A New Approach to Quantum Gravity from a Model of an Elastic Solid

TL;DR

This paper proposes a novel model where the dynamics of an elastic solid in Minkowski space naturally give rise to Dirac, Maxwell, and Einstein equations, suggesting a new approach to quantum gravity through elasticity theory.

Contribution

It introduces a unified elastic model that derives fundamental physics equations, offering a new perspective on quantum gravity from classical elasticity.

Findings

Derivation of Dirac, Maxwell, and Einstein equations from elastic field displacements.

Quantization of elastic displacements leads to quantized fundamental fields.

Explicit solutions of Dirac fields in a 3D elastic model are obtained.

Abstract

We show that the dynamics of an elastic solid embedded in a Minkowski space consist of a set of coupled equations describing a spin-1/2 field, $\Psi$, obeying Dirac's equation, a vector potential, $A_\mu$, obeying Maxwell's equations and a metric, $g_{\mu\nu}$, which satisfies the Einstein field equations. The combined set of Dirac's, Maxwell's and the Einstein field equations all emerge from a simple elastic model in which the field variables $\Psi$, $A_\mu$ and $g_{\mu\nu}$ are each identified as derived quantities from the field displacements of ordinary elasticity theory. By quantizing the elastic field displacements, a quantization of all of the derived fields are obtained even though they do not explicitly appear in the Lagrangian. We demonstrate the approach in a three dimensional setting where explicit solutions of the Dirac field in terms of fractional derivatives are obtained. A higher dimensional version of the theory would provide an alternate approach to theories of quantum gravity.