Discrete Relativistic Electron Dynamics

This is the fifth report on a new research programme investigating the fundamental electromagnetic (EM) interaction. This paper completes the analysis of the interaction between two electrons described in the two previous papers. Each of these electron papers imposed a new, discrete restriction on the EM interaction. This paper now adds two new restrictions to the asynchronous interaction between two electrons. A pair-wise ray-like form of the EM impulse is proposed whose magnitude diminishes linearly with temporal separation to a finite, fixed value. Additionally, the discrete EM interaction is universalized by proposing a simple, new form for quantizing both the dynamical and kinematical activity between interacting pairs of electrons. This constrains both the linear momentum and kinetic energy of the two electrons to be exchanged across each interaction in fixed quanta. This dynamical exchange of quantized action (h/2) replaces Coulomb’s unproven spherical, continuous and instantaneous ‘law’ of electrostatics with a new, unified, discrete and dynamical basis for electromagnetism. This fulfills Maxwell’s quest for extending Newtonian (particle) mechanics to the phenomena of electricity and magnetism but now for all relative distances and speeds: unifying both EM and classical and relativistic mechanics. This new EM model replaces Planck’s arbitrary (mathematical) quantum of action ‘rule’ (first injected mathematically into EM radiation theory and then later into atomic physics) and thereby providing a universal physical explanation for all atomic phenomena. This paper provides the first complete analytical solution of the isolated two-electron interaction – both attraction and repulsion. The present theory shows that negative and positive electrons are two complementary manifestations of the same type of entity, phase-shifted from one another in the timing of their interactions. It is proposed that both forms of the electron execute a four-step transverse, cyclic trajectory across space (in opposite directions). This new physical and mathematical EM model provides a simple, discrete mechanical explanation for the foundational (but mysterious) two-valued quantum phenomenon of electron ‘spin’. Since this motion is sub-microscopic, this may be viewed as the ‘hidden quantum degree of freedom’ that characterizes this most mysterious behavior of the electron. The intrinsic (‘clicking’) motion of the electron is proposed here as the spatial component (where) of the fundamental interaction between pairs of electrons. The other new component is now intimately associated with when and how an electron interacts with other electrons. These ideas result in electrons stepping cyclically through four interaction states (the positron goes through the same four states but in the opposite sequence). This provides novel insights into Dirac’s Equation of the Relativistic Electron while avoiding all taint of negative energy states. This new two-time theory unifies an asynchronous version of Newton’s physics of point particle motion (at all velocities) with all of the experimental phenomena of classical and quantum EM while avoiding use of single-time field theories and their necessary relativistic transformations of space and time. The new theory now forms the foundation for a new quantum theory of atoms, nuclei and elementary particles that is easier to visualize (geometric) while its finite algebraic basis (rather than continuous calculus) make it much easier to calculate and extend than prior continuum theories; the new results of these further extensive investigations will be presented in a series of subsequent papers. * Surrey B.C. Canada (604) 542-2299spsi99@telus.net © H. J. Spencer Version 1.250 16-12-2016 Begun 23-06-2008 (675 KB, 196pp)

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