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Many texts on GR, after introducing the equivalence principle as the equivalence of inertial and gravitational mass, or the equivalence of gravity and acceleration relative to a local inertial frame state an idea along the lines of "the laws of physic can be formulated in a frame-independent manner"

How does this idea follow from the equivalence principle?

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    $\begingroup$ As far as I know, this is the General Principle of Relativity and is independent of any form of the Equivalence Principle. $\endgroup$ – DanielC Aug 21 '17 at 11:42
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It is derived from the fact that the universe is homogeneous and isotropic. There is no preferred direction or position, and therefore physics acts the same no matter which frame you decide to derive them in. Take an inertia tensor example. If we change the "frame" we compute the tensor elements in we will get different equations for each elements, but that doesn't change the actual physics.

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