[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]
Warp drives are not just science fiction. Einstein’s theory of general relativity says they should be possible. Yes, that guy again!
A year ago I told you about some recent developments, and since then warp drives have been in the news several times. In one case the headlines claimed that a physicist had found a warp drive that makes faster than light travel possible without requiring unphysical negative energies. In another case you could read that a “warp drive pioneer” had discovered an “actual, real world warp-bubble”. Seriously? What does that mean? That’s what we’ll talk about today.
First things first, what’s a warp drive. A warp drive is a new method of travel. It brings you from one place to another not by moving you through space, but by deforming space around you. Alright. Easy enough. Just one thing. How do you do that?
Well, Einstein taught us that you can deform space with energy, so you surround yourself with a bubble of energy, which contracts the space before you and expands it behind you. As a result, the places where you want to go move closer to you. So you’re traveling, even though you didn’t move.
Okay. But what’s that bubble of energy made of and where do you get it from? Yes, indeed, good question. That’s why no one has ever built an actual warp drive.
As I explained in my previous video, warp drives are solutions to Einstein’s equations of general relativity. So they are mathematically possible. But that a warp drive is a solution of general relativity does not mean it makes physical sense.
What Einstein’s equations tell you is just that a certain distribution of energy and mass goes along with a certain curved space-time. If you put in a distribution of energy and mass, you get out the curved space-time this would create. If you put in a curved space-time you get out the distribution of energy of mass that you would need to create it. There will always be some energy distribution for which your curved space-time is a solution. But in general those distributions of energy and mass are not physically possible.
There are three different types of weird stuff which we have never seen that can become necessary for warp drives. There is (a) stuff that has negative energy density, (b) stuff that has a weird gravitational behavior which can seem repulsive (c) stuff that moves faster than the speed of light.
The worst type of weird stuff is that with the negative energy density, not only because we’ve never seen that but also because it would make the vacuum unstable. If negative energies existed, one could make pairs of negative and positive energy particles out of nothing, in infinite numbers, which destroys literally everything. So if negative energy existed we wouldn’t exist. We’ll mark that with a red thumb down.
The repulsive stuff isn’t quite as bad. Indeed, physicists have a few theories for such repulsive stuff, though there is no evidence they actually exist. There is for example the hypothetical “inflaton field” which allegedly rapidly expanded our universe just after the big bang. This inflaton field, or rather its potential, can act gravitationally repulsive. And dark energy is also repulsive stuff, if it is stuff. And if it exists. Which it may not. But well, you could say, at least that stuff doesn’t destroy the universe so we’ll mark that with an orange thumb down.
Finally, superluminal stuff, so stuff that moves faster than light. This isn’t all that problematic other than that we’ve never seen it, so we’ll give it a yellow thumb down. It’s just that if you need stuff that moves faster than light to move stuff faster than light then that isn’t super useful.
Now that we have color coded problematic types of energy which makes us look super organized, let us look at whether warp drives require them.
The best known warp drive solution dates back to 1994 and is named the “Alcubiere drive” after the physicist Miguel Alcubierre. The Alcubierre drive requires all of the above, negative energies, repulsive gravity, and superluminal stuff. That’s not particularly encouraging.
Now the big headlines that you saw in March last year were triggered by a press release from the University of Göttingen about the publication of a paper by Erik Lentz. Lentz claimed to have found a new solution for warp drives that does not require negative energies.
The paper was published in the journal Classical and Quantum Gravity, which is a specialized high quality journal. I have published quite a few papers there myself. I mention this because I have seen a few people tried to criticize Lentz’ paper by discrediting the journal. This is not a good argument, it’s a fine journal. However, this doesn’t mean the paper is right.
Lentz claims both in his paper and the press release that he avoided unphysical stuff by stitching together solutions that, to make a long story short, have fewer symmetries than the warp drives that were previously considered. He does not explain why or how this prevents negative energies.
