The use of joint distribution functions for noncommuting observables in quantum thermodynamics is investigated in the light of L. Cohen's proof that such distributions are not determined by the quantum state. Cohen's proof is irrelevant to uses of the functions that do not depend on interpreting them as distributions. An example of this, from quantum Onsager theory, is discussed. Other uses presuppose that correlations betweenp andq values depend at least on the state. But correlations may be fixed by the state (...) even though the distribution varies from one ensemble to another represented by that state. Taking covariance as a measure of correlation, it is shown that the different commonly used joint distributions yield the same correlations for a given state. A general characterization is given for a family of distributions with this same covariance. (shrink)

This paper uses a non-distributive system of Boolean fractions (a|b), where a and b are 2-valued propositions or events, to express uncertain conditional propositions and conditional events. These Boolean fractions, 'a if b' or 'a given b', ordered pairs of events, which did not exist for the founders of quantum logic, can better represent uncertain conditional information just as integer fractions can better represent partial distances on a number line. Since the indeterminacy of some pairs of quantum events is due (...) to the mutual inconsistency of their experimental conditions, this algebra of conditionals can express indeterminacy. In fact, this system is able to express the crucial quantum concepts of orthogonality, simultaneous verifiability, compatibility, and the superposition of quantum events, all without resorting to Hilbert space. A conditional (a|b) is said to be "inapplicable" (or "undefined") in those instances or models for which b is false. Otherwise the conditional takes the truth-value of proposition a. Thus the system is technically 3-valued, but the 3rd value has nothing to do with a state of ignorance, nor to some half-truth. People already routinely put statements into three categories: true, false, or inapplicable. As such, this system applies to macroscopic as well as microscopic events. Two conditional propositions turn out to be simultaneously verifiable just in case the truth of one implies the applicability of the other. Furthermore, two conditional propositions (a|b) and (c|d) reside in a common Boolean sub-algebra of the non-distributive system of conditional propositions just in case b = d, their conditions are equivalent. Since all aspects of quantum mechanics can be represented with this near classical logic, there is no need to adopt Hilbert space logic as ordinary logic, just a need perhaps to adopt propositional fractions to do logic, just as we long ago adopted integer fractions to do arithmetic. The algebra of Boolean fractions is a natural, near-Boolean extension of Boolean algebra adequate to express quantum logic. While this paper explains one group of quantum anomalies, it nevertheless leaves no less mysterious the 'influence-at-a-distance', quantum entanglement phenomena. A quantum realist must still embrace non-local influences to hold that "hidden variables" are the measured properties of particles. But that seems easier than imaging wave-particle duality and instant collapse, as offered by proponents of the standard interpretation of quantum mechanics. (shrink)

Modern insolubility proofs of the measurement problem in quantum mechanics not only differ in their complexity and degree of generality, but also reveal a lack of agreement concerning the fundamental question of what constitutes such a proof. A systematic reworking of the (incomplete) 1970 Fine theorem is presented, which is intended to go some way toward clarifying the issue.

A recent no-go theorem (Frauchiger and Renner in Nat Commun 9(1):3711, 2018) establishes a contradiction from a specific application of quantum theory to a multi- agent setting. The proof of this theorem relies heavily on notions such as ‘knows’ or ‘is certain that’. This has stimulated an analysis of the theorem by Nurgalieva and del Rio (in: Selinger P, Chiribella G (eds) Proceedings of the 15th international conference on quantum physics and logic (QPL 2018). EPTCS 287, Open Publishing Association, Waterloo, (...) 2018), in which they claim that it shows the “[i]nadequacy of modal logic in quantum settings” (ibid.). In this paper, we will offer a significantly extended and refined reconstruction of the theorem in multi-agent modal logic. We will then show that a thorough reconstruction of the proof as given by Frauchiger and Renner requires the reflexivity of access relations (system T). However, a stronger theorem is possible that already follows in serial frames, and hence also holds in systems of doxastic logic (such as KD45). After proving this, we will discuss the general implications for different interpretations of quantum probabilities as well as several options for dealing with the result. (shrink)

The aim of this paper is to give a systematic account of the so-called “measurement problem” in the frame of the standard interpretation of quantum mechanics. It is argued that there is not one but five distinct formulations of this problem. Each of them depends on what is assumed to be a “satisfactory” description of the measurement process in the frame of the standard interpretation. Moreover, the paper points out that each of these formulations refers not to a unique problem, (...) but to a set of sub-problems. (shrink)

Since he proved his theorem in 1982, Fine has been challenging the traditional interpretation of the experimental violation of the Bell Inequalities. A natural interpretation of Fine's theorem is that it provides us with an alternative set of assumptions on which to place blame for the failure of the BI, and opens to a new interpretation of the violation of the BI. Fine has a stronger interpretation for his theorem. He claims that his result undermines the traditional interpretation in terms (...) of local realism. The aim of this paper is to understand and to assess Fine's claim. We distinguish three different strategies that Fine uses in order to support his view. We show that none of these strategies is successful. Fine fails to prove that local realism is not at stake in the violation of the BI by quantum phenomena. (shrink)

The standard axiomatization of quantum mechanics (QM) is not fully explicit about the role of the time-parameter. Especially, the time reference within the probability algorithm (the Born Rule, BR) is unclear. From a probability principle P1 and a second principle P2 affording a most natural way to make BR precise, a logical conflict with the standard expression for the completeness of QM can be derived. Rejecting P1 is implausible. Rejecting P2 leads to unphysical results and to a conflict with a (...) generalization of P2, a principle P3. All three principles are shown to be without alternative. It is thus shown that the standard expression of QM completeness must be revised. An absolutely explicit form of the axioms is provided, including a precise form of the projection postulate. An appropriate expression for QM completeness, reflecting the restrictions of the Gleason and Kochen-Specker theorems is proposed. (shrink)

