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Calin Galeriu
I am an independent researcher who, just like Hermann Minkowski, believes that "physical laws might find their most perfect expression as reciprocal relations between these worldlines." Using 3D Minkowski diagrams, I have extended the geometrical derivation of the relativistic addition of velocities to the most general case, and I have derived the magnetic force between two moving electric charges. Then I realized that the material point particle model was incompatible with a purely geometrical understanding of Special Relativity. Indeed, if electrons were points in Minkowski space, fixed points in a 4D space, how could the electromagnetic Lorentz force depend on their velocity in 3D space? The interaction must be taking place between corresponding infinitesimal segments on the particles' worldlines, just like in Adriaan Fokker's time symmetric electrodynamics. Based on the isomorphism between the equations describing the motion of relativistic point particles and the equations describing the static equilibrium of classical elastic strings, first noticed by Olivier Costa de Beauregard, the worldline of a particle becomes a stationary string under tension. If higher dimensions were allowed, the worldline string could also vibrate. A time symmetrical action-at-a-distance interaction is needed for a good compatibility with the action and reaction principle. The theory I am working on has some surprising consequences: the rest mass of the electron is no longer constant, but its variation averages out to zero, once the interaction is over. By assuming that the rest mass variation does not depend on the path taken, with the help of Stokes' theorem, I have derived the two homogenous Maxwell equations. I have also discovered that the radiation reaction force did not have to be orthogonal to the four-velocity, as it is usually assumed. The variation of the rest mass seems to be related to the special conformal symmetry that Maxwell's equations have. I have also been doing research in the history and philosophy of physics. I have explained the details behind Minkowski's electromagnetic force formula from Space and Time. I have explained how to use special conformal symmetry transformations in order to get the electromagnetic field produced by an electric charge in hyperbolic motion. And I have explained the geometrical origin of the Doppler factor in the Lienard-Wiechert potentials, based on the worldtube theorem of J. L. Synge.
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