The Covariant Relativistic Derivation of De Broglie Relation

TL;DR

This paper offers a covariant relativistic derivation of the de Broglie relation, emphasizing its foundational role in wave-particle duality through special relativity and quantum field theory perspectives.

Contribution

It presents a novel derivation of the de Broglie relation directly from special relativity, connecting quantum hypotheses with relativistic principles.

Findings

Relativistic derivation of de Broglie relation established

Highlights the universality of wave-particle duality

Connects quantum field theory with foundational quantum relations

Abstract

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.