Speeds of light in Stueckelberg-Horwitz-Piron electrodynamics

Abstract

Stueckelberg-Horwitz-Piron (SHP) electrodynamics formalizes the distinction between coordinate time (measured by laboratory clocks) and chronology (temporal ordering) by defining 4D spacetime events xμ as functions of an external evolution parameter τ. As τ grows monotonically, the spacetime evolution of classical events xμ (τ) trace out particle worldlines dynamically and induce the five U(1) gauge potentials through which events interact.In analogy with the constant c that associates a unit of length x0 with intervals of time t in standard relativity, we introduce a constant c5 associated with the external time τ. Whereas the nonrelativistic limit of special relativity can be found by taking c → ∞, we show that 5D SHP goes over to an equilibrium state of Maxwell theory in the limit c5 → 0. Thus, the dimensionless ratio c5/c parameterizes the deviation of SHP from standard electrodynamics, in particular the coupling of events. Put another way, Maxwell theory can be understood as currents and fields relaxing to an equilibrium independent of chronological time as c5τ slows to zero. We find that taking 0 < c5/c < 1 enables the resolution of several longstanding difficulties in SHP theory.