It has been suggested that the Modal Interpretation of Quantum Mechanics (QM) is "incomplete" if it lacks a dynamics for possessed values. I argue that this is only one of two possible attitudes one might adopt toward a Modal Interpretation without dynamics. According to the other attitude, such an interpretation is a complete interpretation of QM as standardly formulated, an interpretation whose innovation is to attempt to make sense of the quantum realm without the expedient of novel physics. Then I explain why this attitude, though available, is unattractive. Without dynamics, the Modal Interpretation vanquishes the measurement problem only, it seems, to succumb to the problem of state preparation. On this view, the Modal Interpretation needs dynamics not to be an interpretation at all, but to be an adequate one. I review reasons to suspect that the dynamics which would best suit the Modal Interpretation--a dynamics equivalent to a set of two time transition probabilities of the sort used to solve the preparation problem--is not a dynamics the interpretation can have. I close with a brief discussion of versions of the Modal Interpretation that may not succumb to the considerations presented here.
It has been suggested that the Modal Interpretation of Quantum Mechanics (QM) is "incomplete" if it lacks a dynamics for possessed values. I argue that this is only one of two possible attitudes one might adopt toward a Modal Interpretation without dynamics. According to the other attitude, such an interpretation is a complete interpretation of QM as standardly formulated, an interpretation whose innovation is to attempt to make sense of the quantum realm without the expedient of novel physics. Then I explain why this attitude, though available, is unattractive. Without dynamics, the Modal Interpretation vanquishes the measurement problem only, it seems, to succumb to the problem of state preparation. On this view, the Modal Interpretation needs dynamics not to be an interpretation at all, but to be an adequate one. I review reasons to suspect that the dynamics which would best suit the Modal Interpretation--a dynamics equivalent to a set of two time transition probabilities of the sort used to solve the preparation problem--is not a dynamics the interpretation can have. I close with a brief discussion of versions of the Modal Interpretation that may not succumb to the considerations presented here.
The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription rule by applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties.
Bas van Fraassen in [4] has recently tried to use modal logic to solve the measurement problem of quantum mechanics. His model is based on a method of expressing quantum states developed by Hugh Everett [1] called the “relative state formulation.” Unfortunately, Everett's mathematics cannot be generalized as van Fraassen requires. The difficulty itself is elementary enough. But a revision of van Fraassen's postulates (such as the one he adopted on p. 341 after he had been told of the problem) can save the mathematics only on pain of making the whole study irrelevant to the physics. I shall explain the dilemma in this note. In a later paper [5], van Fraassen avoids this dilemma by developing an abstract modal interpretation which does not rely on any expression for quantum states.
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.
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.
Modal interpretations of quantum mechanics admit two kinds of state: physical states, which specify the values of observables on a system, and theoretical states, which specify a probability distribution over possible physical states. They appear to use this distinction to deny the projection postulate, claiming that collapse corresponds only to a change from discussing the theoretical state to discussing the physical state. I argue that modal interpretations should adopt a projection postulate at the level of the theoretical state. However, other features of modal interpretations might render the projection postulate immune from the usual objections.
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.