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10 September 2009 Two versions of Maxwell's equations and the nature of light
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Abstract
In this paper, we show that there are actually two versions of Maxwell's equations. The new version is mathematically, but not physically, equivalent to the conventional form. It was missed because of an attempt to give a mathematical fix for a basic physical problem. This second formulation fixes the clock of the field source for all inertial observers. However now, the (natural definition of the effective) speed of light is no longer an invariant for all observers, but depends on the motion of the source. This approach allows us to account for radiation reaction without the Lorentz-Dirac equation, self-energy (divergence), advanced potentials or any assumptions about the structure of the source. This version has a new invariance group which, in general, is a nonlinear and nonlocal representation of the Lorentz group, and provides a natural (and unique) definition of simultaneity for all observers. We briefly review the corresponding particle mechanics. The purpose is to show that there is a (unique) clock for any closed system of physical bodies. This clock provides a unique definition of simultaneity for all events associated with the system. We then discuss our view of the photon within this theory.
© (2009) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Tepper L. Gill and Woodford W. Zachary "Two versions of Maxwell's equations and the nature of light", Proc. SPIE 7421, The Nature of Light: What are Photons? III, 74210O (10 September 2009); https://doi.org/10.1117/12.824191
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