Classical Two-Electron Relativistic Dynamics H. J. Spencer * IV ABSTRACT 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 theory of relativity 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 co-ordinates; 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. 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 Relativistic transform to redefine the foundations of space and time. 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 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 the two interaction times must always be considered in a symmetric manner: the single-time approach can no longer be viewed as a suitable model of reality. * Surrey, B.C. Canada (604) 542-2299 [email protected] © H. J. Spencer Version 1.0 20-06-2008 Begun 21-12-2007 UET4 Classical Two-Electron Relativistic Dynamics ABSTRACT 1. INTRODUCTION & OVERVIEW ...................................................................................... 1 1.1 INTRODUCTION ............................................................................................................ 1 1.1.1 RESEARCH PROGRAMME .................................................................................... 1 Conservative Science ...................................................................................................... 2 Science clings to its Theories .......................................................................................... 2 Maxwell discovered the ‘Truth’ ...................................................................................... 2 Einstein promoted Independence .................................................................................... 2 The Unity of Science ....................................................................................................... 3 Physics is always grounded in Points ............................................................................. 3 Reality involves Entities .................................................................................................. 3 Electrons are Points ........................................................................................................ 3 Existence is All Electrons ................................................................................................ 3 The Fact of the Act .......................................................................................................... 3 1.1.2 THE SECOND PILLAR OF MODERN PHYSICS .................................................. 4 It’s all about Time ........................................................................................................... 4 Einstein also began with Time ........................................................................................ 4 The Centrality of Time, not Geometry ............................................................................ 5 Defining Time .................................................................................................................. 5 Mass & Energy ............................................................................................................... 5 Electricity is the Electron ................................................................................................ 5 Pure Electron Theory ...................................................................................................... 5 Interactions cannot be Continuous ................................................................................. 5 1.1.3 OBJECTIVES ............................................................................................................ 6 1.2 OVERVIEW ..................................................................................................................... 6 1.2.1 A NEW APPROACH TO EM ................................................................................... 6 New EM Theory avoids Relativistic Transforms ............................................................ 6 Philosophy Redux ............................................................................................................ 7 Extending Newton’s Metaphysics ................................................................................... 7 Newton introduced Dualities .......................................................................................... 7 1.2.2 ELECTRODYNAMICS & MOTION ....................................................................... 7 1.2.2.1 Nineteenth Century EM ....................................................................................... 8 1.2.2.2 Experimental Anomalies ..................................................................................... 8 1.2.2.3 Relativistic Transformation Theory .................................................................... 8 1.2.2.4 Einstein’s 1905 Relativity Theory ....................................................................... 9 1.2.3 REACTIONS TO SPECIAL RELATIVITY ............................................................. 9 1.2.3.1 Planck’s Role in Relativity .................................................................................. 9 1.2.3.2 Planck’s Momentum Proposal .......................................................................... 10 1.2.3.3 Resistance to Relativity ..................................................................................... 10 1.2.3.4 Acceptance of Relativity .................................................................................... 10 1.2.3.5 Modern Views on Relativity .............................................................................. 10 1.2.3.6 Experimental Confirmation .............................................................................. 10 2 UET4 1.2.4 METAPHYSICS OF SPECIAL RELATIVITY ...................................................... 10 1.2.4.1 Continuity in Classical Physics ........................................................................ 11 1.2.4.2 Rigid Bodies ...................................................................................................... 11 1.2.4.3 Light as an Entity .............................................................................................. 11 1.2.4.4 The Role of Time ............................................................................................... 11 1.2.4.5 The Principle of Relativity ................................................................................ 11 1.2.4.6 Reference Frames ............................................................................................. 12 1.2.5 DISCRETE CLASSICAL MECHANICS ............................................................... 12 1.2.5.1 Continuum Physics ............................................................................................ 12 1.2.5.2 Classical Electron Metaphysics ........................................................................ 12 1.2.5.3 Finite Difference Mathematics ......................................................................... 13 1.2.5.4 Discrete Classical Physics ................................................................................ 13 1.2.6 TWO-ELECTRON RELATIVISTIC DYNAMICS ................................................ 14 1.2.6.1 Interactions: Directed & Discrete .................................................................... 14 1.2.6.2 Discrete Time Interactions ...............................................................................