On the Origin of the De Broglie Relations and the Wave-Corpuscle Parallelism

Wim Vegt

R. L. Collins

Bruce R. Wheaton

Philippe Orta

This article proposes a conceptual analysis of the reasoning developed by Louis de Broglie in his 1924 thesis Recherches sur la théorie des quanta, particularly the pages devoted to the derivation of the phase wave. By distinguishing the proper frequency associated with the particle at rest, the frequency observed from the stationary frame, and the frequency derived from the relativistic energy of the corpuscle, we show that these different frequencies do not appear to possess the same physical status in de Broglie’s original reasoning. We therefore examine the hypothesis according to which the introduction of the phase wave primarily responds to the necessity of maintaining relativistic coherence between two distinct interpretations of frequency. This study does not challenge the physical validity of the de Broglie relation linking momentum and wavelength, but rather proposes a critical re-examination of the conceptual status of the frequencies involved in the original 1924 construction. Finally, we discuss the possibility of future geometrical or topological reformulations of this relation without explicit recourse to a superluminal hase wave.

Patrick Marquet

Per‐Olov Löwdin

This pedagogical monograph describes some of the fundamental laws of physics. The derivations are, however, obtained from a rather unconventional point of view. The Lorentz transformations and the special theory of relativity are derived without mentioning the phenomenon of light, and the de Broglie relations in the wave-corpuscle parallelism are derived without the help of Planck's constant. By the use of Schrödinger's idea of "quantization as an eigenvalue problem", the foundations of wave mechanics are discussed as a mathematical problem without reference to Planck's constant. Finally, the