Pair production in classical Stueckelberg-Horwitz-Piron electrodynamics

Abstract

In this paper we calculate pair production from bremsstrahlung as a classical effect in Stueckelberg-Horwitz-Piron electrodynamics. In this framework, worldlines are traced out dynamically through the evolution of events x µ (τ) parameterized by a chronological time τ that is independent of the spacetime coordinates. These events, defined in an unconstrained 8D phase space, interact through five τ-dependent gauge fields induced by the event evolution. The resulting theory differs in its underlying mechanics from conventional electromagnetism, but coincides with Maxwell theory in an equilibrium limit. In particular, the total massenergy-momentum of particles and fields is conserved, but the mass-shell constraint is lifted from individual interacting events, so that the standard Feynman-Stueckelberg interpretation of pair creation/annihilation is implemented in classical mechanics.We consider a three-stage interaction which when parameterized by the laboratory clock x 0 appears as (1) particle-1 scatters on a heavy nucleus to produce bremsstrahlung, (2) the radiation field produces a particle/antiparticle pair, (3) the antiparticle is annihilated with particle-2 in the presence of a second heavy nucleus. When parameterized in chronological time τ, the underlying process develops as (1) particle-2 scatters on the second nucleus and begins evolving backward in time with negative energy, (2) particle-1 scatters on the first nucleus and releases bremsstrahlung, (3) particle-2 absorbs radiation which returns it to forward time evolution with positive energy.

A 4+1 Formalism for the Evolving Stueckelberg-Horwitz-Piron Metric

“…It has been shown [16] that the total mass, energy, and momentum of particles and fields are conserved. These equations of motion, along with the τ-dependent field equations, have been used to calculate [17] the Bethe-Heitler mechanism for electron-positron production in classical electrodynamics. A positron (an electron withẋ 0 = cṫ < 0) propagates backward in coordinate time until entering the bremsstrahlung field produced by another electron scattering off a heavy nucleus.…”

“…These equations of motion, along with the τ-dependent field equations, have been used to calculate [17] At coordinate times prior to the particle's turn-around (when E = Mc 2 ṫ = 0) no particles will be observed, but two particles will be observed for subsequent coordinate times, implementing Stueckelberg's picture of pair creation.…”

Mass stability in classical Stueckelberg-Horwitz-Piron electrodynamics

“…In the continuous evolution of an event x µ (τ) from a future trajectoryẋ 0 ≥ c to the pastẋ 0 ≤ −c the event must pass through the spacelike region aroundẋ 0 = 0, whereẋ 2 changes sign. It was shown in [17] that under certain conditions SHP electrodynamics permits these classical pair processes, with no a priori guarantee that the outgoing particles will have identical mass. Small changes in particle mass are similarly relevant to neutrino oscillations [16] and low energy nuclear reactions [21].…”