A question about the self consistency principle

[BadgerBadger92]

TL;DR

Sorry if I posted this in the wrong section.

Can you meet yourself through time travel?

I was watching a video from Neil DeGrasse Tyson on time travel. He said you can’t travel back in time to meet yourself. Is this correct or am I misunderstanding this? Explanations would be greatly appreciated.

I know it’s only a hypothesis, but I was wondering about the answer in terms of the self consistency principle.

 

[pervect]

I don't know what Neil DeGrasse Tyson said, but as far as peer reviewed papers go, I'd recommend the "billard ball paper", "Billard balls in wormhole space-times with closed timelike curves", https://pages.uoregon.edu/imamura/FPS/images/PhysRevD.44.1077.pdf

The result is interesting - in the context of your question, there isn't any paradox in a classical billard ball going back in time and colliding with itself. Rather, it generates an infinte number of solutions where one might expect only one. This relates to what is called the "Cauchy" problem.

 

[pervect]

To add a bit to my previous post to attempt to motivate reading the paper by demonstrating relevance, the wormhole time machine is set up in a way that attempts to mimick the grandfather paradox with billard balls. In the grandfather paradox, you go back in time and shoot your grandfather so you can't be born - in the billard ball revision, you set up a situation where the billard ball will travel back in time and collide with itself in such a way that it can't pass through the wormhole.

But it turns out there are solutions, rather similar to the usual time-travel stories, where the billard ball collides with itself with a glancing blow, enough to deflect it from it's path so that it does not stop itself from going through the wormhole, but rather hits itself with a glancing blow, a self-consistent solution. And, interestingly enough, the authors found an infinite number of such solutions, which says some things about the mathematics of initial value problems around time machines.

 

[Ibix]

I would say it depends very much on what limitations you're putting on yourself. You can write down solutions to Einstein's field equations that include closed timelike curves and paths "near" those curves allow you to meet your past self, as pervect has described in some detail.

However, such solutions tend to require negative energy densities in order to exist which we've never seen. We suspect they can't exist. So you probably can't have the kind of spacetime where the above is possible.

So you can get different answers on this one, depending on whether you think of the kind of thing pervect describes as realistic or not.