Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: inferential probability, ensemble probability, and propensity. Class is the basis of inductive logic; deals with the frequencies of (...) events in repeatable experiments; describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge. (shrink)

Several philosophers of science have claimed that the conceptual difficulties of quantum mechanics can be resolved by appealing to a particular interpretation of probability theory. For example, Popper bases his treatment of quantum mechanics on the propensity interpretation of probability, and Margenau bases his treatment of quantum mechanics on the frequency interpretation of probability. The purpose of this paper is (i) to consider and reject such claims, and (ii) to discuss the question (...) of whether the ψ -function refers to an individual system or to an ensemble of systems. (shrink)

The prime concern of this paper is with the nature of probability. It is argued that questions concerning the nature of probability are intimately linked to questions about the nature of time. The case study here concerns the single case propensity interpretation of probability. It is argued that while this interpretation of probability has a natural place in the quantum theory, the metaphysical picture of time to be found in relativity theory is incompatible with (...) such a treatment of probability. (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)

The difficult issues related to the interpretation of quantum mechanics and, in particular, the “measurement problem” are revisited using as motivation the process of generation of structure from quantum fluctuations in inflationary cosmology. The unessential mathematical complexity of the particular problem is bypassed, facilitating the discussion of the conceptual issues, by considering, within the paradigm set up by the cosmological problem, another problem where symmetry serves as a focal point: a simplified version of Mott’s problem.

In the _The Undivided Universe_, David Bohn and Basil Hiley present a radically different approach to quantum theory. They develop an interpretation of quantum mechanics which gives a clear, intuitive understanding of its meaning and in which there is a coherent notion of the reality of the universe without assuming a fundamental role for the human observer. With the aid of new concepts such as active information together with non-locality, they provide a comprehensive account of all (...) the basic features of quantum mechanics, including the relativistic domain and quantum field theory. It is shown that, with the new approach, paradoxical or unsatisfactory features associated with the standard approaches, such as the wave-particle duality and the collapse of the wave function, do not arise. Finally, the authors make new suggestions and indicate some areas in which one may expect quantum theory to break down in a way that will allow for a test. _The Undivided Universe_ is an important book especially because it provides a different overall world view which is neither mechanistic nor reductionist. This view will ultimately have radical implications not only in physics but also in our general approach to all areas of life. (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)

In the The Undivided Universe, David Bohn and Basil Hiley present a radically different approach to quantum theory.

We summarize a new 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. Our interpretation—which we claim is ultimately compatible with Lorentz invariance—reformulates wave-function collapse in terms of an underlying interpolating dynamics, makes it possible to derive the Born rule from deeper principles, and resolves several open questions regarding ontological stability and dynamics. (shrink)

After about a century since the first attempts by Bohr, the interpretation of quantum theory is still a field with many open questions.1 In this article a new interpretation of quantum theory is suggested, motivated by philosophical considerations. Based on the findings that the ’weirdness’ of quantum theory can be understood to derive from a vanishing distinguishability of indiscernible particles, and the observation that a similar vanishing distinguishability is found for bundle theories (...) in philosophical ontology, the claim is made that quantum theory can be interpreted in an intelligible way by positing a bundle-theoretic view of objective idealism instead of materialism as the underlying fundamental nature of reality. (shrink)

In order to tackle the question posed by the title – notoriously answered in the positive, among others, by Heisenberg, Margenau, Popper and Redhead – I first discuss some attempts at distinguishing dispositional from non-dispositional properties, and then relate the distinction to the formalism of quantum mechanics. Since any answer to the question titling the paper must be interpretation-dependent, I review some of the main interpretations of quantum mechanics in order to argue that the ontology of theories (...) regarding “wave collapse” as a genuine physical process could be interpreted as being irreducibly dispositional. In non-collapse interpretations, on the contrary, the appeal to dispositions is simply a way to reformulate the predictive content of the algorithm of the theory in a fancier metaphysical language. (shrink)

I propose a new class of interpretations, real world interpretations, of the quantum theory of closed systems. These interpretations postulate a preferred factorization of Hilbert space and preferred projective measurements on one factor. They give a mathematical characterisation of the different possible worlds arising in an evolving closed quantum system, in which each possible world corresponds to a (generally mixed) evolving quantum state. In a realistic model, the states corresponding to different worlds should be expected to (...) tend towards orthogonality as different possible quasiclassical structures emerge or as measurement-like interactions produce different classical outcomes. However, as the worlds have a precise mathematical definition, real world interpretations need no definition of quasiclassicality, measurement, or other concepts whose imprecision is problematic in other interpretational approaches. It is natural to postulate that precisely one world is chosen randomly, using the natural probability distribution, as the world realised in Nature, and that this world’s mathematical characterisation is a complete description of reality. (shrink)

Popper's idea of propensities constituting the physical background of predictable probabilities is reviewed and developed by introducing a suitable formalism compatible with standard probability calculus and with its frequency interpretation. Quantum statistical ensembles described as pure cases (“eigenstates”) are shown to be necessarily not homogeneous if propensities are actually at work in nature. An extension of the theory to EPR experiments with local propensities leads to a new and more general proof of Bell's theorem. No joint probabilities (...) for incompatible observables need to be introduced. (shrink)

Spontaneous collapse theories of quantum mechanics turn the usual Schrödinger equation into a stochastic dynamical law. In particular, in this paper, I will focus on the GRW theory. Two philosophical issues that can be raised about GRW concern (i) the ontology of the theory, in particular the nature of the wave function and its role within the theory, and (ii) the interpretation of the objective probabilities involved in the dynamics of the theory. During the (...) last years, it has been claimed that we can take advantage of dispositional properties in order to develop an ontology for GRW theory, and also in order to ground the objective probabilities which are postulated by it. However, in this paper, I will argue that the dispositional interpretations which have been discussed in the literature so far are either flawed or – at best – incomplete. If we want to endorse a dispositional interpretation of GRW theory we thus need an extended account that specifies the precise nature of those properties and which makes also clear how they can correctly ground all the probabilities postulated by the theory. Thus, after having introduced several different kinds of probabilistic dispositions, I will try to fill the gap in the literature by proposing a novel and complete dispositional account of GRW, based on what I call spontaneous weighted multi-track propensities. I claim that such an account can satisfy both of our desiderata. (shrink)

First published in 1995. Routledge is an imprint of Taylor & Francis, an informa company.

This paper is a response to some recent discussions of many-minds interpretations in the philosophical literature. After an introduction to the many-minds idea, the complexity of quantum states for macroscopic objects is stressed. Then it is proposed that a characterization of the physical structure of observers is a proper goal for physical theory. It is argued that an observer cannot be defined merely by the instantaneous structure of a brain, but that the history of the brain's functioning must (...) also be taken into account. Next the nature of probability in many-minds interpretations is discussed and it is suggested that only discrete probability models are needed. The paper concludes with brief comments on issues of actuality and identity over time. (shrink)

Confused ideas about the weirdness of quantum mechanics have sometimes been blamed for the spread of anti-realist positions in philosophy. In this seminar, I shall re-examine the relation between realism and quantum theory. My goal is to argue that one can remain a realist in a reasonably familiar sense, while adopting a theory which amounts to a form of idealism. After sketching the abstract mathematical structure of quantum theory, I will introduce realism and consider (...) some of its problems and some counter-arguments. Next I will look at why quantum theory needs an interpretation and at some of the features common to many proposed interpretations. Then I will discuss some of the gaps in decoherence theory, when it is considered as an interpretation of quantum theory, and I will end with a sketch of my own realist version of idealism in which the fundamental entities are structures which define minds, and the fundamental laws govern the stochastic developments of those structures. (shrink)

A fully micro realistic, propensity version of quantum theory is proposed, according to which fundamental physical entities - neither particles nor fields - have physical characteristics which determine probabilistically how they interact with one another . The version of quantum "smearon" theory proposed here does not modify the equations of orthodox quantum theory: rather, it gives a radically new interpretation to these equations. It is argued that there are strong general reasons for (...) preferring quantum "smearon" theory to orthodox quantum theory; the proposed change in physical interpretation leads quantum "smearon" theory to make experimental predictions subtly different from those of orthodox quantum theory. Some possible crucial experiments are considered. (shrink)

