TO SOME, it might seem that Eric Adelberger is on a wild goose chase. Not only is he trying to disprove Newton鈥檚 law of gravity, which has withstood over 300 years of scrutiny, but for years now every experiment he has done at the University of Washington in Seattle has come up with zilch.
Despite this, Adelberger has no shortage of graduate students keen to help, even though they are all getting null results too. So what鈥檚 going on 鈥� why do they bother? Because the first person to find what they are looking for will make history. Find the blip, and you have proved that gravity leaks out from our world into hidden dimensions.
It might seem like a far-fetched scenario, but it seems to be the best way to explain the strangeness of gravity, a force totally unlike the three others we have observed in the universe 鈥� the electromagnetic, strong and weak forces. For a start, every bit of matter, from the tiniest speck of dust to the greatest star, generates gravity and attracts every other thing. But its most curious aspect is its strength.
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Gravity is vastly weaker than the other three forces. You only have to look at a fridge magnet to see that: even for a fairly heavy magnet, gravity鈥檚 pull 鈥� which is also proportional to the enormous mass of the Earth 鈥� is as nothing compared with the attraction to the fridge door. Nobody has yet managed to explain the huge gulf in strength between gravity and the other forces.
Adelberger鈥檚 search for an explanation began in 1998. That鈥檚 when Nima Arkani-Hamed, now at Harvard University, Savas Dimopoulous from Stanford University in California and Gia Dvali of New York University came up with a hypothesis. The three theorists had been playing with the idea of extra dimensions, because modern theories that unite gravity and the other forces of nature often require that the universe has extra spatial dimensions too tiny for most experiments to observe (快猫短视频, 29 September 2001, page 26).
Arkani-Hamed and his colleagues did some reading and uncovered something intriguing about these extra dimensions. 鈥淭hey dilute any force that goes there,鈥� Arkani-Hamed says. 鈥淭here鈥檚 just a lot more room to spread out, so the forces appear to be weaker.鈥� They realised that this might be the answer to the physicists鈥� puzzlement. But how to find out for sure?
One of the predictions of the theory is that leakage into those extra dimensions might cause gravity to deviate from Newton鈥檚 inverse square law. This law of gravitational attraction says that the mutual pull of two objects decreases in proportion to the inverse of the square of their separation. That鈥檚 because the way gravity varies with distance depends on the number of dimensions the space has.
In three dimensions, the surface area of a sphere surrounding a point mass increases as the square of the radius of the sphere. The idea is that, since the total 鈥渁mount鈥� of gravity reaching successively larger spheres should remain constant, the strength of that gravity therefore falls off like the inverse of the square of the distance. In four dimensions the surface area of a sphere depends on the cube of the radius, in five it鈥檚 the fourth power, and so on. So in higher-dimensional spaces, the force of gravity must dissipate ever more rapidly, which means it will no longer obey Newton鈥檚 inverse square law, but some law in which its strength falls off far more sharply.
Strange attractor
It was a tantalising idea: if our universe has hidden dimensions, then at distances smaller than the size of the dimensions, particles might be attracted to each other in a way that breaks the inverse square law. The only problem is that most physicists think these extra dimensions could be very small indeed, and they believe the size that would make most sense is the so-called Planck length. This is a unit of length arrived at by combining quantum-mechanical and gravitational constants, and is roughly 10-35 metres 鈥� about a hundred-millionth of a trillionth of the size of a proton. However, although many physicists feel the Planck length is the natural scale for the bundled extra dimensions 鈥� and no experiment has ever ruled this out 鈥� it is still only an assumption. And it is one that Arkani-Hamed and his colleagues quickly undermined. They found that the extra dimensions could actually be much larger than the Planck length, without anyone having noticed. If you suppose that the fundamental scale is not the Planck length but rather the scale at which the weak force acts 鈥� changing one type of quark into another 鈥� then the extra dimensions could be as large as a millimetre.
