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).
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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.
That is excellent! Thanks.