Lorentz frames.

In any such frame an infinitesimal interval, here assumed timelike, between two events is expressed asand separates points on a trajectory of a particle (think clock{?}). The same interval can be expressed in coordinates such that at each moment, the particle is at rest. Such a frame is called an instantaneous rest frame, denoted here by the coordinates for each instant. Due to the invariance of the interval (instantaneous rest frames taken at different times are related by Lorentz transformations) one may write

since

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