  We consider the process of changing reference frames in the case where the
reference frames are quantum systems. We find that, as part of this process,
decoherence is necessarily induced on any quantum system described relative to
these frames. We explore this process with examples involving reference frames
for phase and orientation. Quantifying the effect of changing quantum reference
frames serves as a first step in developing a relativity principle for theories
in which all objects including reference frames are necessarily quantum.
