- Update - van der Waals and Casimir: Nima told me an obviously true statement whose validity I did not appreciate although I had to know it because it is apparently explained in the Landau-Lifshitz books. I thought that there were too problematic forces competing with gravity: the Casimir force and the van der Waals forces. In fact, they're the same one-loop effect. The Casimir force is a macroscopic description of the overall effect of van der Waals forces between the atoms of the metallic plates.

What do you need in their experiment? You need a one-meter-long fiber and a hanging gadget whose size is seven centimeters. There are mirrors on the gadget: because they reflect a laser beam, you can measure the orientation of the gadget.

On that gadget, you find a horizontal disk with many holes that respect a Z_{21} symmetry. This disk can rotate relatively to another disk beneath it. In the experiments, it rotates very slowly, with a period comparable to several hours. The existence of holes exerts a gravitational torque on the gadget whose magnitude is periodically oscillating. This effect caused by gravity is still pretty large. Because you want to study deviations from the "1/r^2" force law, you add another disk with holes whose torques exactly cancel the previously discussed torques assuming that Newton's law is exact.

That's a method to measure the hypothetical deviations only. You must be careful about many details - for example, you must insert a thin conducting foil in between the different layers to screen the electromagnetic effects including the Casimir forces. This foil is really thin because eventually you are able to measure the forces at distances slightly below 100 microns.

The deviations are conveniently parameterized as a Yukawa force that is, relatively to Newton's force, suppressed by the factor "alpha.exp(-r/r0)". You measure the angular orientation of your gadget and finally you evaluate the data: you allow the coefficient "alpha", the distance scale of the new force "r0", as well as various parameters of your gadget's mass distribution to vary, and you calculate the best fit.

After having made several versions of their experiment with slightly modified details, they end up with

- alpha = (-0.7 +- 0.9) x 10^{-4}

The intermediate results indicated some effects - equivalent to an additional repulsive force - but these were just 3 sigma effects that disappeared when they tried to do things slightly differently.

They also measure a possible existence of the preferred reference frame and other unusual terms and they can show that the coefficients of the terms responsible for these effects are at least 100,000 times weaker than what you would normally expect if you assumed that CPT and the Lorentz invariance are broken at the Planck scale. While Lee Smolin waits for GLAST to prove his unusual theories that the normal Lorentz invariance is broken, I think that these terrestrial experiments have already falsified these bizarre theories, proving that they were indeed (easily) falsifiable.

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