Środowiskowe Seminarium z Informacji i Technologii Kwantowych

The canonical quantization of gravity leads to the Hamiltonian constraint, that is, physical states of the theory are annihilated by the Hamiltonian. Combined with the Schrodinger equation, the Hamiltonian constraint dictates that the physical states do not evolve in time. This poses a problem for time in the theory: Given that the physical states do not evolve, how do we explain the time evolution we see around us?I will begin by reviewing how the Hamiltonian constraint arises in both classical and quantum mechanics and then introduce the conditional probability interpretation of time, which is a possible answer to the question above. I will then discuss two generalizations of this interpretation which are necessary if it is to be applied to time in quantum gravity.