equations.

If an electromagnetic expression or equation (in which all field quantities must satisfy Maxwell equations) is derived from Maxwell equations without finite-boundary conditions used, then this electromagnetic expression or equation should be applicable to a plane wave, because all field quantities of the plane wave satisfy Maxwell equations. If not, the first thing I would like to do is to check my derivations, including basic assumptions or physical models.

When light propagates in a block of uniform dielectric medium with its dimension much larger the wavelength (Einstein's box), is the light momentum problem beyond the macro-electromagnetic theory? I don’t think so.

[DaleSpam]

You'd better check your statement: What are your grouds? The statement is correct. The principle of relativity is simply that the form of the laws of physics is preserved under boosts. A boost is a diffeomorphism. The form of any tensor equation is preserved under any diffeomorphism. Therefore, any physical law which is written in tensor form is preserved under boosts, and so it is compatible with the principle of relativity.

[keji8341]

The statement is correct. The principle of relativity is simply that the form of the laws of physics is preserved under boosts. A boost is a diffeomorphism. The form of any tensor equation is preserved under any diffeomorphism. Therefore, any physical law which is written in tensor form is preserved under boosts, and so it is compatible with the principle of relativity.

Sciencewatch said "the photon's 4-velocity in a medium, which follows Lorentz transformation, breaks the special principle of relativity instead". That is true or not in your opinion?

[DaleSpam]

Sciencewatch said "the photon's 4-velocity in a medium, which follows Lorentz transformation, breaks the special principle of relativity instead". That is true or not in your opinion?It is not true.

Merely noting that two 3 vectors are parallel in one frame and not in another does not break the principle of relativity. What is important is that the law of physics that gives the relationship between them is the same. When these laws are expressed in tensor form then they are guaranteed to be compatible with the principle of relativity.

What is the tensor law that gives the photons velocity in a medium?

[keji8341]

It is not true.

Merely noting that two 3 vectors are parallel in one frame and not in another does not break the principle of relativity. What is important is that the law of physics that gives the relationship between them is the same. When these laws are expressed in tensor form then they are guaranteed to be compatible with the principle of relativity.

What is the tensor law that gives the photons velocity in a medium?

1. “Merely noting that two 3 vectors are parallel in one frame and not in another does not break the principle of relativity.”

If I did not misunderstand your words, you agree that, observed in the lab frame, the 3D-photon velocity (space component of a photon’s 4-velocity) in a moving medium is NOT parallel to the 3D-wave vector (space component of a wave 4-vector), unless the medium moves parallel to the wave vector.
-----------------

2. “What is the tensor law that gives the photons velocity in a medium?”

If I did not misunderstand the tensor’s definition, the Lorentz covariant photon’s 4-velocity in a dielectric medium, which is widely presented in electrodynamics textbooks to explain Fizeau experiment, is a first-rank tensor.
------------------

3. If I did not misunderstand Sciencewatch’s words, she/he uses this example to show her/his own understanding of the principle of relativity: NOT every sub-physical law can be expressed directly in terms of a 4-vector or 4-tensor. Inversely speaking, even if a “sub-physical law” is expressed in a tensor form, it is NOT guaranteed to be compatible with the principle of relativity.

It is also my understanding: Any “sub-physical laws”, which are even expressed in a tensor form but not compatible with the principle of relativity, are also not allowed (or not comfortable in your elegant words) in the frame of special theory of relativity.

PS:
Master physical laws of relativistic electrodynamics: Time-space coordinates and electromagnetic field-strength tensors obey Lorentz transformations ---> the Maxwell equations keep the same forms in all inertial frames. (Copied from Longlive)

[DaleSpam]

If I did not misunderstand your words, you agree that, observed in the lab frame, the 3D-photon velocity (space component of a photon’s 4-velocity) in a moving medium is NOT parallel to the 3D-wave vector (space component of a wave 4-vector), unless the medium moves parallel to the wave vector.I did not work it out in detail myself. So I can't explicitly agree, but I have no reason to doubt it. I can think of other examples of 3 vectors that are parallel in one frame and not in another, so it is not a surprising or unreasonable claim.

If I did not misunderstand the tensor’s definition, the Lorentz covariant photon’s 4-velocity in a dielectric medium, which is widely presented in electrodynamics textbooks to explain Fizeau experiment, is a first-rank tensor.Yes, but that is not the question. The question is what is the physical law which determines that first-rank tensor?

In particular, the concern is the relationship between the wave vector, the material velocity, and the photon velocity in which the the wave vector and photon velocity are parallel in the material rest-frame and not parallel in other frames.

To determine if this relationship "breaks special relativity" it is necessary to write down the law of physics which determines that relationship and see if the law of physics is different in the different frames. If you write that law down in the form of a tensor equation then you are guaranteed that it will be the same in all frames.

3. If I did not misunderstand Sciencewatch’s words, she/he uses this example to show her/his own understanding of the principle of relativity: NOT every sub-physical law can be expressed directly in terms of a 4-vector or 4-tensor. Inversely speaking, even if a “sub-physical law” is expressed in a tensor form, it is NOT guaranteed to be compatible with the principle of relativity. I don't know what you mean by this. What is a "sub-physical law"? That is an unusual phrase.

Any “sub-physical laws”, which are even expressed in a tensor form but not compatible with the principle of relativity, are also not allowed in the frame of special theory of relativity.Again, I don't know what you mean by the phrase "sub-physical law", but any equation expressed in tensor form is guaranteed to be compatible with the principle of relativity. See post 149 for details.

[Vanadium 50]

This whole thread is nothing but a string of sockpuppets arguing with everyone else. Since one side of this argument is gone and not coming back, we might as well close this.