The Classical Electron Problem
TL;DR: In this paper, the authors construct a parallel image of the conventional Maxwell theory by replacing the observer-time by the proper-time of the source, and show that the origin of radiation reaction is not the action of a charge on itself but arises from inertial resistance to changes in motion.
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Abstract: In this paper, we construct a parallel image of the conventional Maxwell theory by replacing the observer-time by the proper-time of the source. This formulation is mathematically, but not physically, equivalent to the conventional form. The change induces a new symmetry group which is distinct from, but closely related to the Lorentz group, and fixes the clock of the source for all observers. The new wave equation contains an additional term (dissipative), which arises instantaneously with acceleration. This shows that the origin of radiation reaction is not the action of a “charge” on itself but arises from inertial resistance to changes in motion. This dissipative term is equivalent to an effective mass so that classical radiation has both a massless and a massive part. Hence, at the local level the theory is one of particles and fields but there is no self-energy divergence (nor any of the other problems). We also show that, for any closed system of particles, there is a global inertial frame and unique (invariant) global proper-time (for each observer) from which to observe the system. This global clock is intrinsically related to the proper clocks of the individual particles and provides a unique definition of simultaneity for all events associated with the system. We suggest that this clock is the historical clock of Horwitz, Piron, and Fanchi. At this level, the theory is of the action-at-a-distance type and the absorption hypothesis of Wheeler and Feynman follows from global conservation of energy.
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Citations
Two Mathematically Equivalent Versions of Maxwell's Equations
TL;DR: A review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics can be found in this article, where it is shown that there are two versions of Maxwell's equations, one of which fixes the clock of the field source for all inertial observers.
26
Analytic representation of the square-root operator
TL;DR: In this paper, the authors used fractional powers of linear operators to construct a general representation theory for the square-root energy operator of relativistic quantum theory, which is valid for all values of the spin.
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The Analysis of Lagrangian and Hamiltonian Properties of the Classical Relativistic Electrodynamics Models and Their Quantization
TL;DR: In this paper, the Lagrangian and Hamiltonian properties of classical electrodynamics models and their associated Dirac quantizations are studied and a concise expression for the Lorentz force is derived by suitably taking into account the duality of electromagnetic field and charged particle interactions.
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Torsion Fields, Cartan-Weyl Space-Time and State-Space Quantum Geometries, their Brownian Motions, and the Time Variables
TL;DR: In this paper, the relation between spacetime geometries with trace-torsion fields, the so-called Riemann-Cartan-Weyl (RCW) geometry, and their associated Brownian motions is discussed.
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Iso-, Geno-, Hyper-Mechanics for Matter, Their Isoduals, for Antimatter, and Their Novel Applications in Physics, Chemistry and Biology
TL;DR: In this paper, the authors outline the research conducted by various mathematicians, physicists and chemists over the past two decades who have shown that the inverse approach, the construction of new numbers, related new mathematics and consequential new physical theories from open physical, chemical and biological problems, leads to new intriguing formulations of increasing complexity called iso-, geno-and hypermathematics for the treatment of matter in reversible, irreversible and multi-valued conditions, respectively, plus anti-isomorphic images called isodual mathematics for antimatter.
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