The puzzle of how Einstein’s equivalence principle plays out in the quantum realm has vexed physicists for decades. Now two researchers may have finally figured out the key that will allow us to solve this mystery.

Einstein’s physical theories have held up under pretty much every classical physics test thrown at them. But when you get down to the very smallest scales – the quantum realm – things start behaving a little bit oddly.

The thing is, it’s not really clear how Einstein’s theory of general relativity and quantum mechanics work together. The laws that govern the two realms are incompatible with each other, and attempts to resolve these differences have come up short.

But the equivalence principle – one of the cornerstones of modern physics – is an important part of general relativity. And if it can be resolved within the quantum realm, that may give us a toehold into resolving general relativity and quantum mechanics.

The equivalence principle, in simple terms, means that gravity accelerates all objects equally, as can be observed in the famous feather and hammer experiment conducted by Apollo 15 Commander David Scott on the Moon.

It also means that gravitational mass and inertial mass are equivalent; to put it simply, if you were in a sealed chamber, like an elevator, you would be unable to tell if the force outside the chamber was gravity or acceleration equivalent to gravity. The effect is the same.

“Einstein’s equivalence principle contends that the total inertial and gravitational mass of any objects are equivalent, meaning all bodies fall in the same way when subject to gravity,” explained physicist Magdalena Zych of the ARC Centre of Excellence for Engineered Quantum Systems in Australia.

“Physicists have been debating whether the principle applies to quantum particles, so to translate it to the quantum world we needed to find out how quantum particles interact with gravity.

“We realised that to do this we had to look at the mass.”

According to relativity, mass is held together by energy. But in quantum mechanics, that gets a bit complicated. A quantum particle can have two different energy states, with different numerical values, known as a superposition.

And because it has a superposition of energy states, it also has a superposition of inertial masses.

This means – theoretically, at least – that it should also have a superposition of gravitational masses. But the superposition of quantum particles isn’t accounted for by the equivalence principle.

“We realised that we had to look how particles in such quantum states of the mass behave in order to understand how a quantum particle sees gravity in general,” Zych said.

“Our research found that for quantum particles in quantum superpositions of different masses, the principle implies additional restrictions that are not present for classical particles – this hadn’t been discovered before.”

This discovery allowed the team to re-formulate the equivalence principle to account for the superposition of values in a quantum particle.

The new formulation hasn’t yet been applied experimentally; but, the researchers said, opens a door to experiments that could test the newly discovered restrictions.

And it offers a new framework for testing the equivalence principle in the quantum realm – we can hardly wait.

The team’s research has been published in the journal *Nature Physics*.