But then if some axioms suffice for the behavior of pointer orientations (at least when they are observed), rules about the measurement of other observables must be theorems, following from those axioms, not additional axioms.
To achieve highly accurate angular estimates, the precise GNSS carrier phase observables must be employed.
In quantum error correction, information is redundantly stored in a large quantum state space and one or more observables must be monitored to reveal the occurrence of an error, without disturbing the information encoded in an unknown quantum state.
Thus, we know that the memory exhibited by any pair of observables must be greater or equal to the bit count of the most retentive pathway of the pair, and less than or equal to the sum of the bit counts of the two pathways.
As mentioned previously, if computational models are to be validated by experiments such as randomized clinical trials and become predictive of therapeutic interventions, relevant system observables must be included.
Since such structures are not readily observable, they must be discerned from intensive interpretive analysis of myths, language, or texts.
The multiplicity of visible forms in nature, then, is based upon differences in these particles and in their configurations; hence, any observable changes must be reduced to changes in these configurations.
This is a common occurrence since, in general, entities in the world are not directly observable, but must be inferred from some signal.
It rather implies that empirically observable motions must be subject to a priori principles of the understanding (a priori rules of time determination) in order to count as fully objective experience within a unified, temporally determinate objective world.
In fact, according to John Bell (Mermin 1993, p. 805), von Neumann's assumptions (about the relationships among the values of quantum observables that must be satisfied in a hidden-variables theory) are so unreasonable that the "the proof of von Neumann is not merely false but foolish!" Nonetheless, some physicists continue to rely on von Neumann's proof.
