The Alcubierre drive, a theoretical concept for faster-than-light travel, alters the geometry of spacetime, allowing for travel to Alpha Centauri in less than 4.3 years as perceived by observers. However, the distance measured along the path through the warp bubble does not remain invariant; it is indeed less than 4.3 light years due to the ship's worldline being timelike. The discussion emphasizes that while the bubble contracts space ahead, it expands space behind, but this does not negate the overall shortening of distance experienced by the ship. The conversation highlights the necessity of understanding the complex nature of spacetime perturbations and the role of exotic matter in this theoretical framework.
PREREQUISITESPhysicists, theoretical researchers, and science enthusiasts interested in advanced concepts of spacetime, faster-than-light travel, and the implications of general relativity.
And the superluminal velocity with which he did it.PeterDonis said:It's neat that he responded!
Well, with his "normally I don't answer", I wouldn't want to abuse his kindness.PeterDonis said:I would be interested to see his take on the spacetime diagram I mentioned in post #28. I would particularly be interested to see his description of how the Euclidean 3-dimensional spacelike slices he refers to are drawn on that diagram (they would be 1-dimensional spacelike lines on the diagram, which only considers motion in one spatial direction, but that would be sufficient to illustrate his meaning).
I would also be interested in his answer to the issue I have raised several times now: the ship's worldline is timelike, and it takes much less than 4.3 (or 4.1 if we allow for the distance ##d## at the start and end) years for the ship to go from the start point to the end point, so the distance the ship travels must be much less than 4.3 (or 4.1) light years.
There is a comment to be made about this as well. What he means here by "three-dimensional space" is "a surface of constant ##t## in the coordinates in which the metric is standardly written". But while it is true that one can "read off" from his metric, without requiring any calculation, that the metric of such a surface is ##dx^2 + dy^2 + dz^2## (which makes it look like Euclidean 3-space), the intuition that makes us call that surface "three-dimensional space" is that it is a "surface of constant time", i.e., a surface with ##dt = 0##. But for the "warp" case ##v > 1##, the ##t## coordinate is not timelike! That is, ##t## is not a valid "time" coordinate, and surfaces of constant ##t## are not valid "surfaces of constant time".The original metric in my article clearly shows (by construction) that the geometry of three-dimensional space is always perfectly Euclidean.
Yes, I understand that. What I was actually hoping is that someone would be able to find papers in the literature where the issues I have raised are already addressed. Unfortunately I have so far not been able to find any. That is somewhat surprising to me, but it might be that the questions we are discussing have simply not come up in a way that would generate a paper addressing them. "Warp drive" physics is something of a niche field and there might not be many physicists actually taking the time to look at the details.Jaime Rudas said:with his "normally I don't answer", I wouldn't want to abuse his kindness.