A proof is given, at a greater level of generality than previous 'no-go' theorems, of the impossibility of formulating a modal interpretation that exhibits 'serious' Lorentz invariance at the fundamental level. Particular attention is given to modal interpretations of the type proposed by Bub.

According to the modal interpretation, the standard mathematical framework of quantum mechanics specifies the physical magnitudes of a system, which have definite values. Probabilities are assigned to the possible values that these magnitudes may adopt. The interpretation is thus concerned with physical properties rather than with measurement results: it is a realistic interpretation. One of the notable achievements of this interpretation is that it dissolves the notorious measurement problem. The papers collected here, together with the introduction and concluding critical (...) appraisal, explain the various forms of the modal interpretation, survey its achievements, and discuss those problems that have yet to be solved. Audience: Philosophers of science, theoretical physicists, and graduate students in these disciplines. (shrink)

We generalize the modal interpretation of quantum mechanics so that it may be applied to composite systems represented by arbitrary density operators. We discuss the interpretation these density operators receive and relate this to the discussion about the interpretation of proper and improper mixtures in the standard interpretation.

Modal interpretations are hidden-variable, no-collapse interpretations of quantum mechanics that were designed to solve the measurement problem and reconcile this theory with relativity. Yet, as no-go theorems by Dickson and Clifton, Arntzenius and Myrvold demonstrate, current modal interpretations are incompatible with relativity. In the mainstream modal interpretations, properties of composite systems are generally unrelated to the properties of their subsystems. We propose holistic and relational interpretations of properties to explain this failure of (...) property composition. Based on these interpretations, we consider strategies for circumventing Myrvold's theorem, which are also effective against the other two theorems. (shrink)

We study the process of observation (measurement), within the framework of a “perspectival” (“relational,” “relative state”) version of the modal interpretation of quantum mechanics. We show that if we assume certain features of discreteness and determinism in the operation of the measuring device (which could be a part of the observer's nerve system), this gives rise to classical characteristics of the observed properties, in the first place to spatial localization. We investigate to what extent semi-classical behavior of the object (...) system itself (as opposed to the observational system) is needed for the emergence of classicality. Decoherence is an essential element in the mechanism of observation that we assume, but it turns out that in our approach no environment-induced decoherence on the level of the object system is required for the emergence of classical properties. (shrink)

A recent article argues that the modal interpretation of quantum mechanics does not do justice to immediately repeated non-disturbing measurements. This objection has been raised before, but the article presents it in a new, detailed, precise form. I show that the objection is mistaken.

Within many approaches to the interpretation of quantum mechanics, especially modal interpretations, one singles out a particular decomposition of the state vector in order to fix the properties that are well-defined for the system. We present a novel proposal for this preferred decomposition. Given a distinguished factorization of the Hilbert space, it is the decomposition that minimizes the Ingarden–Urbanik entropy from among all product decompositions with respect to the distinguished factorization. We incorporate this choice of preferred decomposition into (...) a framework for modal interpretations and investigate in detail the extent to which it provides a solution to the measurement problem and the extent to which it ensures that measurements whose outcomes are predictable with probability 1 reveal pre-existing properties of the system under investigation. (shrink)

We propose a novel interpretation of natural-language questions using a modal predicate logic of knowledge. Our approach brings standard model-theoretic and proof-theoretic techniques from modal logic to bear on questions. Using the former, we show that our interpretation preserves Groenendijk and Stokhof's answerhood relation, yet allows an extensional interpretation. Using the latter, we get a sound and complete proof procedure for the logic for free. Our approach is more expressive; for example, it easily treats complex questions with operators (...) that scope over questions. We suggest a semantic criterion that restricts what natural-language questions can express. We integrate and generalize much previous work on the semantics of questions, including Beck and Sharvit's families of subquestions, non-exhaustive questions, and multi-party conversations. (shrink)

