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Here a question about terminology. Suppose I have a particle that is moving at velocity $\beta$ in the observer (or laboratory) frame. Now, is it appropriate / legitimate to describe the frame in which such particle is at rest as comoving with the particle? I often found the expression "the reference frame in which the particle is at rest", but in a long manuscript "the reference frame comoving with the particle" makes it more concise.
I ask because the comoving frame is a concept of its own in cosmology.

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Usually, we call frames attached to/or moving with the moving particle 'proper frames' and the particle is obviously in rest in these frames. The definition holds even if the particle is accelerating.

A comoving frame at some time 't', however, is defined as an inertial frame in which the particle is instantaneously at rest at the time 't'.

Note that for an accelerating particle, the proper frame is non-inertial.

Restricting ourselves to STR where we do not consider accelerating frames, the notions of proper frames and comoving frames coincide.

To answer your question, it would be more appropriate to use the term 'proper frame' than 'comoving frame'.

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  • $\begingroup$ I see, thank you, so as long as I am dealing with a special relativity situation the comoving label (as it coincides with the proper frame) is legitimate. $\endgroup$ – cosimoNigro Apr 21 at 8:47

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