How would negative mass interact with gravity?

[Hawksteinman]

Let's assume that negative mass is possible. How would it react with gravity?

Since F=ma, the acceleration would be in the opposite direction to the force applied. Keep this in mind

Now, the gravitational force, F=GMm/r². Usually this force acts towards the centre of the Earth since 'G' is negative, which makes the overall force negative. Negative forces attract.

If mass is negative, then the force would be positive, and act away from the Earth. Positive forces repel. But since the object has negative mass, it accelerates in the opposite direction to the force, so fall towards the Earth!

This makes sense if you think about it because all objects fall at the same rate regardless of mass, even massless objects

Am I right?

 

[DrClaude]

##F=ma## is here only a shorthand for ##F=GMm/r^2## where ##a = GM/r^2##. You therefore cannot use both equations to arrive at different results. (Edit: see my next post below.)

 

[Hawksteinman]

##F=ma## is here only a shorthand for ##F=GMm/r^2## where ##a = GM/r^2##. You therefore cannot use both equations to arrive at different results.

So ma = GMm/r²

Still, doesn't that mean the object will accelerate towards the Earth?

 

[Drakkith]

This makes sense if you think about it because all objects fall at the same rate regardless of mass, even massless objects

Am I right?

There is no "right" here. The reason there isn't is because we've never observed objects with negative mass so we actually don't know how they would behave. And then there's the complication that you're asking about things in terms of classical mechanics when relativity says that gravity isn't a force at all, but a result of the geometry of spacetime. Would an object of negative mass not obey the laws of geometry? I'd say that we just don't know.

 

[DrClaude]

I should have put some more thought before replying. It is correct that the acceleration of gravity will be directed towards the center of the Earth even for negative mass (provided that mass is negative for both gravitational interaction and inertia). I'm not much of a relativist, by I guess that this is also what would be expected from general relativity.