Quantum Physics

   

Two Relativistic Derivations of the Photon Energy-Frequency Relation and Their Pedagogical Significance

Authors: Zilu Liu

This paper presents two novel methods for deriving the photon energy formula. Both methods are strictly rooted in the framework of special relativity, without presupposing quantum theory. Method One rigorously established the proportional relationship between energy and frequency by analyzing the complementarity between the relativistic Doppler effect and the conservation of energy and momentum in Compton scattering, and subsequently determined Planck's constant h through experiments. Method Two derives the photon energy formula naturally by examining the limiting behavior of a massive particle as its velocity approaches the speed of light, incorporating the frequency ratio relationship. These derivations compensate for the deficiency in traditional pedagogy where this formula is introduced merely as a prescriptive conjecture fitting experimental results, providing a profound and unified perspective for understanding this fundamental formula and highlighting the role of relativity as its theoretical foundation, thus holding significant value for physics education.

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[v1] 2026-02-05 20:21:26

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