According to legend, it was Galileo Galilei who first performed one of science’s most famous experiments. After dropping a pair of cannonballs of different weights off the top of the Leaning Tower of Pisa, he heard the two balls hit the ground at the same instant. In this way he proved what physicists would later call the principle of equivalence: all objects fall at the same rate, regardless of their mass or composition, provided there are no forces acting on them other than gravity.
Whether or not Galileo really performed this experiment, it is the prototype of an iconic demonstration in physics, requiring only a pair of weights and a vacuum chamber to eliminate air resistance. The equivalence principle that it demonstrates has meanwhile become a cornerstone of Einstein’s general theory of relativity, the model of gravity that has reigned for nearly a century.
Now two physicists at Stanford University in California, Mark Kasevich and Savas Dimopoulos, are preparing to challenge this whole premise, with a modern Tower of Pisa. Rather less picturesque than the Tuscan original, theirs is a shaft dug 10 metres down from a basement laboratory. Instead of dropping cannonballs, they will launch rubidium atoms upward and watch them fall down again. To measure the rate of descent, they will use an exquisitely sensitive timing method. The result: a test of the equivalence principle and general relativity far more stringent than any that has gone before.
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Why would they want to do that? Because, says Dimopoulos, “there is something big that we don’t understand about gravity”. Researchers believe we may find a breach in the principle of equivalence or general relativity if we look hard enough, and that this would give us a major clue to what is missing. A breach could, for instance, reveal the first evidence for exotic new particles or extra dimensions of space that have long been postulated by theorists, including Dimopoulos. It could help physicists arbitrate between several proposed theories of quantum gravity that strive to unify gravitation with the other forces of nature.
There is a good reason for all this theorising. Although both general relativity and the equivalence principle have never been found wanting in even the most assiduous experimental tests, they do have one big shortcoming: they are strangely incompatible with established quantum theory. All the known forces of nature besides gravity – electromagnetic, strong and weak – are mediated by the exchange of subatomic particles. In other words, these forces come in discrete quantum chunks. Not so with gravity. According to general relativity, gravity is created by the curvature of space-time, something we can’t even see because it is woven into the fabric of our universe, and is apparently smooth and indivisible.
What’s more, every force apart from gravity acts on different particles in different ways. Gravity appears to be indiscriminate: it acts on everything, including light. Even more perplexingly, all signs point to it being more than 30 orders of magnitude weaker than the other forces. This lucky fact is what keeps your chair from falling through the floor, as the electrical bonds that hold together a layer of wood are stronger than the gravitational pull of an entire planet.
Dimopoulos and others proposed in 1998 that gravity operates in extra dimensions of space beyond the three we can see, and that this dilutes its apparent strength in the everyday world. The idea came from string theory, the leading approach to quantum gravity, in which extra dimensions of space contain vibrating loops of “string” that give rise to all the familiar forces and particles. Trouble is, this idea can only be tested if we probe at suitably small scales – something that is technically difficult, to say the least.
Enter Kasevich, who has built up considerable expertise in a technique called atom interferometry, which he has used to measure the acceleration of atoms due to gravity, among other things. This high-precision method became feasible in the mid-1990s, thanks to major advances in the cooling of atoms. In 2002, Kasevich happened to run into Dimopoulos in the departmental coffee room, and the two hatched a plan to use the technique to push general relativity as far as it would go – and possibly discover new physics.
Zero in on gravity
Most tests of relativity have taken the form of observations of what goes on in outer space. This makes them difficult if not impossible to control. “You can’t change the orbital velocity of Mercury,” points out Jason Hogan, a graduate student in Kasevich’s lab. With atom interferometry, more control is possible. “You can change the launch velocity of the atoms in our experiment,” Hogan says. There are other inherent advantages too. “The atom is a very clean system, easily isolated from outside forces,” Kasevich says. That enables the researchers to zero in on the effects of gravity.
