Duality of masses and lifetimes in quantum systems

Abstract

In an earlier work it was shown that the masses (appropriately defined) and the lifetimes of radionuclides, and all the fundamental particles, could be obtained from a single integral parameter. In this paper it is shown that the theory based on Cantor's theory of cardinality is closely related to fractal dimension and is not only numerically consistent with the Fermi theory of β decay and the Gamow theory of a decay but also has wider applicability. The theory suggests a new way of looking at quantum mechanics based on discreteness and continuity. The work of Mitra et al. is used to show that the predictions of QCD on fundamental particles are consistent with the above theory with regard to discreteness.