Short Distances: Newton Still the Man

By Sean Carroll | January 13, 2007 2:18 pm

Torsion Balance 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.

  • Garrett

    Funny to see some string theory go away because of an experiment with a… string.

  • Chad Orzel

    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?)

    I think that because when people talk about extra dimensions and experimental tests of physics beyond the Standard Model, it’s LHC this, LHC that, and nothing at all about the table-top tests that these guys and the various EDM search experiments are doing. The fact that you learned of the result from my blog post (and I learned of it when I read the table of contents of PRL this week) is another indication– the paper hit the arxiv back in November, and nobody said anything. They’re just not on the radar, even for people who work in the field, and it’s a shame.

  • Sean

    Honestly, they very much are on the radar for people who are working in the field. Of course, the LHC will give us enormously more information about TeV-scale physics, in a wealth of detail; so people are rightly excited at that prospect. They’re all very much worth doing.

  • Chad Orzel

    Honestly, they very much are on the radar for people who are working in the field. Of course, the LHC will give us enormously more information about TeV-scale physics, in a wealth of detail; so people are rightly excited at that prospect.

    I don’t deny that the LHC will give more information, and more direct information. And when you get down to it, billion-dollar accelerators are much sexier than torsion pendulum experiments.

    But you’ve probably got another two years (at least) before the LHC is going to provide anything useful, and these guys and the EDM search people are getting results right now (and have put the tightest constraints on the range of possible theories). They deserve some more publicity.

    I’ll admit that I’m highly biased on this question, though, because I’m a low-energy experimental physicist, and I’m sick of accelerator people getting all the press. Also, I know just how impressive the stuff they’re doing is. The concept is deceptively simple, and that probably makes it sound much less impressive to people outside experimental physics, but these really are tour de force experiments. The way they’ve dealt with the many systematic issues involved is nothing short of ingenious, and if I wore a hat, I’d take it off to them.

  • B

    Hi Sean,

    thanks for the info! Glad to hear that rumor about the repulsive force is dead, it really bothered me. Best,


  • Scott H.

    Honestly, they very much are on the radar for people who are working in the field.

    Sean, to play Devil’s advocate (or maybe just Chad’s advocate) here, I have found that people not working in the field often don’t know about these results at all. I’m a huge fan of the Eot-Wash group and try to plug them whenever appropriate; a not uncommon reaction is “Wow, that’s amazing … where did you say that stuff was being done?”

  • Sean

    Outside the field, you might be right. I wish the word was spread more widely — about searches for short-range forces, violations of the equivalence principle, tests of Lorentz invariance, dipole moments, and the LHC. We’re all on the same side.

    At least I didn’t say that Chad was the Devil.

  • Amara

    Thanks! At the EOT-Wash website I found this 1991 paper, discussing experimental results for testing the Equivalence Principle on charged particles. It’s a topic rarely discussed; I wish I knew why.

  • anon

    Having heard several talks on this over the past few years at various places, I’m pretty sure everyone working on gravity or on high-energy physics in general has heard of the Eot-Wash group and knows what they’re doing. The experiments are a real tour-de-force and the engineering needed to make these precise torsion balances is amazing.

    That said, I think the reason the LHC gets more hype in the extra-dimensional context is that the most plausible extra-dimensional models (note I don’t say that they’re likely at all!) tend to be Randall-Sundrum models, which are much easier to test in a particle physics context than in a gravitational one. The torsion balance puts limits on “old” large extra dimension models, like ADD, which almost no one really finds believable these days anyway.

    As for EDMs, I think maybe fewer people are aware of how much the bounds are going to be improved in the near future, but at least a few vocal people are quite excited about the prospects. Does anyone know when, e.g., the Yale group is going to release their next result? EDMs could be the big surprise discovery of the next year or two….

  • Chad Orzel

    As for EDMs, I think maybe fewer people are aware of how much the bounds are going to be improved in the near future, but at least a few vocal people are quite excited about the prospects. Does anyone know when, e.g., the Yale group is going to release their next result?

    The last I heard from them, they were just starting to take data, and hoped to have something to report this year. That was a good six months ago, though, and it’s entirely possible that something has changed.

    (I was a post-doc in a lab down the hall from them, so I try to keep an eye on their progress… Those are way cool experiments, too.)

  • Chad Orzel

    I should add that I think some of the difference between my perception and Sean’s is that we’re using “field” to mean different things– by “people in the field” I pretty much mean “physicists,” not just “people working on gravity.”

  • Christine Dantas

    Other interesting lab experiments for quantum gravity with results published in refereed journals that might be relevant for discussions here are: – Experimental limits for low-frequency space-time fluctuations from ultrastable optical resonators, by S. Schiller et al. (Published: Phys.Rev. D69 (2004) 027504) – Signals for CPT and Lorentz Violation in Neutral-Meson Oscillations, by Alan Kostelecky (Published: Phys.Rev. D61 (2000) 016002) – Gravity-wave interferometers as probes of a low-energy effective quantum gravity, by Giovanni Amelino-Camelia (Published: Phys.Rev. D62 (2000) 024015)

  • Mark

    That might be it Chad. For my part, I certainly see these results quoted and discussed at essentially every conference I go to (particle physics, gravity or cosmology).

