In Griffith's General Relativity there is the following line:

An accelerated particle has no inertial frame in which it is always at rest. However, there is an inertial frame which momentarily has the same velocity as the particle, but which a moment later is of course no longer comoving with it. This frame is the momentarily comoving reference frame (MCRF), and is an important concept. (Actually, there are an infinity of MCRFs for a given accelerated particle at a given event; they all have the same velocity, but their spatial axes are obtained from one another by rotations).

I am not able to understand the last statement.

How is it possible for an accelerated particle to have an infinity of MCRFs at a given event?


The Lorentz transformation allows to change coordinates between inertial reference frames (frames in relative motion with constant velocity). It preserves the spacetime interval between any two events.

The homogeneous Lorentz transformation (no shift in spacetime) is made of a boost in relative velocity and a rotation in space. It has 6 degrees of freedom: 3 directions for the boosts + 3 axis for the rotations.

Providing the relative velocity is the same, if you rotate in space you have an infinity of inertial reference frames at a given event.


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