Why wormholes (probably) don’t exist

The test rig for the Dark Energy Camera (DECam) at Fermilab. I picked this image today because it kinda sorta looks like the wormhole-making machine from the film version of Contact. [Credit: moi]

The test rig for the Dark Energy Camera (DECam) at Fermilab. I picked this image today because it kinda sorta looks like the wormhole-making machine from the film version of Contact. [Credit: moi]

A lot of science fiction plot devices are devoted to getting around the speed of light. In the real Universe, nothing with mass can travel faster than light, which means we can’t travel to distant stars without taking decades, centuries, or longer in transit. So, sci-fi draws from teleportation, hyperdrive, warp drive, and the ultimate cosmic short-cut: wormholes.[1]

In some cases, the source of a science fiction concept actually is in physics — though it rarely looks the same in fiction as in reality. (Ain’t that the truth for so many things?) And of course many scientists are sci-fi fans, who have tried to determine if any of these schemes actually work with physics as we know it. A lot of these calculations are for fun or for curiosity, but whether with serious intent or not, the science is pretty clear: without something unexpected, the speed of light is still the limit. We can’t get from here to a distant star system instantly, no matter how much we want to.[2]

I’m as disappointed by this as anyone, though I won’t let it stop me from enjoying Star Trek and the rest. It’s important to remember that scientists like me don’t shoot down sci-fi ideas because we hate them: we just need to keep ourselves grounded in what successful theories and experiments tell us about the world.

For that reason, I got a little grumpfy last week when a press release from SISSA (Scuola Internazionale Superiore di Studi Avanzati, or the International School for Advanced Studies for those of us who don’t speak Italian) claimed researchers showed that our galaxy could harbor a huge wormhole, powered by dark matter. [ http://arxiv.org/abs/1501.00490 ] Thankfully most outlets didn’t pick up on the story (apart from Universe Today, which loves to run uncritical stories about wild speculative science). However, I got enough questions via Twitter and Facebook that I thought it’s worth going over what established science tells us about wormholes and dark matter.

Briefly stated: wormholes probably don’t exist in real life, for a wide variety of reasons from general relativity and quantum physics. To make matters worse, the way the new paper treats dark matter contradicts a lot of research in cosmology, and flatly is ruled out by existing observations in the Milky Way. Let’s start from the beginning….

What is a wormhole?

A wormhole is a hypothetical link between two points in spacetime, which would manifest itself as something resembling a black hole without an event horizon. (Event horizons are the boundaries preventing anything from exiting once something enters a black hole.) In plain language, if you entered a wormhole, you would emerge in a different place and time; the distance you travel could be far less than than the separation in space. You could even travel back or forward in time using a wormhole, though that’s a complication we don’t need to worry about today. It’s also possible for wormholes to be longer than the distance you want to travel in space, so science fiction astronauts: don’t just blindly drop into a wormhole and hope for the best!

From the “outside”, the simplest wormhole would look like a sphere, though its surface would look very strange, based on its strong gravity and whatever light is passing through it from the other side. If they existed, most wormholes would likely be very small and would evaporate almost as soon as they formed. Anything passing through — even a single photon — disturbs the gravitational structure of the wormhole, causing it to collapse into two infinitely dense concentrations of energy known as “naked singularities”. That leaves us with two questions: could a wormhole form in the first place, and could it be stabilized somehow?

Mathematically, a wormhole is perfectly allowed by the rules of general relativity. But the math isn’t the whole (hole?) story. A wormhole is described using geometry; when you insert that geometrical statement into the machinery of Einstein’s equations of general relativity, you get back a description of what sort of matter or energy would be needed to make a wormhole true. Basically, the structure of spacetime requires something that focuses light as it enters the wormhole, then defocuses it as it exits.

