Radiation-reaction in classical off-shell electrodynamics. I. The above mass-shell case

Aharonovich, I.; Horwitz, L. P.

doi:10.1063/1.3694276

Cited by 14 publications

(10 citation statements)

References 25 publications

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“…Negative m 2 particles are considered as tachyons. The question of how the particle mass avoids unobserved off-shell behavior is an area of current research [43,50,2]. These plane wave states are eigenstates for them 2 =p µp µ operator.…”

Section: Covariant Bohmian Mechanicsmentioning

confidence: 99%

Bohmian Trajectories for Kerr–Newman Particles in Complex Space-Time

Davidson¹

2018

Found Phys

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Complexified Liénard-Wiechert potentials simplify the mathematics of Kerr-Newman particles. Here we constrain them by fiat to move along Bohmian trajectories to see if anything interesting occurs, as their equations of motion are not known. A covariant theory due to Stueckelberg is used. This paper deviates from the traditional Bohmian interpretation of quantum mechanics since the electromagnetic interactions of Kerr-Newman particles are dictated by general relativity. A Gaussian wave function is used to produce the Bohmian trajectories, which are found to be multi-valued. A generalized analytic continuation (GAN) is introduced which leads to an infinite number of trajectories. These include the entire set of Bohmian trajectories. This leads to multiple retarded times which come into play in complex space-time. If one weights these trajectories by their natural Bohmian weighting factors, then it is found that the particles do not radiate, that they are extended, and that they can have a finite electrostatic self energy, thus avoiding the usual divergence of the charged point particle. This effort does not in any way criticize or downplay the traditional Bohmian interpretation which does not assume the standard electromagnetic coupling to charged particles, but it suggests that a hybridization of Kerr-Newman particle theory with Bohmian mechanics might lead to interesting new physics, and maybe even the possibility of emergent quantum mechanics.Keywords Quantum Gravity · Kerr-Newman · Bohm · complex space-time · electron model · emergent quantum mechanics PACS 03.65.Ta · 03.65.Sq · 04.20.Jb · 41.60.-m IntroductionThis paper studies Kerr-Newman charged particles moving along free-particle Bohmian trajectories embedded in complex space-time. These are coupled directly to the electro-2 Mark Davidson magnetic fields in the standard way, and the resulting Liénard-Wiechert potentials are analyzed. This form of coupling is dictated by the theory of general relativity. In the Bohmian interpretation of quantum mechanics, no such coupling of Bohmian particles to classical electromagnetic fields is assumed. Therefore, in this paper, I am deviating from the Bohmian interpretation, but using the Bohmian trajectories nonetheless. The Bohmian interpretation is perfectly consistent, and I do not mean by this to detract from it in any way. Rather I'm trying to see if there is anything to be learned about Kerr-Newman particles in this way. It appears that there might be.Recently Maldacena and Susskind have proposed that quantum entanglement and the Einstein-Rosen bridge might be intimately related to one another [54,69]. They and others argue that gravity may be an emergent phenomenon, and that quantum entanglement is a crucial ingredient of this emergence [65,24,72]. Einstein thought that quantum theory might possibly be derivable from general relativity and electromagnetism. This is clear from some of the statements in the Einstein and Rosen paper [32], as well as many other writings of Einstein dealing with unified field theory ...

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Section: Covariant Bohmian Mechanicsmentioning

confidence: 99%

Bohmian Trajectories for Kerr–Newman Particles in Complex Space-Time

Davidson¹

2018

Found Phys

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“…The second term has spacelike support (x 2 > τ 2 ≥ 0) and vanishes under concatenation, so it may contribute to correlations but not to Maxwell potentials. Terms of this type have been studied in [7].…”

Section: Pre-maxwell Electrodynamicsmentioning

confidence: 99%

Field signature for apparently superluminal particle motion

Land

2015

J. Phys.: Conf. Ser.

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In the context of Stueckelberg's covariant symplectic mechanics, Horwitz and Aharonovich [1] have proposed a simple mechanism by which a particle traveling below light speed almost everywhere may exhibit a transit time that suggests superluminal motion. This mechanism, which requires precise measurement of the particle velocity, involves a subtle perturbation affecting the particle's recorded time coordinate caused by virtual pair processes. The Stueckelberg framework is particularly well suited to such problems, because it permits pair creation/annihilation at the classical level. In this paper, we study a trajectory of the type proposed by Horwitz and Aharonovich, and derive the Maxwell 4-vector potential associated with the motion. We show that the resulting fields carry a signature associated with the apparent superluminal motion, providing an independent test for the mechanism that does not require direct observation of the trajectory, except at the detector.

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Section: Stueckelberg Off-shell Electrodynamicsmentioning

confidence: 99%

Electrostatics in Stueckelberg-Horwitz electrodynamics

Land¹

2013

J. Phys.: Conf. Ser.

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In this paper, we study fundamental aspects of electrostatics as a special case in Stueckelberg-Horwitz electromagnetic theory. In this theory, spacetime events x µ (τ) evolve in an unconstrained 8-dimensional phase space, interacting through five τ-dependent gauge fields induced by the current densities associated with their evolutions. The chronological time τ was introduced as an independent evolution parameter in order to free the laboratory clock x 0 to evolve alternately 'forward' and 'backward' in time according to the sign of the energy, thus providing a classical implementation of the Feynman-Stueckelberg interpretation of pair creation/annihilation. The resulting theory differs in its underlying mechanics from conventional electromagnetism, but coincides with Maxwell theory in an equilibrium limit.After a brief review of Stueckelberg-Horwitz electrodynamics, we obtain the field produced by an event in uniform motion and verify that it satisfies the field equations. We study this field in the rest frame of the event, where it depends explicitly on coordinate time x 0 and the parameter τ, as well as spatial distance R. Calculating with this generalized Coulomb field, we demonstrate how Gauss's theorem and Stoke's theorem apply in 4D spacetime, and obtain the fields associated with a charged line and a charged sheet. Finally, we use the field of the charged sheet to study a static event in the vicinity of a potential barrier. In all of these cases, we observe a small transfer of mass from the field to the particle. It is seen that for an event in the field of an oppositely charged sheet of sufficient density, the event can reverse time direction, providing a specific model for pair phenomena.

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Radiation-reaction in classical off-shell electrodynamics. I. The above mass-shell case

Cited by 14 publications

References 25 publications

Bohmian Trajectories for Kerr–Newman Particles in Complex Space-Time

Bohmian Trajectories for Kerr–Newman Particles in Complex Space-Time

Field signature for apparently superluminal particle motion

Electrostatics in Stueckelberg-Horwitz electrodynamics

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