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It is well known that there exists certain class of physical observables like momentum and position which are common to both classical and quantum mechanics, and has different 'kinds of predictability' depending on if it is classical or quantum . Certain other quantities like charge are common to both classical and quantum physics and have the same 'kinds of determinism' irrespective of if its referring to a classical or a quantum system.What is the fundamental reason behind this partitioning of the set of physical observables that are common to classical and quantum physics on the basis of the kinds of determinism which I have defined below.

p.s By 'kinds of predictability' I refer to the following two types of outcomes a theory can produce:

  1. predictions for individual outcomes

  2. Predictions of ontic probability probability distributions.

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  • $\begingroup$ Well, charge, mass etc. are fixed properties of a particle that never change, they have just one fixed value. They are, in the usual quantum language, not thought of as "observables". Momentum and position are dynamical variables, in contrast. $\endgroup$ Commented Apr 12, 2018 at 10:13

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If you know how to prepare some yet to be determined vector such that there is a family of further measurement's reading that are definitely the readings following a particular state of the wave function, then that state is a physical quantity. No it not circular logic.

Observables are hermitian operators. Those that commute are compatible and some families of them correspond to a complete representation of the Hilbert space. Once you have that it is the maximal information you can ask for.

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