On Alcubierre Warp Drives

OK, I’ve read this article that I’ve been asked about a few times now.

Background (general relativity):
There is a hard limit to speeds that objects can take in special relativity that generalizes to general relativity. This is the famous “you can’t go faster than the speed of light” claim, which, I’d argue, in the case of travel over distances small compared to the curvature of space, is really kind of closer to “moving faster than light doesn’t MEAN anything, it’s a non-concept”

General relativity, however, offers a loophole. Since spacetime is curved, and the curvature can be time-dependent, you can create various schemes where you are basically “surfing” in spacetime, and appear to have travelled faster than light to distant observers. Mexican physicist Miguel Alcubierre worked out one particular exact solution to Einstein’s equation, the fundamental equaiton of general relativity, that allows motion like this.

There are several naïve problems with directly applying this “Alcubierre warp bubble” solution though:

1. The model requires a matter distribution that has a negative energy density, and this is not known to exist
2. The amount of negative energy required in order to safely transport a human with the Alcubierre geometry is something like “negative one times the mass of Jupiter”
3. While the particular Alcubierre geometry does not allow the warp bubble to stop, slow down, or turn, if you allowed these features, it would inevitably enable time travel, grandfather paradoxes and the like. Which, basically ruins the predictability of physics

For these reasons, most physicists have believed Alcubierre-style drives to be unbuildable, in principle. Enter the above cited article.

Background (quantum field theory):

OK, so, the other half of prerequisite to understanding this article is understanding what the Casimir effect is. The real ground basis here is that in quantum mechanics, systems tend to have what is called a “ground state energy.” Most famously, this is represented by the 1s orbital of the electron in a hydrogen atom from chemistry class — the electron can go to this energy level, but it can go no lower in a hydrogen atom. Most quantum mechanical systems with finite energy have some sort of “lowest possible” energy. When you do quantum field theory for the first time, though, you find that you have to treat every point in space like it is a “bound system” in a particular mathematical way that is beyond the scope of this article. This results in an infinite energy for spacetime called the “vacuum energy”. Current QFT frameworks basically sweep this away and say “the only meaningful energies are differences with this vacuum energy,” and then go on with their lives.

Henrik Casimir, however, came up with a clever way of poking the vacuum, so to speak. He realized that if you took two metal conducting plates, you would change the number of possible states available to the system in between the two plates in a way that depended on the distance between them. In particular, you’d end up removing states available to the system, which would mean, basically, that there would be vacuum energies not accessible between the plates — it would look like the energy density between the two plates was, in fact, less than the vacuum energy. He then showed that the plates would exert a force on each other due to this effect. This force was later measured.

The White, et. al. article

So, the above article got published a few days ago. The takeaway of the article in the popular press is “we built a tiny warp bubble.” I believe this claim to be wildly misleading at worst, and missing several Jupiter-sized caveats at best. Here is the basic argument in the paper:

1. We have come up with a novel way of computing the Casimir negative energy density in a system of many, arbitrarily shaped plates
2. We have developed a particular geometry of plates such that they create a “negative energy density” that matches the negative energy density required to create an Alcubierre metric
3. Therefore, we have made a very small warp bubble

But, notice what was left out of the above argument:

1. Any real evidence that “negative energy relative to the QFT vacuum” really means the same thing as “negative energy in General relativity”. In particular, there is no measurement of gravitational effects of Casimir cavities and a demonstration that they are, in fact, negative matter distributions. Note how different the above two approaches are. It is not obvious that they are equivalent.
2. Any measurement of superluminal effects, or even an assertion that they are there.
3. Any analysis of the motion of particles under the influence Alcubierre metric beyond just a naïve matching of the energy density functions

I’d argue that these points are most of the connection that one would have to make between “There is a Casimir force” and “I have a warp bubble,” and I will go back to my claim that the linked article is wildly premature in it’s claims at best.

Errata (edit):

I should note that there are reasonable arguments to believe that the Casimir cavity is not a negative energy density per GR. For one thing, the relationship between vacuum energy and the cosmological constant, which would follow from just treating vacuum energy as “gr mass-energy” has famously produced “physics’s worst prediction” (namely, that the cosmological constant is less than 1/10^100 the size that it “should” be). There is almost certainly more complexity there than just saing “A = B” and calling it a day.

Similarly, someone reading the above might think about “negative mass”, and think “antimatter”, but that is not correct. Antimatter has positive mass for the purposes of general relativity (easy way to see this, a photon can decay to an electron and a positron, but the photon gravitated with a positive mass-energy, so the products have to too, they don’t just cancel). General relativity couples to the four-momentum of matter, and the four-momentum of matter is conserved in decays in quantum field theory.