Self-consistent theory for a plane wave in a moving medium and light-momentum criterion

Abstract

A self-consistent theory is developed based on the principle of relativity for a plane wave in a moving non-dispersive, lossless, non-conducting, isotropic uniform medium. Light-momentum criterion is set up for the first time, which states that the momentum of light in a medium is parallel to the wave vector in all inertial frames of reference. By rigorous analysis, novel basic properties of the plane wave are exposed: (1) Poynting vector does not necessarily represent the electromagnetic (EM) power flow when a medium moves, (2) Minkowski light momentum and energy constitute a Lorentz four-vector in a form of single EM-field cell or single photon, and Planck constant is a Lorentz invariant, (3) there is no momentum transfer taking place between the plane wave and the uniform medium, and the EM momentum conservation equation cannot be uniquely determined without resort to the principle of relativity, and (4) when the medium moves opposite to the wave vector at a faster-than-dielectric light speed, negative frequency and negative EM energy density occur, with the plane wave becoming left-handed. Finally, a new physics of so-called "intrinsic Lorentz violation" is presented as well.

Fantastic quasi-photon and the symmetries of Maxwell electromagnetic theory, momentum-energy conservation law, and Fermat's principle

“…In my theory, Minkowski photon momentum-energy four-vector is shown to be the unique correct four-momentum of light in a medium, given by K µ = (k w , ω/c), where Planck constant is a Lorentz invariant, K µ is the wave fourvector, 3 and k w is the wave vector. K µ indeed does not include "the transferred mass δm", but it is four-vector covariant [5], never leading to any mathematical problems; thus Partanen-coworkers criticism is not pertinent either. 1 In Ref.…”

“…2 In Ref. [5], I showed that Minkowski photon four-momentum is the direct result of Einstein light-quantized electromagnetic (EM) momentum and energy, namely K µ = N −1 p (g M , W em /c), which holds in all inertial frames, and where N p is the photon number density in volume, g M = D × B = N p ( k w ) is the Minkowski EM momentum density vector, and W em = 0.5(D · E + B · H) = N p ( ω) is the EM energy density. It is worthwhile to point out that K µ is constructed based on Einstein light-quantum hypothesis (single photon energy = ω) and the invariance of phase (resulting in the wave four-vector K µ , as shown in footnote 3), while N −1 p (g M , W em /c) is constructed based on Einstein light-quantum hypothesis [EM energy density W em = N p ( ω)] and the Lorentz covariance of field-strength four-tensors to keep Maxwell equations invariant in form in all inertial frames.…”

“…is the metric tensor, X µ = (x, ct) is the time-space four-vector, and K µ = (k w , ω/c) [5]. (It is should be noted that for the plane wave in such a case, the wave vector k w and the angular frequency ω are independent of t and x, and they are of real number.)…”

“…where n > 1 is assumed. In such a case, ω = 0 but n = ∞ [5], resulting in finite n ω = ω(n 2 − 1) 1/2 . Thus the Minkowski photon is stopped there (c/n = 0), with a zero energy (E = ω = 0) and a finite nonzero momentum of |p | = (n 2 − 1) 1/2 ω/c.…”

Is the Abraham electromagnetic force physical?

“…If a plane wave propagates in a lossless, non-dispersive, non-conducting, uniform anisotropic medium, the Abraham momentum conservation equation can be written as [11] …”