Mass stability in classical Stueckelberg-Horwitz-Piron electrodynamics

Land, Martin

doi:10.1088/1742-6596/845/1/012025

Cited by 3 publications

(5 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where T µν Φ is the energy-momentum tensor, and the terms T 5α Φ represent mass density in the field and the flow of mass into spacetime. Inserting the current ( 22) into (33) and using the second Lorentz force equation (19), we find…”

Section: Classical Off-shell Electrodynamicsmentioning

confidence: 99%

“…A simple model of mass variation is a uniformly moving particle undergoing a stochastic perturbation x = uτ → uτ + X(τ) when entering a dense distribution of charged particles [19]. If the typical short distance between charge centers is d then the particle will encounter charges periodically, with a short characteristic period d/ |u|, leading to a high characteristic frequency ω 0 = 2π |u| /d.…”

Section: Mass Interactions and Mass Stabilitymentioning

confidence: 99%

See 1 more Smart Citation

Mass as a dynamical quantity

Land¹

2022

Preprint

View full text Add to dashboard Cite

The Standard Model (SM) ascribes the observed mass of elementary particles to an effective interaction between basis states defined without mass terms and a scalar potential associated with the Higgs boson. In the relativistic field theory that underlies the SM, mass itself, understood as the Lorentz-invariant squared 4-momentum of a particle or field, is fixed a priori, imposing a constraint on possible momentum states. Stueckelberg introduced an alternative approach, positing antiparticles as particles evolving backward in time, thus relaxing the mass shell constraint for individual particles. Further work by Piron and Horwitz established a covariant Hamiltonian mechanics on an unconstrained 8D phase space, leading to a gauge field theory that mediates the exchange of mass between particles, while the total mass of particles and fields remains conserved. In a recently developed extension of general relativity, consistent with this approach, the spacetime metric evolves in a manner that permits the exchange of mass across spacetime through the gravitational field. Mechanisms that restrict mass exchange between particles have also been identified. Nevertheless, mass exchange remains possible under certain circumstances and may have phenomenological implications in particle physics and cosmology.

show abstract

Section: Classical Off-shell Electrodynamicsmentioning

confidence: 99%

Section: Mass Interactions and Mass Stabilitymentioning

confidence: 99%

Mass as a dynamical quantity

Land¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…While mass exchange must be present in any classical theory of pair processes and must also be small to account for standard electromagnetic phenomenology, such a compromise cannot explain the fixed masses of elementary particles. However, it has been shown that under certain circumstances [23] a self-interaction induced through G Correlation has the effect of restoring on-shell evolution in event trajectories and thus returning the particle worldline to the observed fixed mass. As seen in (45) when g 55 = 1, the Green's function has time-like support, permitting the event to interact with the field produced earlier along its worldline.…”

Section: Non-local Field Kinetics ↔ Ensemble Of Eventsmentioning

confidence: 99%

The Particle as a Statistical Ensemble of Events in Stueckelberg–Horwitz–Piron Electrodynamics

Land

2017

Entropy

Self Cite

View full text Add to dashboard Cite

Abstract:In classical Maxwell electrodynamics, charged particles following deterministic trajectories are described by currents that induce fields, mediating interactions with other particles. Statistical methods are used when needed to treat complex particle and/or field configurations. In Stueckelberg-Horwitz-Piron (SHP) electrodynamics, the classical trajectories are traced out dynamically, through the evolution of a 4D spacetime event x µ (τ) as τ grows monotonically. Stueckelberg proposed to formalize the distinction between coordinate time x 0 = ct (measured by laboratory clocks) and chronology τ (the temporal ordering of event occurrence) in order to describe antiparticles and resolve problems of irreversibility such as grandfather paradoxes. Consequently, in SHP theory, the elementary object is not a particle (a 4D curve in spacetime) but rather an event (a single point along the dynamically evolving curve). Following standard deterministic methods in classical relativistic field theory, one is led to Maxwell-like field equations that are τ-dependent and sourced by a current that represents a statistical ensemble of instantaneous events distributed along the trajectory. The width λ of this distribution defines a correlation time for the interactions and a mass spectrum for the photons emitted by particles. As λ becomes very large, the photon mass goes to zero and the field equations become τ-independent Maxwell's equations. Maxwell theory thus emerges as an equilibrium limit of SHP, in which λ is larger than any other relevant time scale. Thus, statistical mechanics is a fundamental ingredient in SHP electrodynamics, and its insights are required to give meaning to the concept of a particle.

show abstract

“…However, one is immediately confronted by conceptual difficulties in attempting to describe even the simple case of low energy Coulomb scattering. First, although the current j α (x, τ) and the potential a α (x, τ) are individually constructed to be vector + scalar representations of O(3,1) on physical grounds, the 5D scalar structure of the electromagnetic action (22) places all five components on the same algebraic footing. This suggests an underlying formal symmetry larger than O(3,1) but containing it as a subgroup: O(4,1) for the choice g 55 = 1 or O(3,2) symmetry for g 55 = −1.…”

Section: Classical Shp Electrodynamicsmentioning

confidence: 99%

“…But while mass exchange must be present in any classical theory of pair processes and must also be small to account for standard electromagnetic phenomenology, such a compromise cannot explain the fixed masses of elementary particles. However, it has been shown that under certain circumstances [22] a self-interaction induced through G Correlation has the effect of restoring on-shell evolution in event trajectories and thus returning the particle worldline to the observed fixed mass. As seen in (44) when g 55 = 1 the Green's function has timelike support, permitting the event to interact with the field produced earlier along its worldline.…”

Section: Non-local Field Kinetics ↔ Ensemble Of Eventsmentioning

confidence: 99%

The Particle as a Statistical Ensemble of Events in Stueckelberg-Horwitz-Piron Electrodynamics <sup>&dagger;</sup>

Land

2017

Preprint

Self Cite

View full text Add to dashboard Cite

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. Classical spacetime events xμ (τ) evolve as τ grows monotonically, tracing out particle worldlines dynamically and inducing the five U(1) gauge potentials through which events interact. Since Lorentz invariance imposes time reversal symmetry on x0 but not τ, the formalism resolves grandfather paradoxes and related problems of irreversibility. The action involves standard first order field derivatives but includes a higher order τ derivative that while preserving gauge and Lorentz invariance removes certain singularities and makes the related QFT super-renormalizable. The resulting field equations are Maxwell-like but τ-dependent and sourced by a current that represents a statistical ensemble of instantaneous events distributed along the worldline. The width λ of this distribution defines a correlation time for the interactions and a mass spectrum for the photons that carry the interaction. As λ becomes very large, the photon mass goes to zero and the field equations become τ-independent Maxwell’s equations. Maxwell theory thus emerges as an equilibrium limit of SHP, in which λ is larger than any other relevant time scale. Particles and fields are not constrained to mass shells in SHP theory, and by exchanging mass may produce pair creation/annihilation processes at the classical level. On-shell evolution with fixed particle masses is restored through a self-interaction associated with the 5D wave equation.

show abstract

Mass stability in classical Stueckelberg-Horwitz-Piron electrodynamics

Cited by 3 publications

References 15 publications

Mass as a dynamical quantity

Mass as a dynamical quantity

The Particle as a Statistical Ensemble of Events in Stueckelberg–Horwitz–Piron Electrodynamics

The Particle as a Statistical Ensemble of Events in Stueckelberg-Horwitz-Piron Electrodynamics <sup>&dagger;</sup>

Contact Info

Product

Resources

About