wormholes, part I

I saw Christopher Nolan's latest film Interstellar a couple weeks ago on opening night. I hadn't even heard about it before, my company just decided to buy us all tickets to see it in IMAX, one of the nice things they do for employees once a month or so. I loved it and it left a big impression on me, and I intend to go back and see it again as soon as I get a chance. (Don't worry, I'm not going to spoil anything about the plot here--the intention of this series of posts is not to talk about the movie but about wormholes.)

I mostly loved it for the story, but also that you see concepts from theoretical physics like time dilation, black holes, and wormholes being applied in a relatively mainstream hollywood movie. Not all of it was very accurate scientifically, but it was still really exciting to see these things show up on the big screen in such a prominent spectacular way.

Lots of people were asking me about the time dilation effects after the movie, and it took me a few days to remember exactly how everything works and do enough back of the envelope calculations, but I eventually came to the conclusion that there is no realistic way in which the effects portrayed could have worked the way they did in the movie. But something similar could have maybe possibly happened if things had been a bit more complicated (for instance if there were two black holes nearby instead of just one). Maybe Kip Thorne (who consulted on the movie) suggested something like this but they decided they didn't care enough about the details to bother getting everything exactly right.

Regarding the wormhole itself, I feel like a bit of a hypocrite for getting excited about it. I've always been annoyed at how big the disconnect is between what the sci-fi community thinks is plausible and what is actually plausible according to our latest and most up to date scientific knowledge. As I've always told people who ask me, traversable wormholes are most likely completely impossible, not something that any civilization no matter how advanced could create. But they show up in sci fi all the time as if all we need to do is gain enough technology and then we can figure out how to build one. Worse, the depictions of them in sci fi are usually nothing like a real wormhole would look like, in the unlikely case it turned out somehow they were possible. At least, in Interstellar, they got this right--a real wormhole would look like a sphere, not like a hoop as I've seen in most sci fi.

After I watched the film, I started thinking about wormholes and the different conversations I've had with people, many of whom tend to be very enthusiastic about the possibility of using them for interstellar travel some day. I always have tried to emphasize that it's very unlikely that they are possible at all, even in principle. But I realized that the truth is--I have never looked into the science behind them deeply enough to know exactly what the reasons for this are, and what possible loopholes there could be that might allow some advanced civilization to build one. So for the past couple weeks I did my due diligence and looked through the current scientific literature to find out what the present state of knowledge is. What is the most solid argument against them being possible--are they almost certainly impossible, or just probably impossible, or is it that we really just don't know whether they are impossible? I think my answer to this is about the same as when I started looking through the literature--they're either very likely impossible or almost certainly impossible depending on who you believe, but as of yet nobody has succeeded in coming up with an absolutely rock solid proof that they are impossible. However, I now know much more of the details than I did a few weeks ago, so I'd like to share them and let you be the judge!

wormholes, part II: Kip Thorne

I started my review of wormholes by reading Kip Thorne's famous paper on them from 1989. Thorne is the T in "MTW" a book by Misner, Thorne, and Wheeler called Gravitation, written in 1973 and still one of the most widely used textbooks on general relativity.

I'm not actually sure whether Kip Thorne believes that wormholes are possible--I assume he would at least lean towards "no" but I have no idea. You might think that because he has written important papers on them and because he consulted on a movie that depicts one, he believes they are. But that doesn't follow, because theoretical physicists often explore ideas that they don't think will work out, to see where they will lead and find the limits of existing theories and uncover new questions or problems with them. I didn't search for comments from him so I don't know what his present take on them is or if it has changed any, but in his 1989 paper he doesn't say they are possible, he just outlines what the conditions would have to be in order for them to be possible.

In his paper, he does three main things. The first is to construct a simple example of a stable traversable wormhole geometrically. In other words, he describes what the shape of space and time would have to be, and what distribution of energy would be needed in order to create this shape. (Remember, the basic idea of general relativity is that matter and energy warp space and time; given any distribution of energy you get a well defined shape of space and time.) Unfortunately he finds that the distribution would have to be quite "exotic", meaning it would require a lot of negative energy, a substance which is very different from ordinary matter and energy. The main question is: could such a substance exist or be created somehow, and if so could it exist in large enough quantities to make a wormhole? At the time, little was known about the answer to this question but a lot more work has been done since which is the topic I focused most of the rest of my reading on.

The second important thing he does in his 1989 paper is to show that if it is possible to create even the simplest kind of wormhole that just connects point A to point B in space, then it is also possible to build a time machine out of the wormhole, that could be used for traveling backwards in time.

So while the fact that a prominent very respectable physicist was even discussing the possibility of wormholes must have been very exciting to the sci fi community, what they may not have realized is that both of these results make wormholes less likely, not more likely. The first because he demonstrated that they depend on a substance not known to exist. And the second because time travel has a whole set of causality and consistency problems that come with it. If it were possible to build a wormhole that couldn't be made into a time machine, that would be much more believable than a wormhole that could be made into a time machine. But sadly, it doesn't seem like the first scenario is possible, at least according to Kip Thorne's 1989 results. However, there is some encouraging news here: in 1992 Stephen Hawking conjectured that there may be weird as of yet unknown effects in physics which act to protect against time travel. (He called this the "Chronology Protection Conjecture".) It seems like pure speculation to me, but if Hawking's suggestion is right then there might plausibly be some mechanism that prevents someone traveling through a wormhole if they plan to travel backwards in time. Like, maybe the wormhole suddenly closes up or becomes unstable. However, I don't think he has much reason to believe this is true other than wishful thinking--it would be nice if some kind of wormhole were possible, without having to face all of the obviously troublesome inconsistencies that time travel brings (grandfather paradox, etc.) So he tried to think of any way in which it could be. This is one way of avoiding that problem, but seems unlikely and doesn't do anything to solve the main problem which is a lack of negative energy.

wormholes, part III: negative energy

So what is this thing called negative energy (also called "exotic matter", and could it exist somewhere, or if it doesn't exist naturally, is there a way we could somehow generate it?

The two main theories of fundamental physics today are General Relativity and Quantum Field Theory. General Relativity was developed as a way to understand the large scale structure of the universe (cosmology, astrophysics, etc), while quantum field theory was developed as a way to understand the small scale structure (quantum mechanics, subatomic particles, etc.) Putting the two together is still a work in progress and string theory so far seems to be the only promising candidate, but it is far from complete.

General Relativity by itself is usually referred to as a "classical" theory of physics, since it doesn't involve any quantum mechanics. But there has been a lot of work using a "semi-classical" theory called Quantum Field Theory in Curved Spacetime. This is basically quantum field theory but where the space the quantum fields live in is allowed to be slightly curved as opposed to perfectly flat. Because this doesn't work once the curvature becomes too strong, it's not a full theory of quantum gravity, and is only regarded as an approximation. But it has been good enough to get various interesting results (for example, the discovery of Hawking radiation).

In General Relativity by itself (usually referred to by string theorists as "classical GR"), there are a number of "energy conditions" which were conjectured early on, specifying what kinds of energy are allowed to exist. The main ones are the strong energy condition, the dominant energy condition, the weak energy condition, and the null energy condition. As I understand it, all of these are satisfied by classical physics. If there were no quantum mechanics or quantum field theory, then it would be easy to say that wormholes are impossible, since negative energy is not even a thing. But in quantum field theory, the situation is much more subtle. In Kip Thorne's 1989 paper he finds that a variant of the weak energy condition (AWEC = averaged weak energy condition) is the one which would need to be violated in order to construct his wormhole. I've seen more recent papers which focus more on ANEC (averaged null energy condition) though, so perhaps there have been wormhole geometries since discovered which only require violation of the null energy condition.

I'm not going to explain what the difference is between all of these different energy conditions. But I should explain the difference between the "averaged" conditions and the regular ("local") conditions. The weak energy condition says that the energy density measured by every ordinary observer at a particular location in space must be zero or positive. The surprising thing about quantum field theory is that this, as well as all of the other local conditions (local means at a particular point) are violated. In other words, in quantum field theory, negative energy is very much "a thing".

But hold your horses for a second there! Because the thing about quantum field theory is that, there are loads of different examples of weird things that can happen on short time scales and at short distances that cannot happen macroscopically. For example, virtual particles exist that travel faster than the speed of light, masses can be imaginary, and energy is not even strictly conserved (there are random fluxuations due to quantum uncertainty). There are particles and antiparticles being created out of the vacuum and then annihilated all the time (quantum foam). There are bizarre things called "ghosts" that can have negative probability (which I won't go into). But when you look at the macroscopic scale, none of these weird effects show up--through very delicate mathematics, they all cancel out and you end up having very normal looking physics on the large scale. It's like if you look at the individual behavior at the microscopic level, everything is doing something completely weird and bizarre. But if you take an average of what's happening, it all gets smoothed out and you have very solid reliable macroscopic properties: energy is conserved, probabilities are positive, everything moves at less than the speed of light, etc. These things have been proven and are well understood. So given everything I know about how quantum field theory works, my intuition would be that something similar happens for negative energy: it's the kind of thing that could happen momentarily on the microscopic scale, but would never be the kind of thing one would expect to see on the macroscopic scale. And that's the main reason I've always told people I don't think wormholes are possible, despite not having reviewed most of the relevant literature related to it until this month.

After reviewing the literature, I have seen that over the past 20 years, the case that negative energy cannot exist macroscopically in our universe has grown stronger. Since the mid 90's the focus has shifted from energy conditions to what are known as "quantum energy inequalities" or QEI's. I read a couple review papers on QEI's, and will try to summarize in my next part. The gist of it is that while negative energy can happen locally, there are limits which can be placed on how negative that energy can be. And the limits depend on what timescale you're looking at. If you want a very negative energy, you will only find that on a very short timescale. If you want only a little bit of negative energy, you might find it on a longer time scale. But once you get to timescales like a second or more, the amount of negative energy you can have at a point is indistinguishably different from zero. There is a related idea called "quantum interest". Quantum interest refers to the fact that: given any negative energy spike there will be some compensating positive energy spike in the near future to compensate it (and make it average out to zero). And the time you have to wait to have this "payback" in the energy balance is shorter the larger the initial spike.

Gotta run for now, but I still have more to summarize on this. To be continued in part IV!