As I understand it, then when I am standing on Earth I feel a force on my feet and is accelerated through spacetime. But what if a person is standing on the other side of Earth. That person is also accelerated. I kind of feel this is strange because it is in a different direction. But I guess it is because I am not allowed to look at it from the Earth frame? Or is it because I can´t use my own local frame to look at the other person?
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Strictly speaking, "local" means an infinitesimally small volume. In practice, it means a volume sufficiently small that space appears to be inertial to experiments. A globe-spanning space does not qualify as local. – David Hammen Jul 02 '18 at 19:04
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When you look at a person around the globe, you see that what he experiences locally over there is equivalent to acceleration. However, the distance between you and him is not increasing. It is not increasing, because the spacetime is curved. Anything that you observe happening locally to him would seem equivalent to his acceleration. However, values that are local neither to you nor to him, such as the distance between you two, are not covered by the equivalence principle (e.g. the distance does not increase despite you two apparently accelerating away from each other). – safesphere Jul 02 '18 at 19:25