Quantum mechanics of time travel
Until recently, most studies on time travel have been based upon classical general relativity. A theory of time travel based upon quantum mechanics requires physicists to solve the time evolution equations for density states in the presence of closed timelike curves (CTC).
Igor Novikov conjectured in the mid-1980s 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.[1]
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.
Entropy and computation[edit]
A related description of CTC physics was given in 2001 by Michael Devin, and applied to thermodynamics.[8][9] The same model with the introduction of a noise term allowing for inexact periodicity, allows the grandfather paradox to be resolved, and clarifies the computational power of a time machine assisted computer. Each time traveling qubit has an associated negentropy, given approximately by the logarithm of the noise of the communication channel. Each use of the time machine can be used to extract as much work from a thermal bath. In a brute force search for a randomly generated password, the entropy of the unknown string can be effectively reduced by a similar amount. Because the negentropy and computational power diverge as the noise term goes to zero, complexity class may not be the best way to describe the capabilities of time machines.