"For a person located inside a hermetically sealed box, there is no difference between being in space with the box accelerating and another person located in a similar box resting in a gravitational field."
What are the implications of Einstein's equivalence principle for physics? And why is it so important to us?
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Einstein equivalence principle is one of the pillars upon which we build up the theory of general relativity. One can formulate it in a more physical way as follows
In an arbitrary gravitational field, at every point of spacetime, we can choose a locally inertial frame such that, in a sufficiently small neighborhood of a point, every physical laws have the same form as the one which they would have in absence of gravity, i.e. they have the form given by special relativity.
This means that, no matter how difficult of a spacetime geometry you're trying to study, you can always go to a locally inertial frame in which the metric tensor assumes the form of the Minkowski metric.
The concept of equivalence principle, as stated before, is the one which links together the geometry of spacetime with physical laws. This is due to the fact that this physical principle is somewhat similar to Gauss axiom of non-euclidean geometries which says that in every point of space one can find a small region in which the rules of Euclidean geometry apply.
