Via Chad Orzel, I see that the latest constraints on short-distance modifications of Newton’s inverse-square law from the Eot-Wash group at the University of Washington have now appeared in PRL. And the answer is: extra dimensions must be smaller than 0.045 millimeters (in any not-too-contrived model).
We used to think that extra dimensions must be enormously smaller than that, if they exist at all. If you have n extra compact dimensions of space, long-ranges forces like gravity and electromagnetism would go from falling off as an inverse-square law, 1/r 2, to something like 1/r 2+n. Gravity is weak and hard to test, but electromagnetism is easy to test, and it behaves quite conventionally down to scales probed by particle accelerators.
In 1998, Arkani-Hamed, Dimopoulos and Dvali realized we could hide extra dimensions that were much larger than that, by positing a three-dimensional brane on which all of the particles of the Standard Model were confined. Then it’s easy to see why electromagnetism wouldn’t notice the extra dimensions: photons couldn’t get there! But gravity can always get there. So it became a big new project to test Newton’s law of gravity at short distances. As a separate motivation for the large-extra-dimensions idea, you could explain why gravity is so weak by imagining that it’s really not so weak at a fundamental level, but gets diluted by the extra dimensions. It all works out perfectly nicely if you have two extra dimensions of about a millimeter in size, which was happily right where the experiments hadn’t quite probed. By now, as you can see, they have been pushed there and beyond.
Which by no means implies that the experiments aren’t worth doing any more — you never know what suprises you might find in regimes where you’ve never looked. The title of the new paper tries to score some motivational points by referring to the “Dark Energy Length Scale.” This notion is a bit less concrete than the size of an extra dimension, but okay. What cosmologists have measured in the case of dark energy is an energy density, about 10-8 ergs per cubic centimeter. But if we multiply by appropriate powers of Planck’s constant and the speed of light, we can convert this density into a length (to the -4th power), and that length turns out to be about 0.08 millimeters. Now, this little bit of dimensional analysis may or may not be connected to anything physical; they reference papers by Beane and by Dvali, Gabadadze, Kolanovic, and Nitti, speculating that this length scale actually corresponds to something important. These ideas are not completely baked, but they’re fascinating, and the important point is that we have a length scale at which stuff happens, and we don’t completely understand what’s going on, so let’s do all the experiments we can to try to dig up some clues.
The other important point about this work is that it puts to rest the vicious rumors we were hearing over a year ago, about which Eric Adelberger (leader of the Eot-Wash group) was nice enough to comment here. Namely, the rumor that they had actually found a weak repulsive force in their data. This is the kind of thing that happens all the time when you’re doing ultra-precise measurements at the very edge of what is possible; unforeseen effects creep in, and it takes time to stamp out everything that shouldn’t be there. These guys are careful, and would never jump up and down about a real effect unless they were truly convinced it was there. If I had been in charge (putting aside for the moment the fact that, if the experiment relied on my technical expertise, the lower limit on the size of extra dimensions would probably be measured in kilometers), I would probably have floated that rumor intentionally, just so people paid attention when the results did come out. Unlike me, Eric Adelberger has enormous integrity, so they just told the honest truth all along.
Chad keeps saying that these experiments don’t get enough credit, but I don’t know why he thinks that. (Chad, why do you think that?) Ever since the idea of large extra dimensions was floated in 1998, everyone working in string theory, particle physics, and cosmology has been very excited by the search for short-range forces, and most everyone knows that the Eot-Wash group is kicking butt within the field. Their 2000 paper, which pushed the limit on extra dimensions below a millimeter for the first time, has hundreds of citations, and Adelberger gets far more invitations to give colloquia and conference talks than he can possibly accept. Some influential theorists have even described the torsion-balance work as one of the most profound experiments in physics. This is not exactly a small, under-the-radar operation. We’re all looking forward to what they do next.