  The topic of quantum reference frames (QRFs) has attracted a great deal of
attention in the recent literature. Potentially, the correct description of
such frames is important for both the technological applications of quantum
mechanics and for its foundations, including the search for a future theory of
quantum gravity. In this letter, we point out potential inconsistencies in the
mainstream approach to this subject and propose an alternative definition that
avoids these problems. Crucially, we reject the notion that transformations
between QRFs can be represented by unitary operators and explain the clear
physical reasons for this. An experimental protocol, capable of empirically
distinguishing between competing definitions of the term, is also proposed. The
implications of the new model, for uncertainty relations, spacetime symmetries,
gauge symmetries, the quantisation of gravity, and other foundational issues
are discussed, and possible directions for future work in this field are
considered.
