The guidance theorem of de Broglie

TL;DR

This paper reviews de Broglie's double solution theory, focusing on the guidance theorem, comparing it with pilot-wave interpretation, and discussing philosophical differences between the two approaches.

Contribution

It rederives and analyzes the guidance theorem within de Broglie's original double solution framework and contrasts it with the de Broglie-Bohm interpretation.

Findings

Guidance theorem is a central element of de Broglie's double solution theory.

De Broglie rejected pilot-wave interpretation in favor of the double solution approach.

Philosophical differences influence the strategies of de Broglie and Bohm.

Abstract

We review some aspects of the double solution theory proposed by de Broglie at the beginning of the quantum era (i.e., in the period 1924-28). We specifically analyze and rederive the so called guidance theorem which is a key element of the full theory. We compare the double solution approach to the most known pilot-wave interpretation, also known as de Broglie-Bohm or Bohmian mechanics. We explain why de Broglie rejected the pilot wave interpretation and advocated the double solution. We also discuss some philosophical issues related to difference of strategies between de Broglie on the one side and Bohm on the other side.