Einstein's equivalence principle confirmed at quantum scale

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For the first time, physicists have measured the tiny quantum shift an object acquires by falling through Earth's gravity — an effect of Einstein's relativity that was predicted almost a century ago but never observed.

Researchers placed ultracold rubidium atoms into a superposition, a quantum state in which a single particle takes two paths at once. In this experiment, one path put the atom in free fall while the other kept it motionless. Recombining the atoms revealed an almost imperceptible difference between the two paths.

The measurement, published Sept. 2 in the journal Science Advances , shows that Einstein's equivalence principle — the idea at the heart of general relativity — still holds when it is pushed into the quantum world, creating a small but tantalizing link between relativity and quantum mechanics .

"The principle says that acceleration and gravity cannot be distinguished locally," Vlatko Vedral , a physicist at the University of Oxford and a co-author of the new study, told Live Science via email.

Einstein's happiest thought

The classic illustration of the equivalence principle is a thought experiment known as Einstein's elevator. A person sealed in a windowless elevator cannot tell whether the floor is pressing against their feet because the elevator is parked motionless on Earth or because it is being accelerated through empty space. Einstein called that realization the "happiest thought" of his life and built general relativity around it.

For heavy, everyday objects, the equivalence principle has been tested to extraordinary precision. Quantum objects are a different matter. They behave like waves, and each wave carries a quantity called phase — essentially, where its crests and troughs sit. Phase cannot be seen directly, but when two versions of the same particle are recombined, any mismatch between their phases shows up as an interference pattern. The two waves reinforce each other in some places and cancel each other out in others, thereby changing the odds of where the particle turns up.

Theory says that a wave in free fall should build up phase relative to an identical wave held still and that this phase should grow with the cube of the falling time. Therefore, doubling the fall time multiplies the effect eightfold. Charles Galton Darwin, a grandson of the famous naturalist, and Earle Kennard both documented this prediction in 1927 ‪—‬ but no one had measured it until now.

An atom that falls and stays still at once

This apparatus, called 2D MOT, feeds the science chamber with cold atoms. (Image credit: Or Dobkowski) Catching the effect required an instrument with one arm genuinely at rest with respect to Earth and the other in genuine free fall ‪—‬ something no previous experiment could supply. Matter-wave experiments going back to the neutron interferometry of the 1970s had measured gravity in other ways, but never with that pair of trajectories.

The team behind the new study, led by physicist Ron Folman at Ben-Gurion University of the Negev in Israel, chilled roughly 20,000 rubidium atoms into an exotic state of matter called a Bose-Einstein condensate , released them from their magnetic trap and ran the interferometer about 113 micrometers beneath an "atom chip" patterned with gold wires only 2 micrometers thick.

Radio and microwave pulses put each atom into a superposition of two magnetic states. A magnetic kick launched one of them upward, and a fraction of a millisecond later, a second pulse made that half insensitive to magnetic fields so that it rose and fell under gravity alone. The other half remained magnetically sensitive and felt a force tuned to cancel gravity exactly, leaving it suspended in place.

At the top of the arc, the two halves of a single atom stood about 7.5 micrometers apart ‪—‬ about seven times the width of the atomic wave itself — before the sequence was reversed to bring them back together. The team named the device the quantum Galileo interferometer, after the scientist who first argued that all objects fall at the same rate.

"Two different accelerations can be superposed, zero [acceleration] and the Earth's gravitational acceleration, and the resulting quantum interference measured," Vedral said.

A phase predicted almost 100 years ago

The researchers tracked the interference signal as they stretched the free-fall time to about 2.4 milliseconds. Across 633 runs over 5.3 hours, they recorded 13 complete oscillations, each one a full cycle of phase built up between the two halves of the atom. The growth followed the cube of the falling time, matching the theoretical model to within about 2.5%.

"The phase between the two elements of the superposition, which grows as the cube of the duration of the experiment and which was predicted a long time ago, in 1927, has now finally been observed for the first time," Vedral said.

The result matters because the same phase can be derived in two completely different ways: One treats gravity as a force acting on a quantum wave; the other moves into the falling frame, where gravity vanishes, and invokes the equivalence principle. Both give the same answer, and that agreement is what allows quantum mechanics and general relativity to coexist.

"They tell us that, at this level of accuracy, there is no conflict between quantum physics and gravity," Vedral said. "In other words, the equivalence principle is perfectly compliant with quantum mechanics."

The difficulty of bringing the two halves back together

The hardest part of the experiment was the recombination. Because the two halves of the atom end up moving at very different speeds, returning them to overlap in both position and motion is extremely demanding. Physicists Marlan Scully, Berthold-Georg Englert and Julian Schwinger named the problem the "Humpty-Dumpty effect." The magnetic fields also curve across the atom cloud, distorting the two halves in different ways.

The contrast of the interference fringes started at 80% for short runs and faded to 20% for the longest run, setting a practical ceiling on how long the experiment can run. The authors also cautioned that their measurement does not rule out every theory in which the equivalence principle breaks down, because some of those theories predict the same phase.

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The team now wants to test the equivalence principle under more general conditions, such as the "same experiment in a rotating frame," Vedral said. "Even more interestingly, performing an experiment in which two such systems are superposed and can gravitationally affect one another" would further test the results, he added.

That last idea points toward one of the field's central open questions. Scaling up the technique from atoms to far heavier objects, such as nanodiamonds, would let physicists ask whether gravity itself follows quantum rules and would open a route to testing the conjecture — championed by study co-author and Nobel laureate Roger Penrose — that gravity is what destroys quantum superpositions in the first place.

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