Gauge invariance and the quantization of mass (of gravitational charge)

Abstract

In a previous paper (referred to as I in the text) it was shown that the Weyl principle of gauge invariance leads to the relationship Gm2 =h{combining short stroke overlay}c for a particle of inertial mass m obeying the Dirac equation, where G is the Newtonian gravitational constant. Instead of interpreting this equation to mean that G takes on the extremely large value h{combining short stroke overlay}c/m2 inside a particle like an electron (as we did in I), we now write it in the form Gm2/c = h{combining short stroke overlay} and treat it as a quantization condition on the square of the gravitational charge √Gm. We show that this same quantization condition can be obtained from an angular-momentum component in the general-relativistic two-body problem as well as from the Machian definition of inertial mass in a rotating universe by using the Dirac-Schwinger procedure for quantizing charge. From this quantization condition we now deduce that the fundamental particle in Nature (the uniton) has an inertial mass equal to about 10-5 g. The possibility of using the uniton to shed light on the mystery of the « missing mass » in the Universe is discussed. Other cosmological implications of the uniton are also discussed and it is suggested that unitons can clear up the solar-neutrino discrepancy. © 1972 Società Italiana di Fisica.