Consistency, Amplitudes and Probabilities in Quantum Theory

Details Consistency, Amplitudes and Probabilities in Quantum Theory Consistency, Amplitudes and Probabilities in Quantum Theory

1998-04-03

arxiv.org/abs/quant-ph/9804012v2

Phys.Rev. A57 (1998) 1572

Physics

Quantum Physics

23 pages, 3 figures (old version did not include the figures)

Scientific paper

10.1103/PhysRevA.57.1572

Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This constraint is expressed in the form of functional equations the solution of which leads to the usual sum and product rules for amplitudes. A consequence is that the Schrodinger equation must be linear: non-linear variants of quantum mechanics are inconsistent. The physical interpretation of the theory is given in terms of a single natural rule. This rule, which does not itself involve probabilities, is used to obtain a proof of Born's statistical postulate. Thus, consistency leads to indeterminism. PACS: 03.65.Bz, 03.65.Ca.

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