![]() Echeverria was a student of Thorne at CalTech, and Thorne also gives a popular-level discussion of this idea in ch. ![]() The Echeverria paper discusses some toy models involving billiard balls, and shows that, surprisingly, one does not always get causality violation despite the presence of CTCs. This is very much like the twin paradox the two mouths are no longer synchronized temporally. So you take one mouth, accelerate it away from the other, and then bring it back. The basic idea is that either mouth of the wormhole can be acted on by gravitational forces (I guess in the sense that it has a certain Komar or ADM mass), and therefore you can manipulate it and move it around (at least in theory, if you had the ability to manipulate huge amounts of matter). There are straightforward arguments to the effect that if wormholes are possible, then CTCs are possible as well. The question assumes that going through a wormhole does not involve FTL velocities, but in fact there is simply no way to define what velocity it would be. (3) Because this is GR, not SR, there is no unambiguous way to define the velocity of an object relative to some other, distant object. One of them is if your spacetime has closed timelike curves (CTCs). There are other reasons besides FTL why you can get causality violation. (2) The basic logic is not that causality violation implies FTL, it's that FTL implies causality violation. Therefore there can't be any complete analysis of this problem in special relativity. (1) Wormholes are a type of curved spacetime. And that would be a matter for another question on this site. But that would mean there is a preferred reference frame in the universe. The only way to prevent me from using a wormhole to travel to the past is to make all wormholes exist in the same reference frame and transport objects using that frame's definition of instantaneous. ![]() But what if at point B I find another wormhole travelling in the green frame that links back to x=0? Or what if I found a way of speeding up the other end of the wormhole? Then I could certainly travel back to 2004. Didn't I already establish that the wormhole uses the definition of instantaneous from its own frame the red one? True, I did say that. I start at x=0, I used the wormhole to travel to some point on the x-axis, I speed up (so shift the green frame so that the green origin is on the x-axis at our chosen point), then I return through the wormhole to x=0 except remember I'm travelling along the x'-axis now. Then I get to point B, accelerate to be in the green frame and go back through the wormhole to our point A at x=0. How does this explain how I can send a message back to 2004? Say I have the wormhole, I enter it in the red frame (let's assume that's the Earth frame). Now if I'm in the green frame and enter the wormhole, I travel along the x-axis and the point I end up is actually in my past (trace a line from somewhere on the x-axis back to the ct'-axis that is parallel to the x'-axis, it leads to the past). So you say "well that's simple, the wormhole isn't moving in my frame so it would make use of my definition of instantaneous". Notice that accordingly, that would put me into the red frame's future (we're just looking at the first quadrant). But what if I enter the wormhole travelling fast enough to be in the green frame? In that frame, instantaneous travel is anything along the x'-axis. The wormhole could take you to any point along it. So now ask yourself that question, when is right now? By the red frame, right now is the x-axis. The red axes represent the reference frame we're in and the green axes represent a reference frame at some high velocity relative to ours. No problem right? No violation of causality? Perhaps, but you need to ask yourself "when is right now at point B?" Consider this diagram: A traveller would arrive the same moment they left, spend some time at point B (it's really a nice place the B-ian people are friendly and the food is great), then use the wormhole to go back to point A. How long would it take to get from point A to point B using it? Let's say it's instantaneous.
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