Clearly, the Time Traveller proceeded, any real body must have extension in four directions: it must have Length, Breadth, Thickness, and–Duration. But through a natural infirmity of the flesh, which I will explain to you in a moment, we incline to overlook this fact. There are really four dimensions, three which we call the three planes of Space, and a fourth, Time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives.
This is often the way it is in physics - our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world. Even worse, there often seems to be a general agreement that certain phenomena are just not fit subjects for respectable theoretical and experimental effort.
Time and space treated symmetrically in relativity; but not in quantum mechanics. We force the issue by quantizing time using the same rules as for space. We use the Feynman path integral formalism, including paths in time on the same basis as paths in space. We use Morlet wavelet decomposition to ensure convergence and normalization of the path integrals. We derive the Schrödinger equation in four dimensions from the path integral expression. We verify we recover standard quantum theory in the non-relativistic, semi-classical, scattering, and bound cases. We propose a number of experimental tests, including the double slit in time, scattering by time-varying fields, and the Aharonov-Bohm effect in time. As most foundational quantum mechanics experiments can be turned into tests of temporal quantization by interchanging time and a space dimension, hundreds of tests are possible.