  In physics one attempts to infer the rules governing a system given only the
results of imperfect measurements. Hence, microscopic theories may be
effectively indistinguishable experimentally. We develop an operationally
motivated procedure to identify the corresponding equivalence classes of
states, and argue that the renormalisation group arises from the inherent
ambiguities associated with the classes: one encounters flow parameters as,
e.g., a regulator, a scale, or a measure of precision, which specify
representatives in a given equivalence class. This provides a unifying
framework and identifies the role played by information in renormalisation. We
validate this idea by showing that it justifies the use of low-momenta n-point
functions as statistically relevant observables around a gaussian hypothesis.
These results enable the calculation of distinguishability in quantum field
theory. Our methods also provide a way to extend renormalisation techniques to
effective models which are not based on the usual quantum-field formalism, and
elucidates the relationships between various type of RG.
