Wormholes and time travel paradoxes

[jack]

I posted a short version of this, but I feel a longer version may get more comprehensive answers. I'm sure I remember a conversation that came to a conclusion once long ago, but not the details.

Suppose you have a stationary wormhole allowing FTL travel. If you can move one end of the wormhole to the other, you get plenty of time travel paradoxes, because the two ends will no longer be synchronised in time -- the one that's travelled will have experienced a shorter journey time, so when they're next to each other, someone entering the other one will exit from that one earlier, opening the question of "can they prevent themselves entering the wormhole".

But suppose you *don't* move the ends of the wormhole. I *think* that FTL + general relativity[1] must mean there's a time travel paradox somewhere for someone. Maybe someone travelling very fast relative to your wormholes? But for whom?

[1] I believe Stellaris DOES have time travel hidden somewhere but in general doesn't try to stay faithful to general relativity :)

Comments

[damerell]

http://www.theculture.org/rich/sharpblue/archives/000089.html is my go-to explanation of it. The important point is that FTL+relativity necessarily implies causality violation; it doesn't matter how the FTL is done, which cuts off at the pass nonsense like Alcubierre "drives".

[jack]

Ah, thank you! That does seem like the explanation I think I remember.

Reading it slowly, I guess what I'm now wondering is, if you have ansibles which only work in one reference frame (say, at rest compared to most of the nearby mass, to get as close to the implicit rules space opera usually assumes this sort of thing works with), can you still construct a paradox? I guess so, if one leg of the triangle in their diagram was someone travelling the slow way, but I'm not sure.

I'm also not sure if I'm confident demonstrating the existence of paradoxes *disproves* FTL. It means we can't dodge the question. But while it does feel suggestive that this will never happen, the explanations "the universe will just never have loops like that" and "if a paradox would occur it just works in some way we haven't figured out yet" both sound plausible to me.

[damerell]

I don't think that helps - I can stick all of ABCD on planets of their own which are moving in the desired fashion. All ansible communication happens between pairs which are at rest relative to each other, and every ansible is at rest relative to the local lump of mass. (We can't get out of this one by saying the local centre of mass moves as C passes B, because they can easily talk at lightspeed over a moderately long distance such that B's planet's gravity doesn't do much at C and vice versa).

If all ansibles only work in _one_ frame, they all must be at rest relative to each other, we've already thrown out relativity because we have a preferred frame of reference - something's special about being stationary relative to the other ansibles.

The thing about causality violation is that not only do we have no evidence it's happened, but it doesn't even have to have happened yet. I'm content enough to say that something is impossible based on our current understanding and observations, because outside of pure maths that's always what "impossible" means.

If one of relativity and causality is going to give way, my money would be on relativity, which at least looks a little shaky around the edges with all this spooky dark matter floating about when we can't see or touch it.