Time Travel, General Relativity & Information Paradoxes

In summary: The Tipler cylinderIn summary, 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.
  • #1
PreposterousUniverse
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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.
 
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  • #2
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).
 
  • #3
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.
 
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But wouldn't such a casual loop violate the principle of conservation of information? If the information has no source?
 
  • #5
Ibix said:
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.
 
  • #6
PreposterousUniverse said:
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.
 
  • #7
PreposterousUniverse said:
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.

Dale said:
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.
 
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  • #8
Vanadium 50 said:
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).
 
  • #9
PeterDonis said:
The Godel universe
But doesn't that have a negative cosmological constant?
 
  • #10
Vanadium 50 said:
doesn't that have a negative cosmological constant?
Yes. Or you can consider that as part of the stress-energy tensor.
 
  • #11
Vanadium 50 said:
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.
 
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FAQ: Time Travel, General Relativity & Information Paradoxes

What is time travel and is it possible?

Time travel is the concept of moving between different points in time, either into the past or the future. While it has been a popular topic in science fiction, it is still a highly debated topic in the scientific community. According to the theory of general relativity, time travel may be possible in certain scenarios, such as traveling at the speed of light or near a black hole. However, it is currently not possible with our current technology and understanding of physics.

How does general relativity relate to time travel?

General relativity is a theory of gravity that describes the relationship between space and time. It is the basis for understanding the concept of time dilation, which is the idea that time can pass at different rates for objects in different gravitational fields. This is important in the context of time travel because it suggests that time can be manipulated by altering the gravitational field around an object.

What is the information paradox and how does it relate to time travel?

The information paradox is a theoretical problem that arises when considering the possibility of time travel. It is based on the idea that if time travel were possible, it would be possible to send information back in time, potentially creating a paradox. For example, if someone were to go back in time and prevent their own birth, it would create a paradox because they would not exist to go back in time in the first place. This paradox challenges the idea of causality and raises questions about the consequences of time travel.

Can time travel be used to change the past?

According to current scientific understanding, time travel cannot be used to change the past. This is due to the concept of causality, which states that an event cannot occur before its cause. Therefore, if someone were to go back in time and attempt to change the past, their actions would have already been accounted for in the present. Additionally, the laws of physics, such as the conservation of energy and momentum, would prevent any major changes to the past.

Are there any real-life examples of time travel?

While time travel is currently not possible, there are some real-life examples that demonstrate the effects of time dilation, which is a key concept in the theory of general relativity. For example, astronauts on the International Space Station experience time at a slightly slower rate than people on Earth due to the difference in gravitational fields. Additionally, atomic clocks on airplanes have been shown to run slightly slower than those on the ground, further supporting the concept of time dilation.

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