Why wormholes (probably) don’t exist

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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.

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.

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

Real-world communication is similarly limited by the speed of light, hence subspace communication and Ursula LeGuin’s ansible. 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. In the movie version, Ellie Arroway travels alone, and if my memory serves, the structure of the wormhole is never explained. This is known in the trade as a horrible simplification. Don’t try this at home, kids.