Consistency of the de Broglie Relations with Special Relativity

James Murray Hill

Tokio Takéuchi

Samuel Bueno Soltau

This paper provides an examination of the de Broglie relation, tracing its historical development from the quantum hypotheses proposed by Planck and Einstein to its covariant relativistic derivation. The discussion begins by situating de Broglie's seminal insight within the early framework of quantum theory. We then reconstruct his original heuristic derivation. The primary focus of this work, however, is the derivation of the de Broglie relation directly from the principles of special relativity, employing the four-momentum formalism. A comparative analysis between the heuristic and relativistic approaches underscores the universality and conceptual coherence of the latter. The paper concludes by highlighting the significance of relativistic mechanics in establishing a consistent foundation for wave-particle duality, further reinforcing this through a quantum field theoretical perspective.

Pieter Wagner

Janez Strnad, W Kuhn

On the occasion of the sixtieth anniversary of Louis de Broglie's thesis, the concept of phase waves, is re-examined. After a brief historical survey a modern conceptual presentation of these waves is described via phase invariance. In this respect de Broglie's hypothesis appears not to be self-consistent. Phase waves in galilean relativity are briefly discussed. As an interesting pedagogical device, inverse phase waves in two-dimensional special relativity are presented. Finally, some remarks are added concerning the development of concepts and theories.

B. Buonaura, F. Selleri