It sounded absurd. Surely such large extra dimensions would have shown up in astronomical or cosmological observations? Apparently not. The team searched the literature and could find no experimental result or phenomenon that depended on gravitational attraction at very small scales. Though they tried to kill off their theory in every way they could think of, they failed. 鈥淚t survived and was consistent with all the experimental results we could imagine,鈥� said Arkani-Hamed.
So these extra dimensions might be accessible to experiments after all. But that鈥檚 not to say they would be easy experiments to perform: gravity is so weak that it is extremely difficult to bring together enough matter to generate a measurable force at a few millimetres of separation. After all, you can鈥檛 play around with things the mass of a planet in an Earth-bound laboratory. Nonetheless, Adelberger and his colleagues have slowly and surely been finding ways to put an upper bound on the size of the hidden extra dimensions.
For this they are standing on the shoulders of giants. The method used by Adelberger鈥檚 team owes much to the way Henry Cavendish first measured the strength of gravity in 1798. Cavendish used a torsion balance, a pair of weights arranged at the ends of a rod like a dumb-bell, and suspended in the middle by a thin wire. When he brought a test mass close to one of these weights, the gravitational attraction caused the bar to turn slightly, twisting the fibre. A mirror mounted on the wire reflected a beam of light, and by observing the motion of the reflected spot, Cavendish could measure the twisting of the wire and calculate the magnitude of the force.
鈥淭he gravitational field in the lab had changed. The pull of water in the rain-soaked earth was enough to upset the calibration鈥�
Adelberger鈥檚 experiment, allowing for two centuries of technological improvement, is pretty much the same. Like Cavendish, Adelberger and his colleagues suspend their apparatus from a wire. In their case the apparatus consists of a pendulum with 10 vertical holes bored symmetrically around the circumference of its base (see Diagram). Immediately below this pendulum are two metal discs called attractors, one above the other, which can be rotated. The attractors also have 10 holes drilled through them, but the holes in the thicker, lower disc are slightly larger, and are offset so that they lie halfway between the holes in the upper disc.
To look for gravitational anomalies, Adelberger simply sets the attractors rotating together. The rotation of the thin upper attractor alone would cause the pendulum to twist back and forth 10 times per rotation (each twist is around one ten-thousandth of a degree). That鈥檚 because the holes in the plates and the pendulum act, mathematically, like negative masses, which you can think of as attracting each other. However, the rotation of the lower, thicker attractor 鈥� or rather its offset holes 鈥� compensates for this. 鈥淵ou can arrange things so the peak of the signal from one plate corresponds to the trough of the signal from the other, so they just cancel out,鈥� Adelberger explains.
The result is that the pendulum should not twist at all, provided gravity follows an exact inverse square law. If, on the other hand, a component of the gravitational force from the lower disc decreases more rapidly with distance, its effect on the torsion balance will be negligible, since it is further away. The forces will no longer cancel exactly, and the pendulum will twist.
Adelberger and his colleagues have tested the idea at ever smaller separations between the pendulum and the attractor discs. So far they have published confirmation that gravity obeys the inverse square law down to around 160 micrometres, which means that any extra dimensions must be curled up smaller than that (Physical Review D, vol 70, p 42004). As yet unpublished results, obtained using a torsion balance with 42 holes amongst other technical improvements, constrain the extra dimensions down to 70 micrometres.
Progress is slow and painful, though. As the distance decreases, the researchers are fighting ever more sensitive effects. Part of the problem is simply the weakness of the signal they are trying to detect. The apparatus must be isolated from any gravitational effect that might nudge the pendulum and twist the wire, swamping the signal from the apparatus itself. The experiments take place in a vacuum to avoid twist induced by collisions with air molecules. Electrostatic attractions might also twist the pendulum: the researchers have attempted to overcome this by coating their apparatus with gold, and by putting a thin sheet of copper foil between the pendulum and the attractors. They have to get rid of almost all vibrations using a highly efficient damping system, and they must even compensate for local variations in the Earth鈥檚 gravitational field, which has thrown up its own difficulties.
