The Importance of Meaningful Conservation Equations in Relativistic Quantum Mechanics for the Sources of Classical Fields

Abstract

Relativistic quantum theory for a free particle, such as the Dirac theory, yields continuity equations for tensor bilinear densities that lead to conservation laws for the physical properties of that particle. It is shown here that the same continuity equations serve as the source equations for classical fields produced by the particle and described by the Clifford algebra C₄. The continuity equations must yield physically meaningful conservation laws in order to produce classical fields which also are physically meaningful and correct. Specifically, the charge-current conservation equation leads directly to the correct classical Maxwell electromagnetic equations if the sign of the charge is indefinite. Similarly, the energy-momentum conservation equation leads to a classical theory of gravity if the sign of the energy tensor is positive-definite. The equations obtained, although very different from those of general relativity, agree with all the current gravitation experiments.

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