## Fact and fiction about negative mass

Sometimes science makes progress by adopting a negative attitude.

Electricity, for instance, would be impossible to understand without realizing that electric charge can be either positive or negative. Negative numbers once seemed a little suspicious, but they’re really useful for companies that lose money or for keeping track of temperatures in Antarctica. Even negative energy, weird as the idea seems, has been experimentally demonstrated.

And since energy is merely matter’s evil twin, you’d think that there would be such a thing as negative mass as well. But so far the evidence for negative mass is negatory. Or nugatory. Nobody has found the slightest sign of anything with negative mass in the real universe.

On the other hand, you can find lots of negative mass in science fiction, where writers have long proposed it as a source of antigravity to propel a spaceship. After all, antigravity is precisely the key property that negative mass would possess. The idea is at least as old as an 1827 science fiction novel called *A Voyage to the Moon*, by Joseph Atterley (a pseudonym for George Tucker, a professor of moral philosophy at the University of Virginia and former U.S. congressman). Atterley’s trip to the moon relied on the antigravity properties of a metal called lunarium.

“There is a principle of repulsion as well as gravitation in the earth,” an Indian sage told Atterley in the novel. It was found deep in a mountain in Burma in the form of a metal “united with a very heavy earth…. This metal, when separated and purified, has as great a tendency to fly off from the Earth, as a piece of gold or lead has to approach it.”

That sounds just like what negative mass would do. It’s the opposite of positive mass, and all positive masses attract each other. So positive mass would repel negative mass, right? Well, not exactly. It’s really a lot more complicated than that, as physicist Richard Hammond writes in a recent paper. A negative mass Newtonian apple would fall down to Earth just like a positive mass apple, he points out. But on a negative mass planet, both positive and negative mass apples would “fall” up.

That sounds weird, but it’s logical. For an ordinary apple, the Earth’s positive mass exerts an attractive force downward, and so, according to Newton’s second law, the apple will accelerate in that direction, toward the Earth. For a negative mass apple, the force would be negative, and therefore upward. But the acceleration would also be negative — that is, in the opposite direction of the force. So the negative mass apple would still fall downward.

Negative mass wouldn’t always behave like positive mass, though. Suppose you shot a negative mass bullet at a brick wall. When the bullet hits the wall, the wall exerts a force against the bullet, trying to push it back toward the gun. This force will accelerate the neg-mass bullet in the other direction — that is, through the wall. So no matter how thick the wall is, the bullet will speed right through it.

“This would explain why negative mass on earth has not been found,” writes Hammond, of the University of North Carolina at Chapel Hill. “First, it would fall to the earth. Then it would receive a mighty boost as it drills its way through the earth, being flung out far above the escape velocity on the other side.”

Of course, if the Earth itself consisted of negative mass, all the equations (and therefore the forces) are reversed, and all objects, whether positive mass or negative would “fall” upward.

At this point, you should ask what happens when two objects of the same mass-magnitude, one positive and one negative, find themselves in the same neighborhood. Do they repel or attract?

A detailed analysis of that question was worked out by Hermann Bondi in 1957. Bondi, an Austrian-born physicist who went to Cambridge in England shortly before World War II, was most famous for developing the steady-state theory of the universe (with Fred Hoyle and Thomas Gold). Perhaps more significantly he was also a major player in developing interest in Einstein’s general theory of relativity during the 1950s.

Bondi worked out the general relativistic math for the case of two bodies, one with ordinary (positive) mass and one negative. Positive mass attracts all masses, so Body P (positive mass) attracts Body N (negative mass). But negative mass repels all masses, so Body P would fly away from Body N. So N tries to get closer to P, because P attracts it, while P tries to get farther away from N, because N repels it. Consequently N chases P across the universe at an ever accelerating speed.

All this is very interesting, but also probably moot, as there doesn’t seem to be any reason to believe that negative mass actually exists. But that doesn’t stop physicists from speculating (or even theorizing) about it. After all, scientists cannot say what 85 percent of the matter in the universe is made of. Nor do they know how to reconcile the best theory of gravity, general relativity, with the best theory of matter, quantum theory. So it would seem a little premature to say negative mass is impossible. And in fact, a candidate for something with negative mass (sort of, possibly) has been around for decades: antimatter. (I’ll get to that.)

But even if by some chance negative mass does exist, using it for an antigravity shield still seems dubious. To counter the gravitational pull of the Earth, a negative mass carpet could be put in place (the carpet itself would fall to the ground). Then any mass would float above it. But to cancel out the Earth’s gravity over a space of just one square meter, you’d need a carpet with a negative mass of 70 billion kilograms.

“Thus we could float an object of any mass,” writes Hammond, “but it would take the (negative) mass of a small asteroid to make one square meter, so we may rule out this form of antigravity.”