We come from the future
We come from the future

# Negative Mass: The Nuttiest Thing Never Seen

Negative mass has never been observed and most likely never will be observed. However, if it were, you would be able to ride it to work one day.

Negative mass sounds like a cover band that plays Antimatter tunes. The rip off of the name is unmistakable and potentially confusing. Both concepts pair an existing, common, physical substance with a negation of that substance. That's where the similarities end. Antimatter is an observed, if rare, substance. Negative Mass is what you get when you let physicists play around with positive and negative signs without supervision.

The name ‘negative mass,' is a straightforward result of the concept of negative mass. Most mass is like a sleepy toddler. When pushed, accelerates in the same direction of the push, ambling off groggily. Negative mass, however, is like an angry soccer hooligan. When pushed it accelerates in the opposite direction of the push. It pushes back towards you, and maybe takes a swing or two.

When you push, you exert a force on the object, and in physics, force equals mass times acceleration. A push (in a positive direction) will make the positive mass accelerate in the same, positive, direction.

F=m x a

With negative mass, though, a push in a positive direction will make the mass accelerate in the opposite, negative direction.

F=m x (-a)

Here's the problem. A positive number multiplied by a negative number always produces a negative number, so the equation would look like this:

-F=m x (-a)

But we've already defined the force as in the positive direction. So the only way to make the equation work is if the mass is negative.

F= (-m) x (-a)

And so we have negative mass.

No negative mass has been observed on earth, but there is a possibility it can fall to earth. Yes, gravity from positive mass affects negative mass the same way it would affect regular mass. Negative mass would fall towards earth, although it would fall away from any other negative mass object.

But how would a person pick up negative mass? Any upward force exerted on negative mass would push it more firmly into the ground. The only way to pick it up would be to push down on it with more force than gravity was exerting on it. In other words, the only way to pick up a, say, two pound block of negative mass would be to push down on it with over two pounds of force until it reached a height at which a person could carry it – with their hand on top of it, of course.

The idea is impossible, and impractical, but I can't help but think of people flying lightweight negative mass bikes (Or brooms. Brooms would be awesome.) to work and parking them on the ceiling of a specially designed garage. Maybe someday.

But probably not.

### DISCUSSION

Hypnosifl

I think this article contains some major mistakes. It is not true that negative masses would always move in the opposite direction as the force exerted on them, at least not if we're talking about a gravitational force—in fact negative mass objects would be pulled in the same direction by gravity from a positive-mass planet as positive mass objects are. You can see this from the Newtonian gravity equation, which says if you have a mass m being pulled by the gravitational field of a mass M (say m is the mass of a small object and M is the mass of a planet), the force on m in the direction of the center of M (at distance r from M) is given by:

F = ma = GMm/r^2

The reason all objects accelerate at the same rate in the Earth's gravity (as discovered by Galileo) can be seen from this equation—the m can be cancelled out, giving the simple equation:

a = GM/r^2

So, it doesn't matter whether the mass of the mass m is negative or positive, it'll accelerate towards the center of M with this magnitude either way (you can also see that negative mass should fall downward in the presence of gravity using Einstein's equivalence principle, since this should be equivalent to negative mass moving inertially inside a rocket whose floor is accelerating upwards in deep space with no gravity). On the other hand, the same reasoning says that in the gravitational field of a negative-mass object with mass M, all other objects would be accelerated away from the center of M, regardless of whether the mass of the other objects was positive or negative, so in this case you would have a sort of antigravity.

Things would get interesting if you had two masses opposite in sign (one negative and one positive) but equal in magnitude in deep space with no other sources of gravity, the negative mass would continually accelerate towards the positive mass while the positive mass would accelerate away from the negative mass at exactly the same rate, so they would maintain a constant distance from one another while their speed increased without bound (but this would not violate conservation of energy or momentum since the negative mass would have a momentum and energy that was negative and which always cancelled out the momentum and energy of the positive mass).

Also, negative mass is not complete fantasy. In relativity any region of space with negative energy density can also be considered to have negative mass by E=mc^2, and negative energy densities are seen between parallel plates in the Casimir effect. For example, see this lecture by Steven Hawking, where right below the diagram showing the Casimir plates he writes:

Because there are fewer virtual particles, or vacuum fluctuations, between the plates, they have a lower energy density, than in the region outside. But the energy density of empty space far away from the plates, must be zero. Otherwise it would warp space-time, and the universe wouldn't be nearly flat. So the energy density in the region between the plates, must be negative.

We thus have experimental evidence from the bending of light, that space-time is curved, and confirmation from the Casimir effect, that we can warp it in the negative direction.