What happens when we quantize time? Speaker(s): Alexander Smith
Abstract: The lesson of general relativity is background independence: a physical theory should not be formulated in terms of external structures. This motivates a relational approach to quantum dynamics, which is necessary for a quantum theory of gravity. Using a covariant POVM to define a time observable, I will introduce the socalled trinity of relational quantum dynamics comprised of three distinct formulations of the same relational quantum theory: evolving constants of motion, the PageWootters formalism, and a symmetry reduction procedure. The equivalence between these formulations yields a temporal frame change map that transforms between the dynamics seen by different clocks. This map will be used to illustrate a temporal nonlocality effect that results in a superposition of time evolutions from the perspective of a clock indicating a superposition of different times. Then, a timenonlocal modification to the SchrÃ¶dinger equation will be shown to manifest when a system is coupled to the clock that is tracking its evolution. Such clocksystem interactions should be expected at some scale when the gravitational interaction between them is taken into account. Finally, I will examine relativistic particles with internal degrees of freedom that constitute a clock that tracks their proper time. By evaluating the conditional probability associated with two such clocks reading different proper times, I will show that these clocks exhibit a novel quantum time dilation effect when moving in a superposition of different momenta.
Date: 10/12/2019  9:00 am
Collection: Indefinite Causal Structure
