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Cambridge University Press eBooks

Properties, states, measurement outcomes and effective states

Pieter E. Vermaas

Published Feb 5, 2010• 0 citations
Publisher

Abstract

Starting with a more philosophical review, I discuss how modal interpretations describe reality. Firstly, it is shown that they describe states of affairs which need not be observable. Secondly, I underpin my position that in order to be metaphysically tenable, interpretations need only to satisfy the criteria of Consistency and Internal Completeness. Thirdly, I analyse how properties, states and measurement outcomes are related to one another within the modal descriptions of reality. Finally, I show how modal interpretations recover the standard formulation of quantum mechanics if one defines, in addition to the true states, so-called effective states of systems. Noumenal states of affairs The aim of an interpretation of quantum mechanics is, as I said in the introduction, to provide a description of what reality would be like if quantum mechanics were true. This formulation underlines two aspects of interpretations. Firstly, interpretations intend to construe quantum mechanics in terms of a description of reality and not merely in terms of the outcomes of measurements. Secondly, this description need not be correct. The objective is only to prove that there exists a construal of quantum mechanics which yields an acceptable description of reality. And because it is already difficult enough to give such a proof of existence, it is not (yet) the aim of interpretations to provide the one and only correct description of reality. The above formulation, however, disregards another aspect of interpretations of quantum mechanics, namely that they describe states of affairs which need not always be observable.

DOI
10.1017/cbo9780511608230.016

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Starting with a more philosophical review, I discuss how modal interpretations describe reality. Firstly, it is shown that they describe states of affairs which need not be observable. Secondly, I underpin my position that in order to be metaphysically tenable, interpretations need only to satisfy the criteria of Consistency and Internal Completeness. Thirdly, I analyse how properties, states and measurement outcomes are related to one another within the modal descriptions of reality. Finally, I show how modal interpretations recover the standard formulation of quantum mechanics if one defines, in addition to the true states, so-called effective states of systems. Noumenal states of affairs The aim of an interpretation of quantum mechanics is, as I said in the introduction, to provide a description of what reality would be like if quantum mechanics were true. This formulation underlines two aspects of interpretations. Firstly, interpretations intend to construe quantum mechanics in terms of a description of reality and not merely in terms of the outcomes of measurements. Secondly, this description need not be correct. The objective is only to prove that there exists a construal of quantum mechanics which yields an acceptable description of reality. And because it is already difficult enough to give such a proof of existence, it is not (yet) the aim of interpretations to provide the one and only correct description of reality. The above formulation, however, disregards another aspect of interpretations of quantum mechanics, namely that they describe states of affairs which need not always be observable.
In this final part I analyse the modal interpretations from a more philosophical point of view. In Chapter 12 I start by arguing that modal interpretations describe noumenal states of affairs and that therefore metaphysically tenable interpretations need only to meet the criteria of Consistency and Internal Completeness. Then I analyse the relations between properties, states and outcomes of measurements in the modal description of reality. I end by discussing how modal interpretations, when restricted to the description of measurement outcomes, recover the standard formulation of quantum mechanics. Chapter 13 concerns the relations between the properties ascribed to composite systems and subsystems. I show that the property ascriptions of the bi and spectral modal interpretations can be characterised as holistic and non-reductionistic, whereas the property ascription of the atomic modal interpretation is non-holistic and to a large extent reductionistic. I argue that notwithstanding the lack of reductionism, the bi and spectral modal interpretations are empirically adequate and metaphysically tenable. I also discuss the possibility of saving the metaphysical tenability of the atomic modal interpretation by taking holistic properties as dispositional properties. In Chapter 14 I give a survey of the possibilities and impossibilities of modal interpretations and in Chapter 15 I end with general conclusions.
As a last step towards general conclusions, I collect and assess the more important results obtained in the previous chapters. In the next and final chapter I then consider the question of whether the modal descriptions of reality meet the demands of being well developed, empirically adequate and metaphysically tenable. Indefinite properties and inexact magnitudes The bi, spectral and atomic modal interpretations do manage to interpret quantum mechanics by providing a description of what reality could be like in terms of systems possessing properties. Moreover, if one accepts the full property ascription (5.12) as developed in Section 5.4, this description of reality satisfies a number of desirable conditions. However, these modal interpretations do not simultaneously ascribe all the possible properties to a system. Instead they select at each instant a specific subset of the properties pertaining to a system and ascribe only these. And the properties which are not selected are taken to be indefinite. This possibility that properties of systems are sometimes not definite is in itself not that problematic for in some cases it is perfectly understandable what this means. Consider again the example of a tossing coin. During the toss the properties ‘heads’ and ‘tails’ can be said to be indefinite and this can be understood as meaning that these two properties are applicable only to coins which lie on surfaces. However, in other cases it is less clear what is going on.
In Part one the description of reality by modal interpretations has been developed as far as possible. In this part I determine whether modal interpretations are empirically adequate by considering their descriptions of measurements. In Chapter 10 I focus on the measurement problem. After a measurement,according to our observations, the measurement device displays a definite outcome. Such an outcome is traditionally called a pointer reading and the question is whether modal interpretations manage to ascribe such pointer readings. In the standard formulation of quantum mechanics one predicts by means the Born rule the probabilities and the correlations with which measurements have outcomes. In Chapter 11 I discuss whether modal interpretations can reproduce these empirically correct predictions.
This book is about how to understand quantum mechanics by means of a modal interpretation. Modal interpretations provide a general framework within which quantum mechanics can be considered as a theory that describes reality in terms of physical systems possessing definite properties. Quantum mechanics is standardly understood to be a theory about probabilities with which measurements have outcomes. Modal interpretations are relatively new attempts to present quantum mechanics as a theory which, like other physical theories, describes an observer-independent reality. In this book, Pieter Vermaas summarises the results of this work. The book will be of great value to undergraduates, graduate students and researchers in philosophy of science, and physics departments with an interest in learning about modal interpretations of quantum mechanics.
The modal interpretation explained here construes the mathematical formalism of quantum mechanics in terms of physical properties (``be-ables,'' ``existents'') in such a way that the property attribution reflects the mathematical structure as much as possible---no additional structure is superimposed on the formalism. We generalize the interpretation by specifying a dynamics of physical properties, and also extend it while replying to recent objections by Albert and Loewer 2 [Proceedings of the 1990 Biennial Meeting of the Philosophy of Science Association, edited by A. Fine, M. Forbes, and L. Wessels (Philosophy of Science Association, East Lansing, MI, 1990), Vol. 1, p. 277], and by Elby [Found. Phys. Lett. 6, 5 (1993)]. I also discuss questions relating to relativistic aspects and casuality.
Orthodox quantum mechanics includes the principle that an observable of a system possesses a well-defined value if and only if the presence of that value in the system is certain to be confirmed on measurement. Modal interpretations reject the controversial ‘only if’ half of this principle to secure definite outcomes for quantum measurements that leave the apparatus entangled with the object it has measured. However, using a result that turns on the construction of a Kochen–Specker contradiction, I argue that modal interpretations cannot deliver a metaphysically tenable conception of properties in quantum mechanics unless they also abandon the less controversial ‘if’ half of the orthodox principle.