Relativistic implications of entropy and purity

TL;DR

This paper explores how quantum entropy and purity influence relativistic effects and geodesic motion, revealing a new geometric structure and implications for phenomena like Hawking radiation.

Contribution

It introduces a novel framework linking quantum entropy and purity to non-Riemannian geometry in relativistic contexts, expanding understanding of quantum-gravitational interactions.

Findings

Entropy and purity affect geodesic motion under gravity.

A non-Riemannian geometry is required when quantum correlations are present.

A new Minkowski structure emerges on entanglement subspaces.

Abstract

A quantum object is extended by virtue of quantum uncertainty. Subjected to gravity, it therefore experiences tidal forces and other relativistic effects. As a result, entropy and purity affect geodesic motion and acquire weight, an observation that has broad implications from free-fall experiments to Hawking radiation. If the object's position is quantum correlated in at least two directions, a complete description of its geodesic motion requires non-Riemannian geometry of a form controlled by the entropy and purity of its state. In addition, the analysis reveals a new Minkowski structure on a subspace of entanglement degrees of freedom.