  In the context of constrained quantum mechanics, reference systems are used
to construct relational observables that are invariant under the action of the
symmetry group. Upon measurement of a relational observable, the reference
system undergoes an unavoidable measurement "back-action" that modifies its
properties. In a quantum-gravitational setting, it has been argued that such a
back-action may produce effects that are described at an effective level as a
form of deformed (or doubly) special relativity. We examine this possibility
using a simple constrained system that has been extensively studied in the
context of quantum information. While our conclusions support the idea of a
symmetry deformation, they also reveal a host of other effects that may be
relevant to the context of quantum gravity, and could potentially conceal the
symmetry deformation.
