Where Do Closed Timelike Curves Go?

[TimeCurtis2289]

OK, I've read a lot of articles on Closed Timelike Curves, and they all say confusing things. Take this part off of Wikipedia for example:

Orbits around high-density objects with extreme gravitational forces are an example of such a closed loop. An object in such an orbit would repeatedly return to the same point in spacetime if it stays in free fall.

And which point in spacetime would that be? I'm starting to get the feeling that going on a Closed Timelike Curve would not send you to a requested time.

That's what I'm confused about. What point in spacetime would the object go to? Would it go to multiple points?

 

[pervect]

OK, I've read a lot of articles on Closed Timelike Curves, and they all say confusing things. Take this part off of Wikipedia for example:

Orbits around high-density objects with extreme gravitational forces are an example of such a closed loop. An object in such an orbit would repeatedly return to the same point in spacetime if it stays in free fall.

And which point in spacetime would that be? I'm starting to get the feeling that going on a Closed Timelike Curve would not send you to a requested time.

That's what I'm confused about. What point in spacetime would the object go to? Would it go to multiple points?

A CTC would be a "time loop", i.e. for instance the fictional idea in "Groundhog day" or "12:01" (if you've seen either of those movies).

However, it seems extremely doubtful that there would be any "memory" of pervious iterations of the loop in reality, unlike in the fictional treatments.

The fictional treatments might correspond best to an almost-but-not-quite closed timelike curve. A true CTC would be totally closed and unable to evolve (at least classically).

 

[Chris Hillman]

If you mention WP, link to the article, but its NOT A RELIABLE SOURCE

Hi, TimeCurtis2289, welcome to PF!

OK, I've read a lot of articles on Closed Timelike Curves, and they all say confusing things.

You should have said: see the Wikipedia article on Closed timelike curve, which reads in part:

Orbits around high-density objects with extreme gravitational forces are an example of such a closed loop. An object in such an orbit would repeatedly return to the same point in spacetime if it stays in free fall.

Sure, that's nonsense: even in regions of spacetimes which do contain some CTCs, most timelike curves (possible world lines) are not closed.

Wikipedia is inherently unstable and unreliable; since I am a former Wikipedian who cofounded what turned into this WikiProject, my criticisms (far too complex and far too OT* to discuss here) cannot be easily dismissed as the product of failure to understand how WP (doesn't) work or as arising from hostility towards the stated goal of Wikipedia.

[*I claim the paragraph above is not at OT as some might think since the OP seems to have implicitly criticized the dubious utility of WP in this thread ]

IMO, you shouldn't ever behave as if you think it might be a reliable source; it is not and most likely never will be. If you are willing to swear a solemn oath that you'll never use WP again, I can elaborate on what pervect said.

(I'm kidding. But only just barely.)

 

[TimeCurtis2289]

OK, I'll admit, Wikipedia was a horrible source to go to. I won't use Wikipedia ever again!

 

[Chris Hillman]

Do you have enough background in gtr to follow a discussion of some specific examples of CTCs in specific exact solutions such as the Van Stockum dust?

 

[TimeCurtis2289]

Do you have enough background in gtr to follow a discussion of some specific examples of CTCs in specific exact solutions such as the Van Stockum dust?

gtr? what's gtr? I'm new to this science thing, I used to be a filmmaker, and I'm using the filmmaker thing as a disguise.

 

[AlphaNumeric2]

GTR = General Theory of Relativity.

 

[TimeCurtis2289]

Yes I read an article that told me about that weird ball and rubber model and another that explains the special relativity theory. I understand both the general theory of relativity and special relativity.

 

[TimeCurtis2289]

well, are you going to explain or not? Sorry if I'm acting impatient.

 

[cristo]

Yes I read an article that told me about that weird ball and rubber model and another that explains the special relativity theory. I understand both the general theory of relativity and special relativity.

That's not really answered Chris' question, though: reading an article "about a weird ball and rubber" is not, I suspect, enough background on which to understand a response. We shall wait and see, however.

 

[TimeCurtis2289]

That's not really answered Chris' question, though: reading an article "about a weird ball and rubber" is not, I suspect, enough background on which to understand a response. We shall wait and see, however.

Basically, I read about the general theory of relativity, and I understood it.

 

[robphy]

Basically, I read about the general theory of relativity, and I understood it.

Can you provide a specific reference to what you have read?

 

[TimeCurtis2289]

Can you provide a specific reference to what you have read?

I read http://archive.ncsa.uiuc.edu/Cyberia/NumRel/GenRelativity.html"

 

[pervect]

I read this article here.

OK, do you know that CTC stands for "Closed Timelike Curve".

I'll assume there's nothing that strikes you as mysterious about a closed curve. (Though perhaps that's a bad assumption. It's not particularly clear to me how to answer "where does a closed curve go?" - does the question even make sense?).

Now, if you know what a closed curve is, and you also know the difference between a timellike and a spacelike curve, I think we're home free and you'll be able to answer your own questions. Otherwise, you might have to ask "what is the difference between a timelike curve and a spacelike one?".

 

[TimeCurtis2289]

Now, if you know what a closed curve is, and you also know the difference between a timellike and a spacelike curve, I think we're home free and you'll be able to answer your own questions. Otherwise, you might have to ask "what is the difference between a timelike curve and a spacelike one?".

Yeah, it's an object's worldline that turns into a loop. Like tiing the two ends of a string together.

 

[pervect]

Yeah, it's an object's worldline that turns into a loop. Like tiing the two ends of a string together.

Yep, the worldline of an object is an example (one of the best examples) of a timelike curve. And if you have an actual object that follows a particular CTC, the object's worldline would be a closed curve.

While there is certainly a lot more to GR than "rubber sheets", you seem to have a perfectly good understanding of what a CTC is.