Non-Moving Wormhole & Moving Observer: Paradoxes?

[vemvare]

I've recently come across the claim that if the mouths of a hypothetic wormhole don't move in relation to each other, then paradoxes in the form of closed timelike curves cannot be demonstrated to occur, even if an observer moves at relativistic speed relative to them.

Is this true? I want to be able to graph this, but I don't know how to insert the observer itself to see if it can create paradoxes (as opposed to just seeing things as happening in reverse, which is easily demonstrated), rather than it's relativistic timeframe.

(Do ignore the obvious question how the wormhole mouths got to be in different places. )

 

[bcrowell]

I've recently come across the claim that if the mouths of a hypothetic wormhole don't move in relation to each other, then paradoxes in the form of closed timelike curves cannot be demonstrated to occur, even if an observer moves at relativistic speed relative to them.

Several points need clarification here.

1) The discussion of observers is irrelevant. The existence or nonexistence of CTCs in a spacetime has nothing to do with observers.

2) Where did you find this claim? Has it been stated somewhere in exact language?

3) Which of the following are they claiming? (a) It is possible to write down a metric for a spacetime in which there is a wormhole, the mouths don't move, and there are no CTCs. (b) Given a state with a wormhole, it can't be manipulated in order to form CTCs.

Statement 3b would be false: Morris, Thorne, and Yurtsever, "Wormholes, time machines, and the weak energy condition," Phys Rev Lett 61 (1988) 1446 .

 

[vemvare]

1. Then how do you see if there is a CTC? I'm a beginner in the field and I've only quite recently understood why the most basic form of CTC's even occur, by drawing lines in Minkowski diagrams. One thing I've even more recently begun to perhaps understand is that relativity seems to be explainable by a wider range of models/metrics, so that observable relativistic effects can be shown to occur, and what happens when/if c is in some way exceeded is depends on the model used.

2. Modern hard-sf trope. Naturally I have no a great ability to distinguish between informed and uninformed claims as I'm not informed myself. As in "reviewed papers", no, not that I know of.

3. I will look at this paper, see if I can make some sense out of it. I'm sorry that I didn't reply earlier, when someone takes the time to reply to my "noobish" question I feel I should. Well, I'm currently studying mechanics, so, I'll get there eventually :)

 

[PeterDonis]

how do you see if there is a CTC?

Whether or not CTCs are present is a geometric fact about the spacetime. You check it by looking at the geometry, which means looking at the mathematical description of the spacetime.

relativity seems to be explainable by a wider range of models/metrics

This is not really the right way to state it. What I think you mean is that there are a wide range of models/metrics that are solutions to the Einstein Field Equation, which is the central equation of General Relativity. This is true, and some of those solutions have CTCs in them, others don't. bcrowell's questions #3a and #3b are asking about particular types of solutions.

what happens when/if c is in some way exceeded

I'm not sure why you bring this in. CTC stands for closed timelike curve; that means an observer can have that curve as his worldline while always moving slower than $c$.