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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.

Their thinking begins by pointing out the important distinction between kinematics, which is concerned purely with motion not how it arises, and dynamics which focuses on the origin of motion. In the classical world, this has no bearing on the effects of inertial and gravitational mass.

However, in the quantum world, the way states are prepared has huge significance. They point out, for example, that the wave function of a particle in a box does not depend on mass at all whereas the energy wave function of a harmonic oscillator depends on the square root of the mass.

That leads to an interesting idea: that it is possible to create combinations of gravitational and electromagnetic boxes and oscillators in which inertial and gravitational mass play different roles.

It turns out that physicists already play with exactly this kind of set up: the so-called atom trampoline, in which a matter wave falls under the influence of gravity but is bounced by an electromagnetic force. They calculate that the energy eigenvalues of the atom are proportional to the (gravitational mass)^2/3 but to the (inertial mass)^-1/3.

That’s an amazing result. The kind of energy spectroscopy of atoms or Bose Einstein Condensates that can spot this difference ought to be achievable, if not now, then very soon within the next few years.

If successful, these kinds of investigations will provide an entirely new way of studying the nature of mass and, perhaps more importantly, of investigating the puzzling relationship between general relativity and quantum mechanics.

For example, cosmologists will want to know how inertial and gravitational mass behaves in the most extreme conditions in the Universe, such as inside black holes.

That promises an exciting few years ahead.

Ref: arxiv.org/abs/1006.1988: Inertial And Gravitational Mass In Quantum Mechanics


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