Wave-particle duality in general relativity

TL;DR

This paper establishes a direct correspondence between general relativity metrics and quantum wave equations, providing a new perspective on wave-particle duality and clarifying the relationship between quantum and classical mechanics.

Contribution

It introduces a novel method linking spacetime metrics to quantum wave equations, offering a natural explanation for wave-particle duality and the connection between quantum and relativistic mechanics.

Findings

Maxwell's equation for photons derived from the metric

Dirac's equation approximated from the metric for massive particles

Provides a clearer understanding of wave-particle duality and initial conditions

Abstract

In this paper a one to one correspondence is established between space-time metrics of general relativity and the wave equations of quantum mechanics. This is done by first taking the square root of the metric associated with a space and from there, passing directly to a corresponding expression in the dual space. It is shown that in the case of a massless particle, Maxwell's equation for a photon follows while in the case of a particle with mass, Dirac's equation results as a first approximation. Moreover, this one to one correspondence suggests a natural explanation of wave-particle duality. As a consequence, the distinction between quantum mechanics and classical relativistic mechanics is more clearly understood and the key role of initial conditions is emphasized. PACS NUMBERS: 03.65, 04.60