(where Thorne taught), arrived at a solution to the problem that managed to avoid any inconsistencies. 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. This blow alters its trajectory by just the right degree, meaning it will travel back in time with the angle required to deliver its younger self the necessary 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 situation. 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. Echeverria, Klinkhammer, and Thorne published a paper discussing these results in 1991; 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. This only applies to initial conditions outside of the chronology-violating region of spacetime, which is bounded by a Cauchy horizon. 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. 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—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, 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. The authors of "Cauchy problem in spacetimes with closed timelike curves" write: Assumptions The Novikov consistency principle assumes certain conditions about what sort of time travel is possible. Specifically, it assumes either that there is only one timeline, or