An inexpensive crystal makes a fine quantum time machine

[Philip Thrift]

https://physicstoday.scitation.org/doi/10.1063/PT.3.4335

From a theoretical perspective, there’s nothing paradoxical about the idea of making a later measurement first and an earlier measurement second. One need only write down a factor of e^iHt/ℏ in between their two operators, where H is the system’s Hamiltonian, to represent the rewinding of time. (Forward-propagating time, in contrast, is represented by e^–iHt/ℏ.)

Experimentally, it’s also possible, at least in principle, to turn back the clock on any quantum system. A quantum state has a unique backward trajectory in time, just as it has a unique forward trajectory, and an ably chosen combination of measurements can extract information about what that trajectory is. Despite their apparent oddity, OTO [out-of-time-order] commutators can make both mathematical and physical sense.

@philipthrift

[Lawrence Crowell]

This is actually quite interesting. The OTO measurements indicating entanglement increase means there is an evolution towards nonlocality. It should be mentioned that QFT with equal time commutators and Wightman conditions do not consider this. This seems to point to how there can be a duality between the localized state, such as the localized spins of fluorine, and nonlocal entangled states.

LC