The Mass-Frequency Equivalence Principle: Deriving de Broglie's Matter Waves from Fundamental Constants

For a century, de Broglie's relation  \lambda = h/p  has stood as a foundational yet inexplicable postulate of quantum mechanics, describing the wave nature of matter without a physical mechanism. This paper derives the de Broglie wavelength from a more fundamental principle: the mass-frequency equivalence relation  dm/df = h\mu_0\varepsilon_0 . We demonstrate that this relation, derived from the unification of Planck's quantum law ( E = hf ) and Einstein's mass-energy equivalence ( E = mc^2 ), naturally decomposes into linear and vibrational components. This decomposition provides a physical picture of the electron as a helical spacetime path, where the interference between its Compton-frequency oscillation and its linear motion naturally generates the de Broglie wave. Thus, de Broglie's postulate is shown not to be fundamental, but a necessary consequence of the deeper unification of quantum mechanics, special relativity, and electromagnetism.