The Planck aether hypothesis: An attempt for a finitistic non-Archimedean theory of elementary particles

The Planck aether, discovered by Max Planck in 1911 as the zero point vacuum energy, is here assumed to consist of a densely packed assembly of positive and negative Planck mass particles (positive and negative masses, not positive and negative electric charges), each occupying a Planck length volume, subject to Newton s mechanics, locally interacting by the Planck force. Like Leibniz's monads the Planck mass particles have no 'windows', and are not the source of long-range forces, which arise from collective excitations of the Planck aether. This novel theory explains both quantum mechanics and the theory of relativity as asymptotic low energy approximations, and gives a spectrum of particles greatly resembling the standard model. Einstein's gravitational and Maxwell's electromagnetic equations are unified by the symmetric and antisymmetric wave mode of a vortex sponge, Dirac spinors result from gravitationally interacting bound positive-negative mass vortices, which explains why the mass of an electron is so much smaller than the Planck mass. The phenomenon of charge is for the first time explained to result from the zero point oscillations of Planck mass particles bound in vortex filaments.