Abraham's light momentum breaks special relativity?

[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.

 

[Dale]

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).
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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.
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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.

 

[Dale]

Well, Dale is also good to read. And uses clear approaches which makes it understandable for us laymen

Thanks, 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.

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“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.

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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.

 

[Dale]

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?

 

[Dale]

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.
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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.
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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)

 

[Dale]

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.