The term observer in special relativity refers most commonly to an inertial reference frame. Less often it may refer to an arbitrary non-inertial reference frame; in particular, a Rindler frame is sometimes called an "accelerating observer". In such cases an inertial reference frame may be called an "inertial observer" to avoid ambiguity. Note that these uses differ significantly from the ordinary English meaning of "observer". Reference frames are inherently nonlocal constructs, covering all of space and time or a nontrivial part of it; thus it does not make sense to speak of an observer (in the special relativistic sense) having a location. Also, an inertial observer cannot accelerate at a later time, nor can an accelerating observer stop accelerating.
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