Time Travel, General Relativity & Information Paradoxes

[PreposterousUniverse]

General relativity permits some exact solutions that allow for time travel. Some of these exact solutions describe universes that contain closed timlike curves, or world lines that lead back to the same point in spacetime.

I wondered if these solutions also permits Causal loops? Such as the one given as an example by Allan Everett: where one suppose a time traveler copies a mathematical proof from a textbook, then travels back in time to meet the mathematician who first published the proof, at a date prior to publication, and allows the mathematician to simply copy the proof. In this case, the information in the proof has no origin.

 

[Ibix]

I think stable time loops of that variety are permitted, yes. Although (a) it may be the case that "you can't get there from here" and we can't have them in this universe although other spacetimes may allow it, and (b) Hawking proposed the "chronology protection conjecture" which says that GR may allow this but more general theories will prevent it (rather like Newtonian physics allows travel at arbitrary speeds but relativity places it in a larger framework that both forbids faster than light travel and explains why Newtonian physics is OK with it).

 

[Dale]

GR doesn’t describe the generation of proofs, so that is not something that the theory can have an opinion on. GR will neither rule it out nor assert it is possible.

 

[PreposterousUniverse]

But wouldn't such a casual loop violate the principle of conservation of information? If the information has no source?

 

[Vanadium 50]

I think stable time loops of that variety are permitted, yes

I don't know that that's true. They require things like an infinite cylinder. I believe the thinking that a large but finite cylinder will work is not something confirmed by calculation.

 

[Dale]

But wouldn't such a casual loop violate the principle of conservation of information? If the information has no source?

I am not at all sure that information is conserved in such a spacetime.

 

[PeterDonis]

the principle of conservation of information?

The only possible formulation of that principle in GR is that the spacetime geometry is unique for a given solution. The solutions under discussion meet that criterion.

If you want to talk about "information" in the sense that "information theory" uses the term, i.e., in terms of bits, the only physics context in which that concept makes sense is quantum mechanics, since you need QM to explain why there can even be things like bits in the first place. Classical physics cannot explain such a concept.

I am not at all sure that information is conserved in such a spacetime.

I am not sure there is any useful concept of information that can even be formulated in the context of GR other than the one I described above.

 

[PeterDonis]

I don't know that that's true. They require things like an infinite cylinder.

Not all spacetimes with CTCs or closed causal loops in GR require such things. The Godel universe is the best known example of a solution of the EFE that has CTCs but has the same finite stress-energy tensor at every point and is completely regular (no singularities anywhere).

 

[Vanadium 50]

The Godel universe

But doesn't that have a negative cosmological constant?

 

[PeterDonis]

doesn't that have a negative cosmological constant?

Yes. Or you can consider that as part of the stress-energy tensor.

 

[Ibix]

I don't know that that's true. They require things like an infinite cylinder. I believe the thinking that a large but finite cylinder will work is not something confirmed by calculation.

That's the kind of thing I was meaning by "can't get there from here". If we are free to specify arbitrary initial conditions like the Tipler cylinder (an infinitely long cylinder that's always been rotating a constant rate) then we can have CTCs in our model universe. It's not clear that they can exist in the spacetime we see around us, so whether they can exist as anything other than a mathematical toy is an open question.