Testing the robustness of the Page-Wootters construction with system-clock interactions

In quantum theory, the concept of time rests on shaky ground.

One way to address this problem is to remove the usual background time parameter as a primitive entity and explain its emergence via correlations between physical systems. This approach was adopted by Page and Wootters [1], who showed how time can emerge in a stationary quantum universe from the correlations between two of its subsystems, one of them acting as a clock for the other (the system of interest). Crucially, Page and Wootters assumed that the system of interest does not interact with the clock.

In this talk, I will consider more realistic scenarios where the system and the clock are coupled. I will show how system-clock interactions affect the Page-Wootters construction and discuss some implications for the energy, purity and entanglement of the state of the universe. I will also present a simple model where these interactions lead to an interesting "time-reversal" effect.

[1] D. N. Page and W. K. Wootters, Phys. Rev. D27, 2885 (1983).