We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum
clock. This allows us to bypass some of the problems of previous proposals, and to obtain a …

We draw a picture of physical systems that allows us to recognize what “time” is by requiring
consistency with the way that time enters the fundamental laws of Physics. Elements of the …

The local conservation of a physical quantity whose distribution changes with time is
mathematically described by the continuity equation. The corresponding time parameter …

We present a covariant quantum formalism for scalar particles based on an enlarged Hilbert
space. The particular physical theory can be introduced through a timeless Wheeler DeWitt …

We consider a global quantum system (the “Universe”) satisfying a double constraint, both
on total energy and total momentum. Generalizing the Page and Wootters quantum clock …

Time in quantum mechanics is peculiar: it is an observable that cannot be associated to an
Hermitian operator. As a consequence it is impossible to explain dynamics in an isolated …

We consider a quantum universe composed of a small system S and a large environment. It
has been demonstrated that, for the vast majority of randomly chosen wave functions of the …

Equilibrium statistical mechanics provides powerful tools to understand physics at the
macroscale. Yet, the question remains how this can be justified based on a microscopic …

Textbook quantum mechanics treats time as a classical parameter and not as a quantum
observable with an associated Hermitian operator. For this reason, to make sense of usual …

We discuss some fundamental properties of discrete system-time history states. Such states
arise for a quantum reference clock of finite dimension and lead to a unitary evolution of …