Old and New Ideas in the Theory of Quantum Measurement

Abstract

The conceptually simplest interpretation of the quantum-mechanical wave function is that adopted by most textbooks. In the celebrated book by Dirac¹ one reads — each state of a dynamical system at a particular time corresponds to a ket vector... if the ket vector corresponding to a state is multiplied by any complex number, not zero, the resulting ket vector will correspond to the same state (pages 16, 17). And later — a measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured (page 36). Similar sentences can be found, e. g., in the book by Messiah² (pages 249 and 251). In the above statements the term state refers to a single system, not to a statistical ensemble of systems. This emerges clearly from the second statement, concerning reduction, which is quite incomprehensible in this form if the ket vector is not referred to a single system. In most textbooks the wave function up to a factor is interpreted just in this way — as the state of the single considered system.