Why is that bodies in a box accelerating uniformally in space that is sufficiently removed from gravitational fields fall identically to bodies in a box located in a homogeneous gravitational field (e.g., on Earth)
Answer
We don't know. The equivalence principle is based on a fundamental assumption that interial mass is the same as gravitational mass. We have verified this assumption in numerous experiments (e.g., the classic feather vs hammer experiment done on the Moon by David Scott).
On this assumption, we have also built a more complete theory of gravitation (GR) that explained/predicted thitherto unexplained/unknown phenomena (e.g., black holes, gravitational waves, gravitational lensing etc.). It all works out and seems correct but we still do not know why the two masses should be equal. For all we know, there is a deeper connection lurking in somewhere.
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