It has been suggested, on the one hand, that quantum states are just states of knowledge; and, on the other, that quantum theory is merely a theory of correlations. These suggestions are confronted with problems about the nature of psycho-physical parallelism and about how we could define probabilities for our individual future observations given our individual present and previous observations. The complexity of the problems is underlined by arguments that unpredictability in ordinary everyday neural functioning, ultimately (...) stemming from small-scale uncertainties in molecular motions, may overwhelm, by many orders of magnitude, many conventionally recognized sources of observed ``quantum'' uncertainty. Some possible ways of avoiding the problems are considered but found wanting. It is proposed that a complete understanding of the relationship between subjective experience and its physical correlates requires the introduction of mathematical definitions and indeed of new physical laws. (shrink)

The interpretation of quantum mechanics is discussed from the viewpoint of quantum logic (QL). QL is understood to concern the possible properties that can be ascribed to a physical system SYS. The micro-state of SYS at any given moment t is identified with the set of all properties actualized by SYS at time t. Minimal adequacy requirements are proposed for all interpretations of micro-states. A strict interpretation is defined to be one according to which the properties (...) ascribable to SYS are individuated by the projection operators on the associated Hilbert space. Two strict interpretations are examined. Kochen's interpretation is also discussed, and it is argued that it is not a strict interpretation. (shrink)

I examine some problems standing in the way of a successful `field interpretation' of quantum field theory. The most popular extant proposal depends on the Hilbert space of `wavefunctionals.' But since wavefunctional space is unitarily equivalent to many-particle Fock space, two of the most powerful arguments against particle interpretations also undermine this form of field interpretation. IntroductionField Interpretations and Field OperatorsThe Wavefunctional InterpretationFields and Inequivalent Representations 4.1. The Rindler representation 4.2. Spontaneous symmetry breaking 4.3. Coherent representations (...) The Fate of Fields in Interacting QFTConclusions. (shrink)

This is a philosophical paper in favor of the many-worlds interpretation of quantum theory. The necessity of introducing many worlds is explained by analyzing a neutron interference experiment. The concept of the “measure of existence of a world” is introduced and some difficulties with the issue of probability in the framework of the MWI are resolved.

We use the primitive ontology framework of Allori et al. to analyze the quantum information-theoretic interpretation of Bub and Pitowsky. There are interesting parallels between the two approaches, which differentiate them both from the more standard realist interpretations of quantum theory. Where they differ, however, is in terms of their commitments to an underlying ontology on which the manifest image of the world supervenes. Employing the primitive ontology framework in this way makes perspicuous the differences between (...) the quantum information-theoretic interpretation, and the various realist interpretations of quantum theory. It also allows us to identify a sense in which the commitments of quantum information-theoretic interpretation are underspecified. Several possible ways of completing the interpretation are presented, and it is suggested that the most likely strategy would leave the information-theoretic interpretation such that it would fail to qualify as a theory, according to the primitive ontology approach. (shrink)

The concept of "fitness" is a notion of central importance to evolutionary theory. Yet the interpretation of this concept and its role in explanations of evolutionary phenomena have remained obscure. We provide a propensity interpretation of fitness, which we argue captures the intended reference of this term as it is used by evolutionary theorists. Using the propensity interpretation of fitness, we provide a Hempelian reconstruction of explanations of evolutionary phenomena, and we show why charges (...) of circularity which have been levelled against explanations in evolutionary theory are mistaken. Finally, we provide a definition of natural selection which follows from the propensity interpretation of fitness, and which handles all the types of selection discussed by biologists, thus improving on extant definitions. (shrink)

Popper wrote extensively on the quantum theory. In Logic der Forschung he devoted a whole chapter to the topic, while the whole of Volume 3 of the Postscript to the Logic of Scientific Discovery is devoted to the quantum theory. This volume entitled Quantum Theory and the Schism in Physics incorporated a famous earlier essay, ‘Quantum Mechanics without “the Observer”’ . In addition Popper's development of the propensity interpretation of probability was (...) much influenced by his views on the role of probability in quantum theory, and he also wrote an insightful critique of the 1936 paper of Birkhoff and von Neumann on nondistributive quantum logic. (shrink)

