http://www.technologyreview.com/blog/arxiv/25331/
http://arxiv.org/abs/1006.1988
The equivalence principle is one of the more fascinating ideas in modern science. It asserts that gravitational mass and inertial mass are identical. Einstein put it like this: the gravitational force we experience on Earth is identical to the force we would experience were we sitting in a spaceship accelerating at 1g. Newton might have said that the m in F=ma is the same as the ms in F=Gm1m2/r^2.
This seems eminently sensible. And yet it is no more than an assertion. Sure, we can measure the equivalence with ever increasing accuracy but there is nothing to stop us thinking that at some point the relationship will break down. Indeed several modifications to relativity predict that it will.
One important question is what quantum mechanics has to say on the matter. But physicists have so far been unable to use quantum theory as a lever to tease apart the behaviour of inertial and gravitational mass.
All that changes today with the extraordinary work of Endre Kajari at the University of Ulm in Germany and a few buddies. They show how it is possible to create situations in the quantum world in which the effects of inertial and gravitational mass must be different. In fact, they show that these differences can be arbitrarily large.
What would be the impact if inertial mass is different than gravitational mass? Would it mean that objects with different masses don't fall down equally fast? I would assume they still do. Suppose inertial mass Mi and gravitational mass Mg are not equal but Mi = 1.000000001 Mg. Then
F=Mi * a with F the force, a the acceleration and
F= - Mg * g with g the gravitational constant on earth
This means that
a=1.000000001 * g.
Henceforth, objects with different masses still fall equally fast.
If Mi and Mg are not related by a simple factor, but if Mi=Mg^1.0000001 then
a=(Mi^(-0.0000001)) g
In this case there is a difference. Therefore, my question is: what do people mean by the statement
that inertial mass might be different than gravitational mass. They mean they differ by a factor different than one or their relation is more complicated?
Interesting. Foreshadows of science fiction/fact or simply the illusion?
The potential application that comes to mind is some sort of energy producing machine involving accelerating something in gravity. For example, if it took less energy to lift an object that it gives off when it falls we could make a quantum energy generator.
Of course it would probably work the other way if at all; more energy to lift than it gives off when it falls, converting mass to heat or something.