Time operator and quantum projection evolution

In this paper, we consider time as a dynamical variable. In particular, we present the explicit realization of the time operator within four-dimensional nonrelativistic spacetime. The approach assumes including events as a part of the evolution. The evolution is not driven by the physical time, but it is based on the causally related physical events. The usual Schrödinger unitary evolution can be easily derived as a special case of the three-dimensional projection onto the space of simultaneous events. Also the time—energy uncertainty relation makes clear and mathematically rigorous interpretation.