A null 4-vector ε°σμε, based on Dirac's relativistic electron equation, is shown explicitly for a plane wave and various Coulomb states. This 4-vector constitutes a mechanical “model” for the electron in those states, and expresses the important spinor quantities represented conventionally byn, f, g, m, j, κ,1, ands. The model for a plane wave agrees precisely with the relation between velocity and phase gradient customarily used in quantum theory, but the models for Coulomb states contradict that relation.

Spinor equations, previously found valid and interesting in dealing with plane waves of light, are applied to spherical waves. It is found that the spinors pertaining to light do not form outgoing spherical waves, as the vectors do, but they can form standing spherical waves, which the vectors usually cannot. The spinors disclose details (“hidden variables”) which are hidden from the accepted theories of the subatomic scale.