  • Simon DeDeo

    Just to prop up a colleague’s work — Dimitrios Psaltis at Arizona actually beat this limit first with an entirely different and very clever test involving black hole lifetimes:

    For the record (and Dimitrios is far too modest — I think! — to say this) — he submitted the work before the eotwash group came out with theirs, but the paper was held up in PRL reviewing.

    Anyway, of course it’s science and it doesn’t matter who “got there first”, but I think it is very interesting to see that there are competitive constraints coming from an entirely different sector.

  • Simon DeDeo

    PS: not “beat the limit”, sorry — but definitely competitive (eotwash get 0.045 mm, DP came up with 0.08 mm).

    The era of “human scale” numbers in quantum gravity is coming to an end…

    I should reiterate since Chad is here that my comments here are made good-naturedly and without wishing to in any way diminish the incredible eotwash achievements.

  • Jack

    Sorry, I’m a bit lost. Can we say that these results are a fatal/nearly fatal blow to the large non-warped extra dimensions scenario?

  • Sean

    Jack — no, not really, we can just say what the limit is, as above. The “favorite” place to have two large extra dimensions was at a millimeter, and that’s now ruled out. But the models can be saved by increasing the six-dimensional Planck scale, or by having more than two large dimensions.

    Simon — I haven’t read the paper, but the abstract refers to the AdS curvature radius in warped models, which isn’t exactly the same as the radius of the extra dimensions in ADD models (where the compactification is flat). Maybe it would also apply.

  • a

    The Eot-Wash experiments are very interesting for many issues, but they never had any possibility of observing extra-dimensional 6d gravity: this specific signal was already excluded by astrophysics. This was recognized long ago, see e.g. the PDG review, page 8.

  • Charles T

    I come down on Sean’s side in this debate. I am not a physicist at all – just someone previously educated in maths with an interest in physics in general and quantum gravity in particular. Eot-Wash gets plenty of publicity in the popular press such as New Scientist.

    It includes a good anecdote about how melting snow on the surrounding mountains upset the calibration of their equipment between summer and winter. I think this gives a good idea of the incredible sensitivity of their experiment.

    I think it should very apparent to an educated layman with a passing interest in quantum gravity that this is serious and important work and one of the very few experiments that is directly probing the predictions of and putting constraints on some quantum gravity models.

    For the record, I am also very interested in following recent tabletop results that hint at axion-photon mixing and I am looking forward to following up some of the other links in the posts above from Christine Dantas and others.

    Thanks for another interesting post.

  • Matt

    Anyone brave enough to attempt to answer an extra-dimensional question from a non-scientist?

    I understand the rationale behind positing extra dimensions in small scales to explain anomalies in gravity. Mostly. But if those dimensions disappear at the observable level, what are cosmologists talking about when they discuss the “shape” of the universe?

    E.g., the soccer ball shape, or the horn shape? I always picture the “shapes” as a three dimensional analog in a higher-dimensional space. Or, more accurately, I picture a two-dimensional world on a piece of paper, wrapped into a horn shape, or whatever, where the “shape” exists only in a higher dimension than what the 2D paper dwellers are aware of. Then I try to do the same thing +1 dimension, so our 3D universe wrapped into a 4D horn or soccer ball. Is that not an accurate analogy?

    If not, how can 3D space be warped or shaped, without a higher spacial dimension to warp in?

  • Sean

    Matt, the small-dimensions idea and the shape-of-the-universe idea are not directly related. When cosmologists talk about the shape of the universe, it’s the three big and noticeable dimensions they’re talking about.

    And space can definitely be warped without being embedded in something bigger. It’s hard to visualize, I know. If the whole universe were the surface of a two-dimensional sphere, we could still tell (even if we couldn’t step outside to an extra dimension), for example because initially parallel lines would eventually come together.

  • Matt


    Thanks for the clarification. I hate having my mental analogies taken from me. I’ll try to come up with something new.

  • Simon DeDeo

    Sean — yes, very true. I believe Dimitrios’ measurement is sensitive to what eotwash is not, and vice versa.

  • Alex R

    This is very neat stuff, but I don’t see why it’s all that surprising that their work is not that widely known.

    After all, they do beautiful, incredibly precise experiments that lead to, at least so far… null results.

    Now, null results are important and interesting in themselves, especially when they are sufficiently precise to exclude promising fundamental theories. But it requires a certain kind of abstract mind to get excited by them.

  • Shantanu

    (Sean, for some reason when I posted this comment previously, it was rejected by a spam filter)
    Anyhow I am between Sean and Chad on this. The EOTWASH experiment is definitely
    on everyone’s radar. However there are many other excellent table top gravity experiments
    which get very little attention and are never discussed anywhere. One example I can think
    of is the neutron COW experiment. I know that many high energy physicists and even
    people working in gravity do not even know what the acronym “COW” stands for, even though
    this fascinating experiment (at the interface of gravity and foundations of quantum mechanics) was first done more than 30 years ago.

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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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