Nothing But Uncertainty

Over at Backreaction, Bee has a nice post about uncertainty, in the technical sense, not the quantum sense. The context is news stories about science, which typically do a terrible job of handling the uncertainties and caveats that are an essential part of science.

Properly dealing with uncertainty is one of the hardest parts of science. Which is why I’m particularly impressed by people who spend their whole careers measuring nothing but uncertainties– looking for an electric dipole moment for the electron, or parity non-conservation, or Lorentz violation, or any of a bunch of other things that may not exist. Such as deviations from the inverse square law of gravity. As ZapperZ notes, there’s a new result here (the official journal link is at the bottom of the post; this goes to the freely available arXiv preprint), putting a new limit on the possible size of “extra” dimensions of space: if they’re there, they’re probably smaller than 10 microns, or about a tenth of the diameter of a human hair.

As with all such experiments, this one is a tour de force, using a silicon cantilever as a gravity detector. Here’s the experimental apparatus as depicted in their paper:

There’s some background information in this old post about a different measurement of the inverse square law at short distances (I have a better graphic in Chapter 10 of the current book draft, which covers the same topic), but the basic idea is that it may be possible to detect the “extra” dimensions of space predicted by some exotic physics theories through their effect on gravity. If the dimensions are large enough, and if gravity is not confined to our usual four dimensions (three of space, one of time), then the force of gravity should get dramatically stronger when two attracting objects are separated by a small enough distance.

Making such a measurement requires two things: a way to get two test masses really close together, and a way to measure the force between them. The Stanford group responsible for the new result has a clever solution to this: they use tiny gold bars (about 100 microns square by 1 millimeter long) as the perturbing mass, and a tiny bit of gold (about 1 microgram) at the end of a silicon cantilever as their test mass. They detect the force between the gold bars and the test mass by looking at how the cantilever vibrates in response to the tiny gravitational force between the bits of gold. The whole experiment is done at cryogenic temperatures (10-20 K), to minimize other possible sources of noise, and they did extensive checks to exclude the possibility of magnetic or electric forces, and even the Casimir effect.

To make it easier to see a signal, their test masses are arranged in an alternating pattern of heavier gold barns and lighter silicon ones, and this pattern is moved back and forth beneath the cantilever. They can readily predict the force experienced by the test mass, provided that gravity follows the inverse-square law known since the time of Isaac Newton. If large extra dimensions exist, though, the force should deviate from their prediction, and that’s what they’re looking for.

And what did they measure? Well, they measured zero. They did not see any significant deviation from Newton’s inverse-square law, down to separations of about 30 microns between the gold bars and the test mass.

Of course, this null measurement isn’t an absolute– they can only say that there is no deviation within the uncertainty of their experiment. Possible deviations from Newtonian gravity are expressed in terms of a parameter α, which can vary with the “range” of the extra force (which is related to the size of the extra dimensions). The results are summarized in this plot:

That’s a little confusing to look at at first, but it’s a plot of possible values of α as a function of the range (given the symbol λ). Anything in the shaded region has been excluded with 95% confidence– that is, those are the values we know with confidence that α can’t have. The white regions are still possible, and the dotted lines indicate the predicted values for α according to various exotic theories.

The result of this particular experiment was to exclude the region shaded in green. They’ve improved the limit by about half an order of magnitude in α for a range of ten microns– a small shift in the total excluded region, maybe, but still a significant achievement.

Of course, the work here is never done– there’s still white on the plot, and there are still theories that might be viable. And, indeed, the conclusion of the paper includes a few suggestions of ways that they might be able to push this even further– to make an even better measurement of zero.

Obviously, this sort of work requires a certain type of personality. I have the utmost respect for the people who do this sort of thing, mostly because I know I could never do it myself.

And, of course, to return to the opening point, this work should make people who do climate change research happy: no matter how much trouble you may have getting people to accept the uncertainties in your work, these guys have it much work– they’re dealing with nothing but uncertainty, from start to finish…

Geraci, A.A., Smullin, S.J., Weld, D.M., Chiaverini, J., Kapitulnik, A. (2008). Improved constraints on non-Newtonian forces at 10Â microns. Physical Review D, 78(2) DOI: 10.1103/PhysRevD.78.022002