Abraham's light momentum breaks special relativity?

[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.