What Are Closed Timelike Curves and Common Misunderstandings About Them?

[L Drago]

TL;DR

It is said that in Einstein's relativity it is possible to time travel in past by using CTCs closed time like curves.

Are there any images to show CTC such as many images are available in Google to show curvature of general relativity. As far as I understand two points of space time fabric are curved and joined . If we travel from one point to future we will again come back to the same point and now we are in past. But we will be stuck in a loop.

Please point out what misunderstanding I have and give some authentic articles to learn about CTCs

 

[martinbn]

Did you search for such images and articles?

 

[L Drago]

Did you search for such images and articles?

I searched got random images and the closest one of space time fabric I got was of a wormhole. Please kindly point out what I am misunderstanding in my thread summary.

 

[Ibix]

Closed timelike curves aren't really time travel. A timelike curve is the type of path any particle with mass follows through spacetime. A closed one is one that forms a loop, so its past is also its future. They are not possible in general, only in some solutions of Einstein's field equations that happen to allow them in some regions. And the existence of closed timelike curves makes it difficult to define "past" and "future" in such solutions, since the causal future and causal past overlap.

There are closed timelike curves in the interior of Kerr black holes. They're probably an artefact of general relativity going wrong, so probably they don't exist in real black holes, only in our models.

Be wary of images purporting to "show" curvature. Most are plots of Flamm's paraboloid, which is an embedding of a spacelike plane and has very little to do with gravity.

 

[L Drago]

Closed timelike curves aren't really time travel. A timelike curve is the type of path any particle with mass follows through spacetime. A closed one is one that forms a loop, so its past is also its future. They are not possible in general, only in some solutions of Einstein's field equations that happen to allow them in some regions. And the existence of closed timelike curves makes it difficult to define "past" and "future" in such solutions, since the causal future and causal past overlap.

There are closed timelike curves in the interior of Kerr black holes. They're probably an artefact of general relativity going wrong, so probably they don't exist in real black holes, only in our models.

Be wary of images purporting to "show" curvature. Most are plots of Flamm's paraboloid, which is an embedding of a spacelike plane and has very little to do with gravity.

 

[L Drago]

This means a loop is created in Ctc. I don't trust pop Sci images they are showing wormholes and not pointing out exactly CTC which I was asking. That's why I asked in forum.

 

[javisot20]

The fact is that we have Einstein's equations, I suppose you are familiar, these equations have many qualities, but among all the ways to divide those solutions you can think of "physical solutions" and "non-physical solutions. A physical solution meets all the energy conditions, unlike a non-physical solution that fails one, several, or all the energy conditions. The ctc's are among non-physical solutions.

Think of a system that evolving into the future (not unusual), eventually ends up reaching a configuration in its past.

 

[L Drago]

The fact is that we have Einstein's equations, I suppose you are familiar, these equations have many qualities, but among all the ways to divide those solutions you can think of "physical solutions" and "non-physical solutions. A physical solution meets all the energy conditions, unlike a non-physical solution that fails one, several, or all the energy conditions. The ctc's are among non-physical solutions.

Think of a system that evolving into the future (not unusual), eventually ends up reaching a configuration in its past.

Yeah I have thought that suppose we are walking from present forward as it is a circular loop we keep walking towards the future but again reach our then present which is now our past. Hence, I think we will be forever stuck in this loop.

 

[PeterDonis]

Yeah I have thought that suppose we are walking from present forward as it is a circular loop we keep walking towards the future but again reach our then present which is now our past. Hence, I think we will be forever stuck in this loop.

This is basically how a CTC works, yes.

For an extreme example of a spacetime with CTCs, look up the Godel universe. It has a CTC through every single event.

 

[L Drago]

This is basically how a CTC works, yes.

For an extreme example of a spacetime with CTCs, look up the Godel universe. It has a CTC through every single event.

Means I can search for Godel universe in Google. Hope I am not mislead Ed by pop Sci in Google again

 

[L Drago]

Means I can search for Godel universe in Google. Hope I am not mislead Ed by pop Sci in Google again

This is basically how a CTC works, yes.

For an extreme example of a spacetime with CTCs, look up the Godel universe. It has a CTC through every single event.

Thank you for the suggestion

 

[PeterDonis]

Means I can search for Godel universe in Google. Hope I am not mislead Ed by pop Sci in Google again

The Wikipedia article on the Godel metric is a decent starting point:

https://en.wikipedia.org/wiki/Gödel_metric