ψ Superposition and Quantum Rules

The superposition rule for probability amplitudes ψ is not a separate ad hoc assumption of a physical character but is a formal consequence of the arrangement of the states of a system in sets of mutually orthogonal states linked by probabilities of transition. Nor do the quantum prescriptions of Born and Schrödinger have to be introduced as ad hoc assumptions; they can be deduced as consequences of (a) the superposition rule, and (b) the definition of conjugates q and p as leading to a constant probability density in qp-space, a quality known from classical statistical mechanics. Quantum theory can thus be deduced from a nonquantal background.