One summer, one of Adelberger鈥檚 students went to great lengths to measure gravitational variations caused by factors such as the surrounding hills and mountains, so she could compensate for them by strategically placing large masses around the laboratory. A few months later she checked her experiment again and found that the gravitational field in the lab was no longer uniform. It took a while for her to realise what had happened: Seattle rain.
The main difference between summer and winter in Washington state is that there鈥檚 even more rain in the winter 鈥� a lot more. A quick calculation confirmed that the gravitational pull of the water in the rain-soaked earth was enough to upset her careful calibration. But all is not lost. Ultimately, the Washington team believe they can exclude subtle effects like this and explore distance scales of a few hundredths of a millimetre.
Torsion balances are not the only way forward. Groups at Stanford and the University of Colorado have constructed what amount to microscopic tuning forks made from single crystals of silicon. If you set one of these tuning fork vibrating and then bring a test mass up close to it, the gravitational attraction subtly changes the pitch of the tuning fork, and this change reflects the strength of the force. But again, errors can creep in.
Aside from eliminating stray vibrations, the experimenters have to watch out for electromagnetic fields and other effects. Even the ghostly Casimir force, caused by pairs of particles and antiparticles that spontaneously pop into existence out of the 鈥渆mpty鈥� space of the quantum vacuum, is far greater than the gravitational force and must be carefully accounted for. Preliminary measurements have still revealed no evidence of any deviation from the inverse square law down to the 10-micrometre scale.
Exotic merger
An even stranger test of gravitation is being carried out by a group at the National Institute of Standards and Technology at the University of Colorado, Boulder. Jeffery McGuirk and his colleagues are using one of the most exotic states of matter yet created by physicists. They cool a cloud of rubidium atoms to within a few billionths of a degree above absolute zero and watch them merge to form something that behaves like a single quantum object: a Bose-Einstein condensate.
鈥淭he reason we like Bose-Einstein condensates is that they are very small and very cold,鈥� McGuirk says. Very cold means that there is virtually no thermal vibration to obscure the force measurements. And very small means they are great for probing gravity at short distances.
In their experiment, McGuirk and his colleagues suspend a spherical drop of Bose-Einstein condensate in a magnetic field. The drop is about three thousandths of a millimetre in diameter, and contains roughly 100,000 atoms. Then they bring the condensate near a small glass test mass, which causes it to oscillate. 鈥淭he condensate particles kind of roll back and forth like balls in a bucket,鈥� says McGuirk. By taking a series of pictures of the sloshing condensate they can determine the frequency of the oscillation. As with the tuning forks, this frequency depends on the gravity of the test mass.
There is a catch, however. At these scales the Casimir force is about a billion times as strong as gravity 鈥� or at least the version that follows Newton鈥檚 inverse square law 鈥� giving a huge random noise effect. 鈥淭he only experiments that are sensitive to Newtonian gravity take place on a longer distance scale,鈥� McGuirk says. 鈥淏ut that doesn鈥檛 mean that these measurements can鈥檛 say something about effects beyond Newtonian gravity.鈥�
At small enough distances, McGuirk reasons, the curled-up dimensions might create some kind of anomaly in the condensate鈥檚 reaction to the test mass. There is also a chance that such experiments might reveal something about the fundamental nature of gravity 鈥� we still don鈥檛 know whether there is a gravitational particle or 鈥済raviton鈥�, the equivalent of electromagnetic photons. At small scales, something exotic like this may create enough extra force to show up over the Casimir background noise.
As yet, McGuirk and his colleagues have not published any results. In fact, all the various efforts to measure gravity at short distances have so far only confirmed Newton鈥檚 centuries-old leap of faith.
But nobody is disappointed, it seems. Though discovering new physics would be nice 鈥� Stockholm is a beautiful city to visit 鈥� Adelberger and all the others in this field are happy whatever the results. 鈥淲e鈥檝e extended the regime where we know what nature is doing substantially,鈥� Adelberger says. 鈥淚t would be wonderful if you actually had a stunning new discovery. But even if nature doesn鈥檛 roll its dice that way, you鈥檝e still done a lot.鈥�
