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

TL;DR

This paper demonstrates that Minkowski's light momentum and energy form a Lorentz four-vector in media, unlike Abraham's, which breaks conservation laws, and clarifies the correct light momentum using Maxwell equations and boundary conditions.

Contribution

It proves Minkowski's momentum always forms a Lorentz four-vector and introduces a boundary-condition approach to validate light momentum definitions independently of relativity.

Findings

Minkowski's momentum and energy form a Lorentz four-vector in media.

Abraham's momentum cannot form a Lorentz four-vector and violates conservation laws.

The boundary-condition matching approach confirms Minkowski's momentum as correct.

Abstract

By analyzing the Einstein-box thought experiment with the principle of relativity, it is shown that Abraham's light momentum and energy in a medium cannot constitute a Lorentz four-vector, and they consequentially break global momentum and energy conservation laws. In contrast, Minkowski's momentum and energy always constitute a Lorentz four-vector no matter whether in a medium or in vacuum, and the Minkowski's momentum is the unique correct light momentum. A momentum-associated photon mass in a medium is exposed, which explains why only the Abraham's momentum is derived in the traditional "center-of-mass-energy" approach. The EM boundary-condition matching approach, combined with Einstein light-quantum hypothesis, is proposed to analyze this thought experiment, and it is found for the first time that only from Maxwell equations without resort to the relativity, the correctness of light momentum definitions cannot be identified. Optical pulling effect is studied as well.