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In this paper fields of quantum reference frames based on gaugetransformations of rational string states are described in a way that,hopefully, makes them more understandable than their description in an earlierpaper. The approach taken here is based on three main points: (1) There are alarge number of different quantum theory representations of natural numbers,integers, and rational numbers as states of qubit strings. (2) For eachrepresentation, Cauchy sequences of rational string states give arepresentation of the real (and complex) numbers. A reference frame isassociated to each representation. (3) Each frame contains a representation ofall mathematical and physical theories that have the representations of thereal and complex numbers as a scalar base for the theories. These points andother aspects of the resulting fields are then discussed and justified in somedetail. Also two different methods of relating the frame field to physics arediscussed.Comment: 24 pages, 5 figures; submitted to proceedings, 3rd Feynman Festival,  University of Maryland, 200

Fields of quantum reference frames based on different representations of rational numbers as states of qubit strings