A discussion on a possibility to interpret quantum mechanics in terms of general relativity

TL;DR

This paper explores a theoretical framework where general relativity and quantum mechanics can be unified by modeling quantum particles with specific spacetime curvatures and transformations, suggesting a possible geometric interpretation of quantum phenomena.

Contribution

It proposes a method to reconcile general relativity with quantum mechanics by using spacetime metrics and curvature assumptions to derive quantum behavior from geometric principles.

Findings

Quantum particles can have positive or negative spacetime curvature.

Quantisation involves introducing the imaginary unit i, transforming spacetime structures.

Positive curvature relates to Riemannian spacetime, negative to pseudo-Riemannian spacetime.

Abstract

It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum particle so that the line element of the particle can be transformed entirely to that of the Minkowski spacetime, which is assumed by a quantum observer, and the spacetime dynamics of the particle described by a Minkowski observer takes the form of quantum mechanics. Spacetime structure of a quantum particle may have either positive or negative curvature. However, in order to be describable using the familiar framework of quantum mechanics, the spacetime structure of a quantum particle must be "quantised" by an introduction of the imaginary number $i$. If a particle has a positive curvature then the quantisation is equivalent to turning the pseudo-Riemannian spacetime of the particle into a Riemannian spacetime. This means that it is assumed the particle is capable of measuring its temporal distance like its spatial distances. On the other hand, when a particle has a negative curvature and a negative energy density then quantising the spacetime structure of the particle is equivalent to viewing the particle as if it had a positive curvature and a positive energy density.