**4.4 Wave mechanics**

In the wave mechanical interpretation of quantum mechanics, field boundaries are not specified. Nevertheless fields are a part of wave functions, and field boundaries must be included in a fully relativistic theory of electrodynamics. To satisfy that requirement, we interpret the wave function Ψ *r* !, *t* as combining an electron or other particle, and a force *ε r* !, *t* , that are separated by field boundaries. A wave function composed in this manner as a composite of two physical components may be used to describe the interaction of particles in both bound and free states. Whereas in classical theory forces are three-dimensional vectors with direction and magnitude, in a fully relativistic theory they are four-dimensional and symmetric in the coordinates. They have orientation in space-time, but not direction, with magnitude determined by the instantaneous separation of field boundaries according to (1). Thus force is the continuous application of a discrete form. All interactions of electrodynamics may be conceived of in this way in terms of fields and their boundaries.

## **5. Discussion**

Although the wave function contains all that can be known about a particle, the preceding fully relativistic interpretation of atomic structure indicates the presence of internal characteristics that are *in principle* unknown to observers. The field model, described by (1) and confirmed experimentally by slow or stopped light phenomena, includes internal processes in its description of the wave function that are temporarily restricted from external expression due to field boundaries. The characteristics cannot be accessed because the fields vanish at the field boundaries. Due to the unobserved processes, quantum theory predicts the occurrence of instantaneous action-at-a-distance events such as the collapse of the wave function and other macroscopic phenomena that exist outside of our consciousness. However, if wave functions are interpreted in a fully relativistic theory, we conclude that these phenomena are only unusual when interpreted in abstract space with respect to continuous time parameters.

The detection events that form the basis of optical theory are due to energy emissions that occur at singular points in time and are referred to as "photons" due to their discrete nature. If energy absorption evolves according to Eq. (2), as the integration of a Lagrangian density over a region of space-time, then excitation is a continuous process that results from field superposition during the discrete time period τ. Therefore in a fully relativistic theory, interference effects are due to the instantaneous reinforcement and cancelation of superposed photons of the type described in (2), and the statistical nature of quantum mechanics that is observed in experiments such as double-slit interference is due to time averages. A fully relativistic optical theory will account for interference effects as they evolve in real space and time.
