Temporal interference of relativistic bosons

In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the temporal structure of the evolution of quantum systems is ill-defined. We present an extension to the model, in which the time evolution is based on the projection postulate rather than the unitary operator. This approach is in agreement with all other aspects of quantum mechanics and allows to discuss time as an observable. Using this framework we present a description of the temporal double-slit experiment in which a~single particle interferes with itself from a different instant of time. Such behaviour has already been observed experimentally but lacked a consistent theoretical explanation.
Comment: This paper has been merged with arxiv:1910.11198