How the quantum emerges from gravity

TL;DR

This paper proposes a geometric theory of gravity on Riemann-Cartan spacetime with torsion, unifying Dirac and Einstein equations as limiting cases, suggesting a common underlying framework for microscopic and macroscopic physics.

Contribution

It introduces a Riemann-Cartan geometric framework that unifies Dirac and Einstein equations as different limits, incorporating torsion into gravity.

Findings

Dirac equation emerges as torsion-dominated, gravity-free limit

Proposes a unified geometric framework for gravity and quantum mechanics

Suggests a common underlying theory for microscopic and macroscopic physics

Abstract

The dynamics of a massive, relativistic spinning particle could be described either by the Dirac equation or by the Kerr solution of Einstein equations. However, one does not know a priori as to which of the two systems of equations should be used in a given situation, and the choice is dictated by experiments. It is expected that the Dirac equation holds for microscopic masses, and the Kerr solution for macroscopic masses. This suggests that Einstein gravity and the Dirac theory are limiting cases of a common underlying theoretical framework. Here we propose that such a framework is provided by a geometric theory of gravity on a Riemann-Cartan spacetime, which includes torsion. The Dirac equation emerges as the torsion dominated, gravity-free limit of this framework.