Novikov self-consistency principle: Difference between revisions

Revision as of 11:24, 16 December 2023

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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 Polchinski's scenario, the billiard ball is fired into the [[wormhole]] at an angle such that, if it continues along its path, it will exit in the past at just the right angle to collide with its earlier self, knocking it off track and preventing it from entering the wormhole in the first place. Thorne would refer to this scenario as "[[Polchinski's paradox]]" in 1994.<ref name = "timewarps">{{cite book | last = Thorne | first = Kip S. | author-link = Kip Thorne | title = [[Black Holes and Time Warps]] | publisher = W. W. Norton | year= 1994 | isbn = 0-393-31276-3}}</ref>{{rp|510–511}}

Upon considering the scenario, Fernando Echeverria and Gunnar Klinkhammer, two students at [[California Institute of Technology|Caltech]] (where Thorne taught), arrived at a solution to the problem, that lays out the same elements as the solution Feynman and Wheeler<ref>{{cite journal | first=John | middle=Archibald | last=Wheeler | first2=Richard | middle2=Phillips | last2=Feynman | title=Classical Electrodynamics in Terms of Direct Interparticle Action | journal = Reviews Of Modern Physics | volume = 21 | year=1949 | issue=3 | pages=425-433}}</ref> termed the "glancing blow" solution, to evade inconsistencies arising from causality loops. 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.<ref name = "timewarps" />{{rp|511–513}}

Echeverria, Klinkhammer, and Thorne published a paper discussing these results in 1991;<ref>{{cite journal | first=Fernando | last= Echeverria |author2=Gunnar Klinkhammer |author3=Kip Thorne | url=http://authors.library.caltech.edu/6469/ | title=Billiard balls in wormhole spacetimes with closed timelike curves: Classical theory | journal = Physical Review D | volume = 44 | year=1991 | issue=4 | doi= 10.1103/PhysRevD.44.1077 | pages=1077–1099| pmid= 10013968 |bibcode = 1991PhRvD..44.1077E }}</ref> 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.<ref name = "earman">{{cite book | last = Earman | first = John | title = Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes | publisher = Oxford University Press |year= 1995 | isbn = 0-19-509591-X}}</ref>{{rp|184}} This only applies to initial conditions outside of the chronology-violating region of spacetime,<ref name = "earman" />{{rp|187}} which is bounded by a [[Cauchy horizon]].<ref>{{cite book | last = Nahin | first =Paul J. | title = Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction | publisher =American Institute of Physics |year= 1999 | pages = 508 | isbn = 0-387-98571-9}}</ref> 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.