This paper presents a general formal semantic scheme for the interpretation of quantum mechanics, in terms of which van Fraassen's Copenhagen and anti-Copenhagen variants of the modal interpretation are examined. The general character of the modal interpretation is motivated in a discussion of classical statistical mechanics, the distinction being made between statistical states and micro-states. The notion of a quasi-classical (micro) state is introduced in a discussion of the theorem of Gleason and Kochen and Specker. It is shown (...) that, according to the anti-Copenhagen variant, the class of micro-states coincides with a special class of quasi-classical states. The paper concludes with two general criticisms of the anti-Copenhagen variant. (shrink)

Two of the main interpretative problems in quantum mechanics are the so-called measurement problem and the question of the compatibility of quantum mechanics with relativity theory. Modal interpretations of quantum mechanics were designed to solve both of these problems. They are no-collapse (typically) indeterministic interpretations of quantum mechanics that supplement the orthodox state description of physical systems by a set of possessed properties that is supposed to be rich enough to account for the classical-like behavior of macroscopic (...) systems, but sufficiently restricted so as to avoid the no-hidden-variables theorems. But, as recent no-go theorems suggest, current modal interpretations are incompatible with relativity. In this paper, we suggest a strategy for circumventing these theorems. We then show how this strategy could naturally be integrated in a relational version of the modal interpretation, where quantum-mechanical states assign relational rather than intrinsic properties. (shrink)

Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an important motif is to stay close to the standard formalism of quantum mechanics and to refrain from introducing new structure by hand. In this paper we explain how this programme can be made concrete. In particular, we show that (...) the Born probability rule, and sets of definite-valued observables to which the Born probabilities pertain, can be uniquely defined from the quantum state and Hilbert space structure. We discuss the status of probability in modal interpretations, and to this end we make a comparison with many-worlds alternatives. An overall point that we stress is that the modal ideas define a general framework and research programme rather than one definite and finished interpretation. (shrink)

En este ensayo me propongo dos cosas: a) indicar las razones por las cuales la interpretación predicativa de la teoría de la forma de Platón no es la más adecuada. b) proponer una interpretación alternaiva ¿también predicativa¿ pero más completa, agregando el concepto de modalidad. Creo que la última interpretación se encuentra más cerca del espíritu del texto original, en el sentido que estoy convencido de que algunas de las principales intuiciones que subdeterminan la teoría de las formas de Platón (...) están más desarrolladas y fijas en el lenguaje (por supuesto en un lenguaje diferente) por tal comentario explicativo. Más aún, en esta manera están asociadas ¿sugiriendo una relación histórica¿ a consideraciones actuales en relación al objetivo del conocimiento científico ya que están formuladas en términos modales (es decir, nomotéticos). (shrink)

Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an important motif is to stay close to the standard formalism of quantum mechanics and to refrain from introducing new structure by hand. In this paper we explain how this programme can be made concrete. In particular, we show that (...) the Born probability rule, and sets of definite-valued observables to which the Born probabilities pertain, can be uniquely defined from the quantum state and Hilbert space structure. We discuss the status of probability in modal interpretations, and to this end we make a comparison with many-worlds alternatives. An overall point that we stress is that the modal ideas define a general framework and research programme rather than one definite and finished interpretation. (shrink)

An outstanding problem in so-called modal interpretations of quantum mechanics has been the specification of a dynamics for the properties introduced in such interpretations. We develop a general framework (in the context of the theory of stochastic processes) for specifying a dynamics for interpretations in this class, focusing on the modal interpretation by Vermaas and Dieks. This framework admits many empirically equivalent dynamics. We give some examples, and discuss some of the properties of one of (...) them. This approach is applicable to a wider class of theories, in particular, those using (discrete) strict effective—as in decoherence theory—superselection rules. (shrink)

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. (shrink)

I investigate the character of the definite properties defined by the Basic Rule in the Vermaas and Dieks' (1995) version of the modal interpretation of quantum mechanics, specifically for the case of the continuous model of decoherence by Joos and Zeh (1985). While this model suggests that the characteristic length that might be associated with the localisation of an individual system is the coherence length of the state (which converges rapidly to the thermal de Broglie wavelength), I show in (...) an exactly soluble case that the definite properties that are possessed with overwhelming probability in this modal interpretation are delocalized over the entire spread of the state. (shrink)

