Novikov self-consistency principle

Novikov intended it to solve the problem of paradoxes in time travel, which is theoretically permitted in certain solutions of general relativity that contain what are known as closed timelike curves.

Novikov discussed the possibility of closed timelike curves (CTCs) in books he wrote in 1975 and 1983,[1] offering the opinion that only self-consistent trips back in time would be permitted.

Among the co-authors of this 1990 paper were Kip Thorne, Mike Morris, and Ulvi Yurtsever, who in 1988 had stirred up renewed interest in the subject of time travel in general relativity with their paper "Wormholes, Time Machines, and the Weak Energy Condition",[4] which showed that a new general relativity solution known as a traversable wormhole could lead to closed timelike curves, and unlike previous CTC-containing solutions, it did not require unrealistic conditions for the universe as a whole.

[5]: 509 By way of response, physicist Joseph Polchinski wrote them a letter arguing that one could avoid the issue of free will by employing a potentially paradoxical thought experiment involving a billiard ball sent back in time through a wormhole.

In the revised scenario, the ball from the future emerges at a different angle than the one that generates the paradox, and delivers its younger self a glancing blow instead of knocking it completely away from the wormhole.

Later analysis by Thorne and Robert Forward illustrated that for certain initial trajectories of the billiard ball, there could actually be an infinite number of self-consistent solutions.

[6]: 511–513 Echeverria, Klinkhammer, and Thorne published a paper discussing these results in 1991;[8] in addition, they reported that they had tried to see if they could find any initial conditions for the billiard ball for which there were no self-consistent extensions, but were unable to do so.

[10] This could mean that the Novikov self-consistency principle does not actually place any constraints on systems outside of the region of space-time where time travel is possible, only inside it.

However, the Novikov self-consistency principle is intended to go beyond just the statement that history must be consistent, making the additional nontrivial assumption that the universe obeys the same local laws of physics in situations involving time travel that it does in regions of space-time that lack closed timelike curves.

[3]Similarly, physicist and astronomer J. Craig Wheeler concludes that: According to the consistency conjecture, any complex interpersonal interactions must work themselves out self-consistently so that there is no paradox.

As soon as the machine is activated, a so-called "fixed-point" of F, an input which produces an identical output, usually signaling a perfect answer, appears (by an extraordinary coincidence!)

[...] If the iteration does not converge, that is, if F has no fixed point, the computer outputs and inputs will shut down or hover in an unlikely intermediate state.Physicist David Deutsch showed in 1991 that this model of computation could solve NP problems in polynomial time,[13] and Scott Aaronson later extended this result to show that the model could also be used to solve PSPACE problems in polynomial time.

[14][15] Deutsch shows that quantum computation with a negative delay—backwards time travel—produces only self-consistent solutions, and the chronology-violating region imposes constraints that are not apparent through classical reasoning.

In consequence, Tolksdorf and Verch argue that Deutsch's condition is not sufficiently specific to allow statements about time travel scenarios or their hypothetical realization by quantum physics.