Table of Contents
Turn attention to comparison of temporal quantization with standard quantum theory
Two questions:
Correct reductions in various limits
If true, why not seen
Focus on first here
Before doing so, look briefly at second: might this have been seen by chance? Absense of evidence is not proof of absence, but it is evidence of absence.
Working answer to second that:
In general, both halves of scattering experiment have to be time dependent, or expected effects will average out. This is a given in space oriented experiments: beams and gates are normally defined in space, but are often allowed to run for extended periods of time, no boundary in time
Hard to see what we are not looking for
Look at a number of limits:
_nonrel: Non-relativistic limit– gives quick check on overall sanity of the approach and checks the scale of the Lagrangian.
Semi-classical: Semi-classical approximation– for standard quantum theory, semi-classical approximation provides most natural connection to classical mechanics. As with respect to time, temporal quantization is to standard quantum theory as standard quantum theory is to classical mechanics, look at the semi-classical approximation for temporal quantization.
Stationary solutions: Stationary states– we get the standard quantum theory solutions by looking at the stationary (with respect to laboratory time) solutions of temporal quantization.
Stationary solutions with non-singular potentials: Scattering.
Stationary solutions with singular potentials (bound systems): Bound states.