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On the contrary, in an accelerated elevator in free space, bodies would fall with the same acceleration (because of their inertia), just as if there were a gravitational field.
The Einstein Equivalence Principle (EEP)
Einstein's great insight was to postulate that this "vanishing" of gravity in free-fall applied not only to mechanical motion but to all the laws of physics, such as electromagnetism...
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In any freely falling frame, therefore, the laws of physics should (at least locally) take on their special relativistic forms. This postulate is called the Einstein equivalence principle (EEP). One consequence is the gravitational red shift, a shift in frequency ?f' for a light ray that climbs through a height ?h' in a gravitational field, given by where ?g' is the gravitational acceleration...
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