wormholes and causality violations

[insane_alien]

i'm going through a bit of a stargate obsession phase just now and i was reading up about wormhole on the web. nearly every site(well, sites that actually correspond to the physics we all know and love) says that a wormhole violates causality because the information arrives before it is sent.

now, i've thought about this and done some maths and i must be missing something because i can't figure out how that would happen.

 

lets say we have a colony on some planet around alpha centauri and we've either discovered or made a wormhole. and we'll say c=300000000 ms^-1 to keep the math simple.

 

normal radio communication would require 4 years to reach the colony and another 4 for you to get the reply. now, if you use a wormhole of say 300000000 m then the radio waves would take just over a second to get there (assuming a distance between transmitter and wormhole entrance) so it would be like talking to somebody on the moon(roughly). so, how does this violate causality? the alpha centauri colony doesn't recieve the transmission before earth sent it. if they sent a reply earth wouldn't recieve it before they sent the question.

 

so, what am i missing?

[timo]

In flat spacetime, points whose connection line has a velocity (=direction; velocity in 3D is a direction in 4D, roughly speaking) >c can obtain a reversed time-ordering under Lorentz transformations. Take two points (t1, x1) and (t2,x2) with t2>t1. If their connection line is <=c, then t2>t1 in all frames of reference. If v>c, then there are frames of reference in which t1>t2. So if an event at (t2,x2) is caused by an event at (t1,x1) you have the puzzling effect that some people (in a suitable frame of reference) might see the effect happen before the cause. That´s usually considered as impossible, hence the statement that all dependencies should propagate <=c so that the effect happens after the cause independently of the frame of reference (except for explicit inversion of the time axis, of course).

Now what does this have to do with black holes? I have no idea. Black holes are defenitely not flat space time, hence the argument cannot remain unchanged. I sometimes have the feeling that results from flat spacetime are just carried over to curved spacetime where they, not surprisingly, result in puzzling effects - but it´s also well possible that the argumentation is not related to the causality problem in SR I mentioned above.

 

Two notes on black holes and attempted time-travel scenarios:

1) You can double the spacetime of the black hole solution resulting in a "white hole" on the other side. It´s just a dirty mathematical trick (allowing negative values for a variable whose physical interpretation is a radius) but does not violate any rules other than that it doesn´t seem to make sense. Now, someone had the glorious idea that this new spacetime is just the old one and that you have a double-mapping of spacetime (like if you desribe a circle by letting your angle run from 0° to 720°). In that case, the white hole could be somewhere else in space and you might (after some small modifications to the metric which are not compatible to any known physical processes) find a way to pass from the black side to the white one and effectively taking a shortcut. Taking the shortcut and then completely ignoring that there is a black hole, you could then apply the causality statement from above (which is rather cynical because you just got to your destination so fast because it doesn´t apply) you can then can construct a statement of violating causality.

2) In above, I spoke of nonrotating, noncharged black holes which is the simplemost case. Rotating black holes have a slightly different spacetime, notably additional singularities called ring singularities. They are slightly different from the main singularity (event horizont). I think ajb somewhere gave a link to a paper about how these singularities might be used for time-travel.