Measurement and Classical Regime in Quantum Mechanics

Abstract

In this article, I shall focus on two of the main problems raising interpretational issues in quantum mechanics, namely the notorious measurement problem (discussed together with the theory of measurement in section 4) and the equally important but not quite as widely discussed problem of the classical regime (discussed together with decoherence in section 3). The two problems are distinct, but they are both intimately related to some of the issues arising from entanglement and density operators, which are thus briefly reviewed in section 2. A few fundamentals are rehearsed in section 1. The article will aim to be fairly non-technical in language, but modern in outlook and covering the chosen topics in more depth than most introductory treatments.The philosophy and foundations of quantum mechanics offer many more examples of live research issues, and much progress has been achieved recently in such traditional approaches as collapse theories, pilot-wave theories and Everett interpretations, and in the (time-honoured but recently revived) area of axiomatic reconstructions of the theory. Recent years have

On the transition from the quantum to the classical regime for massive scalar particles: A spatiotemporal approach

“…For this NDWF the mean kinetic energy does not coincide with the vanishing classical kinetic energy 1 2 m˙ x 2 ψn (t) = 0. Note, finally, that the force F ψn (t) appearing in Eq.…”

“…As noted in Ref. [1], the notion of 'collapse' of the wave functions requires position wave functions with a finite support (inside the apparatus). Physically, this is connected to the fact that an arbitrarily precise measurement of position requires arbitrarily strong coupling to the system and an arbitrarily large amount of energy.…”

“…See Refs. [1][2][3][4][5][6][7] as a sample of extensive bibliography on these subjects and the associated issues of the uniqueness of outcomes, of Born's probability rule, of the acceptance or non-acceptance of the collapse of the wave function as a real process (in connection with the interpretation of the wave function itself) and of the eigenvalue-eigenvector link. In this vast literature, however, the discussion is often characterized by imprecise, purely verbal statements which do not help to characterize the conceptual heart of the problem discussed.…”

“…This citation reflects Bohr's legacy very well (see Refs. [1,2]), namely the need for some classical distinction between the quantum system and the apparatus needed by the praxis of experimentalists. While the measuring instrument may of course be described as a quantummechanical system, it is only possible to explain its capacity to function as a measure instrument on the assumption that the resulting traces of the interaction between object and instrument can be described in terms of an exchange of energy and momentum in space and time (i.e.…”

Decoherence and Intertheory Relations in Quantum Realism

“…Instead, I just want to show sufficient disagreement on the terms and conditions of the problem. For example, Bacciagaluppi (2013) considers the measurement problem as a separate problem to the quantum-classical limit (in the sense of the limit between the classical regime and the regime of quantum mechanics), and argues that the solution to one problem does not solve the other. Bacciagaluppi argues that decoherence does not solve the measurement problem and that decoherence recovers predictions of classical mechanics merely instrumentally.…”