  In the absence of an external frame of reference physical degrees of freedom
must describe relations between systems. Using a simple model, we investigate
how such a relational quantum theory naturally arises by promoting reference
systems to the status of dynamical entities. Our goal is to demonstrate using
elementary quantum theory how any quantum mechanical experiment admits a purely
relational description at a fundamental level, from which the original
"non-relational" theory emerges in a semi-classical limit. According to this
thesis, the non-relational theory is therefore an approximation of the
fundamental relational theory. We propose four simple rules that can be used to
translate an "orthodox" quantum mechanical description into a relational
description, independent of an external spacial reference frame or clock. The
techniques used to construct these relational theories are motivated by a
Bayesian approach to quantum mechanics, and rely on the noiseless subsystem
method of quantum information science used to protect quantum states against
undesired noise. The relational theory naturally predicts a fundamental
decoherence mechanism, so an arrow of time emerges from a time-symmetric
theory. Moreover, there is no need for a "collapse of the wave packet" in our
model: the probability interpretation is only applied to diagonal density
operators. Finally, the physical states of the relational theory can be
described in terms of "spin networks" introduced by Penrose as a combinatorial
description of geometry, and widely studied in the loop formulation of quantum
gravity. Thus, our simple bottom-up approach (starting from the semi-classical
limit to derive the fully relational quantum theory) may offer interesting
insights on the low energy limit of quantum gravity.
