The SCOP-formalism: an Operational Approach to Quantum Mechanics

We present the SCOP-formalism, an operational approach to quantum mechanics. If a State-COntext-Property-System (SCOP) satisfies a specific set of 'quantum axioms', it fits in a quantum mechanical representation in Hilbert space. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter N. In the case N = 2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N arrow right infinity the system is classical. For the intermediate cases it is impossible to define an orthocomplementation on the set of properties. Another interesting feature is that the probability of a state transition also depends on the context which induces it This contrasts sharply with standard quantum mechanics for which Gleason's theorem states the uniqueness of the state transition probability and independent of measurement context We show that if a SCOP satisfies a Gleason-like condition, namely that all state transition probabilities are independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented.