Can the Abraham Light Momentum and Energy in a Medium Constitute a Lorentz Four-Vector?

Changbiao Wang^{*}

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References

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[18] According to the principle of relativity, all inertial frames are equivalent for descriptions of physical laws, and Maxwell equations have the same form in all inertial frames. Accordingly, the Abraham EM momentum density vector and energy density must have the same definitions in all inertial frames (although observed in the medium-rest frame the medium is stationary and the refractive index is isotropic while observed in the lab frame the medium is moving and the index is anisotropic). Consequently, the Abraham photon momentum and energy, given by Equation (A-3), must have the same form in all inertial frames. In addition, keep in mind (the basic mathematical result of Lorentz transformation) that the scalar product of any two of four-vectors is a Lorentz invariant. Thus if Equation (A-3) were a four-vector, then would be a Lorentz invariant because the Planck constant h must be a Lorentz invariant. But is a wave four-vector, and must be a Lorentz invariant. From this it follows that both and are Lorentz invariants; thus leading to an incorrect mathematical (physical) result: both the photon’s frequency and the medium refractive index are Lorentz invariants.

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