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Electromagnetic fields and charges in 3+1 spacetime derived from symmetry in 3+3 spacetime

J. E. Carroll
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Abstract

Maxwells classic equations with fields, potentials, positive and negative charges in 3+1 spacetime are derived solely from the symmetry that is required by the Geometric Algebra of a 3+3 spacetime. The observed direction of time is augmented by two additional orthogonal temporal dimensions forming a complex plane where i is the bi-vector determining this plane. Variations in the transverse time determine a zero rest mass. Real fields and sources arise from averaging over a contour in transverse time. Positive and negative charges are linked with poles and zeros generating traditional plane waves with right-handed E, B, with a direction of propagation k. Conjugation and space-reversal give left-handed plane waves without any net change in the chirality of 3+3 spacetime. Resonant wave-packets of left- and right- handed waves can be formed with eigen frequencies equal to the characteristic frequencies (N+1/2)fO that are observed for photons.

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J. E. Carroll. 2004-09-01. Electromagnetic fields and charges in 3+1 spacetime derived from symmetry in 3+3 spacetime. https://arxiv.org/abs/math-ph/0404033

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