2 ms·

I don't see how this can avoid violating causality. When analyzing this sort of thing, the method by which one travels faster than light doesn't matter at all.

I don't see how this can avoid violating causality. When analyzing this sort of thing, the method by which one travels faster than light doesn't matter at all. Warp drives, hyperspace, or magic carpet, it's all the same. The mere fact that one can do it is sufficient to violate causality. With any method, any method at all, that transmits information or objects faster than light, one can construct a scenario in which Event A precedes Event B in one reference frame but B precedes A in another reference frame. I'm sorry I don't have a brief example to post here, but everything I've ever read about this supports this view. I'd love to be wrong. I grew up looking at the stars from my back yard, watching Star Trek on its first run, and hoping that the stars would be in reach in my lifetime. But the Universe isn't here to please me and if FTL is really impossible, well, I'll live.

DennisP 13y ago
Nobody seems to have poked any holes in the math since Alcubierre first published, and it's not for lack of attention. I'm not sure what they say about causality, but there's been some work suggesting causality doesn't have to be absolute. Imagine a billiard table, with a wormhole that curves and goes three seconds backward in time. You aim a billiard ball through the wormhole, such that it will emerge earlier and knock itself off the path, never entering the wormhole, and creating a paradox. But what actually happens is, the ball emerges on a slightly altered trajectory, striking itself a glancing blow, and the ball enters the wormhole. And why did it emerge with an altered trajectory? Because it was struck a glancing blow. Physicists have worked out some math on this, and haven't managed to find any scenario that results in inconsistency. http://en.wikipedia.org/wiki/Novikov_self-consistency_principle http://en.wikipedia.org/wiki/Novikov_self-consistency_princi...
yk 13y ago
You are confusing special relativity and general relativity. In special relativity you are ( sort of) right. In general relativity you can find shortcuts in the way we measure distances. The trick is, that speed can either denote a local property, as measured by your speedometer, or a global property, that is distance traveled divided by time. And the light speed limit only applies to the local property. So if you can find a spacetime that contains a shortcut, then you can increase the distance traveled faster than the speed of light. ( And there is nothing in general relativity to stop you, since it only requires you to move locally slower than the speed of light.) An example for this would be a expanding universe ( and for simplicity let me assume that the expansion only starts a some time t1.) So you travel from t0 to t1 with constant velocity v < c. And you are then at some point x=v(t1-t0). Then you stop and expansion sets in. You stay in place at x, as measured relative to some point nearby, but the distance to your original starting point increases, since space itself is expanding. And there is nothing to stop this increase to be faster than the speed of light. The other thing is the "sort of" parenthesis, the Lorentz transformation is directly linked to the causal structure of special relativity. A statement like "if* you could go faster than the speed of light, then you could violate causality" is somewhat nonesensical, since if you could go faster than the speed of light, then you would break local Lorentz invariance and therefore you break your very definition of causality.
- rootbear 13y ago
  Thank you for explaining the GR vs SR aspect of this. I was somewhat aware that the no-FTL rule was different in GR but I didn't really understand how. I'll have to look into this more and now I know where to start. I'm not sure I follow the second part, about Lorentz invariance, but my physics is decades old, so that's not surprising. Time to do more reading.
  - yk 13y ago
    Sorry for the botched formatting (HN is for some reason not showing me a edit link :/ ) A quite interesting paper on the topic is McMonigal & al. [1], it is a bit technical but they discuss the Alcubierre warp drive quite nicely. To elaborate on the second paragraph about special relativity, one way to define Lorentz transformations is, that they are the transformations which preserve the causal structure of Minkowsky space. On the other hand, the speed limit is a direct consequence of the Lorentz transformations. So the causal structure and the speed limit are directly related. To look again at the argument that a velocity larger than the speed of light implies causality violation: The moment you argue that a speed faster than the speed of light is possible, you implicitly change the meaning of causality. Then you use the Lorentz transformations to conclude that in on frame of reference event A precedes B and that event B precedes A in another. So you first deny the special status of the Lorentz transformation, just to go on and use Lorentz transformations. And my take on this is a strong maybe, the moment you start talking about local Lorentz invariance violation, anything goes. Perhaps there is causality violation, perhaps not, but this depends on your specific meaning of 'causality' and 'faster than light' and not very much on special relativity. [1] http://arxiv.org/abs/1202.5708 http://arxiv.org/abs/1202.5708