In this paper we critically review the various attempts that have been made to understand quantum field theory. We focus on Teller's (1990) harmonic oscillator interpretation, and Bohm et al.'s (1987) causal interpretation. The former unabashedly aims to be a purely heuristic account, but we show that it is only interestingly applicable to the free bosonic field. Along the way we suggest alternative models. Bohm's interpretation provides an ontology for the theory--a classical field, with (...) a quantum equation of motion. This too has problems; it is not Lorentz invariant. (shrink)

Single-case and long-run propensity theories are among the main objective interpretations of probability. There have been various objections to these theories, e.g. that it is difficult to explain why propensities should satisfy the probability axioms and, worse, that propensities are at odds with these axioms, that the explication of propensities is circular and accordingly not informative, and that single-case propensities are metaphysical and accordingly non-scientific. We consider various propensity theories of probability and their prospects in light of these (...) objections. We argue that while propensity theories face challenges, these challenges do not undermine their validity as prospective interpretations of probability in science. (shrink)

How can we explain the strange behavior of quantum and relativistic entities? Why do they behave in ways that defy our intuition about how physical entities should behave, considering our ordinary experience of the world around us? In this article, we address these questions by showing that the comportment of quantum and relativistic entities is not that strange after all, if we only consider what their nature might possibly be: not an objectual one, but a conceptual one. This (...) not in the sense that quantum and relativistic entities would be human concepts, but in the sense that they would share with the latter a same conceptual nature, similarly to how electromagnetic and sound waves, although very different entities, can share a same undulatory nature. When this hypothesis is adopted, i.e., when a conceptuality interpretation about the deep nature of physical entities is taken seriously, many of the interpretational difficulties disappear and our physical world is back making sense, though our view of it becomes radically different from what our classical prejudice made us believe in the first place. (shrink)

This paper expands on, and provides a qualified defence of, Arthur Fine's selective interactions solution to the measurement problem. Fine's approach must be understood against the background of the insolubility proof of the quantum measurement. I first defend the proof as an appropriate formal representation of the quantum measurement problem. The nature of selective interactions, and more generally selections, is then clarified, and three arguments in their favour are offered. First, selections provide the only known solution to the (...) measurement problem that does not relinquish any of the explicit premises of the insolubility proofs. Second, unlike some no-collapse interpretations of quantum mechanics, selections suffer no difficulties with non-ideal measurements. Third, unlike most collapse interpretations, selections can be independently motivated by an appeal to quantum propensities. IntroductionThe problem of quantum measurement2.1 The ignorance interpretation of mixtures2.2 The eigenstate–eigenvalue link2.3 The quantum theory of measurementThe insolubility proof of the quantum measurement3.1 Some notation3.2 The transfer of probability condition (TPC)3.3 The occurrence of outcomes condition (OOC)A defence of the insolubility proof4.1 Stein's critique4.2 Ignorance is not required4.3 The problem of quantum measurement is an idealisationSelections5.1 Representing dispositional properties5.2 Selections solve the measurement problem5.3 Selections and ignoranceNon-ideal selections6.1 No-collapse interpretations and non-ideal measurements6.2 Exact and approximate measurements6.3 Selections for non-ideal interactions6.4 Approximate selections6.5 Implications for ignoranceSelective interactions test quantum propensities7.1 Equivalence classes as physical ‘aspects’: a critique7.2 Quantum dispositions7.3 Selections as a propensity modal interpretation7.4 A comparison with Popper's propensity interpretation. (shrink)

In a series of papers, a many-minds interpretation of quantum theory has been developed. The aim in these papers is to present an explicit mathematical formalism which constitutes a complete theory compatible with relativistic quantum field theory. In this paper, which could also serve as an introduction to the earlier papers, three issues are discussed. First, a significant, but fairly straightforward, revision in some of the technical details is proposed. This is used as an (...) opportunity to introduce the formalism. Then the probabilistic structure of the theory is revised, and it is proposed that the experience of an individual observer can be modelled as the experience of observing a particular, identified, discrete stochastic process. Finally, it is argued that the formalism can be modified to give a physics in which no constants are required. Instead, “constants” have to be determined by observation, and are fixed only to the extent to which they have been observed. (shrink)

The Everett interpretation of quantum theory requires either the existence of an infinite number of conscious minds associated with each brain or the existence of one universal consciousness. Reasons are given, and the two ideas are compared.

