Mechanical Model of Maxwell’s Equations and of Lorentz Transformations

We present a mechanical model of a quasi-elastic body (aether) which reproduces Maxwell’s equations with charges and currents. Major criticism (in: Sommerfeld, Mechanics of deformable bodies, lectures on theoretical physics, Academic Press, Inc., London, 1964) against mechanical models of electrodynamics is that any presence of charges in the known models appears to violate the continuity equation of the aether and it remains a mystery as to where the aether goes and whence it comes. We propose a solution to the mystery—in the present model the aether is always conserved. Interestingly it turns out that the charge velocity coincides with the aether velocity. In other words, the charges appear to be part of the aether itself. We interpret the electric field as the flux of the aether and the magnetic field as the torque per unit volume. In addition we show that the model is consistent with the theory of relativity, provided that we use Lorentz–Poincare interpretation (LPI) of relativity theory. We make a statistical-mechanical interpretation of the Lorentz transformations. It turns out that the length of a body is contracted by the electromagnetic field which the molecules of this same body produce. This self-interaction causes also delay of all the processes and clock-dilation results. We prove this by investigating the probability distribution for a gas of self-interacting particles. We can easily extend this analysis even to elementary particles.