‘There is no conflict between quantum physics and gravity’: Physicists prove Einstein’s equivalence principle holds true at quantum scales

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.

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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.

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This apparatus, called 2D MOT, feeds the science chamber with cold atoms.

(Image credit: Or Dobkowski)

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 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.

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.