The modal interpretation of quantum mechanics has two variants: the Copenhagen variant (CV) and the anti-Copenhagen variant (ACV). Healey uses the Bell-Wigner locality condition to criticize the latter, which I do not advocate. 2 The conclusions of Healey's admirably written article are therefore welcome to me. But if I had wished to advocate the ACV, I do not think that his arguments would have dissuaded me. Specifically, as I shall explain, we should distinguish between Physical Locality and Metaphysical Locality. (...) The first principle is unexceptionable, but Healey needs the second for his reductio. At the end I shall briefly indicate why I reject the ACV and advocate instead the Copenhagen variant. (shrink)

A number of arguments have been given to show that the modal interpretation of ordinary nonrelativistic quantum mechanics cannot be consistently extended to the relativistic setting. We find these arguments inconclusive. However, there is a prima facie reason to think that a tension exists between the modal interpretation and relativistic invariance; namely, the best candidate for a modal interpretation adapted to relativistic quantum field theory, a prescription due to Rob Clifton, comes out trivial when applied to a (...) number of systems of physical interest. However, it is far from clear whether this difficulty for the modal interpretation is traceable to relativistic invariance per se or to the infinite number of degrees of freedom involved. In any case, the proponents of the modal interpretation have work to do. (shrink)

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes but leaves the theory’s basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory permits assuming that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture (...) of states and Hilbert-space trajectories to the more realistic case of open quantum systems despite the generic development of entanglement. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure—which we call subsystem space—that we believe merits further study. We conclude with a summary, a list of criteria for future work on quantum foundations, and further research directions. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text. (shrink)

I review the modal interpretation of quantum mechanics, some versions of which rely on the biorthonormal decomposition of a statevector to determine which properties are physically possessed. Some have suggested that these versions fail in the case of inaccurate measurements, i.e., when one takes tails of the wavefunction into account. I show that these versions of the modal interpretation are satisfactory in such cases. I further suggest that a more general result is possible, namely, that these versions of (...) the modal interpretation never encounter the sort of trouble that has been claimed to arise in the case of inaccurate measurement. (shrink)

An outline for a modal interpretation in terms of possible worlds is presented. The so-called Schmidt histories are taken to correspond to the physically possible worlds. The decoherence function defined in the histories formulation of quantum theory is taken to prescribe a non-classical probability measure over the set of the possible worlds. This is shown to yield dynamics in the form of transition probabilities for occurrent events in each world. The role of the consistency condition is discussed.

One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (given that (...) the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability. (shrink)

An outline for a modal interpretation in terms of possible worlds is presented. The so-called Schmidt histories are taken to correspond to the physically possible worlds. The decoherence function defined in the histories formulation of quantum theory is taken to prescribe a non-classical probability measure over the set of the possible worlds. This is shown to yield dynamics in the form of transition probabilities for occurrent events in each world. The role of the consistency condition is discussed.

This paper proposes a logic, motivated by modal interpretations, in which every quantum mechanics propositions has a truth-value. This logic is completely classical, hence violates the conditions of the Kochen-Specker theorem. It is shown how the violation occurs, and it is argued that this violation is a natural and acceptable consequence of modal interpretations. It is shown that despite its classicality, the proposed logic is empirically indistinguishable from quantum logic.

This paper proposes a logic, motivated by modal interpretations, in which every quantum mechanics propositions has a truth-value. This logic is completely classical, hence violates the conditions of the Kochen-Specker theorem. It is shown how the violation occurs, and it is argued that this violation is a natural and acceptable consequence of modal interpretations. It is shown that despite its classicality, the proposed logic is empirically indistinguishable from quantum logic.