Why wormholes (probably) don’t exist

Sometimes you’ll hear wormholes referred to as “Einstein-Rosen bridges”, referring to a 1935 paper by Billy Bob Albert Einstein and Nathan Rosen. John Archibald Wheeler and his colleagues did a lot of work on wormholes in the 1950s and ’60s, but their real entrance into the popular imagination came through Carl Sagan’s novel Contact. Through correspondence with gravitational physicist Kip Thorne, Sagan worked out a science fiction device: alien technology enabled the opening of a temporary wormhole between Earth and a distant star system, allowing the novel’s protagonist and her companions to cover many light-years of distance in a matter of hours.[3]

As Thorne describes in his book Black Holes and Time Warps, the alien tech required some form of “exotic matter”. Sagan didn’t need to worry about the details for Contact, but Thorne did: to make a real-world wormhole to defocus light paths, you need negative energy density to keep the tunnel from collapsing. (Thorne also consulted on the recent film Interstellar, which also involves astronauts traveling via wormhole.) That follows directly from general relativity.

Nothing we know of possesses negative energy density. Dark energy, for example, has positive energy density, even though it has negative pressure. Some quantum fluctuations can be interpreted that way, though they are very tiny on the scale we’d need to build a useful wormhole. So, quantum gravity might let us have microscopic wormholes that pop in and out of existence, but that doesn’t help us travel to Vega.
In fact, it’s really hard to imagine what negative energy density even means. All matter we know about has positive energy density (guaranteed in part by E = mc2), which is why Thorne invoked hypothetical “exotic” matter in his wormhole papers, but there’s good reason to think such stuff doesn’t exist in the real world. There’s even a mathematical theorem in general relativity stating that the total energy in a volume of spacetime must be positive or zero. If there’s any negative energy density around, it must be counterbalanced by a greater amount of positive energy density in the same general region.[4]

Why our galaxy isn’t a giant transit system

All of this is general background for the new paper announced last week. The authors claim they can describe the motion of matter in spiral galaxies if they have huge wormholes at their centers. The exotic matter required to hold these wormholes open is none other than the invisible dark matter that makes up 85 percent of all mass in the cosmos. This paper has been peer-reviewed and accepted for publication in Annals of Physics, but it has a lot of problems.

First, most dark matter out there cannot have negative energy density, or else the Universe couldn’t make galaxies. We also have a pretty good handle on the total dark matter density for the entire Universe via measurements of the cosmic microwave background. Maybe some could be “exotic”, but that’s not the stuff we usually mean by dark matter, which is sluggish and nearly non-interacting. (See this Physical Review Letters paper for more on constraining dark matter properties using astronomical observations.)

But let’s say the exotic matter is something other than dark matter. Even there, the wormhole hypothesis runs into trouble. The authors attempt to reproduce the rotation of matter in a spiral galaxy using a modified version of the wormhole geometry, but their evidence takes the form of side-by-side graphs on vastly different axis scales. There is no direct numerical comparison in their model to real data; instead, they say “our proposed curve and observed curve profile for tangential velocity are almost similar to each other” and “our assumption is more or less justified.” That’s not very um…precise language. I might get away with that sort of thing in a blog post, but with the magnitude of the claim the authors are making, I’d expect much better from a peer-reviewed published paper.

Orbits around the Milky Way’s central black hole, as obtained using the Keck telescope in Hawaii. [Credit: Keck/UCLA Galactic Center Group]

Orbits around the Milky Way’s central black hole, as obtained using the Keck telescope in Hawaii. [Credit: Keck/UCLA Galactic Center Group]

Finally, their model depends on a rather striking assertion: that the wormhole diameter is the size of the dark matter core (a region at the center of the galaxy where the dark matter density levels off rather than climbing forever). While there are several estimates of the size of this core, it’s probably pretty big, maybe even encompassing the orbit of the Sun. It seems like a rather large omission not to note that we actually are inside a wormhole’s throat, but maybe I’m missing something. Additionally, we have mapped the Milky Way pretty well to the center, where we can literally plot the orbits of stars around the central black hole. (If you want to learn more about that, please sign up for my new class on gravity and orbits, starting next week.)

