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My question is: is m (invariant mass) frame-independent also if
non-inertial reference frames are considered? I would tend to think
so but I can't justify it; special relativity starts with the
postulates explicitly dealing with inertial frames. Would then all
the linked notions (like energy-momentum four-vector) share this
crucial restriction?
OTOH special relativity can deal with accelerating systems, at least
in some situations: e.g. the twin paradox can be understood
completely in terms of special relativity as shown by former Phys-L
postings (also by John D. in <http://www.av8n.com/physics/twins.htm>)