Among the coauthors of this 1990 paper were Kip Thorne, Michael Morris, and Ulvi Yurtsever, who in 1988 has stirred up renewed interest in the subject of time travel in general relativity with their paper Wormholes, time machines, and the weak energy condition,[2] 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. After discussions with another coauthor of the 1990 paper, John Friedman, they convinced themselves that time travel need not lead to unresolvable paradoxes, regardless of what type of object was sent through the wormhole.[3]
In response, another physicist named Joseph Polchinski sent them a letter in which he argued that one could avoid questions of free will by considering a potentially paradoxical situation involving a billiard ball sent through a wormhole which sends it back in time. In this scenario, the ball is fired into a wormhole at an angle such that, if it continues along that path, it will exit the wormhole in the past at just the right angle to collide with its earlier self, thereby knocking it off course and preventing it from entering the wormhole in the first place. Thorne deemed this problem "Polchinski's paradox".[4]
After considering the problem, two students at Caltech (where Thorne taught), Fernando Echeverria and Gunnar Klinkhammer, were able to find a solution beginning with the original billiard ball trajectory proposed by Polchinski which managed to avoid any inconsistencies. In this situation, the billiard ball emerges from the future at a different angle than the one used to generate the paradox, and delivers its younger self a glancing blow instead of knocking it completely away from the wormhole, a blow which changes its trajectory in just the right way so that it will travel back in time with the angle required to deliver its younger self this glancing blow. Echeverria and Klinkhammer actually found that there was more than one self-consistent solution, with slightly different angles for the glancing blow in each case. Later analysis by Thorne and Robert Forward showed that for certain initial trajectories of the billiard ball, there could actually be an infinite number of self-consistent solutions.[5]
Echeverria, Klinkhammer and Thorne published a paper discussing these results in 1991;[6] 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. Thus it is plausible that there exist self-consistent extensions for every possible initial trajectory, although this has not been proven.[7] It should be noted, though, that this only applies to initial conditions which are outside of the chronology-violating region of spacetime,[8] which is bounded by a Cauchy horizon.[9] This could mean that the Novikov self-consistency principle does not actually place any constraints on systems outside of the region of spacetime where time travel is possible, only inside it.
Even if self-consistent extensions can be found for arbitrary initial conditions outside the cauchy horizon, the finding that there can be multiple distinct self-consistent extensions for the same initial condition—indeed, Echeverria et al. found an infinite number of consistent extensions for every initial trajectory they analyzed[7]—can be seen as problematic, since classically there seems to be no way to decide which extension the laws of physics will choose. To get around this difficulty, Thorne and Klinkhammer analyzed the billiard ball scenario using quantum mechanics,[10] performing a quantum-mechanical sum over histories (path integral) using only the consistent extensions, and found that this resulted in a well-defined probability for each consistent extension.
