A Geometric Approach to the Quantum Mechanics of de Broglie and Vigier

TL;DR

This paper presents a relativistic causal interpretation of quantum mechanics based on a geometric theory of gravitation and electromagnetism, deriving particle and wave components from Einstein's equations.

Contribution

It introduces a geometric model that extends de Broglie and Vigier's causal interpretation by deriving quantum features from Einstein's equations instead of wave equations.

Findings

Provides a solution to the de Broglie variable mass problem

Develops a geometric framework for quantum mechanics

Aligns causal interpretation with relativistic gravitation theories

Abstract

Following de Broglie and Vigier, a fully relativistic causal interpretation of quantum mechanics is given within the context of a geometric theory of gravitation and electromagnetism. While the geometric model shares the essential principles of the causal interpretation initiated by de Broglie and advanced by Vigier, the particle and wave components of the theory are derived from the Einstein equations rather than a nonlinear wave equation. This geometric approach leads to several new features, including a solution to the de Broglie variable mass problem.