In this article we discuss the contextual character of quantum mechanics in the framework of modal interpretations. We investigate its historical origin and relate contemporary modal interpretations to those proposed by M. Born and W. Heisenberg. We present then a general characterization of what we consider to be a modal interpretation. Following previous papers in which we have introduced modalities in the Kochen-Specker theorem, we investigate the consequences of these theorems in relation to the (...) class='Hi'>modal interpretations of quantum mechanics. (shrink)

The aim of this paper is to consider in what sense the modal-Hamiltonian interpretation of quantum mechanics satisfies the physical constraints imposed by the Galilean group. In particular, we show that the only apparent conflict, which follows from boost-transformations, can be overcome when the definition of quantum systems and subsystems is taken into account. On this basis, we apply the interpretation to different well-known models, in order to obtain concrete examples of the previous conceptual conclusions. Finally, we consider the (...) role played by the Casimir operators of the Galilean group in the interpretation. (shrink)

Recent no go theorems by Dickson and Clifton (1998), Arntzenius (1998) and Myrvold (2002) demonstrate that current modal interpretations are incompatible with relativity. In this paper we propose strategies for how to circumvent these theorems. We further show how these strategies can be developped into new modal interpretations in which the properties of systems are in general either holistic or relational. We explicitly write down an outline of dynamics for these properties which does not pick out (...) a preferred foliation of spacetime. (shrink)

In his logical exegesis of Descartes’ cogito, Hintikka has claimed that, formulated as an inference, it would be question--begging and that it is best understood as a performance, But (1), Hintikka’s discussion of an inferential interpretation omits reference to the possible relevance ofmodalities, and (2), Hintikka assumes that to beg the question is to assume what one is trying to prove. Question-begging is better understood in terms of how evident the premisses are in relation to the conclusion. In this paper (...) I construct a modal inferential interpretation, defend itagainst any charge of question-begging, and outline a system of quantified modal logic which would validate it. (shrink)

In his logical exegesis of Descartes’ cogito, Hintikka has claimed that, formulated as an inference, it would be question--begging and that it is best understood as a performance, But (1), Hintikka’s discussion of an inferential interpretation omits reference to the possible relevance ofmodalities, and (2), Hintikka assumes that to beg the question is to assume what one is trying to prove. Question-begging is better understood in terms of how evident the premisses are in relation to the conclusion. In this paper (...) I construct a modal inferential interpretation, defend itagainst any charge of question-begging, and outline a system of quantified modal logic which would validate it. (shrink)

A Benacerraf–Field challenge is an argument intended to show that common realist theories of a given domain are untenable: such theories make it impossible to explain how we’ve arrived at the truth in that domain, and insofar as a theory makes our reliability in a domain inexplicable, we must either reject that theory or give up the relevant beliefs. But there’s no consensus about what would count here as a satisfactory explanation of our reliability. It’s sometimes suggested that giving such (...) an explanation would involve showing that our beliefs meet some modal condition, but realists have claimed that this sort of modal interpretation of the challenge deprives it of any force: since the facts in question are metaphysically necessary and so obtain in all possible worlds, it’s trivially easy, even given realism, to show that our beliefs have the relevant modal features. Here I show that this claim is mistaken—what motivates a modal interpretation of the challenge in the first place also motivates an understanding of the relevant features in terms of epistemic possibilities rather than metaphysical possibilities, and there are indeed epistemically possible worlds where the facts in question don’t obtain. (shrink)

Any realist interpretation of quantum theory must grapple with the measurement problem and the status of state-vector collapse. In a no-collapse approach, measurement is typically modeled as a dynamical process involving decoherence. We describe how the minimal modal interpretation closes a gap in this dynamical description, leading to a complete and consistent resolution to the measurement problem and an effective form of state collapse. Our interpretation also provides insight into the indivisible nature of measurement—the fact that you can't stop (...) a measurement part-way through and uncover the underlying 'ontic' dynamics of the system in question. Having discussed the hidden dynamics of a system's ontic state during measurement, we turn to more general forms of open-system dynamics and explore the extent to which the details of the underlying ontic behavior of a system can be described. We construct a space of ontic trajectories and describe obstructions to defining a probability measure on this space. (shrink)

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. (shrink)

The connective of realisation associates propositions with names of contexts, at which they are said to be realised. Realisation is usually understood as relativised truth-connective, thus under mo...