DennisP 13y ago

Nobody seems to have poked any holes in the math since Alcubierre first published, and it's not for lack of attention. I'm not sure what they say about causality, but there's been some work suggesting causality doesn't have to be absolute. Imagine a billiard table, with a wormhole that curves and goes three seconds backward in time. You aim a billiard ball through the wormhole, such that it will emerge earlier and knock itself off the path, never entering the wormhole, and creating a paradox. But what actually happens is, the ball emerges on a slightly altered trajectory, striking itself a glancing blow, and the ball enters the wormhole. And why did it emerge with an altered trajectory? Because it was struck a glancing blow. Physicists have worked out some math on this, and haven't managed to find any scenario that results in inconsistency. http://en.wikipedia.org/wiki/Novikov_self-consistency_principle http://en.wikipedia.org/wiki/Novikov_self-consistency_princi...

yk 13y ago

You are confusing special relativity and general relativity. In special relativity you are ( sort of) right. In general relativity you can find shortcuts in the way we measure distances. The trick is, that speed can either denote a local property, as measured by your speedometer, or a global property, that is distance traveled divided by time. And the light speed limit only applies to the local property. So if you can find a spacetime that contains a shortcut, then you can increase the distance traveled faster than the speed of light. ( And there is nothing in general relativity to stop you, since it only requires you to move locally slower than the speed of light.) An example for this would be a expanding universe ( and for simplicity let me assume that the expansion only starts a some time t1.) So you travel from t0 to t1 with constant velocity v < c. And you are then at some point x=v(t1-t0). Then you stop and expansion sets in. You stay in place at x, as measured relative to some point nearby, but the distance to your original starting point increases, since space itself is expanding. And there is nothing to stop this increase to be faster than the speed of light. The other thing is the "sort of" parenthesis, the Lorentz transformation is directly linked to the causal structure of special relativity. A statement like "if* you could go faster than the speed of light, then you could violate causality" is somewhat nonesensical, since if you could go faster than the speed of light, then you would break local Lorentz invariance and therefore you break your very definition of causality.

rootbear 13y ago
Thank you for explaining the GR vs SR aspect of this. I was somewhat aware that the no-FTL rule was different in GR but I didn't really understand how. I'll have to look into this more and now I know where to start. I'm not sure I follow the second part, about Lorentz invariance, but my physics is decades old, so that's not surprising. Time to do more reading.
- yk 13y ago
  Sorry for the botched formatting (HN is for some reason not showing me a edit link :/ ) A quite interesting paper on the topic is McMonigal & al. [1], it is a bit technical but they discuss the Alcubierre warp drive quite nicely. To elaborate on the second paragraph about special relativity, one way to define Lorentz transformations is, that they are the transformations which preserve the causal structure of Minkowsky space. On the other hand, the speed limit is a direct consequence of the Lorentz transformations. So the causal structure and the speed limit are directly related. To look again at the argument that a velocity larger than the speed of light implies causality violation: The moment you argue that a speed faster than the speed of light is possible, you implicitly change the meaning of causality. Then you use the Lorentz transformations to conclude that in on frame of reference event A precedes B and that event B precedes A in another. So you first deny the special status of the Lorentz transformation, just to go on and use Lorentz transformations. And my take on this is a strong maybe, the moment you start talking about local Lorentz invariance violation, anything goes. Perhaps there is causality violation, perhaps not, but this depends on your specific meaning of 'causality' and 'faster than light' and not very much on special relativity. [1] http://arxiv.org/abs/1202.5708 http://arxiv.org/abs/1202.5708