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Continuous Natural Vector Theory of Electromagnetism H UET2 Continuous Natural Vector Theory of Electromagnetism H. J. Spencer * II ABSTRACT A new algebraic representation is used to immediately recover all the major results of classical electromagnetism. This new representation (‘Natural Vectors’) is based on Hamilton’s quaternions and completes the original attempt by Maxwell to use this powerful, non-commutative algebra in the final presentation of his theory in his Treatise. The foundational hypothesis here is that the principal electromagnetic variables are best represented by Natural Vectors, rather than the conventional 3D vectors defined by ‘real numbers’. The present results avoid all use of the field concept and validate the retarded scalar and vector potentials approach first introduced by L. V. Lorenz, who combined Gauss’s 1845 suggestion of the finite speed of interaction with Newton’s action-at-a-distance model of physics into a charge-potential model of electromagnetism in 1867. This new approach demonstrates the primacy and physical significance of the ‘Lorenz gauge’. Not withstanding Maxwell’s aether theory, the present results are based on the continuous charge-density substance model of electricity that is used today to develop Maxwell’s Equations for classical electromagnetism. The present analysis also demonstrates that Helmholtz’s ‘fluid’ model of electricity is one of the few that can result in an electromagnetic ‘explanation’ for the phenomenon of light. Unlike algebraic Minkowski 4-vectors, the more powerful 4-dimensional covariant Natural Vectors used here generate all the differential equations normally found in classical electromagnetism in an immediate and direct algebraic manner. This new theory focuses on the remote interaction between charges, which then appears both as variations in the charge-density and the potentials “traveling at light-speed across space”. Surprisingly, this same result also appears for the current-density; this suggests that the conventional interpretation of this major symbol in Maxwell’s Equations needs to be questioned further. * SPSI, Surrey, B.C. Canada (604) 542-2299 [email protected] © H. J. Spencer Version 2.3 25-07-2012 Version 2.0 30-11-2007 Version 1.0 16-06-2007 UET2 Continuous Natural Vector Theory of Electromagnetism ABSTRACT ........................................................................................................................................... 1 1. INTRODUCTION & OVERVIEW ................................................................................................. 9 1.1 INTRODUCTION ....................................................................................................................... 9 1.1.1 RESEARCH PROGRAMME ............................................................................................... 9 A Major Paradigm Shift ............................................................................................................. 9 Maxwell’s Introductions ............................................................................................................ 9 Einstein just wanted to understand Electrons ............................................................................ 9 Newton’s Introduction to Principia ........................................................................................... 9 The Continuum Hypothesis ...................................................................................................... 10 The Continuum Fallacy ............................................................................................................ 10 Physics: Two, One, Zero Objects ............................................................................................. 10 The Four Basic Concepts ......................................................................................................... 10 Euclidean Theory ..................................................................................................................... 10 Relying on Visualization .......................................................................................................... 10 1.1.2 OBJECTIVES ..................................................................................................................... 11 The Value of Natural Vectors in EM ........................................................................................ 11 The Value of Philosophy & History ......................................................................................... 11 Investigating the Charge-Potential EM Model ........................................................................ 11 1.1.3 PHILOSOPY IS IMPORTANT .......................................................................................... 11 Modern Physics rejects Philosophy ......................................................................................... 11 Feynman View of Physics ........................................................................................................ 11 Maxwell’s View of Science ....................................................................................................... 12 Defining Reality ....................................................................................................................... 12 ‘Schoolmen’ prefer the Plenum ............................................................................................... 12 Aether, not Ether ...................................................................................................................... 12 Human Bias .............................................................................................................................. 12 1.1.4 HISTORY IS IMPORTANT .............................................................................................. 12 Nineteenth Century EM Mythology ......................................................................................... 12 History is always Important ..................................................................................................... 13 A Brief History of Electricity ................................................................................................... 13 Maxwell’s Treatise ................................................................................................................... 13 Maxwell started with the Potentials ......................................................................................... 13 Not the Maxwell-Hertz Equations ............................................................................................ 13 1.1.5 THE RISE OF FIELD THEORY ....................................................................................... 14 Maxwell’s Philosophical Introductions ................................................................................... 14 Maxwell rejects Action-at-a-Distance ..................................................................................... 14 Infinite Decimal Numbers are not Real ................................................................................... 14 Continuous Matter in 19th Century .......................................................................................... 14 Misdirection of Natural Philosophy ......................................................................................... 14 1.2 OVERVIEW .............................................................................................................................. 15 1.2.1 THEORETICAL PHYSICS IS METAPHYSICS .............................................................. 15 Philosophy must be Explicit ..................................................................................................... 15 Maxwell’s Natural Philosophy Questions ............................................................................... 15 The Principle of ‘Least Change’ .............................................................................................. 15 1.2.2 METAPHYSICS OF ELECTROMAGNETISM ............................................................... 15 The Necessity of Metaphysics .................................................................................................. 15 Aetherial EM Metaphysics ....................................................................................................... 16 Contemporary Views on Classical EM .................................................................................... 16 EM Alternatives to Maxwell ..................................................................................................... 16 1.2.3 MAXWELL-HEAVISIDE AETHER THEORY ............................................................... 16 1.2.4 MODERN CLASSICAL ELECTRODYNAMICS ............................................................ 17 1.2.5 SUMMARY OF CONTINUOUS NATURAL VECTORS ............................................... 17 1.2.6 THE CNV ELECTROMAGNETIC MODEL .................................................................... 17 1.2.7 SUMMARY AND CONCLUSIONS ................................................................................. 17 2. METAPHYSICS OF ELECTROMAGNETISM .......................................................................... 18 2.1 THE NECESSITY OF METAPHYSICS .................................................................................. 18 The Goal of Physics ................................................................................................................. 18 2.1.1 NATURAL PHILOSOPHY ..............................................................................................
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