Geometric Electro-Magnetic Field Equations for Particles with Charge and Spin
POSTER
Abstract
The complete and self-consistent "Maxwell" equations are displayed algebraically, describing (time-delayed} force and torque interactions between moving particles with charge and spin. The algebra is the 4-level Grassmann linear algebra describing 3D Euclidean space, starting from 4 independent points to generate structures for lines, planes, and volumes.
With this full algebra, two forces can add to become a torque, and two flows can add to become a circulation. With similar clarity, the algebra describes the motional (v/c) "transformations" between vector electric E and vortical magnetic B through simple motion of the 4th origin point, without "space-time algebra" effects. Thus, the algebra can explicitly distinguish between conduction currents and the orthogonal spin/circulation currents; and between dynamic effects such as spin-transfer torque, and entropic effects such as conduction resistance or magnetization damping.
Geometrically, the two fundamental lengths in electro-magnetism are the classical electron radius Re = e2/mec2 = 2.82 pm; and the "Compton wavelength" Dv = ħc /mec2 = 386 pm. Re scales the electric interaction energy between two charges, and Dv characterizes the vortical diameter (twice Bohr magneton) of a single electron spin. Significantly, a single propagating E-M wave necessarily links both together, with E = B in magnitude. Moreover, as a bi-vector, B squares to negative, making E2 + B2 = 0; and two oppositely propagating waves are required to transfer energy from one particle to another.
Understanding these geometrical structures can substantially clarify the complexity of probability wave function analysis.
Poster at NNP.ucsd.edu /GeoLocCau2 .
With this full algebra, two forces can add to become a torque, and two flows can add to become a circulation. With similar clarity, the algebra describes the motional (v/c) "transformations" between vector electric E and vortical magnetic B through simple motion of the 4th origin point, without "space-time algebra" effects. Thus, the algebra can explicitly distinguish between conduction currents and the orthogonal spin/circulation currents; and between dynamic effects such as spin-transfer torque, and entropic effects such as conduction resistance or magnetization damping.
Geometrically, the two fundamental lengths in electro-magnetism are the classical electron radius Re = e2/mec2 = 2.82 pm; and the "Compton wavelength" Dv = ħc /mec2 = 386 pm. Re scales the electric interaction energy between two charges, and Dv characterizes the vortical diameter (twice Bohr magneton) of a single electron spin. Significantly, a single propagating E-M wave necessarily links both together, with E = B in magnitude. Moreover, as a bi-vector, B squares to negative, making E2 + B2 = 0; and two oppositely propagating waves are required to transfer energy from one particle to another.
Understanding these geometrical structures can substantially clarify the complexity of probability wave function analysis.
Poster at NNP.ucsd.edu /GeoLocCau2 .
Publication: The electric fields and "lightning jets" of the Sun and solar wind", Physics of Plasmas, 30, 102903 (2023); doi: 10.1063/5.0139215 .<br>Preprints and posters at NNP.ucsd.edu .
Presenters
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Charles Fred Driscoll
University of California, San Diego
Authors
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Charles Fred Driscoll
University of California, San Diego