The Enigma of the muon and tau solved by Emergent Quantum Mechanics?

Abstract

This paper addresses the long-standing question of how it may be explained that the three charged leptons (the electron, muon and tau particle) have different masses, despite their conformity in other respects. In the field of Emergent Quantum Mechanics non-singular electron models are being revisited, and from this exploration has come a possible answer. In this paper a deformable droplet model is considered. It is shown how the model can be made self-consistent, whilst obeying the laws of momentum and energy conservation as well as Larmor's radiation law. The droplet appears to have three different static equilibrium configurations, each with a different mass. Tentatively, these three equilibrium masses were assumed to correspond with the measured masses of the charged leptons. The droplet model was tuned accordingly, and was thereby completely quantified. The dynamics of the droplet then showed a "De Broglie-like" relation p = K/λ. Beat patterns in the vibrations of the droplet play the role of the matter waves of usual quantum mechanics. The value of K, calculated by the droplet theory, practically equals Planck's constant: K ≅ h. This fact seems to confirm the correctness of identifying the three types of charged leptons with the equilibria of a droplet of charge.