P=h/λ? W= hv? A Riddle Prior to any Attempt at Grand Unification

Abstract

It is shown that: (a) De Broglie’s quantum relation W = mc 2 = hv does not have the same relativistic variance as Einstein’s quantum relation W = hv assumed for light, (b) If “matter waves” possess physical reality and permit a local representation of microphenomena then, instead of p = h/λ, another relation has to be admitted, which numerically differs significantly from p = h/λ only for nearly null values of the relative velocity of observation u, but the difference becoming infinite for u = 0. Then quantum mechanics has to be reorganized. However, the splitting of the quantum relation subsists if the Einstein variance of macroscopic mass and mechanical energy holds rigorously also at the microscopic level of description, (c) If furthermore the same variance is valid for a quantum of light energy and a quantum of heavy energy, then the definition of a micro-mass must involve a factor that depends on the phase velocity of the corresponding corpuscular wave; notwithstanding the tiny numerical difference with Einstein’s definition introduced by this factor, this modified definition of micromass, if true, requires reconstruction of also the relativistic representation, at the basic microscopic level of description. In either case—(b) alone, or (b) and (c)— a real and local nature assigned to the corpuscular field would entail a deeply unified representation of fields and heavy matter, at the microscopic, macroscopic, or cosmic level of description.