Does E *always *equal mc²? University of Arizona physicist Andrei Lebed suspects not – and plans to try and check.

Einstein’s famous equation describes the fact that energy and mass are essentially the same thing and can be converted into one other. It’s since been validated in countless experiments and calculations – indeed, many technologies including mobile phones and GPS navigation depend on it.

But, says Lebed, it may not always be true, if inertial mass and gravitational mass aren’t, as generally believed, the same thing.

According to the accepted view, there’s no difference between the mass of a moving object that can be defined in terms of its inertia, and the mass bestowed on that object by a gravitational field. The idea was first introduced by Galileo Galilei, and has been confirmed with a very high level of accuracy.

“But my calculations show that beyond a certain probability, there is a very small but real chance the equation breaks down for a gravitational mass,” says Lebed.

If one measures the weight of quantum objects often enough, he says, the result will be the same in the vast majority of cases. However, a tiny portion of those measurements give a different reading, in apparent violation of E=mc².

This has physicists puzzled – but could make sense if gravitational mass was not the same as inertial mass.

“Most physicists disagree with this because they believe that gravitational mass exactly equals inertial mass,” says Lebed. “But my point is that gravitational mass may not be equal to inertial mass due to some quantum effects in General Relativity, which is Einstein’s theory of gravitation. To the best of my knowledge, nobody has ever proposed this before.”

According to Lebed, the curvature of space could make gravitational mass different from inertial mass – and this means it would be possible to test his theory away from Earth, where space is no longer curved, but flat.

It would mean measuring the weight of the simplest quantum object, a single hydrogen atom, which only consists of a nucleus, a single proton and a lone electron orbiting the nucleus.

Sometimes, the electron whizzing around the atom’s nucleus jumps to a higher energy level and then falls back. According to E=mc², the hydrogen atom’s mass will change along with the change in energy level. Away from the curvature caused by the Earth, though, this wouldn’t be able to happen.

“In this case, the electron can occupy only the first level of the hydrogen atom. It doesn’t feel the curvature of gravitation,” says Lebed.

“Then we move it close to Earth’s gravitational field, and because of the curvature of space, there is a probability of that electron jumping from the first level to the second. And now the mass will be different.”

Instead of measuring weight directly, these energy switching events could be detected by their emitted photons, or light.

What Lebed wants to do is send a small spacecraft with a tank of hydrogen and a sensitive photo detector into space. Here, the relationship between mass and energy is the same for the atom, but only because the flat space doesn’t permit the electron to change energy levels.

“When we’re close to Earth, the curvature of space disturbs the atom, and there is a probability for the electron to jump, thereby emitting a photon that is registered by the detector,” he says.

According to Lebed, his work is the first proposition to test the combination of quantum mechanics and Einstein’s theory of gravity in the solar system.

“There are no direct tests on the marriage of those two theories,” he says. “It is important not only from the point of view that gravitational mass is not equal to inertial mass, but also because many see this marriage as some kind of monster. I would like to test this marriage. I want to see whether it works or not.”