Quantum Theory of Individual Electron and Photon Interactions: Electromagnetic Time Dilation, the Hyper-Canonical Dirac Equation, and Magnetic Moment Anomalies Without Renormalization (original) (raw)
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viXra, 2017
Dirac’s seminal 1928 paper “The Quantum Theory of the Electron” is the foundation of how we presently understand the behavior of fermions in electromagnetic fields, including their magnetic moments. In sum, it is, as titled, a quantum theory of individual electrons, but in classical electromagnetic fields comprising innumerable photons. Based on the electrodynamic time dilations which the author has previously presented and which arise by geometrizing the Lorentz Force motion, there arises an even-richer “hyper-canonical” variant of the Dirac equation which reduces to the ordinary Dirac equation in the linear limits. This advanced Dirac theory naturally enables the magnetic moment anomaly to be entirely explained without resort to renormalization and other ad hoc add-ons, and it also permits a detailed, granular understanding of how individual fermions interact with individual photons strictly on the quantum level. In sum, it advances Dirac theory to a quantum theory of the electron...
Quantum Wave Mechanics as the Magnetic Interaction of Dirac Particles
It is shown that a wave mechanical quantum theory can be derived from relativistic classical electrodynamics, as a feature of the magnetic interaction of Dirac particles modeled as relativistically circulating point charges. The magnetic force between two classical point charges, each undergoing relativistic circulatory motion of small radius compared to the separation between their centers of circulation, and assuming a time-symmetric electromagnetic interaction, is modulated by a factor that behaves similarly to the Schr\"odinger wavefunction. The magnetic force between relativistically-circulating charges has been shown previously to have a radially-directed inverse-square part of similar strength to the Coulomb force, and sinusoidally modulated by the phase difference of the charges' circulatory motions. The magnetic force modulation in the case of relatively moving centers of charge circulation solves an equation formally identical to the time-dependent free-particle Schr\"odinger equation, apart from a factor of two on the partial time derivative term. Considering motion in a time-independent potential obtains that the modulation also satisfies an equation formally similar to the time-independent Schro\"dinger equation. Using a formula for relativistic rest energy advanced by Osiak, the time-independent Schr\"odinger equation is solved exactly by the resulting modulation function. The significance of the quantum mechanical wavefunction follows straightforwardly from these observations. After considering the modification of Wheeler-Feynman absorber theory required by the adoption of Minkowski-Osiak relativity, the model is extended to obtain the full complex Schr\"odinger wavefunction.
Dirac's equation and the nature of quantum field theory
Physica Scripta, 2012
This paper reexamines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics vis-à-vis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantum-mechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (high-energy) experimental quantum physics vis-à-vis that of quantum mechanics and the (low-energy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.
The Lorentz-Dirac Equation and the Physical Meaning of the Maxwell's Fields
1995
Classical Electrodynamics is not a consistent theory because of its field inadequate behaviour in the vicinity of their sources. Its problems with the electron equation of motion and with non-integrable singularity of the electron self field and of its stress tensor are well known. These inconsistencies are eliminated if the discrete and localized (classical photons) character of the electromagnetic interaction is anticipatively recognized already in a classical context. This is possible, in a manifestly covariant way, with a new model of spacetime structure, shown in a previous paper 1^{1}1, that invalidates the Lorentz-Dirac equation. For a point classical electron there is no field singularity, no causality violation and no conflict with energy conservation in the electron equation of motion. The electromagnetic field must be re-interpreted in terms of average flux of classical photons. Implications of a singularity-free formalism to field theory are discussed.