Not that atoms are easy to work with. The experiment taking shape at Stanford blends the Tower of Pisa method with ultra-modern technology (). In the interferometer shaft, a few million rubidium atoms will be cooled by lasers to a few millionths of a degree above absolute zero. Then they will be launched upwards by a precisely tuned blast of laser light from below. This is already impressive – imagine trying to kick a cloud – but the really mind-bending part of the story is what happens next.
According to the weird laws of quantum physics, each rubidium atom is in two places at once. If you tune the laser just right, “half” of the atom is launched upwards rapidly by the laser blast, and “half” of it is launched more slowly. While the atom is in this strange combination state, it is hit by a second blast of laser light that acts like the mirror image of the first: it excites the slow half of each atom’s split personality, and slows down the fast half. After 1.3 seconds – the time it takes for the atom to rise to the top of the 10-metre vacuum chamber and fall back down again – the two halves catch up with each other and merge, thanks to a third, coordinating laser blast (see Diagram).
Except that they don’t exactly merge – they interfere with each other, and hence the instrument is an interferometer. According to quantum physics, each atom behaves like a wave as well as a particle, and its history is encoded in its “phase”, the exact timing of the wave’s vibrations in space. When a wave interacts with itself after taking two different paths, it produces a distinctive pattern of bands called interference fringes.
Red balls, green balls
How will these show up in the experiment? Imagine, for simplicity, that each half of each rubidium atom’s split personality is a ball of a different colour: green for the ones that started out fast and then slowed down, and red for those that started out slow and then speeded up. It looks as if you have launched a million red balls and a million green balls, and you might think you would see a million red balls and a million green balls coming back down. But that’s not what happens. Each atom’s quantum oscillations make it appear to change from red to green and back many times per second. Because of the interference, the researchers might detect two million red balls in one place, and two million green balls in another. According to general relativity, gravity will slow down these oscillations by millions of cycles over the course of one second. Any discrepancies due to violations of the equivalence principle, if they exist, will be much smaller – a shift of less than a millionth of a cycle – but still detectable.
What this means is that Kasevich and Dimopoulos can take two isotopes of rubidium with different atomic masses – rubidium-85 and rubidium-87, directly analogous to Galileo’s light cannonball and heavy cannonball – and see whether gravity acts upon them in exactly the same way. If it doesn’t, it would shake the foundations of relativity and perhaps usher in the era of quantum gravity. If the equivalence principle holds up, the researchers plan to test several unconfirmed predictions of relativity (see “What Einstein knew”).
It’s unlikely to be plain sailing. “Whoever commits himself or herself to doing these experiments must cultivate a spirit of patience,” says Francis Everitt, the leader of NASA’s Gravity Probe B, a different test of general relativity. Because the effects being sought are so tiny, every possible source of error must be either eliminated or calculated with extreme accuracy. A triple shielding of metal will insulate the atoms from Earth’s magnetic field. Massive pieces of lead will be placed around the lab to correct for variations in Earth’s gravitational field. Even one person walking around the lab could contaminate the results. “The whole history of these experiments is that all of your effort goes into controlling the systematic problems,” says Eric Adelberger of the University of Washington, Seattle, whose team has performed tests of how gravity behaves at distances below 1 millimetre. “It’s not so easy.”
Assuming the Stanford experiment can be made to work, it could open a whole new window into gravitational phenomena. “There must be more fundamental physics to be done with it,” says Peter Graham, a graduate student working with Dimopoulos. Initially, the researchers expect to verify the principle of equivalence to 1 part in 1015, a 300-fold improvement over the best measurements to date (see “How low can you go?”).
In a more advanced experiment, they plan to test gravity’s effects at short range. They will bring a small mass made of iron or silicon, say, to within a fraction of a millimetre of the rubidium-atom fountain in the shaft. If two equal masses of iron and silicon are shown to have different gravitational effects on the atoms, as recorded by the proportion of “red balls” and “green balls”, it would signal a violation of the principle of equivalence.
