Quantum mechanics allows one to independently select both the initial and final states of a single system. Such pre- and postselection reveals novel effects that challenge our ideas about what time is and how it flows.
Aharonov, Yakir, Sandu Popescu, and Jeff Tollaksen. "A Time-symmetric Formulation of Quantum Mechanics." Physics Today 63.11 (2010). doi: 10.1063/1.3518209
American Institute of Physics