# Infinite Acceleration, Conservation of Energy, and Negative Mass

1. Jul 28, 2014

### Raze

I've read that the Alcubierre Drive depends on the existence of negative mass, but I've seen that physicists say it could violate the conservation of energy. Their reasoning is that basically a negative mass and positive mass would interact in a perpetual motion sort of way that eternally decreases entropy, that they'd accelerate infinitely.

I was wondering if someone here could help do a kinematics demonstration of that and why such perpetual motion would come of it and why it violates conservation of energy.

I guess I'll start my own attempt to understand with Newton's gravitational law. Suppose these two particles (one with negative mass) are close enough that if they were normal they'd attract.

F = -Gm1m2/r2

except m2 < 0, so I'll add a negative sign.

Then F = Gm1m2/r2

which should mean they repel away from each other, right? If that negative sign were still there, we could have

a = -F/m1 = -Gm2/r2, ​

which would mean they would accelerate at a constant rate until they hit each other, right? If the negative is removed, that means they'd accelerate at a constant rate away from each other, right? Then how is this infinite acceleration? It seems it's just a constant acceleration away from each other.

Or is it that merely adding a negative sign isn't enough to describe how negative mass would behave? If it were more like negative mass always repels negative mass, and positive mass always attracts positive mass, then would mixing the two would result in a repulsive AND attractive force? If so I can see why that could be a conundrum.

But if the masses were of different magnitude, wouldn't either the repulsive or attractive force win out, resulting in more or less "normal" energy situations? And if the masses were of equal magnitude, wouldn't the repulsion and attraction exactly cancel in this scenario? (resulting in a net of zero kinetic energy)

2. Jul 29, 2014