Classical Two-Electron Relativistic Dynamics (UET4)

This is the fourth report on a new research programme investigating the electromagnetic interaction. In contrast to the previous paper in this series, which analyzed the continuous interaction of pairs of charged point particles, this paper focuses on the hypothesis that the inter-electron interaction only occurs discontinuously over time. This new hypothesis is in response to the previous results showing that all continuous interaction (force) theories between point particles that exhibit inertial resistance to changes in their motion are inconsistent with asynchronous forms of action-at-a-distance or equivalently, interactions limited to points 'on their mutual light-cone'. It is shown here that the conventional approach to the Special Relativity Theory (SRT) has been based on an implied merger of two distinct but incompatible theories. The continuous electric charge model (now used to develop Maxwell's Equations of classical electromagnetism) leads directly to Relativistic Transformations of the space and time coordinates ; while Planck's 1906/7 Proposal for redefining an inertial point particle's momentum came to replace classical Newtonian mechanics with its central concept of invariant particle mass. However, both of these theories are fatally flawed: electricity is not continuous but is particulate (point electrons with finite and discrete charge and mass values) while Planck's relativistic derivation relied on a mysterious constant force that contradicts both the inverse square Coulomb force or the Heaviside velocity-sensitive force that are central to electromagnetism. Most readers will be deeply disturbed to realize that one of the most cherished theories of modern physics has been severely edited by revisionist history, driven by sociological pressures, over the last 75 years as this paper revisits the almost forgotten history of the evolution of SRT and describes both the initial, widespread rejection and the eventual, reluctant acceptance of this revolutionary theory. Furthermore, clear philosophical criticisms have rarely been answered, while the lack of empirical evidence is " simply underwhelming ". An alternative model is now proposed here for the basic interaction between pairs of electrons that is shown to be consistent with classical electromagnetism and provides an alternative (but now readily understandable) physical explanation for the dynamical results of relativity without requiring the SRT (Lorentz) transform to redefine the foundations of space and time. A detailed expanded form of the finite-difference calculus is developed herein, which is then used to replace the traditional mathematical toolset of change (calculus), to investigate the comprehensive, relativistic dynamics of pairs of electrons; an ancient problem that has long resisted solutions under the traditional assumption that all material objects (including electrons) only interact through continuous (EM) forces. Physicists now must make a choice: they can continue to use continuum mathematics (grounded in the traditional calculus used to describe local but mass-less field theories that cover all of space and time, subject to the bizarre interpretations of special-relativity). Alternatively, theoretical physics can return to the physical models of impulse interactions between point particles (described by the mathematics of finite differences acting within the passive, but common-sense, view of space and time, introduced by Newton in the Principia), but now acknowledging that the fundamental interaction is asynchronous. This latter choice means that two interaction times must always be considered in a symmetric manner: the simple, single-time approach (used in physics since Newton) can no longer be viewed as a suitable model of reality.