In other words, classically, probabilities add; quantum mechanically, the probability amplitudes add, leading to the presence of the extra product terms in the quantum case. What this means is that in quantum theory, even though always only one of the various outcomes is obtained in any given observation, some aspect of the non -occurring events, represented by the corresponding complex-valued quantum amplitudes, plays a role in determining the overall probabilities. Indeed, the observed quantum interference (...) effects are correctly captured by the quantum statistical description only because of the presence of these product terms. Therefore, in a realistic construal of quantum theory, if we treat the superposed Ψ function as representing the real state of an individual quantum system, these quantum amplitudes need to be given an ontological status. (shrink)

The attempt to derive (rather than assume) the statistical postulate of quantum theory from the many-universes interpretation of Everett and De Witt is analyzed The many-universes interpretation is found to be neither necessary nor sufficient for the task.

The paper provides a new critical perspective on the propensity interpretation of fitness, by investigating its relationship to the propensity interpretation of probability. Two main conclusions are drawn. First, the claim that fitness is a propensity cannot be understood properly: fitness is not a propensity in the sense prescribed by the propensity interpretation of probability. Second, this interpretation of probability is inessential for explanations proposed by the PIF in evolutionary biology. Consequently, (...) interpreting the probabilistic dimension of fitness in terms of propensities is neither a strong motivation in favor of this interpretation, nor a possible target for substantial criticism. (shrink)

Jeff Bub has developed an information-theoretic interpretation of quantum mechanics on the basis of the programme to reaxiomatise the theory in terms of information-theoretic principles. According to the most recent version of the interpretation, reaxiomatisation can dissolve some of the demands for explanation traditionally associated with the task of providing an interpretation for the theory. The key idea is that the real lesson we should take away from quantum mechanics is that the ‘structure (...) of in- formation’ is not what we thought it was. In particular a feature of the new structure is intrinsic randomness of measurement, which allegedly dissolves a significant part of the measurement problem. I argue that it is difficult to find an appropriate argument to support the claim that measurement is intrinsically random in the relevant sense. (shrink)

The axiomatic approaches of quantum mechanics and relativity theory are compared with approaches in which the theories are thought to describe readings of certain measurement operations. The usual axioms are shown to correspond with classes of ideal measurements. The necessity is discussed of generalizing the formalisms of both quantum mechanics and relativity theory so as to encompass more realistic nonideal measurements. It is argued that this generalization favours an empiricist interpretation of the mathematical formalisms over (...) a realist one. (shrink)

This paper investigates the possibiity of developing a fully micro realistic version of elementary quantum mechanics. I argue that it is highly desirable to develop such a version of quantum mechanics, and that the failure of all current versions and interpretations of quantum mechanics to constitute micro realistic theories is at the root of many of the interpretative problems associated with quantum mechanics, in particular the problem of measurement. I put forward a propensity micro realistic (...) version of quantum mechanics, and suggest how it might be possible to discriminate, on expermental grounds, between this theory and other versions of quantum mechanics. (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)

How can we explain the strange behavior of quantum and relativistic entities? Why do they behave in ways that defy our intuition about how physical entities should behave, considering our ordinary experience of the world around us? In this article, we address these questions by showing that the comportment of quantum and relativistic entities is not that strange after all, if we only consider what their nature might possibly be: not an objectual one, but a conceptual one. This (...) not in the sense that quantum and relativistic entities would be human concepts, but in the sense that they would share with the latter a same conceptual nature, similarly to how electromagnetic and sound waves, although very different entities, can share a same undulatory nature. When this hypothesis is adopted, i.e., when a conceptuality interpretation about the deep nature of physical entities is taken seriously, many of the interpretational difficulties disappear and our physical world is back making sense, though our view of it becomes radically different from what our classical prejudice made us believe in the first place. (shrink)

Recently it has been shown that transformations of Heisenberg-picture operators are the causal mechanism which allows Bell-theorem-violating correlations at a distance to coexist with locality in the Everett interpretation of quantum mechanics. A calculation to first order in perturbation theory of the generation of EPRB entanglement in nonrelativistic fermionic field theory in the Heisenberg picture illustrates that the same mechanism leads to correlations without nonlocality in quantum field theory as well. An explicit transformation is (...) given to a representation in which initial-condition information is transferred from the state vector to the field operators, making the locality of the theory manifest. (shrink)