Observer dependence of entanglement in "nonrelativistic" quantum mechanics

TL;DR

This paper demonstrates that observer dependence of spin entropy, previously shown in relativistic contexts, also appears in nonrelativistic quantum mechanics when energy is weighted by $E=mc^2$, highlighting its soft relativistic nature.

Contribution

It reveals that the observer dependence of spin entropy can be derived within nonrelativistic quantum mechanics by considering energy weighting, broadening the understanding of this phenomenon.

Findings

Observer dependence of spin entropy appears in nonrelativistic quantum mechanics.

Weighting energy as $E=mc^2$ is key to this effect.

The result is a specific case of a more general class of systems.

Abstract

It was recently shown that, in general, the von Neumann spin entropy of fermionic particles is not invariant under Lorentz boosts. We show that an analogous result can be recovered (at the lowest order of $v^2 /c^2$) using plain nonrelativistic quantum mechanics provided one uses that energy weighs: $E=m c^2$. This should (i) help to moderate the skepticism on the observer-dependence of the spin entropy of fermionic particles, (ii) emphasize the soft relativistic nature of this result, and (iii) show that this is a particular case of a more general class of systems, since our calculation only assumes a nonrelativistic particle endowed with an internal degree of freedom.