Modal interpretations of quantum mechanics

OLIMPIA LOMBARDI; DENNIS DIEKS

STANFORD ENCYCLOPEDIA OF PHILOSOPHY

STANFORD UNIVERSITY

Lugar: Stanford; Año: 2012 vol. 2012 p. 1 - 40

1095-5054

The roots of the modal interpretations can be found in certain works of Bas van Fraassen of the 1970s, where the distinction between the quantum state and what he called the value state of the system is introduced: the quantum state tells us what may be the case, that is, which physical properties the system may possess; the value state represents what actually is the case.  The relationship between the quantum state and the value state is probabilistic.  Therefore, the quantum state is the basis for modal statements, that is, statements about what possibly or necessarily is the case. On the basis of this original idea, in the 1980s several authors presented realist interpretations which, in retrospect, can be regarded as elaborations or variations on van Fraassen?s modal themes (for an overview and references, see Dieks & Vermaas, 1998).  However, each one of them proposed its own rule of property-ascription. For instance, in the so-called Kochen-Dieks modal interpretation (Kochen, 1985; Dieks, 1988), the biorthogonal (Schmidt) decomposition of the pure quantum state of the system picks out the definite-valued observables.  The Vermaas-Dieks version (Vermaas & Dieks, 1995), a generalization of the Kochen-Dieks interpretation to mixed states, is based on the spectral resolution of the reduced density operator: the range of the possible properties of a system and their corresponding probabilities are given by the non-zero diagonal elements of the spectral resolution of the system?s reduced state, obtained by partial tracing.  In turn, the so-called atomic modal interpretation (Bacciagaluppi & Dickson, 1999) is based on the assumption that there exists a special set of disjoint systems, which are the building blocks of all other systems, and that set fixes a preferred factorization of the Hilbert space; the properties of a system supervene on the properties ascribed to its ?atomic? subsystems.  More recently, and as a response to some difficulties in the account of non-ideal measurements, Gyula Bene and Dennis Dieks (2002) have developed a perspectival version of the modal interpretation, according to which properties are not monadic but have a relational character: following the original idea of Kochen (1985), systems have properties ?as witnessed? by a larger system. In this section we are not interested in the differences among the members of the modal family, but rather in the features that they share. In particular, all the modal interpretations agree on the following points: ·  The interpretation is based on the standard formalism of quantum mechanics. ·  The interpretation is realist, that is, it aims at describing how reality would be if quantum mechanics were true. ·  Quantum mechanics is a fundamental theory, which must describe not only elementary particles but also macroscopic objects. ·  Quantum mechanics describes single systems: the quantum state refers to a single system, not to an ensemble of systems. ·  The quantum state of the system (pure state or mixture) describes the possible properties of the system and their corresponding probabilities, and not the actual properties (given by van Fraassen?s value state).  The relationship between the quantum state and the actual properties of the system is probabilistic. ·  Systems possess actual properties at all times, whether or not a measurement is performed on them. ·  A quantum measurement is an ordinary physical interaction.  There is no collapse: the quantum state always evolves unitarily according to the Schrödinger equation. ·  The Schrödinger equation gives the time evolution of probabilities, not of actual properties.