  We present a comprehensive study, using both analytical and numerical
methods, of measurement-induced localization of relational degrees of freedom.
Looking first at the interference of two optical modes, we find that the
localization of the relative phase can be as good for mixed states - in
particular for two initially Poissonian or thermal states - as for the
well-known case of two Fock states. In a realistic setup the localization for
mixed states is robust and experimentally accessible, and we discuss
applications to superselection rules. For an ideal setup and initial Fock
states we show how a relational Schr\"{o}dinger cat state emerges, and
investigate circumstances under which such a state is destroyed. In our second
example we consider the localization of relative atomic phase between two Bose
Einstein condensates, looking particularly at the build up of spatial
interference patterns, an area which has attracted much attention since the
work of Javanainen and Yoo. We show that the relative phase localizes much
faster than was intimated in previous studies focusing on the emerging
interference pattern itself. Finally, we explore the localization of relative
spatial parameters discussed in recent work by Rau, Dunningham and Burnett. We
retain their models of indistinguishable scattering but make different
assumptions. In particular we consider the case of a real distant observer
monitoring light scattering off two particles, who records events only from a
narrow field of view. The localization is only partial regardless of the number
of observations. This paper contributes to the wider debate on relationism in
quantum mechanics, which treats fundamental concepts - reference frames and
conservation laws - from a fully quantum and operational perspective.
