Decoherence-Free Entropic Gravity for Dirac Fermion

TL;DR

This paper extends entropic gravity models to Dirac fermions, showing that quantum coherence is maintained in strong coupling regimes and that spin remains unaffected, supporting the emergent gravity hypothesis.

Contribution

It introduces a relativistic model for entropic gravity with Dirac fermions, demonstrating coherence preservation and analyzing antiparticle behavior in free fall.

Findings

Quantum coherence is maintained for Dirac fermions in strong coupling.

Spin is unaffected by entropic gravity effects.

Antigravity phenomena are explained as zitterbewegung effects, not violations of equivalence.

Abstract

The theory of entropic gravity conjectures that gravity emerges thermodynamically rather than being a fundamental force. One of the main criticisms of entropic gravity is that it would lead to quantum massive particles losing coherence in free fall, which is not observed experimentally. This criticism was refuted in [Phys. Rev. Res. 3, 033065 (2021)], where a nonrelativistic master equation modeling gravity as an open quantum system interaction demonstrated that in the strong coupling limit, coherence could be maintained and reproduce conventional free-fall dynamics. Moreover, the nonrelativistic master equation was shown to be fully compatible with the qBounce experiment for ultracold neutrons. Motivated by this, we extend these results to gravitationally accelerating Dirac fermions. We achieve this by using the Dirac equation in Rindler space and modeling entropic gravity as a thermal bath thus adopting the open quantum systems approach as well. We demonstrate that in the strong coupling limit, our entropic gravity model maintains quantum coherence for Dirac fermions. In addition, we demonstrate that spin is not affected by entropic gravity. We use the Foldy-Wouthysen transformation to demonstrate that it reduces to the nonrelativistic master equation, supporting the entropic gravity hypothesis for Dirac fermions. Also, we demonstrate how antigravity seemingly arises from the Dirac equation for free-falling antiparticles but use numerical simulations to show that this phenomenon originates from zitterbewegung thus not violating the equivalence principle.