Principles same as in case of standard quantum theory, but applied in time and energy dimensions.
For instance, fast chopper implies large uncertainty in energy.
In general require an estimate of how uncertain the initial wave function is in quantum time, to make a prediction. Three methods here:
For free particles, estimate dispersion in energy from dispersion in momentum: Estimates of uncertainty in time/energy.
For bound states, estimate dispersion in time from orbit times: Estimate of uncertainty in time.
For single slit, estimate dispersion in time based on time gate open: Slits in time.
Have looked at a set of approximations here
An exact solution of the path integrals or of the Schrödinger equation includes these paths, perhaps along the lines developed by Moshinsky: [Moshinsky-1951], [Moshinsky-1952].
Or we could use the approach of Marchewka and Schuss: [Marchewka-1996], [Marchewka-1999b].
We could also solve exactly by using discrete grid for paths, then summing over these paths using techniques from discrete analysis, i.e. generating functions and the like. See [Feller-1968], [Feller-1971], [Graham-1994]. In some ways, this is the most intuitive approach, most consistent with temporal quantization.
However each of these approaches represents a separate project in its own right.
And there is a further benefit to use of approximations: avoids excessive dependence on specifics of temporal quantization.
Experiments here intended to falsify temporal quantization, not to explore it.
Relatively few experiments directly aimed at time: in addition to Lindner's, also [Godoy-2002]with diffraction in time.
Most foundational experiments can be turned into a test of "fuzzy" time by interchanging time and one of the space dimensions
Variation on Aharonov-Bohm experiments with time dependent solenoid.
Tunneling: a quantum cat nervous about the occasional appearances of hydrocyanic acid in its chamber might understandably choose to tunnel past the times when the acid is present.
Gates in energy rather than time.
Quantum electrodynamics variations, i.e. refinements of the particle-particle scattering experiments. Would enable correct treatment of Møller scattering; see if improvement in divergences extends to quantum electrodynamics.
Needed to do correct job on bound state experiments; have looked at doing photon mass to zero estimates; not hard but not entirely persuasive.
Variations on EIT, slow light, quantum Zeno effect, quantum eraser,...
Use of astronomical scales.
Rather than a straight interchange of time and space dimensions; look at mixing, as in relativistic scattering experiments (thanks to Andy Love for suggesting this).
Variations on Michelson-Morley experiment in time possible, looking at quantum effects off-axis, with a time and space dependent shutter at the front.