Decoherence, the Measurement Problem, and Interpretations of Quantum Mechanics by Maximilian Schlosshauer

Author:Maximilian Schlosshauer [Schlosshauer, Maximilian]
Language: eng
Format: epub
Published: 2011-02-17T05:00:00+00:00

1. Everett branches and the preferred basis problem

tinuum of narrow Gaussian-type wavepackets (for exam-

ple, the coherent states of harmonic oscillator models,

Stapp (2002, p. 1043) demanded that “a many-worlds see K¨

ubler and Zeh, 1973; Zurek et al. , 1993)—that are interpretation of quantum theory exists only to the ex-not necessarily orthogonal (i.e., the Gaussians may overtent that the associated basis problem is solved”. In the lap), Stapp considers this approach to the preferred basis context of relative-state interpretations the preferred ba-problem in relative-state interpretations as not satisfac-sis problem is not only much more severe than in the

tory. Zurek (private communication) has rebutted this

orthodox interpretation (if there is any problem at all), criticism by pointing out that a collection of harmonic

but also more fundamental than in many other inter-

oscillators that would lead to such overcomplete sets of pretations for several reasons: (1) The branching occurs Gaussians cannot serve as an adequate model of the hu-continuously and essentially everywhere; in the general

man brain (and it is ultimately only in the brain where

sense of measurements understood as the formation of

the perception of denumerability and mutual exclusive-

quantum correlations, every newly formed such correla-

ness of events must be accounted for; cf. Sec. II.B.3); tion, whether it pertains to microscopic or macroscopic

when neurons are more appropriately modeled as two-

systems, corresponds to a branching.

(2) The onto-

state systems, the issue raised by Stapp disappears (for logical implications are much more drastic, at least in

a discussion of decoherence in a simple two-state model, those relative-state interpretations that assume an ac-see Sec. III.D.2).13

tual “splitting” of worlds or minds, since the choice of The approach of using environment-induced superse-the basis determines the resulting “world” or “mind” as

lection and decoherence to define the Everett branches

a whole.

has also been critized on grounds of being “conceptually The environment-based basis superselection criteria

approximate” since the stability criterion generally leads of the decoherence program have frequently been emonly to an approximate specification of a preferred ba-

ployed to solve the preferred basis problem of relative-

sis and can therefore not give an “exact” definition of

state interpretations (see, for example, Butterfield, 2001;

the Everett branches (see, for example, the comments

Wallace, 2002, 2003a; Zurek, 1998). There are several by Kent, 1990; Zeh, 1973, and also the well-known anti-advantages in appealing to a decoherence-related ap-

FAPP position of Bell, 1982). Wallace (2003a, pp. 90–91) proach in selecting the preferred Everett bases: First,

has argued against such an objection as

no a priori existence of a preferred basis needs to be

postulated, but instead the preferred basis arises natu-

(. . . ) arising from a view implicit in much discus-

rally from the physical criterion of robustness. Second, sion of Everett-style interpretations: that certain

the selection will be likely to yield empirical adequacy concepts and objects in quantum mechanics must

since the decoherence program is solely derived from the either enter the theory formally in its axiomatic

well-confirmed Schrödinger dynamics (modulo the possi-

structure, or be regarded as illusion. (. . . ) [In-

bility that robustness may not be the universally valid

stead] the emergence of a classical world from

criterion). Lastly, the decohered components of

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