Talk:Alcubierre metric/Archive 1

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Criticism of May 2005 Version of this Article

This article is seriously misleading in one important respect.

The Alcubierre spacetimes are a certain family of Lorentzian spacetimes, but they are not solutions of the Einstein field equation.

Every Lorentzian manifold has, mathematically speaking, a well-defined Einstein tensor, which you can compute from its Riemann curvature tensor. To be a solution of the EFE, this must agree (up to a certain constant factor) with a physically reasonable matter tensor. Consider two easy examples:

1. vacuum solutions are easy to recognize, since the matter tensor vanishes identically in a vacuum region, so vacuum solutions have purely a mathematical characterization: they are Lorentzian manifolds whose Einstein tensor vanishes (equivalently, whose Ricci tensor vanishes).

2. electrovacuum solutions (no mass-energy other than the field energy of an electromagnetic field) must have Einstein tensors which agree with matter tensors having the form appropriate for an electromagnetic field (as described in Maxwell's theory). Furthermore, their definition must include specifying an antisymmetric second order tensor field Fab, and this must not only satisfy (a curved spacetime version of) Maxwell's equations but must rise to a stress-energy tensor (according to Maxwell's theory, and following some general principles for getting from a field equation to the corresponding contribution to the matter tensor), and of course this stress-energy tensor must match the Einstein tensor computed directly from the Riemann tensor.

There are other kinds of classical fields which one can propose besides classical electromagnetism, and there are other types of solutions which arise from the notion of a perfect fluid or from a nonzero cosmological constant, but AFAIK (and few years ago I read the ENTIRE literature on warp drives) there is no well-defined classical field theory which gives contributions to the matter tensor which could match the Einstein tensor of a nontrivial Alcubierre spacetime.

Put in other words: in principle, we could take any Lorentzian spacetime, compute its Einstein tensor, and declare this to be the 'matter tensor' of some funky field. But this would be an absurd procedure, since it would imply that every Lorentzian spacetime is a 'solution' of the EFE! If we allowed this, gtr would be unfalsifiable-- hence useless! Of course, it is not useless, because in fact physicists have stringent expectations about what can stand as a legal matter tensor.

Einstein himself had a rather stringent notion of 'solution' in mind, similar to what I described above in the special case of 'electrovacuum'. Others with a more speculative turn of mind have proposed to allow matter tensors which merely satisfy one or more of a list of energy conditions which may (or may not) characterize some properties shared by all (or some) known matter tensors which everyone would agree are acceptable, such as electromagnetic field energy/momentum/stress, or a perfect fluid.

Accordingly, I propose to rewrite this article to correct the mistaken impression. ---Chris Hillman

Neutralized the wording a bit. Mathematically the Alcubierre metric is a solution of the Einstein field equations. Now one could argue that the definition of the EFF includes certain conditions on physically reasonableness, but I would argue that this is a different issue.
Also I disagree about the statement on falsibility. Mathematically the EFF *is* unfalsibility because it is consistent. The physical question is whether or not EFF matches observations. To illustrate the point I'm making, you can't argue on mathematical grounds that Newtonian physics is incorrect. However it is incorrect, because the predictions don't match observerations.

Roadrunner 1 July 2005 04:54 (UTC)


Hi, Roadrunner, we might have an edit conflict since I was actually modifying the page just now, not knowing that you were also doing so. Did you know that the new Wiki software has a problem? I didn't want to lose my work and couldn't see what you did, so maybe we should avoid making drastic changes for a few days to the article and discuss our difference of opinion here.

I have extensively discussed elsewhere the question of what it means to be a "solution" of the EFE. See for example the article on exact solutions in general relativity. Can you read that (and hopefully the CQG papers I cited) before making any drastic changes in the article? Again, because of the edit conflict problem with current Wikiware, let's try to settle this on the talk page, since neither of us want to lose a lot of work if an edit conflict messes up the article itself!

-- CH (talk) 1 July 2005 05:39 (UTC)

Notes on Revised Version of This Article

OK, I rewrote the article and added citations to the series of CQG papers. A bibliographic note: according to Broeck, the proper way to parse his name is Broeck, Chris Van Den. ---CH

I added a bit more about the interpretation of the warp bubble and pointed out a significant difference between the Alcubierre and Notario warp drives. I still think the existing article on Alcubierre drive should be deleted, since I think this one adequately describes the concept. However, there might be some reason for a similar article on Notario warp drives, since these spacetimes are significantly different from the Alcubierre warp drives.

I think the present version fairly describes the currently dubious status of warp bubbles in the research literature, but could add much more detail in support of my comments regarding the apparently "unphysical" energy flux near an Alcubierre bubble, and their suspiciously "spontaneous" appearance and disappearance. If anyone is greatly interested in seeing that, say so here and I'll add it to my list---CH (talk) 1 July 2005 04:37 (UTC)

Is GTR Falsifiable?

Hi again, User:Roadrunner,

I've been looking everywhere for my "statement on falsifiability" and can't find it. Unless you mean what I said about "divide Gab by 8π and declare the result to be the stress-energy of the spacetime" in the article on exact solutions of Einstein's field equations. If so, I think you missed my point. If we allowed any symmetric second rank tensor field on any Lorentzian spacetime to be a "solution" to the EFE, we would have no nonsolutions whatever! That would mean that any observation whatever could be declared to "agree with theory". ---CH (talk) 1 July 2005 06:36 (UTC)

Time travel? Not neccessarily

Hi, 63.201.230.31 from SBC, the statement you added is meaningless as stated, and the page you cited certainly doesn't imply anything about time travel in the sense of closed timelike curves. In fact, the ADM form of the metric guarantees that Alcubierre style warp drive spacetimes do not admit any closed timelike curves, if that is what you had in mind. Hint: construct a simplified two-dimensional warp drive using a compact bump function with metric in ADM form as in the Alcubierre spacetimes. Draw some light cones. Study the nature of the timelike geodesics. You will see that in fact the ADM form guarantees that they cannot turn around in time. ---CH (talk) 00:01, 12 October 2005 (UTC)