The Universe is a slippery little weasel: we are often surprised by new discoveries. However, the likelihood of wrongness increases with the grandiosity of the claim. For large stable wormholes of the type claimed in this paper (or the types in Interstellar, Contact, Deep Space Nine, and other science fiction) we need to be wrong about a lot of different things that touch on several branches of fundamental science. We would need general relativity to be wrong in its own claims about itself, and we would need to fundamentally revise the way we interpret astronomical data. Much as I love the idea of wormholes, I love the reliability of general relativity — and reality — more.

Notes

  1. Real-world communication is similarly limited by the speed of light, hence subspace communication and Ursula LeGuin’s ansible.
  2. Despite discovering the mathematical equations describing a kind of “warp drive”, Miguel Alcubierre is one of the biggest critics of the people trying to build a working example. As he rightfully has pointed out, his calculations pretty much show warp drive is impossible in the real world, for similar reasons to those showing why wormholes probably aren’t real. I wrote about why “warp drives” won’t work for Slate.
  3. In the movie version, Ellie Arroway travels alone, and if my memory serves, the structure of the wormhole is never explained.
  4. This is known in the trade as a horrible simplification. Don’t try this at home, kids.

19 Responses to “Why wormholes (probably) don’t exist”


  1. 1 Carrie January 26, 2015 at 15:43

    My 13-year-old son will be very disappointed.

  2. 2 Mike January 26, 2015 at 16:44

    As a scientist, I find more sci-fi weirdness of the “we have highly intelligent robots, but still need people to fly the ship” variety. Don’t get me started on how you can use hand-tools to fix faster than light ships. That doesn’t even apply to my car!

  3. 3 Brett January 27, 2015 at 02:02

    Wormholes always seemed like an unnecessary complication in SF stories. Just say something about “hyperspace”, make the rules consistent, and then don’t talk about it again.

  4. 4 Tokyo Tengu January 27, 2015 at 05:56

    Well, if wormholes don’t work, find something else! I want off this dirtball.

  5. 5 Sue Bonner January 28, 2015 at 13:59

    I think it’s important to never say never. Things that were science fiction decades and centuries ago are science fact today. One of the examples given in the article is warp drive. We don’t have the technology to do it today, but maybe in the future it will be possible. By saying it will never happen diminishes the motivation to study the possibility.

    • 6 Matthew R. Francis January 28, 2015 at 16:24

      I won’t say “never”, but it’s important also to remember that the theories saying wormholes don’t exist are the same theories that are very well tested. It’s the same deal with warp drive (and in fact you’d need “exotic matter” for that too). I won’t say either of those are impossible, but we would need some profoundly new concepts, ones that can’t be accommodated in general relativity and quantum physics, the two most successful theories in physics. That’s a big step, and one that can’t be taken lightly.

      • 7 Zach Merrill January 29, 2015 at 10:21

        Maybe the concepts can be accommodated once general relativity and quantum physics are unified? Just a thought…I love this stuff!

  6. 8 Lewis Joule-Newton January 28, 2015 at 15:44

    wait. you are making a broad claim based on what seems to be your belief about wormholes. where, exactly, is your peer reviewed paper that proves that wormholes CAN not “exist”?

    • 9 Matthew R. Francis January 28, 2015 at 16:33

      If you want to see why wormholes can’t exist, you need to start with studying general relativity. I recommend Hartle’s book ( http://www.goodreads.com/book/show/17301.Gravity ); he has a section on wormholes, including some clear statements about why they probably don’t exist.

      To see why energies need to be positive in general relativity (while wormholes need negative energy density), the most important paper is this one by Ed Witten: http://dx.doi.org/10.1007/BF01208277, which I linked in the blog post. It’s not an easy paper to read, since it requires some advanced math, but with that under your belt, you can see clearly why any exotic matter of the kind needed to make wormholes conflicts with general relativity.

      The main thing, though, is that this isn’t my opinion: I’m not presenting any original research here. It’s all based on work done by other people over a period of several decades.

      • 10 Polychronis Iliakis January 30, 2015 at 04:27

        Didn’t Einstein himself and several other scientist counteract the validity of concepts such as quantum entanglement for decades, until they were proven horribly wrong? I agree with you on the fact that this peer review paper could be wrong, and probably is, however I am at a point where I would not dismiss anything based on previous theories and ideas. Everyone can and will be wrong at some point.

