Speeds of light and mass stability in Stueckelberg-Horwitz-Piron electrodynamics

It is well-known that the 5D gauge structure of Stueckelberg-Horwitz-Piron (SHP) electrodynamics permits the exchange of mass between particles and the fields induced by their motion, even at the classical level. This phenomenon presents two closely related problems: (1) What accounts for the stability of the measured masses of the known particles? (2) Under what circumstances can real particles evolve sufficiently off-shell to account for mass changing phenomena such as flavor-changing neutrino interactions and low energy nuclear reactions? To approach these questions, we introduce a constant $c_5$ associated with the invariant time $\tau$, in analogy with the constant $c$ that associates a unit of length with intervals of time $t$ in standard relativity. It follows that electromagnetic mass exchange can be a small effect, in proportion to $c_5 / c$. We show that this structure permits a classical self-interaction that tends to restore on-shell propagation. Finally we propose a model in which a particle evolving through a complex charged environment can acquire a significant mass shift for a short time.