Such a violation, though sure to be controversial, could bolster any number of alternative models of gravity. String theorists have long proposed that gravity is conveyed by particles that they call “moduli”, which represent vibrations of space-time. This is consistent with Einstein’s idea that gravity is produced by the curvature of space-time, but one key difference is that the moduli vibrate in extra dimensions that radiate out from our everyday four-dimensional space-time like the petals of a rose. Also, the moduli, unlike Einstein’s gravity, have the quantum property of spin, which means they should interact with different particles in different ways, and so violate the equivalence principle.
Shape of things to come
Recent experiments by Adelberger suggest that any curled-up extra dimensions must be smaller than 44 micrometres in length (Physical Review Letters, vol 98, p 021101). If Dimopoulos’s idea is correct, the effects of quantum gravity – including a violation of the equivalence principle – should become visible, even in our own space-time, at some distance below this. If the researchers observe gravity being conveyed by moduli, their interactions with particles like electrons and quarks could reveal the size and shape of the extra dimensions they come from. Quantum gravity, once seen as untestable, would begin to fall within the realm of experiments.
The first evidence of relativity’s failings might show up before then, however, courtesy of Gravity Probe B. Launched in 2004, the satellite-based experiment was designed to test the principle in general relativity that the Earth’s rotational energy should generate its own gravitational field. Any discrepancy there could point to new physics. The Gravity Probe B team is due to announce its results within the next few weeks, while Kasevich and Dimopoulos will not even start collecting data until the middle of the year. Coincidentally, Kasevich is working in a lab that was once used by Gravity Probe B researchers, before they moved to a new building. There is no collaboration between the two groups, but also no rivalry. “They will be complementary experiments,” says Everitt. “In my view as a hard-nosed experimentalist, almost any new test is worth doing.”
In the end, whether atom interferometry upholds general relativity or illuminates a more fundamental path to quantum gravity, it will certainly provide theorists with food for thought. “Not all discoveries come from new concepts. Some come from new technological marvels,” says Dimopoulos. “Right now, with the atom interferometer, we’re in an era where technology has gotten way ahead of the theory.” It’s time to make use of it, he says, so that theorists can catch up.
What Einstein knew
Although a violation of the equivalence principle would be an epochal discovery, the Stanford University researchers are prepared for the much more likely outcome that the principle will hold up. If so, they will go on to test two predictions of general relativity that have never been confirmed, for lack of measurement precision. First, a slow-moving object should feel a slightly different gravitational force from a fast-moving one. Second, Earth’s gravity itself should gravitate. The latter is a consequence of Einstein’s E = mc2, which says energy and mass are interchangeable. If that is so, the energy in Earth’s gravitational field should produce a bit of its own gravity, just as mass does. Each of these effects should be just detectable by the Stanford experiment.
How low can you go?
Since Galileo’s time, tests of the equivalence principle – the idea that gravity acts on all matter in the same way – have delved down to ever tinier levels. In the early 20th century, the physicist Loránd Eötvös demonstrated it to an accuracy of 5 parts in a billion (109) by placing two masses of different materials on either side of a “source mass” attached to one arm of a torsion balance – an arm suspended from its centre on a wire. If the mass were attracted more to one material than the other, the arm would swing slightly in its direction, against the resistance of the wire.
At the University of Washington, Seattle, Eric Adelberger’s team has updated the Eötvös experiment by putting the torsion balance on a smoothly rotating platform. In this set-up, any difference in the source mass’s attraction to the two test masses would cause the arm to oscillate like a horizontal pendulum; the oscillations would build up over time, making them easier to detect. The “Eöt-Wash” experiment has so far found no violation of the equivalence principle: any difference in the gravitational acceleration of the two masses is at most 3 parts in 1013.
Other modern tests have been astrophysical. In 1971, Apollo 15 astronaut David Scott performed the Galileo experiment on the moon, dropping a hammer and an eagle feather at the same time. Sure enough, they landed in spooky unison. More seriously, Apollo astronauts also installed mirrors on the moon, which could be used to measure the Earth-moon distance to millimetre precision. These lunar ranging tests have confirmed that Earth and the moon respond to the sun’s gravity in identical ways, to within 1 part in 1012.
In other words, the equivalence principle remains watertight – so far.
