What remains of the killing-your-earlier-self paradox in general
relativistic time travel worlds is the fact that in some cases the
states on edgeless spacelike surfaces are ‘overconstrained’, so that one
has less than the usual freedom in specifying conditions on such a
surface, given the time-travel structure, and in some cases such states
are ‘underconstrained’, so that states on edgeless space-like surfaces
do not determine what happens elsewhere in the way that they usually do,
given the time travel structure.
There can also be mixtures of those
two types of cases. The extent to which states are overconstrained
and/or underconstrained in realistic models is as yet unclear, though it
would be very surprising if neither obtained. The extant literature has
primarily focused on the problem of overconstraint, since that, often,
either is regarded as a metaphysical obstacle to the possibility time
travel, or as an epistemological obstacle to the plausibility of time
travel in our world. As we have discussed, using responses and
counterresponses, it is not entirely clear that it is indeed an
epistemological or a metaphysical obstacle.
It is true that our world
would be quite different from the way we normally think it is, if states
were overconstrained given the time travel structure. If anything,
underconstraint seems even more bizarre to us than overconstraint.
However, time travel is quite strange to begin with, and it does not
appear to be a terribly strong additional argument against time travel
that it has strange consequences.
Source:
http://plato.stanford.edu/entries/time-travel-phys/#4
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