# Weighing the implications of negative-mass antimatter

Antimatter is anti- a lot of things, but it’s not supposed to be antigravity.

An antimatter particle does have the opposite electric charge of its ordinary matter counterpart. But the mass of both particles should be precisely equal. When an antiparticle meets its ordinary particle partner, they annihilate in a burst of energy, equal to their masses squared in accordance with Einstein’s famous formula E=mc^{2}.

Because you get energy out by destroying antimatter, you have to put energy in to create antimatter, which implies that antimatter’s mass must be positive. That’s one reason why most physicists immediately dismiss the idea that antimatter could have negative mass.

But thanks to some technical complications in the definition of mass, the case is not closed. To figure out whether such a thing as negative mass is possible in the universe, you have to know what kind of mass you’re talking about.

Sometimes you’ll hear physicists say there are two kinds of mass: inertial and gravitational. But actually mass is more like Gaul — it can be divided into three sorts: inertial mass, active gravitational mass and passive gravitational mass.

Inertial mass represents an object’s resistance to changes in its state of motion. (That’s the type of mass that particles acquire by interacting with the Higgs field, the source of the Higgs boson.) Active gravitational mass is the source of a gravitational field; passive gravitational mass is the mass that a field acts on.

In Newton’s physics, active and passive gravitational mass must be equal, by virtue of his third law of motion (the one about equal and opposite reactions). But for Newton it seemed to be just a happy coincidence that gravitational mass equaled inertial mass (which is the mass in Newton’s second law, about force and acceleration). Einstein, though, required inertial and gravitational mass to be equal — that was the principle on which he based his theory of gravity, general relativity.

If gravitational and inertial mass are equal, then antimatter can’t have negative gravitational mass, because it certainly has positive inertial mass. But suppose general relativity turns out not to be the last word on gravity. Then antimatter, despite having positive inertial mass, might still have negative gravitational mass.

That’s why several teams are doing or planning experiments to find out.

“In a world in which physicists have only recently discovered that we cannot account for most of the matter and energy in the universe, it would be presumptuous to categorically assert that the gravitational mass of antimatter necessarily equals its inertial mass,” physicists from the ALPHA collaboration at the European research laboratory CERN wrote in a recent paper.

Physicists have debating this point for decades. Some have contended that negative-gravity antimatter would violate the law of conservation of energy. But that argument apparently doesn’t hold up to advanced analysis invoking quantum physics. And you can’t very well say it must be so because general relativity says so, because the whole point is to test general relativity to see if it’s really right. And after all, since general relativity does not reconcile itself with quantum physics very well, something has to give somewhere.

If antimatter does possess negative gravitational mass, the gravitational force on an antiatom would point up, and so it would “fall” upward (because its inertial mass is positive, it accelerates in the direction of the force). But it’s not exactly easy to measure which way antiatoms fall. One problem is making antimatter atoms in the first place, but that has been done at CERN.

Still, apparatus of extreme delicacy is required to test the effect of gravity on antimatter. One early attempt, reported this year in *Nature Communications* by the ALPHA team, recorded the demise of 434 antihydrogen atoms confined in a magnetic trap. When the magnetism is turned off, the antiatoms collide with the walls of the container and annihilate. If antiatoms fall up instead of down, more of the annihilations should occur near the top of the container than the bottom.

That sounds simpler than it is. It’s a very complex experiment. The location of an annihilation depends on all sorts of things, such as how fast the magnetic field decays after it’s turned off and the energy possessed by the individual atoms. All those factors make the results rather imprecise.

If all went well, such an experiment could determine the precise ratio of antimatter’s gravitational to inertial mass. If Einstein’s general relativity is right, inertial and gravitational mass are identical, so that ratio would be exactly equal to 1. If antimatter has negative gravitational mass (of equal magnitude), that ratio would be –1. So far, the best the ALPHA experiment can conclude is that the ratio is probably no more than 110 or less than –75, which doesn’t exactly come close to answering the question.

Refinements in the technique may someday narrow that range. And there are other proposals, such as one using muonium (an antimuon plus electron) that might offer better precision. (A muonium experiment would have the additional benefit of testing whether antileptons behave the same way with respect to gravity as antiquarks, the main components of antihydrogen atoms.)

If any of the proposed experiments succeed in identifying negative mass of some sort, it won’t be the first time that taking a negative idea seriously led to an important discovery. Antimatter itself was first imagined by the physicist Paul Dirac only after he decided to take the idea of negative energy seriously, not to mention the even more bizarre notion of negative probabilities.

“Negative energies and probabilities should not be considered as nonsense,” Dirac declared in a lecture in 1941. “They are well-defined concepts mathematically, like a negative sum of money.” So maybe negative mass should not be considered as nonsense, either. But you shouldn’t bet on it. You’d probably end up with a negative sum of money.