Abraham 光動量違反狹義相對論嗎？

背景：光在媒質中的動量是爭論了一百多年的尚未解決的問題，愛因斯坦本人也參與了這一爭論。目前主流科學家認為：光的Abraham動量和Minkowski動量都是正確的 Phys. Rev. Lett. 104, 070401 (2010)，都有實驗支持：Phys. Rev. Lett. 101, 243601 (2008)；Physical Review Letters. Vol.94, issue 17, 2005, pp.170403。然而，從下面的討論看出，Abraham動量在理論上是和狹義相對論矛盾的，主流科學家用巧妙的方法極力違避這個問題。

Abraham's light momentum breaks special relativity? http://www.physicsforums.com/showthread.php?t=541846

Sciencewatch: 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?

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DaleSpam: We have already established through the review article I posted (Rev.Mod.Phys.79:1197-1216 (2007); http://arxiv.org/abs/0710.0461 ) 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.

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

Sciencewatch: 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)

DaleSpam: 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.

Sciencewatch: 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. （評註：避免讀者想起 動量-能量4維矢量。）

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

DaleSpam: You are correct in the above. Abraham's momentum is not covariant. If you want a covariant momentum then use Minkowski.