Quantum mechanics of time travel

Until recently, most studies on time travel have been based upon classical general relativity. Coming up with a quantum version of time travel requires physicists to figure out the time evolution equations for density states in the presence of closed timelike curves (CTC).

Novikov^[1] had conjectured that once quantum mechanics is taken into account, self-consistent solutions always exist for all time machine configurations, and initial conditions. However, it has been noted such solutions are not unique in general, in violation of determinism, unitarity and linearity.

The application of self-consistency to quantum mechanical time machines has taken two main routes. Novikov's rule applied to the density matrix itself gives the Deutsch prescription. Applied instead to the state vector, the same rule gives nonunitary physics with a dual description in terms of post-selection.