Time Running Backwards, and Where It Stops: Superoscillations of Proper Time and the Memory of the Environment

arXiv:2611.12971v1 Announce Type: new Abstract: A quantum system prepared in a superposition of proper times - a clock whose worldline is superposed, or a clock at rest in a superposed gravitational potential - evolves, in each branch, by the same dynamics for a different duration. Post-selecting the control that sets the proper time turns the superposition into a superoscillation of the time-dilation factor: the system is found to have evolved for a proper time $\alpha_w t$, where the weak value $\alpha_w$ may exceed unity, vanish, or be negative - the quantum time-translation machine of Aharonov, Anandan, Popescu and Vaidman. We ask how far back such a machine can run an irreversible process.