Just one month later, in April 2021, another paper came out, this one by Shaun Fell and Lavinia Heisenberg. They made a similar claim like Lentz, namely that they’d found a warp drive solution that doesn’t require unphysical stuff by using a configuration that has fewer symmetries than the previously considered ones. The Fell and Heisenberg paper got published in the same journal and is mathematically more rigorous than Lentz’. But it didn’t come with a press release and didn’t make headlines.
Now, those new warp drive solutions, from Lentz and Fell and Heisenberg are in the same general class as the Alcubierre drive, which is called the Natario class, named after Jose Natario. In May last year, a third warp drive paper appeared, this one by Santiago, Schuster, and Visser. The authors claim to have proved that all warp drives in the Natario class require negative energies and are therefore not physical. So that means, the new solutions are all bad, bad, and bad.
Why the disagreement? Why do those people say it’s possible, and those prove it’s impossible. Well, in their paper, Santiago and coauthors point out that the other authors omitted a necessary check on their derivation. After that, Fell and Heisenberg revised their paper and now agree that their warp drive require negative energies after all. Lentz also revised his paper but still claims that he doesn’t need negative energies. It’s unclear at the moment how he wants to escape the argument in the Santiago paper.
Now, the Santiago paper has not yet gotten published in a journal. I’ve read it and it looks good to me but in all honesty I didn’t check the calculation. If this result holds up, you may think it’s bad news because they’ve ruled out an entire class of warp drives. But I think it’s good news because their proof tells us why those solutions don’t work.
Just to give you the brief summary, they show that these solutions require that the integral over the energy density is zero. This means if it’s non-zero anywhere, it has to be negative somewhere. If they’re correct, this would tell us we should look for solutions which don’t have this constraint.
Okay, so the situation with the new solution from Lentz isn’t entirely settled, but if the proof from the Santiago paper is right then Lentz’ solution also has a negative energy problem. The Santiago paper by the way does not apply to the more general class of warp drives from Bobrick and Martire, which I talked about in my earlier video. The issue with those more general warp drives is that they’re somewhat unspecific. They just say we need several regions with certain properties, but one doesn’t really know how to do that.
Those general warp drives can be divided into those that move faster than light and those that move slower than light. The ones that move faster than light still require stuff that moves faster than light, so they’re still problematic. The ones that stay below the speed of light however don’t seem to have any obvious physical problem. You might find it somewhat disappointing that a warp drive stays below the speed of light and I can see that. But look at it this way: if we could at least travel with nearly the speed of light that would already be great progress.
So the claim that Lentz found a warp drive solution which allows faster than light travel without negative energies is highly questionable. But what’s with the headlines that said someone had actually built a warp drive? Well that turns out to be just bad science communication.
In July last year, a paper was published by a group with the lead author Harold White. They had done a computer simulation of certain nanostructures. And in that simulation they found a distribution of energies similar to that of the Alcubierre drive. This can happen because on very short distances the Casimir effect can give rise to energy densities that are effectively negative. So, not only did they not actually build the thing, it was a computer simulation, it’s also an in-medium effect. It’s kind of like a simulation of a simulation and definitely not an “actual” warp drive.
Where does this leave us? The big picture is that warp drives are getting some serious attention from researchers who work on general relativity. I think this is a good development. We certainly have a long way to go, but as they say, every journey begins with a first step. I think warp drives are a possibility that’s worth investigating. If you want to work on warp drives yourself, check out Gianni Martire’s website, because he is offering research grants and tells me he has to get rid of the money fast.
Having said that, I think those people all miss the point. If you want to have a propulsion mechanism the relevant question isn’t whether there is some energy distribution that can move an object. The question is how efficiently can you convert the energy into motion. You want to know what it takes to accelerate something. At present those papers basically say if you throw out stuff that way, then the space-ship will go that way because momentum is conserved. And that is probably correct, but it’s not exactly a new idea.