Definitions

noninertial

Noninertial reference frames

The noninertial reference frames referred to a particular case which is the Lorentz frame that showed to be not inertial frames at rest on Earth. So if special relativity is to be valid in a gravitational field, it's naturally to take a guess of that the 'laboratory' frame at rest on Earth is a Lorentz frame, but the followed from the argument of Schild (1967), easily shows that the assumption to be false.

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