I think my "blogicidal tendencies", the weird habit of ending and restarting this blog, might one day require deeper analysis, perhaps using Freud's concept of Todestrieb, usually translated as "death wish". Or one could understand it as an example of the "halting problem" - not even the author can determine with certainty if and when this blog will halt ...
But this blog post is really about something else - the possible existence of closed timelike curves (CTC).
Hawking famously proved that CTCs within classical general relativity require either ...
a time machine of infinite size (example: Tipler cylinder) or
exotic matter, violating the weak energy condition (example: wormholes) or
a (naked) singularity (example: Bonnor metric) or
they are hidden behind a horizon (example: Kerr metric). (*)
As far as I know, cosmic censorship prohibiting naked singularities is still an open question (with several examples and counterexamples) and the question if quantum field theories obey the weak energy condition is not settled either. Furthermore, the existence of CTCs would still be unsettling even if "hidden" behind horizons; a brave observer, willing to plunge e.g. into a large rotating blackhole, perhaps motivated by a "death wish", would be able to experience them.
Therefore an important question is how CTCs would change computability theory and fortunately Scott has already some answers. Spoiler alert: He talks about the "halting problem".
(*) S. Hawking, Phys. Rev. D46, p. 603; F. Tipler, Phys. Rev. D9, p. 2203; W. Bonnor, Class. Quant. Grav. 19 (2002), p.5951
added later: There is an interesting proposal of a time machine by Amos Ori, but I have to admit that I do not understand (yet) how exactly he circumvents the Hawking result (see also this and that).
In case you wonder, yes an exact string theory model of CTCs has been investigated and this "may also support the possibility that CTCs may be viable in some physical situations".
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