Gravity as Classical Effect in Generalized Relativistic Quantum Mechanics on Flat Background

TL;DR

This paper explores how classical gravity emerges from a generalized relativistic quantum mechanics framework with two times, linking effective metrics to correlations in a flat background.

Contribution

It introduces a novel approach connecting classical gravitational effects to correlations in a generalized relativistic quantum mechanics with two times.

Findings

World lines correspond to geodesics in weak gravity limit

Effective metrics arise from correlations between canonical variables

Classical gravity effects emerge from flat background quantum mechanics

Abstract

We study classical limit for quantum mechanics with two times and temperature, which describes a generalized dynamics of relativistic point mass. In this theory, thermodynamic time means a parameter of evolution, whereas geometric time is one of space-time coordinates. We identify world lines in this theory with geodesic lines for the same point mass in standard General Relativity in its weak gravity limit. In identification performed, effective metrics is generated by weak correlations between canonical variables of the originally flat relativistic mechanics, i.e. between its space-time coordinates and moments.