The principle of equivalence - that, locally, you can\'t distinguish between a u

Question

The principle of equivalence - that, locally, you can't distinguish between a uniform gravitational field and a noninertial frame accelerating in the sense opposite to the gravitational field - is dependent on the equality of gravitational and inertial mass. Is there any deeper reason for why this equality of "charge corresponding to gravitation" (that is, the gravitational mass) and the inertial mass (that, in newtonian mechanics, enters the equation F=ma) should hold? While it has been observed to be true to a very high precision, is there any theoretical backing or justification for this? You could, for example (i wonder what physics would look like then, though), have the "charge corresponding to electromagnetic theory" equal to the the inertial mass, but that isn't seen to be the case.

Explanation / Answer

This is a tricky question. Fundamentally, this is the motivation of general relativity (and all metric theories of gravity)--if all masses interact with a gravitational field in the same way, then, in a sense, the motion of a particular mass is determined by the local gravitational field, independently of the mass. This then leads you into explaining the gravitational "force" as an emergent property of the local spacetime curvature.

But then, what came first? The explanation of gravity as curvature, or the equivalence of gravitational and inertial mass? In a way, they are just dual pictures of the same thing.

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