Consistency and Linearity in Quantum Theory

Abstract

Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two answers must agree. The constraint is expressed in the form of functional equations the solution of which leads to the usual sum and product rules for amplitudes. An immediate consequence is that the Schrodinger equation must be linear: non-linear variants of quantum mechanics violate the requirement of consistency. PACS: 03.65.Bz, 03.65.Ca.

References in corpus (5)

• Quantum Logic and the Histories Approach to Quantum Theory
• Consistent Histories and Quantum Reasoning
• Consistency, Amplitudes and Probabilities in Quantum Theory
• Quantum Mechanics as Complex Probability Theory
• Is Complex Probability Theory Consistent with Bell's Theorem?

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