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.
Highlights
The problem is well known: why do three types of charged leptons exist, and what determines the mass ratios between them? An anecdote about the famous physicist Rabi tells that, after the discovery of the muon by Anderson (1936), his reaction was “who ordered that?”
The relation between Em.quantum mechanics (QM) and QM is analogous to the relation between kinetic gas theory and thermodynamics, the latter is excellent for actual calculations, whilst the former reveals the connection with classical mechanics
It may be concluded that the relation between the momentum and the wavelength of the droplet model is quantitatively in good agreement with De Broglie’s relation in QM
Summary
The problem is well known: why do three types of charged leptons exist (the electron, the muon and the tau particle), and what determines the mass ratios between them? An anecdote about the famous physicist Rabi tells that, after the discovery of the muon by Anderson (1936), his reaction was “who ordered that?”. The model of electrons obtained may, despite the absence of a separate core, be considered to be a deformable version of the relativistically rigid charge distributions studied by Lorentz Thanks to this fact, the analysis of the model owes much to Lorentz and Yaghjian’s theories. Complementary to the time-averaging, an apparent force should be included to obtain a consistent simplification of the real situation All this leads to a droplet model, with a surface-tension-like containment force (not a real physical force but an apparent force belonging to the level of the time-averaged model only).
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