Relativity Implies Quantization: A Pedagogical Derivation of the Energy-Frequency Relation from the Massless Limit

The relation E = hν is traditionally introduced in introductory physics as an ad hoc hypothesis by Planck or Einstein to explain blackbody radiation or the photoelectric effect. This pedagogical approach often leaves students with the impression that quantum mechanics is disjoint from classical relativity. In this paper, we present a purely relativistic derivation of the proportionality between energy and frequency. By analyzing the transformation properties of a massive particle’s energy in the limit m → 0 and comparing them with the relativistic Doppler effect, we demonstrate that E ∝ ν is the unique solution required to satisfy Lorentz invariance. This derivation uses elementary algebraic expansions suitable for undergraduates and highlights the deep structural connection between spacetime symmetries and quantum dispersion relations.