HOW MANY FUNDAMENTAL CONSTANTS DOES QUANTUM PHYSICS NEED?

Abstract

Of the four familiar constants c, [Formula: see text], [Formula: see text] and ℏ (expressed in SI or other "ordinary" units) used in quantum mechanics and quantum electrodynamics, only three are independent because [Formula: see text], [Formula: see text] and ℏ occur in quantum equations and their predictions only as the ratios [Formula: see text] and [Formula: see text]. If one defines the inertial mass of any particle absolutely and operationally as its rest frame de Broglie frequency, the constant quantity [Formula: see text], where [Formula: see text] is its measured de Broglie wavelength when it has speed v and Lorentz factor γ, then electric charge becomes dimensionless and ℏ disappears from all quantum expressions; classical and quantum equations can then be written in terms of only three fundamental constants — c, the frequency me and the dimensionless e — and involve only two base units, those of length and time. This suggests that quantization rules, whose "scale" is given by ℏ, can also be eliminated from the theoretical framework and that it is therefore possible to construct a single unified theory of classical and quantum phenomena.