## Negative Mass

Posted in: Gravity Simulator, Lesson Time! | May 29, 2014 | No Comments

This week, I want to talk about negative mass.  Wait… negative mass?  Like antimatter?

No.

Antimatter, in spite of its ‘anti’ name, still has a positive mass.  An electron and an antielectron (positron) have opposite charge, but they have the same mass.  Charge flips to negative, mass stays the same.

If antimatter is out of the picture — what in the world does have negative mass?  Well, nothing really that we know of.  It would take a very strange, exotic form of matter to have negative mass.  The closest we come is with the complex Casimir Effect.  But let’s imagine that a chunk of negative mass does exist.  What do we know about it?

First off, negative masses would have… negative energies.  When an object is moving, it has a kinetic energy equal to 1/2*m*v^2.  If the mass is negative, the kinetic energy is negative.  Even when you look at E = mc^2, the rest energy of matter, you’d find that the negative mass would lead to negative energy here, too!

Strange stuff.  The faster it goes, the less energy it has.  The more you have of it, the less energy you’ve got.

Gravity Time!

What would a negative mass mean for gravity?  Well, we can check this out in the Gravity Simulator.  Two planets with positive mass will, of course, attract.

Load this Scene in the Simulator: [ForceGr: r^(-2),Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: -125,y0: 0,vx: 0,vy: 0,t0: 0,who: 4,m: 1000,c: 1], [x0: 0,y0: 0,vx: 0,vy: 0,t0: 0,who: 4,m: 1000,c: 1]

This is because the force between them is:

Where m and M represent their masses.  Positive masses mean a positive force, which in this case means the objects pull towards each other.

What about negative masses?  Suppose we had two planets with negative mass.

Looking at the equation above, if we change m to -m and M to -M… the equation doesn’t change at all!  (Negative*Negative = Positive!) So they should attract as before, right?

Load this Scene in the Simulator: [ForceGr: r^(-2),Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: 50,y0: 0,vx: 0,vy: 0,t0: 0,who: 4,m: -1000,c: 1], [x0: 75,y0: 0,vx: 0,vy: 0,t0: 0,who: 4,m: -1000,c: 1]

Wrong!

There’s an extra bit of the puzzle we’ve left out.  The force hasn’t changed, but the acceleration has.  To figure out how something will move, we use F=ma.  The force is equal to the mass times acceleration.  Even if the force hasn’t changed in our example… if the sign of the mass has flipped, the sign of the acceleration has to flip.  So instead of the pulling force making the planets accelerate together… they accelerate apart.

With all that in mind, the final puzzle is: what happens when you have a positive mass and a negative mass.  Will they attract?  Will they repel?

The test is easy to do (Note, you can do all these tests and MORE in the Gravity Simulator):

Load this Scene in the Simulator: [ForceGr: r^(-2),Qual: 1,Zoom: 1,xSet: 0,ySet: 0], [x0: 125,y0: 2.5,vx: 0,vy: 0,t0: 0,who: 4,m: -1000,c: 1], [x0: 90,y0: 2.5,vx: 0,vy: 0,t0: 0,who: 4,m: 1000,c: 1]

…whoa.  Why did that happen?  You’ve now got enough information to figure that one out.

As a final note, it would seem that having two planets suddenly zoom off the screen, ever faster, would violate Conservation of Momentum, or Conservation of Energy.  But in fact, it doesn’t.  As the positive mass gains positive kinetic energy, the negative mass gains negative kinetic energy.  They cancel out.

Same with the momentum.  Both planets may start moving in the same direction in that gif above, but the planet with negative mass has its momentum moving to the right.  (Momentum = m*v, so flipping the sign of the mass flips the direction of the momentum).  So even with strange negative masses around, conservation laws stay intact.

Will we ever really encounter a chunk of negative mass?  Who can say.  But at least we can make some good predictions about how we’d expect it to behave.

-Andy

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