## Thursday, February 16, 2012

### Gravitational mass vs inertial mass

I've heard a lot of physicists and people interested in physics noting that inertial mass and gravitational mass seem to be different phenomena and there's no clear reason why the two should end up being exactly the same magnitude.
First consider the following thought experiment. Suppose you have two perfectly hard spheres of the same mass that start out a distance apart and gravitationally attract to one another, when they eventually collide they both reverse direction and eventually end up in the same configuration that they started, motionless. All the energy was originally from their potential energy based on gravitational mass, turned into kinetic energy based on inertial mass, and then their gravitational attraction gradually slowed them down to return to the same state.All the while the system as a whole had the same total energy.
Now if something could have more gravitational mass than inertial mass the balls would attract to one another and collide but not go back to the original state they would bounce a shorter and shorter distance apart each collision until they were eventually fused together. This would result in the final system having less energy than what it started with which in an isolated system can't happen.
And the opposite is if the gravitational mass were less than the inertial mass then every time they collided they would end up ever farther apart and going faster to get there which would eventually end up with both masses having infinite kinetic energy.
So you see this thought experiment shows that they have to be the same based on conservation of energy.