Speaker
Description
The time-of-arrival problem asks for a probability distribution for when a quantum particle reaches a specified location. It has been the subject of decades of debate, exemplifying the lack of a self-adjoint time observable in quantum theory. In the Page–Wootters framework, time is a relational quantity, emerging from correlations between a system and a clock induced by a global Hamiltonian constraint. We construct a time-of-arrival distribution by inverting the Page-Wootters approach, asking what time a clock reads given that the particle arrives at some fixed position. The result coincides with a common approach to the time-of-arrival problem, suggesting a potential relational interpretation to the latter. Our investigation provides a relational description of the time-of-arrival problem, applying the abstract Page-Wootters formalism to a concrete physical problem, and revealing some complications with the canonical interpretation of the Page-Wootters formalism as a theory of conditional probabilities.
(The manuscript corresponding to this abstract is in its final stages and will be uploaded to arXiv soon.)