Even though there is no experimental evidence, that the Alcubierre drive works. The Einstein field equations permit this solution. For Gravitoelectromagnetism there are hints and ongoing efforts to test those hypotheses. See the up to date wikipedia articles on the Alcubierre Drive and Gravitoelectromagnetism. But whether there will or won't be experimental evidence does not matter for my question. My question is: Are the approximate Gravitoelectromagnetism equations sufficient to explain the Alcubierre Drive?
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$\begingroup$ If one could explain the Alcubierre Drive with the familiar looking Gravitoelectromagnetism equations, that would be awesome. One reason why that might not be the case, is that in electromagnetism there does not exist, to my knowledge any similar concept. All of this is highly speculative, because at least for the Alcubierre Drive there is no experimental evidence so far. $\endgroup$– v217Commented Jan 2, 2015 at 10:38
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2$\begingroup$ Like I said, it doesn't matter which theory you use to break momentum conservation in. It's plain false in all of them. $\endgroup$– CuriousOneCommented Jan 2, 2015 at 10:42
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$\begingroup$ @CuriousOne the conservation of momentum follows from translation invariance. If you break translation invariance, conservation of momentum goes too. Isn't that exactly what the Alcubierre drive is doing by deforming spacetime? $\endgroup$– John DvorakCommented Jan 2, 2015 at 11:13
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$\begingroup$ GR without gravitational waves is completely identical to Newtonian gravity in the far field, so the internal structure of the bubble shouldn't play any role for an observer who is far enough away. Such an observer can measure the center of mass of any volume of space the bubble moves in. If the bubble moves real mass, the center of mass has to move (at any velocity!). That, of course, can not happen unless momentum conservation is violated or unless the drive produces e.g gravitational waves to make up for that... but those can only travel at c! $\endgroup$– CuriousOneCommented Jan 2, 2015 at 11:22
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It isn't obvious to me why there should be any relationship between the Alcubierre Drive and gravitoelectromagnetism. The Alcubierre drive is a valid solution provided you can lay your hands on some exotic matter, but then if you have a stock of exotic matter to hand all sorts of problematic solutions to GR are possible. The conclusion that most of us draw is that while exotic stress-energy tensors can be written down, they don't correspond to physical reality. It's like putting a negative mass into Newton's equations - it can be done, but you won't get any meaningful output. Anyhow, gravitomagnetism isn't required.
answered Jan 2, 2015 at 11:16
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1$\begingroup$ 1st: Gravitomagnetism is certainly not required. (The Alcubierre drive is a child of the Einstein Field Equations.) The question was motivated by the idea that the Acubierre drive might be easier to understand, if explained within the framework of Gravitomagnetism. $\endgroup$– v217Commented Jan 2, 2015 at 12:25
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2$\begingroup$ @user22207: no, the Alcubierre drive is already easy to understand - as metrics go it's a pretty simple one - and I know of no way to simplify it farther. The problem is understanding even simple metrics requires a conceptual leap that requires a lot of work. If you're looking for a simple way in then I'm afraid there isn't one. The good news is that the effort is worth it when the light finally dawns. $\endgroup$ Commented Jan 2, 2015 at 12:29
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$\begingroup$ 2nd: The experiments done at Nasa to search for experimental evidence for the Alcubierre drive did not need the concept of "exotic matter". en.wikipedia.org/wiki/… $\endgroup$– v217Commented Jan 2, 2015 at 12:33
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$\begingroup$ @user22207: (1) NASA is an abbreviation, capitals are required (2) the experiment you refer to is inconclusive. $\endgroup$ Commented Jan 2, 2015 at 15:24
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$\begingroup$ @user22207: the Alcubierre metric is a straightforward piece of mathematics and is uncontroversial. It requires a stress-energy tensor that contains exotic matter. Sonny White and co have hypothesised that if the universe contains extra dimensions then the curvature caused by a suitably chosen electric field could look like exotic matter in our 4D slice of the higher dimensional spacetime. Their calculations are described in this paper. Most of us would regard their ideas as highly speculative. $\endgroup$ Commented Jan 2, 2015 at 15:35