Could an observer prove he is in a CTC?

[Passionflower]

I think an interesting question is: could an observer prove he is in a CTC?

Intuitively I would think the answer is no.

But I am interested in proofs, conjectures or opinions.

[bcrowell]

In general, I would expect that any property of spacetime that is invariant under diffeomorphisms would be observable. Since the fact that CTCs exist through a given point P is invariant under diffeomorphisms is diff-invariant, I would think that the answer to your question would be yes.

As a method of checking, I suppose you could sent out a cloud of test particles from P in all directions in P's future light cone. Let's say that these test particles consist of glass bottles with notes inside addressed to yourself. If some of them arrive very close to P, just as you're sending them, then P has CTCs through it.