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From what little I know of general relativity, the equality of inertial and gravitational mass is an axiom of the theory. I suspect that this precludes GR from unifying them in the same sense as electric, magnetic and weak interactions are unified as the electroweak force.

But since the two appear to be equal under staggeringly precise measurements, there must be some interest in constructing a theory of mass and motion which fundamentally unifies the two, that is, makes the separation nonsensical / impossible.

Are there any particularly outstanding attempts in this regard, even if the resulting theories are known to fail to correspond to our universe in some other important way?

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General relativity already unifies these two concepts, as you said. –  C.R. Jul 17 '12 at 2:49
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up vote 2 down vote accepted

The equivalence of gravitational and inertial mass is one of the ideas that inspired general relativity, but it's not an axiom of the theory. Instead, it's a consequence of the interpretation of gravity as spacetime curvature. You could say that GR was designed from the ground up such that the equivalence principle would come out of it.

Given the success of general relativity, there hasn't been much of any effort devoted to finding an alternate explanation for the equivalence principle.

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Oh I see. I got the wrong impression from a comment by Luboš Motl: "... gravitational mass is the same as inertial mass is called the principle of equivalence. In GR, this principle is a postulate - an assumption". –  romkyns Jul 17 '12 at 10:18
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