Quantum Measurement, Probability, and Logic

In the centuries preceding the development of quantum mechanics, the conception of mechanical systems as objects existing independently of conscious agents and possessing physical magnitudes that can, in principle, be arbitrarily well specified was rarely questioned by physicists. In classical mechanics, that is, that of the tradition of Newton, Lagrange, and Hamilton, the full set of physical magnitudes describing each physical system is precisely determined at all times by a collection of six parameters, the dynamical variables of vector position $\vec{q}$ and vector momentum $\vec{p}$, together constituting the state $(\vec{q},\vec{p})$, in accordance with Hamilton’s partial differential equations for the Hamiltonian function $H(\vec{q},\vec{p})$, and all imprecision of state specification is entirely due to the ignorance of agents as to this objective state.