The quantummechanical wave equations from a relativistic viewpoint

TL;DR

This paper derives quantum mechanical wave equations from a relativistic perspective using Einstein's General Relativity, showing that Schrödinger's Equation is relativistically covariant and providing new insights into Dirac's Equation and electron behavior.

Contribution

It introduces a relativistic derivation of quantum wave equations based on the Equivalence Principle, challenging traditional approaches and explaining antiparticles and wave propagation in curved spacetime.

Findings

Schrödinger's Equation is relativistically covariant.

Klein-Gordon Equation becomes obsolete for spinless particles.

A quantitative analysis of the electron jitter phenomenon.

Abstract

A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy relationship for moving particles. It is shown that Schrodinger's Equation, if properly formulated, is relativisticly covariant. This makes the critisized Klein-Gordon Equation for spinless massparticles obsolete. Therefore Dirac's Equation is presented from a different viewpoint and it is shown that the relativistic covariance of Schrodinger's Equation gives a natural explanation for the dual energy outcome of Dirac's derivation and for the nature of antiparticles. The propagation of wave functions in an energy field is studied in terms of propagation along geodesic lines in curved space-time, resulting in an equivalent formulation as with Feynman's path integral. It is shown that Maxwell's wave equation fits in the developed framework as the massless limit of moving particles. Finally the physical appearance of electrons is discussed including a quantitative calculation of the jitter phenomenon of a free moving electron.