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I am looking for some fresh references on the Chronology Protection Conjecture. I am aware of this question, but the answer there seems to resort to energy conditions. But, weren't they shown violated in QFT, even in averaged format?

I heard physicists are mostly "uncomfortable" with CTCs (right?). What is currently the most accepted "working hypothesis" which prevents CTCs?

Some mathematical details would be much appreciated as I am a mathematician.

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Dismissing all closed timelike curves from just physical arguments is hard since a lot of them are fairly benign (such as the classic timelike cylinder where two spacelike hypersurface of a globally hyperbolic spacetime are identified), but those are usually not considered very problematic since you can always just go to the universal cover without issues. Other spacetimes with non-compact chronology violating regions can also be fairly benign and are harder to disprove, short of finding out initial conditions for the universe.

The common type of CTCs argued against are the ones which can be constructed by experiment, so-called compactly generated chronology horizons. Chronology horizons are as you may know a type of Cauchy horizon leading to a chronology violating region, and a chronology horizon is compactly generated if its null generators remain in a compact region of spacetime at some point in the past (this usually means that they all stem from some closed null geodesic, called a fountain).

It has been shown [1] that, in a compactly generated Cauchy horizon, there are points called base points which are past terminal accumulation points of the null generators (either points on the closed null geodesics or accumulation points if the spacetime is causal but has imprisoned curves). In such a case, the Klein-Gordon equation is singular at those points, which leads the stress-energy tensor to be divergent.

This is the current big argument for chronology protection : in such cases, the perturbation to the vacuum is such that the stress-energy tensor diverges, so that the solution is meaningless : obviously such a thing would disrupt the solution before the formation of a time machine.

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  • $\begingroup$ "While the KRW theorem is undoubtedly of fundamental importance for semi-classical quantum gravity, it does not serve as an effective no-go result for Thornian time machines ... The KRW theorem functions as a no-go result by providing a reductio ad absurdum with a dubious absurdity: roughly, if you try to operate a Thornian time machine, you will end up invalidating semi-classical quantum gravity." -- from the Stanford Encyclopedia. Vesser's fresher work also claims semi-classical arguments are not enough for a valid no-go result. On the other hand ... [cont.] $\endgroup$ – Rubi Shnol Oct 16 '18 at 13:07
  • $\begingroup$ ... don't CTCs actually lead to a whole variety of peculiar phenomena such as hypercomputation, perpetuum mobile, etc.? $\endgroup$ – Rubi Shnol Oct 16 '18 at 13:08
  • $\begingroup$ CTCs don't allow for hypercomputations unless you also allow for other fairly unphysical things (such as infinite memory). And yes, the story may be different with quantum gravity, but as far as I'm aware I can't think of any paper on the topic of chronology violation when gravity is quantized. $\endgroup$ – Slereah Oct 16 '18 at 13:11
  • $\begingroup$ How about unbounded energy growth (since conservation is violated)? Or is this case ruled out by consistency? Also, can you give a comment on my citation of the Stanford Encyclopedia? Furthermore, Visser mentioned some QG approaches where causality is preserved, such as causal sets and lattice GQ. $\endgroup$ – Rubi Shnol Oct 16 '18 at 15:26
  • $\begingroup$ Conservation of energy is no more violated in a causal spacetime than in an acausal one (some spacetimes with CTCs even have timelike Killing vectors). The effect to look out for is runaway blueshifting near the chronology horizon, which can be avoided with appropriate initial conditions but not once quantum effects are taken into account. And most QG approaches are causal, yes, since they're built from quantum formalisms in which causality is assumed as an axiom. For a few of them (such as string theory or covariant quantum gravity), chronology protection is unknown. $\endgroup$ – Slereah Oct 18 '18 at 11:52

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