I agree with your assessment, but you're still missing my point. Following your analogy, what I'm saying is not that 1+1=3, but that we're not really using the plus operator here.
I think we both agree that wormholes do not violate causality. By creating a wormhole, you are connecting two points in space with a shortcut. As a result, traveling through a wormhole is not even FTL -- there are two paths to the destination and the shorter path is so much shorter that you can beat light that goes on the longer path. You would still lose to light if light also took the shortcut.
That's essentially what I'm arguing -- that the Alcubierre drive somehow warps space so that if you're traveling in one, you're not actually going faster than light, but through a makeshift wormhole. It isn't FTL.
Highly unlikely to be realistic, but the premise still obeys causality.
Can I talk to you offline? How can I message you on this forum?
I feel like I'm missing something. The FAQ defines FTL as "getting to a location faster than light" but what if light is taking a suboptimal path? Assuming wormholes exist, depending on your frame of reference, it would take light different times to get to the destination.
The FAQ says to consider the case of someone shooting a bullet through a wormhole and killing someone faster than light could have transmitted that information through the long way. I don't see how it's a problem. The light would have also traveled through the wormhole and it would have been possible to know that information. I guess my point is, with the wormhole, the "correct" distance between A and B is no longer the long way.
The way it sounds to me, it's as if I shot a bullet straight at someone at 0.99999c and it killed him, but now you're saying that violates causality because of this star that is between you and the victim and it would have taken light longer to traverse around the star than my bullet.
Special Relativity only applies if the space between A and B is relativity flat. As long as space is flat in the vicinity, then the predictions of Special Relativity hold true. It doesn't matter if you made some weird topological wormhole that provides a shorter path. If Special Relativity has shown you how to, for instance, make a closed causal curve in the flat part of the space, using the events that occur in the flat part of the space, then SR will be correct in that prediction. The fact that there are non-flat parts of space elsewhere that were used to facilitate the aforementioned events in the flat part, is irrelevant to SR.
If, on the other hand, you are talking about cosmological wormholes that might let you travel some place that is far, far away--e.g., outside our Hubble sphere--then Special Relativity might not apply. For instance if the reason we can have a wormhole is because
space ever-so-slowly curves back onto itself, and there ends up being a short little bridge between two pieces of the universe that turn out to be very close to each other in the space that encloses our 3D space, but far away when measured as an ant crawls within our space, then Special Relativity won't be of use because the space between A and B is not flat. But in that case, GR lets you violate causality with such wormholes, even if you can no longer analyze the issue with SR:
You can write to me at doug at alum.mit.edu, but I can't provide much deep insight to GR, as my knowledge of it isn't much more than that of a knowledgeable layperson. I only really understand SR and when it can be applied.
I think we both agree that wormholes do not violate causality. By creating a wormhole, you are connecting two points in space with a shortcut. As a result, traveling through a wormhole is not even FTL -- there are two paths to the destination and the shorter path is so much shorter that you can beat light that goes on the longer path. You would still lose to light if light also took the shortcut.
That's essentially what I'm arguing -- that the Alcubierre drive somehow warps space so that if you're traveling in one, you're not actually going faster than light, but through a makeshift wormhole. It isn't FTL.
Highly unlikely to be realistic, but the premise still obeys causality.