The Dirac equation is a cornerstone of quantum mechanics that fully describes the behaviour of spin ½ particles. Recently, the energy momentum relationship has been reconsidered such that |E|^2 = |(m0c^ 2)| 2 + |(pc)| 2 has been modified to: |E| 2 = |(m0c^2)|^2-|(pc)|^2 where E is the kinetic energy, moc^2 is the rest mass energy and pc is the wave energy for the spin ½ particle. This has been termed the 'Hamiltonian approach' and with a new starting point, the original Dirac equation has been derived: and the modified covariant form found is where h/2π = c = 1. The behaviour of spin ½ particles is found to be the same as for the original Dirac equation. The Dirac equation will also be expanded by setting the rest energy as a complex number, |(m0c 2)| e^jωt
Schrödinger Theory of Electrons in Electromagnetic Fields: New Perspectives
Computation
The Schrödinger theory of electrons in an external electromagnetic field is described from the new perspective of the individual electron. The perspective is arrived at via the time-dependent "Quantal Newtonian" law (or differential virial theorem). (The time-independent law, a special case, provides a similar description of stationary-state theory). These laws are in terms of "classical" fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. The laws reveal the following physics: (a) in addition to the external field, each electron experiences an internal field whose components are representative of a specific property of the system such as the correlations due to the Pauli exclusion principle and Coulomb repulsion, the electron density, kinetic effects, and an internal magnetic field component. The response of the electron is described by the current density field; (b) the scalar potential energy of an electron is the work done in a conservative field. It is thus path-independent. The conservative field is the sum of the internal and Lorentz fields. Hence, the potential is inherently related to the properties of the system, and its constituent property-related components known. As the sources of the fields are functionals of the wave function, so are the respective fields, and, therefore, the scalar potential is a known functional of the wave function; (c) as such, the system Hamiltonian is a known functional of the wave function. This reveals the intrinsic self-consistent nature of the Schrödinger equation, thereby providing a path for the determination of the exact wave functions and energies of the system; (d) with the Schrödinger equation written in self-consistent form, the Hamiltonian now admits via the Lorentz field a new term that explicitly involves the external magnetic field. The new understandings are explicated for the stationary state case by application to two quantum dots in a magnetostatic field, one in a ground state and the other in an excited state. For the time-dependent case, the evolution of the same states of the quantum dots in both a magnetostatic and a time-dependent electric field is described. In each case, the satisfaction of the corresponding "Quantal Newtonian" law is demonstrated.
The New Relativistic Quantum Theory of the Electron
In this paper we introduce a framework to unify quantum and special relativity theories conforming the principle of causality through a new concept of fundamental particle mass based on new models of both stochastic process and elementary particles as concentrated energy localized on the surface of 3-dimensional sphere-form (2-manifold without boundary). The natural picture of fundamental connection between quantum and special relativistic aspects of particles is described by the existence of the intrinsic random vibrating motion of an elementary particle in a quantum-sized volume (Planck scale) directly connected with a spin phenomenon, which is playing fundamental role as internal time. The results show that fir st, relativistic effects fundamentally relate to dynamic aspects of a particle. Second, new equations indicate antiparticle (antimatter) must have positive energy. Third, these are different from the Dirac's equation exhibiting an electric moment in a pure imaginary. Our equation presents a real electric moment. We also show that the antiparticles only present in strong potential causing the non-symmetry reality between matter and antimatter in the universe.
viXra, 2016
We summarize how the Lorentz Force motion observed in classical electrodynamics may be understood as geodesic motion derived by minimizing the variation of the proper time along the worldlines of test charges in external potentials, while the spacetime metric remains invariant under, and all other fields in spacetime remain independent of, any rescaling, i.e., regauging of the charge-to-mass ratio q/m. In order for this to occur, time is dilated or contracted due to repulsive and attractive electromagnetic interactions respectively, in very much the same way that time is dilated due to relative motion in special relativity and due to gravitational fields in general relativity, without contradicting the well-corroborated experimental content of standard electrodynamic theory and both special and general relativity. As such, it becomes possible to lay an entirely geometrodynamic foundation for classical electrodynamics in four spacetime dimensions, in which mechanical motions and objects are merely promoted into canonical motions and objects in accordance with well-established local symmetry principles. Further, when we consider the self-interactions of individual leptons understood to be responsible for the magnetic moment anomalies, and upon identifying a universal relation between time and energy whereby all forms of energy dilate (or contract) time regardless of their kinetic or interaction origin, it is shown how these magnetic moment anomalies which are quintessential hallmarks of quantum field theory, both measure and empirically validate electromagnetic time dilation, and are a direct and immediate consequence of local abelian and non-abelian gauge symmetries.