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The British Journal for the Philosophy of Science

The Preferred-Basis Problem and the Quantum Mechanics of Everything

Jeffrey Alan Barrett

Published May 17, 2005• 32 citations
Publisher

Abstract

Jereon Vink ([1993]) argued that there are two options for what he called a realistic solution to the quantum measurement problem: (1) select a preferred set of observables for which definite values are assumed to exist, or (2) attempt to assign definite values to all observables simultaneously (1810–1). While conventional wisdom has it that the second option is ruled out by the Kochen-Specker theorem, Vink nevertheless advocated it. Making every physical quantity determinate in quantum mechanics carries with it significant conceptual costs, but it also provides a way of addressing the preferred basis problem that arises if one chooses to pursue the first option. The potential costs and benefits of a formulation of quantum mechanics where every physical quantity is determinate are herein examined. 1. The preferred-basis problem 2. How to solve the preferred-basis problem 3. Relativistic constraints 4. Conclusion

DOI
10.1093/bjps/axi114

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Philosophia Scientae•Jan 1, 2015•0 citations
Jereon Vink ([1993]) argued that there are two options for what he called a realistic solution to the quantum measurement problem: (1) select a preferred set of observables for which definite values are assumed to exist, or (2) attempt to assign definite values to all observables simultaneously (1810–1). While conventional wisdom has it that the second option is ruled out by the Kochen-Specker theorem, Vink nevertheless advocated it. Making every physical quantity determinate in quantum mechanics carries with it significant conceptual costs, but it also provides a way of addressing the preferred basis problem that arises if one chooses to pursue the first option. The potential costs and benefits of a formulation of quantum mechanics where every physical quantity is determinate are herein examined. 1. The preferred-basis problem 2. How to solve the preferred-basis problem 3. Relativistic constraints 4. Conclusion
The preferred basis problem is mentioned in the literature in connection with the measurement problem and with the Many World Interpretation. It is argued that this problem actually corresponds to two inequivalent problems: (i) the preferred-decomposition problem, i.e., what singles out a preferred decomposition of a suitable state vector of a system as the sum of a finite or countable set of vectors?, and (ii) the preferred-representation problem, i.e., what singles out a preferred representation for the Hilbert space of a system? In this paper the preferred-decomposition problem is addressed and two processes, namely decoherence and permanent spatial decomposition (PSD), are examined and compared as possible solutions to this problem. It is shown that, perhaps contrary to common belief, in realistic situations decoherence is not sufficient to solve the preferred-decomposition problem. PSD is the (hypothesized) tendency of the wave function of the universe to decompose into permanently non-overlapping wave packets. Three phases can be roughly identified as composing PSD: Microscopic decomposition, amplification, and interaction with the environment. Decoherence theory considers only the interaction with the environment and ignores the first two phases. For this reason PSD is fundamentally different from decoherence and, unlike decoherence, provides a simple and non-elusive solution to the preferred-decomposition problem.
One understanding of the Niels Bohr's interpretation of quantum mechanics suggests that the measurement problem arises because an observer description of reality is incomplete due to lack of complete access to an entire system of observed and observer. In general, an additional and external measuring observer is required to access the entire system. Inevitable entanglement between observers, measurement apparatus and measured objects is key to such an understanding of the measurement problem. Quantum mechanics only provides a complete `incomplete' description of reality. Nevertheless, some issues, especially providing an account of why a preferred measurement basis arises, remain. Replacing relations between observed and observer in relational quantum mechanics with those between effective (approximate) theories, one arrives at a more clear understanding of why the measurement problem arises and how a preferred measurement basis is determined. The measurement problem exists because of measurement apparatus limitations, which only allow us to formulate and verify effective theories that inevitably neglect some details of nature.
The Kochen–Specker theorem establishes that noncontextual, globally consistent assignments of definite values to quantum observables are mathematically impossible. While this result places a fundamental constraint on pre-measurement value assignments, it does not by itself specify why observable values should exhibit contextuality or how the pre-measurement domain should be conceptually understood. This paper examines the Kochen–Specker theorem from the perspective of the Intrinsic Observability Framework (IOF), with particular emphasis on the relationship between contextuality and accessibility. In the IOF, observable values are not regarded as pre-existing entities awaiting discovery. Instead, the pre-measurement domain is characterized by potential observability, and measurement grants accessibility, thereby establishing observability and making observable values operationally meaningful. From this perspective, different measurement contexts generally participate in distinct accessibility conditions. Even when the same observable appears in distinct compatible sets, the conditions under which its observable value is operationally established are not necessarily identical. Contextuality can therefore be understood not merely as a restriction on global value assignment, but as a natural consequence of accessibility-dependent observability. The Kochen–Specker impossibility of constructing a single noncontextual global value map is thus interpreted as reflecting the attempt to combine observable values established under distinct accessibility conditions into a context-independent description. The IOF does not modify the mathematical content of the Kochen–Specker theorem or the standard quantum formalism. Rather, it provides an accessibility-based conceptual account of the contextual structure revealed by the theorem while explicitly characterizing the pre-measurement domain. Finally, the relationship between the IOF and representative interpretations of quantum mechanics is compared to clarify the distinct conceptual role of accessibility-dependent observability within quantum foundations.
The basic thesis of this book is that there is no quantum measurement problem. I do not mean by this that the apparent paradoxes of quantum mechanics arise because we fail to recognize ‘that quantum theory does not describe physical reality’ (Fuchs and Peres 2000a). Quantum theory describes reality just fine, like any other scientific theory worth taking seriously: describing (and explaining) reality is what the scientific enterprise is about. Nor do I mean that we have found solutions to the problem, ways to modify or supplement quantum mechanics so that the paradoxes are removed. I don’t actually think that we have found any very satisfactory solutions in this sense (at least not in the relativistic domain) but that isn’t my theme: even if we did have these modifications, they would be ways of changing from quantum physics, which supposedly does have a measurement problem, to some other theory, which supposedly doesn’t.
The semantics underlying the propositional structure of Hilbert space quantum mechanics involves an inherent ambiguity concerning the impossibility of assigning definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. Although the preceding Kochen-Specker result forbids a global, absolute assignment of truth values to quantum mechanical propositions, it does not exclude ones that are contextual. In this respect, the Bub-Clifton “uniqueness theorem” is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a suitable “preferred” observable. It is suggested that the most natural choice of the latter, especially for confronting the problem of truth valuation in quantum mechanics, results in the determinateness of the observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The resulting account of truth is compatible with a realist conception of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature.