Classical and quantum gravity from relativistic quantum mechanics

TL;DR

This paper shows that multi-particle quantum systems described by Poincaré group representations can exhibit correlations that resemble gravitational interactions, deriving a gravitational constant consistent with empirical values.

Contribution

It introduces a novel connection between relativistic quantum mechanics and gravity, deriving gravitational interactions from Poincaré group representations.

Findings

Correlations in multi-particle systems mimic gravitational interactions.

Derived gravitational constant matches empirical value.

Links quantum mechanics with conformal gravity field equations.

Abstract

It is common practice to describe elementary particles by irreducible unitary representations of the Poincar\'e group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincar\'e group. Representations of the Poincar\'e group are characterised by fixed eigenvalues of two Casimir operators corresponding to a fixed mass and a fixed angular momentum. In multi-particle systems (of massive spinless particles), fixing these eigenvalues leads to correlations between the particles. In the quasi-classical approximation of large quantum numbers, these correlations take on the structure of a gravitational interaction described by the field equations of conformal gravity. A theoretical value of the corresponding gravitational constant is calculated. It agrees with the empirical value used in the field equations of general relativity.