      • 11 Matthew R. Francis January 30, 2015 at 08:14

        On the contrary, Einstein (along with Boris Podolsky and Nathan Rosen) discovered entanglement, but used it as an argument against quantum physics. He didn’t like the idea, but recognized it was a natural consequence of quantum theory, which is why he proposed an alternative model to preserve things the way he wanted them. That alternative model (which goes under the unmemorable name of “local hidden variables”) has been ruled out by experiment.

        Einstein was wrong on entanglement, but he wasn’t just making stuff up. He could have been right, but the key was that he discussed testable consequences both of entanglement and its alternative. (Admittedly the original test is probably impossible to do in practice, but others figured out a way to generalize it.)

      • 12 Matthew R. Francis January 30, 2015 at 08:23

        To reiterate, it’s not opinions that count in science. Sure, our theories are all incomplete and may always be (though that’s a philosophical argument, and I’m no philosopher). But that’s not the same thing as saying anything is possible. It’s not! We have literal centuries of research on Newton’s laws, and have shown that they work very well. Are they complete? No, we have to modify them for the very small, the very high energy, and the very strong gravity. However, they aren’t “wrong”, even if they aren’t the whole story. It’s likely general relativity will need to be modified; how is an open question, but there are limits to what we can do and still be consistent with experiment and observation. If we do discover that (say) dark energy leads to a new theory of gravity, that doesn’t invalidate the previous results of general relativity. It just says GR holds in some regimes but breaks down in others. It doesn’t mean everything we thought before was wrong.

  7. 13 Luis Edgardo Luiggi Sanchez January 28, 2015 at 23:23

    If negative energy existed would it break the law of conservation of energy? Would negative energy cancel out positive energy? Does a multiverse allow for negative energy?

    • 14 Matthew R. Francis January 29, 2015 at 08:16

      Negative energy doesn’t violate conservation, but it has other problems. In both classical and quantum physics, systems want to move toward a minimum energy configuration. Since negative energy is always less than zero, you end up with runaway collapses.

      The problem of negative energy in the early versions of quantum theory was big enough that Dirac postulated something crazy to get rid of it: a new type matter with positive energy, but otherwise opposite to the normal stuff we know. He was right: we now call his crazy idea “antimatter”.

      So, the lesson is: any theory containing negative energy is going to run into trouble. Usually we try to go out of our way to get rid of negative energy!

  8. 15 Jerrid Wolflick January 29, 2015 at 01:17

    Here is an interesting preprint discussing the ideas of wromholes

    http://arxiv.org/abs/1501.00490

  9. 17 Doug Bell January 29, 2015 at 23:49

    Assuming dark energy exists and that it is responsible for the accelerating expansion of the universe, wouldn’t it be feasible within the laws of physics to harness dark energy to warp space around a stationary ship–expanding space in the direction of travel and collapsing it behind the ship? Since expansion of space is not limited by the speed of light, the entire ship would be transported along with the region of space it occupied.

    • 18 Matthew R. Francis January 30, 2015 at 08:03

      That’s the basic idea behind the “warp drive” equation Miguel Alcubierre found. However, dark energy isn’t the right stuff for it: dark energy still has positive energy density, so it doesn’t create the kind of bubble you want.

  10. 19 Dipanjan Chakraborty January 31, 2015 at 04:45

    I’m not agree wit your blog…u cant say its impossible ever…may b we r knowing the rules of science are wrong enough yet…coz 1 thing is in this universe is real that everything is illusion….sooo my dear nothing is impossible…and you should know before writing this blog that there is no rest point in this universe how u can say that nothing can exceed light speed…although photonic boom has speed much more than light beam….and we are already a point mass in this universe that are in actually brownian motion…so from an imaginary rest point the relative speed is far far greater than light…and a far more interisting thing is that a secret energy(dark energy) is helping us to move our 3d world into the universe….


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