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?

 

[Dale]

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.

 

[Dale]

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?

 

[Dale]

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.

 

[Dale]

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 .

 

[Dale]

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 dilation 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 dilation 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...

 

[Dale]

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.

 

[Dale]

In principle, one can construct infinite kinds of such tensors, resulting in infinite momentum-conservation equations

Exactly. The choice between them being arbitrary.

 

[yoron]

It's interesting.

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.

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?

 

[Dale]

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.

 

[Dale]

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).

 

[Dale]

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.

http://strathprints.strath.ac.uk/27285/1/AbMinkPhil.pdf

 

[Dale]

we have also removed the need for
further rival forms

I 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?

 

[Dale]

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.

 

[Dale]

I cannot find that they have a statement such as Abrahams momentum is no contraindication to SR

Do 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.