Proper-Time Formulation of Relativistic Dynamics

Abstract

It will be argued that Minkowski's implementation of distances is inconsistent. An alternative implementation will be proposed. In the new model the proper time of an object is taken as its fourth coordinate. Distances will be measured according to a four dimensional Euclidean metric. In the present approach mass is a constant of motion. A mass can therefore be ascribed to photons and neutrinos. Mechanics and dynamics will be reformulated in close correspondence with classical physics. Of particular interest is the equation of motion for the proper time momentum. In the classical limit it reduces to the classical law of conservation of (kinetic+potential) energy. In the relativistic limit it is similar to the conservation of energy of the theory of relativity. The conservation of proper time momentum allows for an alternative explanation for Compton scattering and pair annihilation. On the basis of the proper time formulation of electrodynamics also an alternative explanation will be offered for the spectra of hydrogenic atoms. The proper time formulation of gravitational dynamics leads to the correct predictions of gravitational time dilation, the deflection of light and the precession of the perihelia of planets. For this no curvature will be needed. That is, spacetime is flat everywhere, even in the presence of sources of gravitation. Some cosmological consequences will be discussed. The present approach gives a new notion to energy, antiparticles and the structure of spacetime. The contents of the present paper will have important implications for the foundations of physics in general.