- #1

belliott4488

- 662

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We all know how the effects of gravity are described by the curvature of spacetime - rubber sheets and all that - as well as the equivalence of inertial and gravitational mass. Those basic concepts have always made me think of the inertia of a massive object as somehow being the result of the curvature of spacetime. First of all - is that even a correct idea? More to the point, though - how do you account for the inertia of an object that is accelerated by a non-gravitational force? Does spacetime still get curved in such a way that the object accelerates in inverse proportion to its mass, or does that come about purely in the non-relativistic way (i.e. F = ma)?

As a concrete example, let's say we have a small mass with an electric charge in a uniform electric field, far from any other massive object, so that spacetime is relatively flat. The object will accelerate uniformly, which should mean that in some sense it's locally equivalent to a uniform gravitational field, but is there actually any curvature of spacetime?