Since the Bloch energy eigenstate functions determine the energy of space-time, we must seek to express the metric in terms of the Bloch wave functions.

The metric tensor of four-space in the k-th band is therefore associated with the Bloch energy eigenstate functions of the quantum vacuum as follows:

We expand this speed scalar potential using the energy eigenstate basis

Using the time scale [T.sub.[beta]], the time evolution in the energy eigenstate basis was found from Schrodinger-type equation to be

However, for t [greater than or equal to] 0 the particle state, which is no longer an

energy eigenstate, is given by a superposition of the

energy eigenstates [[psi].sub.k](x) (k = [square root of (E)]) of the potential [V.sub.2](x), i.e., [36]

A time interval [DELTA]t can be associated with the time function t during which is measured the energy eigenstate function E which itself has a certain width [DELTA]E, with both widths ([DELTA]) satisfying (10).

For example, we consider the impact of [DELTA]t on the observation of [[tau].sub.n], the lifetime of an atom in energy eigenstate n, and the impact of [DELTA]E on the transition energy [E.sub.mn], for a transition between states n and m during spectral line emission.

The instant-form vacuum is defined as the lowest

energy eigenstate of the instant-form Hamiltonian.

The resonant transition is controlled by

energy eigenstates of the particle which is strongly related to the particle geometry.

Finally, the assumption that the PV is a degenerate state implies that the Planck-particle

energy eigenstates are full.

The proton wave function could as usual be written as a superposition of

energy eigenstates