  State representations summarize our knowledge about a system. When
unobservable quantities are introduced the state representation is typically no
longer unique. However, this non-uniqueness does not affect subsequent
inferences based on any observable data. We demonstrate that the inference-free
subspace may be extracted whenever the quantity's unobservability is guaranteed
by a global conservation law. This result can generalize even without such a
guarantee. In particular, we examine the coherent-state representation of a
laser where the absolute phase of the electromagnetic field is believed to be
unobservable. We show that experimental coherent states may be separated from
the inference-free subspaces induced by this unobservable phase. These physical
states may then be approximated by coherent states in a relative-phase Hilbert
space.
