Closed Time-Like Curves: Principles & Observations

[Paul Colby]

Hi,

If I understand correctly, closed time like curves (CTC) are world lines that close upon themselves. What would an observer measure to demonstrate a CTC?

 

[Sorcerer]

I looked this up and what I found suggest that this probably doesn't have a suitable B level answer.

I did find this thesis:

The Cauchy Problem in Spacetimes With Closed Timelike Curves

 

[Paul Colby]

Thanks for the reference. Not certain how it relates to potential experiments which might demonstrate a CTC. Seems to me that one would have to demonstrate events which reoccur or a related phenomena that implies such which itself would have to be reoccurring. Wouldn't showing reoccurrence imply memory or records of past events? Maybe this is the point we mumble something obscure about QM and move along.

 

[Grinkle]

Wouldn't it require something very obvious and easily observable to be causing the curve to exist, like a wormhole?

 

[Paul Colby]

Wouldn't it require something very obvious and easily observable to be causing the curve to exist, like a wormhole?

Sure, but I think this side steps the question I really want to ask but find hard to articulate clearly. One may, for example, take a flat Minkowski space-time and impose periodic boundary conditions creating a model with CTC. How would one go about demonstrating or refuting a CTC in such a model when locally it's the same as one without a CTC? In GR events exist as a set and are given labels, coordinates. In practice, an event is only observable when something happens at those coordinates. As this example seems to show, CTC is only an artifact of bad event labeling.

 

[PeterDonis]

One may, for example, take a flat Minkowski space-time and impose periodic boundary conditions creating a model with CTC. How would one go about demonstrating or refuting a CTC in such a model when locally it's the same as one without a CTC?

You would have to find a way of probing the global topology of the spacetime; the CTC version of Minkowski spacetime that you describe is not simply connected, whereas ordinary Minkowski spacetime is simply connected.

As this example seems to show, CTC is only an artifact of bad event labeling.

No, it isn't; the two spacetimes you describe have different topologies and are therefore different manifolds.

 

[Paul Colby]

No, it isn't; the two spacetimes you describe have different topologies and are therefore different manifolds.

They are different manifolds for certain, globally. My use of "locally the same" I believe is correct if I recall my topology classes.

The only observations I can think of that would tell us this would be the non periodic nature of observed events. How would we observe periodic ones if all things are periodic including the experimenter?

You would have to find a way of probing the global topology of the spacetime;

I know of no nonlocal measurements that are not in some way comprised of local ones. So is the answer, no they are not observable?

 

[PeterDonis]

My use of "locally the same" I believe is correct if I recall my topology classes.

Locally you can't tell one topology from another; locally all manifolds look like a small piece of $R^4$ (or $R$ of whatever dimension you are working with).

I know of no nonlocal measurements that are not in some way comprised of local ones.

Comprised of local measurements made at different points in the manifold. Combining the results from such measurements can tell you things that measurements made at just one point in the manifold will not tell you.