# Harold White's analysis applied to the Natario warp drive

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There are two solutions to Einstein's equations that allow for warp drive. One is the Alcubierre warp drive and the other is the Natario warp drive (http://arxiv.org/abs/gr-qc/0110086). What is the difference? Is the Natario warp drive better suited for a real life application than the Alcubierre warp drive? (If possible when one knows all the facts) Here is a paper in which something of this is explained I think. They apply Harold White's analysis to the Natario warp drive and arrive at similar conclusions. Sadly I know too little about this to understand it. Maybe someone who understands this can write an answer to my questions. https://hal.archives-ouvertes.fr/hal-00844801/document (And BTW: In QFT there are also violations of energy conditions)

Here is another paper which discusses if the Casimir effect can generate a Natario warp drive (conclusion: yes): https://hal.archives-ouvertes.fr/hal-00981257/document

edited Nov 24, 2014

Hi WolfnSheepsSkin, I have corrected the link to the first paper, as it did not work first.

However I have to say that it is known that warp drives are cool science fiction gadgets but will never work in the real world, so I am not sure if this question is really appropriate for PhysicsOverflow. Voting to close.

Asking for the mathematical differenc of the two solutions to the Einstein equations and its physics interpretation might indeed be an interesting valuable question. What distracted me most is the term "real-world application"...

BTW it needs 3 closevotes to really close a question, so experts about the topic may still put down nice answers to explain the difference at present.

See this blog post and this question for as to why "warp drives" do not work.

The SE question is based on a popular article of a popular magazine. To express it politely, popular media channels are often not reliable sources of correct information about physics at all. The answers I still have to look at.
No, QFT doesn't violate any sort of energy conditions. If you try to treat virtual particles like they're classical balls actually tumbling around, then yes, but that's just an incorrect thing to do. The actual solutions to GR don't just involve negative energy formally in some middle step in a particular calculation method, they require it to be explicitly observable and manipulable, which is very different.

In an answer to a similar question on Quora, Lumo has explained in some detaill that even the classical version of the weakest energy condition prevents "real-world" warp-drives, and not even the best engineering technicques can to anything about it.

I know that many things on Quora are not graduate-level, but I think Lumo's answer is good ...

If someone is still interested in this, here is an update from Harold White, at the end he answers some questions:

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These ideas are of no scientific value, for the following reason: if you consider General Relativity in reverse, as a theory of stress-tensors given a geometry, then any geometry is a solution of Einstein's field equation by simply setting

$$T_{\mu\nu} = 8\pi G_{\mu\nu}$$

For your given metric. In other words, whatever metric you make up, you get a stress tensor which corresponds to this. There is no restriction from General Relativity on the allowed geometry without further energy conditions.

What that means is that if I have any manifold with metric g(x), and a differentiable curve x(t), and I wish to shrink the proper time for traversing that curve to as close to zero as I like, all I have to do is choose a tube perpendicular to the curve, and multiply the metric in the interor by any function of the radial coordinate interpolating from a small value to 1 that I like:

$$g\rightarrow g*f(r)$$

where r is the radial tube-distance to the curve. As long as the tube is small, and f is constant as a function of the curve proper time, this will look like a relatively fixed "object" traveling along the curve, your "warp engine", which magically reduces the metric on the interior so that the curve can be traversed as quickly as you like. You simply choose f(r) to interpolate from the small number (the inverse warp factor) at 0, where it is completely flat, to 1 at some small radius R, where it is also completely flat. And there you have it, a warp drive!

None of this nonsense construction can be said to be a solution of General Relativity, neither the Alcubierre solution nor the solution in this White paper, because there are no conditions from General Relativity without energy conditions. Every geometry works. So it is trivial to construct Warp drives, and if I were in the business I could make up a new "warp drive" every day for all eternity, by choosing a different function f, or making angular dependence, whatever.

The physical content of classical General Relativity requires at least the null energy condition, so that the warp drive does not violate the black hole area law, which is the second law of thermodynamics. All these drives allow you to travel faster than light, and therefore escape a horizon, and so all of them violate the null energy condition. Without this, the weakest condition, there is no content to GR, so there is no content to these claims. They are simply inventions.

answered May 4, 2015 by (7,550 points)

Thank you Ron.

@WolfInSheepSkin: I didn't really construct a "warp drive" in the answer, because the thing I did just shrinks the proper time to traverse an already timelike curve, but I explained the principle behind these constructions--- without energy conditions GR is an empty theory. You can reduce the proper time to traverse a curve just by zig-zagging near the speed of light near the curve, so what I did is not a warp drive at all (but it's the same idea as the Alcubierre business). A real warp-drive would start with a spacelike curve and change the metric around the spacelike curve so that it becomes timelike and reattach it to the surrounding space. But since you can do anything you want without energy conditions, you can modify the geometry however you want, there isn't much content to it. There is a question of whether such a thing would necessarily affect the causal structure--- the nesting of light cones--- whether it can be thought of as a fixed drive moving along the now-timelike curve, or whether it will pile up a larger and larger shock-wave of cut-through light cones as it moves. In any case, despite the faultiness of my answer, the basic principle is correct--- if your purported solution does not obey any energy conditions, it is difficult to say that you have done anything at all. You need to demonstrate that there is a sense in which you obey a physical constraint of some kind. I will think about the spacelike curve issue, I think you do the same thing, by choosing a tube around the spacelike curve, and tipping the light cones over to make the spacelike curve timelike, and there are no issues.

Alright Ron, what about the higher dimensional Chung-Fresse model where a toroidal energy distribution can lead to a negative pressure and that can be created with strong electromagnetic fields?

http://www.earthtech.org/publications/davis_STAIF_conference_2.pdf

(8 pages)

http://arxiv.org/abs/hep-th/0508246

(13 pages)

I'm only familiar with basic GR and all that. So I'm not sure if your answer applies also to this model. Would me make happy if you can answer this. (of course you can answer it in any verbose detail you want)

@WolfInSheepsSkin: The White and Davis paper is again doing content free stuff, because of lack of energy conditions. But Frasca's paper is completely different and should be an entirely separate question, it has nothing to do with this Alcubierre stuff, and it is superficially more plausible. On a quick skim I didn't see much content, although the content I saw superficially looked ok at first glance. The main claimed result, spatially homogenous conditions near singularities, is something that was known since the 1960s in the USSR and was part of what was called the "Mixmaster model", and it was the pre-inflation best-guess theory of homogeneous initial conditions (unlike inflation, it doesn't work). Whether Frasca is reproducing this or doing something else, I don't know, but ask! Certainly it would be a nice question here, or for reviews.

Ok, great. Thank you.

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Hi, I think Whites approach has nothing to do with the usual arguments against a warp drive. I heard that it is somehow related to this paper: http://arxiv.org/abs/hep-th/0508246 (which has only 13 page, so I assume people here are capable of reading it) And that the idea is to induce a local modification of space-time using a strong oscillating electric field at a high frequency and prove that there is an effect through the interferometer.
answered Jan 5, 2015 by (-40 points)
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Alright, here is another video that might explain what is going on at NASA. Any comments?

answered Apr 23, 2015 by (-40 points)

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