by Felix Zhou

Image credit: Quantum Bits ©Argonne National Laboratory, CC BY-NC-SA 2.0

Well, it depends on what you mean by how much. Obviously, something with a mass of -1kg has that much matter in it. If you mean how much as in how much it’s worth in value, well, any negative mass would be invaluable to modern physics research. Also, negative mass *might…maybe…possibl*y… produce endless acceleration (we’ll get to that ludicrous scenario in a bit).

## Negative Gravity?

First, let’s talk about gravity. Everything with mass both causes and experiences a gravitational force, and gravity is always attractive…for positive masses. But what if mass is negative?

## Pull It Away

Newton’s Second Law tells us that how much something accelerates depends on mass. Something with more mass is harder to accelerate. Logically, then, a negative mass should have negative acceleration, moving in the opposite direction you’d expect it to. In other words, if you push negative matter,* it will move towards you.*

But Newtonian gravity is accurate only for normal everyday events, and negative mass most definitely is not a normal, everyday event. To understand gravity for negative masses, we should use relativity.

## Relativistic Negative Gravity

Einstein’s gravity says that gravity isn’t really a force, but more of a distortion in spacetime that curves otherwise straight, constant speed, paths. Positive mass causes spacetime to curve inwards, so everything bends towards it, like a ball rolling into a funnel, regardless of mass. Similarly, negative mass curves spacetime the other way, forming a hill rather than a dent. Everything bends away like a ball rolling up and then back down the side of a hill.

Therefore: positive mass attracts everything gravitationally, and negative mass repels everything.

## Now for the Crackpot Moment

Now what? This. We put a positive mass on the left and a negative mass to the right. The positive mass pulls the negative mass to the left, and the negative mass pushes the positive mass away…to the left. The two objects form a system that accelerates together indefinitely; this means they can get to arbitrarily high speeds, blasting right through the light barrier like paper. The objects’ energies and momenta exactly cancel to zero, though, so the physics that prevent acceleration to FTL aren’t technically broken.

If that weren’t cool enough, negative mass is the only type of matter that can hold open a wormhole.

If that sounds too absolutely insane to be true, it kind of is. There are some problems for negative mass:

- We’ve never seen negative mass and common sense says we likely never will. In fact, it’s quite common that a theory technically allows for something that will never actually be possible because of some other laws of physics.
- This type of “perpetual motion” violates thermodynamics and the energy conditions of relativity very badly. However, that can’t prove that negative mass
*must not*exist per se, and there are other theories that avoid runaway motion. - The sheer preposterous of this scenario is a pretty good sign that our boring positive mass is the only kind there is.

## The Negative Mass That Wasn’t

So that’s it? Disappointing. But *effective* negative mass is still very useful for physics research.

Effective negative mass is pretty much what it sounds like: mass that is normal, but behaves like negative mass under some circumstances.

In fact, scientists have already made an effective negative mass substance by cooling normal matter to extreme temperatures to form a weird state of matter called a Bose-Einstein condensate. The resulting substance, because of strange quantum things, can sometimes accelerate in the opposite direction of a force, just like real negative mass would.

## But Imitation Negative Mass Is Cool Too

While not as epic as endless acceleration, effective negative mass as a concept allows physicists to understand areas of the universe that are rather, ah, *extreme*. This includes areas within neutron stars and the weirdness that is the quantum realm, potentially giving us great swaths of fun new knowledge.

And this is what will lead to fun discoveries and technologies. Bose-Einstein condensates and other weird behaviours of matter are very real; the wildly counterintuitive quantum world is very real. Research into extreme substances like Bose-Einstein condensates is quite useful in developing quantum technology, which is pretty exciting too.

I think the problem is that we’re so focused on the exotic types of matter, we don’t really give ordinary matter a chance to be amazing.

Negative mass, currently, has no place outside highly speculative physics.

Ordinary matter is real, and already has the potential to give us advancements yet unimaginable.

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