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Measurement as Representation: 1. The Physical Correlate

Bas C. van Fraassen

Published Aug 7, 2008• 0 citations
Publisher

Abstract

Abstract This chapter explores measurement ‘from above’: that is, looking for a view that we can have after the measurement procedures, concepts, and theories have stabilized. This resting point in the conceptual and scientific development is fleeting and momentary — yet marking a context in which some things can be taken for granted pro tem, where it makes sense to ask about the world-picture of currently accepted physical theory. The physical conditions of possibility for measurement, the general theory of measurement, and what cannot count as measurement in a theoretical context are discussed, drawing on general lessons derived from 20th-century foundations of physics.

DOI
10.1093/acprof:oso/9780199278220.003.0007

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Abstract This chapter explores measurement ‘from above’: that is, looking for a view that we can have after the measurement procedures, concepts, and theories have stabilized. This resting point in the conceptual and scientific development is fleeting and momentary — yet marking a context in which some things can be taken for granted pro tem, where it makes sense to ask about the world-picture of currently accepted physical theory. The physical conditions of possibility for measurement, the general theory of measurement, and what cannot count as measurement in a theoretical context are discussed, drawing on general lessons derived from 20th-century foundations of physics.
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The usual analytic approach to differential geometry was explored in the early 18th century using the defining notion of limit.With the advent of topos theory in the late 20th century, it has been possible to rediscover without the use of limits the differential and integral calculus, and its development into Synthetic Differential Geometry (SDG), in mathematical universes other than that represented by set theory.These universes obey a subtle but well understood generalisation of classical logic: intuitionistic logic.This thesis presents an exploration of the construction of quantum mechanics in the context of SDG.Chapter 1 introduces SDG, intuitionistic logic, topos theory and a particular topos used in the thesis.Chapter 2 explores the new logical perspective afforded by topos theory and SDG in describing the quantum world from an intuitionistic viewpoint.We build a working quantum-mechanical model using topos theory and analyse the physical and philosophical relevance of the logical steps taken, and account for the consistency of the model with its set-theoretic predecessor by suggesting a certain physical interpretation for the mathematics.In chapter 3, we analyse the extension of this quantum mechanics to state spaces with an infinite number of dimensions, and the associated use of various mathematical constructions that are taken for granted in set theory.Chapter 4 reaches an important proof of the lack of validity of the Spectral 4 The Spectral Theorem 108 4.1 Proof of Failure 4.2 The Internal Logic of the Spectral Theorem 4.3 Measurement-Enforced Validity 5 Conclusions 118 5.
In quantum mechanics, the measurement problem is commonly regarded as reason for deep concern. It seems that, either, the problem can be solved and there is hope for quantum mechanics, or the theory better be left behind in search of another one. We investigate the prospect of finding a solution to the measurement problem—within quantum mechanics, as well as in theoretical frameworks beyond it. As we do so, there emerges a perspective on doing physics drawing from considerations in the philosophy of language and in epistemology. Developing this perspective for further aspects in physics reveals: The notion of a system is similarly problematic. Eventually, the question arises whether these are problems of specific physical theories, or rather of specific stances towards physics. In this regard, we examine in particular the role and understanding of assumptions.
Abstract This chapter attempts to bring the foregoing foundational discussion of QM∞ to bear on issues in the philosophy of science more generally construed. Taking one lesson of the foregoing foundational discussions to be that no single interpretation of QM∞ is adequate to the myriad explanatory and developmental demands faced by theories of QM∞, the chapter draws morals for scientific realism and related issues. One moral is that there might be no single structure or interpretation belief in which is warranted by the many successes of a physical theory. Another is that a physical theory might be best understood, not in terms of a unique set of physically possible worlds specified antecedently to the messy business of applying that theory, but in terms of many different such sets, indexed to contexts of application. A third moral is that semantic indecision of the sort just described could be an empirical virtue, insofar as semantically indecisive theories are more flexibly responsive to diverse sets of empirical demands.