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.
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.
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.
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.
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.
During many years since the birth of quantum mechanics, instrumentalist interpretations prevailed: the meaning of the theory was expressed in terms of measurements results. However, in the last decades, several attempts to interpret it from a realist viewpoint have been proposed. Among them, modal interpretations supply a realist non-collapse account, according to which the system always has definite properties and the quantum state represents possibilities, not actualities. But the traditional modal interpretations faced some conceptual problems when addressing imperfect measurements. The modal-Hamiltonian interpretation, on the contrary, proved to be able to supply an adequate account of the measurement problem, both in its ideal and its non-ideal versions. Moreover, in the non-ideal case, it gives a precise criterion to distinguish between reliable and non-reliable measurements. Nevertheless, that criterion depends on the particular state of the measured system, and this might be considered as a shortcoming of the proposal. In fact, one could ask for a criterion of reliability that does not depend on the features of what is measured but only on the properties of the measurement device. The aim of this article is precisely to supply such a criterion: we will adopt an informational perspective for this purpose.During many years since the birth of quantum mechanics, instrumentalistinterpretations prevailed: the meaning of the theory was expressed in terms of measurementsresults. However, in the last decades, several attempts to interpret it from a realist viewpointhave been proposed. Among them, modal interpretations supply a realist non-collapseaccount, according to which the system always has definite properties and the quantum staterepresents possibilities, not actualities. But the traditional modal interpretations faced someconceptual problems when addressing imperfect measurements. The modal-Hamiltonianinterpretation, on the contrary, proved to be able to supply an adequate account of themeasurement problem, both in its ideal and its non-ideal versions. Moreover, in the non-idealcase, it gives a precise criterion to distinguish between reliable and non-reliable measurements.Nevertheless, that criterion depends on the particular state of the measured system, and thismight be considered as a shortcoming of the proposal. In fact, one could ask for a criterionof reliability that does not depend on the features of what is measured but only on theproperties of the measurement device. The aim of this article is precisely to supply such acriterion: we will adopt an informational perspective for this purpose.
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.
Let's return to the three demands I have imposed on the bi, spectral and atomic modal interpretations. The first was the demand that these interpretations should provide well-developed descriptions of reality. And a first conclusion is that the bi, spectral and atomic modal interpretations indeed provide the necessary starting points to develop them. That is, they all describe reality by means of well-defined property ascriptions: for all it is clear on which points these descriptions of reality need improvement, and for all one has the means to make a start with these improvements. A second conclusion is, however, that the success with which the bi, spectral and atomic modal interpretations can be developed varies. The results with regard to the full property ascription to a single system are in my opinion satisfactory for all three interpretations (Chapter 5). But with regard to the correlations between the properties ascribed to different systems the results start to diverge. For the atomic modal interpretation such correlations can be given (Section 6.4). But for the spectral modal interpretation it is proved that such correlations do not always exist for the properties ascribed to non-disjoint systems (Section 6.3). And for the bi modal interpretation correlations are unknown or, when one accepts Instantaneous Autonomy, Dynamical Autonomy for measurements and Empirical Adequacy (Section 3.3), do not exist as well (Section 6.3). Only if one adopts perspectivalism, that is, if one assumes that one can simultaneously only consider the properties of two disjoint systems in the bi modal interpretation and of n disjoint systems in the spectral modal interpretation, these two interpretations give all the defined correlations.