In this paper I consider the problem of interpreting quantum mechanics. I argue that this problem has evolved in part into the problem of selecting tenable interpretations from a set of available interpretations. We lack the means to make this selection. There is consensus that interpretations should be consistent and empirically adequate. But these conditions are not particularly discriminative. Other conditions may be discriminative but are not generally accepted. I propose two new conditions for selecting tenable interpretations, motivated by the (...) use of quantum mechanics in technology. The first requires that interpretations ascribe the physical properties to technical artefacts that are entailed by the ascription of technical functions to those artefacts. The second requires that they ascribe the physical properties represented by engineering sketches of those artefacts. I consider the example of quantum teleportation in some detail. Introduction The problem of interpreting quantum mechanics Technical functions Decoders in quantum teleportation Engineering sketches Conclusions Appendix: Quantum teleportation. (shrink)

Previous work has shown that the problem of measurement in quantum mechanics is not correctly seen as one of understanding some allegedly univocal process of measurement in nature which corresponds to the projection postulate. The present paper introduces a new perspective by showing that how we are to understand the nature of the change of quantum mechanical state on measurement depends very sensitively on the interpretation of the state function, and by showing how attention to this dependence can greatly sharpen (...) the problems and relations between them. In particular, the problems take a form resembling their traditional formulation only on an inexact value interpretation, according to which the state function attributes inexact values of quantities to systems. On other interpretations we can apply (with various drawbacks) the subensemble idea, according to which a discontinuous change of quantum mechanical description results on measurement simply because we need a new state function to describe a new object. (shrink)

Fine has recently proved the surprising result that satisfaction of the Bell inequality in a Clauser-Horne experiment implies the existence of joint probabilities for pairs of noncommuting observables in the experiment. In this paper we show that if probabilities are interpreted in the von Mises-Church sense of relative frequencies on random sequences, a proof of the Bell inequality is nonetheless possible in which such joint probabilities are assumed not to exist. We also argue that Fine's theorem and related results do (...) not impugn the common view that local realists are committed to the Bell inequality. (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)

Arthur Fine's use of prism models to provide local and deterministic accounts of quantum correlation experiments is presented and analyzed in some detail. Fine's claim that "there is... no question of the consistency of prism models... with the quantum theory" (forthcoming, p. 16) is disputed. Our criticisms are threefold: (1) consideration of the possibility of additional analyzer positions shows that prism models entail unacceptably high rejection rates in the relevant experiments; (2) similar considerations show that the models are at best (...) only superficially local and deterministic; and (3) in any case, Fine extracts the quantum correlation statistics from prism models only by resurrecting conceptual problems similar to those that his models were to designed to solve. (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)

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)

In this paper, possible objections to the propensity microrealistic version of quantum mechanics proposed in Part I are answered. This version of quantum mechanics is compared with the statistical, particle microrealistic viewpoint, and a crucial experiment is proposed designed to distinguish between these to microrealistic versions of quantum mechanics.

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)

The work of Gleason and of Kochen and Specker has been thought to refute a naïve realist approach to quantum mechanics. The argument of this paper substantially bears out this conclusion. The assumptions required by their work are not arbitrary, but have sound theoretical justification. Moreover, if they are false, there seems no reason why their falsity should not be demonstrable in some sufficiently ingenious experiment. Suitably interpreted, the work of Bell and Wigner may be seen to yield independent arguments (...) for the falsity of naïve realistic approach to quantum mechanics. Quantum mechanics is no more like classical statistical mechanics than its creators thought it was. (shrink)

Can quantum theory provide examples of metaphysical indeterminacy, indeterminacy that obtains in the world itself, independently of how one represents the world in language or thought? We provide a positive answer assuming just one constraint of orthodox quantum theory: the eigenstate-eigenvalue link. Our account adds a modal condition to preclude spurious indeterminacy in the presence of superselection sectors. No other extant account of metaphysical indeterminacy in quantum theory meets these demands.

The ArgumentThis paper argues that Einstein subscribed to three distinct kinds of interpretations of the quantum theory: subjective, instrumental, and hidden variables interpretations. We explore the context and ihe content of Einstein's thinking over these interpretations, emphasizing Einstein's conception of his role not only as a critic of the new quantum theory but also as a guide pointing the way to better physics.

This article reexamines Einstein's views concerning ensembles and the quantum state function, by way of responding to criticism on this topic. The response calls attention to the range of interpretations found in Einstein's writings, and their function, and emphasizes the nonspecificity of his discussions. It also offers some guidelines for scholarship and criticism in this area.

En esta tesis hacemos un análisis comparativo de las distintas interpretaciones de la mecánica bohmiana en relación con el realismo científico. En primer lugar discutimos si cabe encontrar una interpretación de la teoría que satisfaga el requisito de que toda entidad real existe en el espacio físico tridimensional. Luego, discutimos el desempeño de las distintas interpretaciones de la teoría en relación con el principio de fiabilidad de la medida. Finalmente, analizamos el argumento de las trayectorias surrealistas. De acuerdo con este (...) argumento, una interpretación realista de las trayectorias bohmianas es insostenible puesto que se dan situaciones en las que dichas trayectorias difieren de lo indicado por los detectores de camino. En relación con esta última cuestión derivamos unas condiciones precisas de ocurrencia de las trayectorias surrealistas y defendemos que, si bien es posible que las trayectorias bohmianas difieran de lo indicado por los detectores de camino, no se sigue de ello que una interpretación realista de las mismas sea insostenible. Puesto que siempre cabe encontrar una interpretación de la mecánica bohmiana que satisface los requisitos realistas discutidos, concluimos a favor del vigor realista de la teoría. Además, puesto que la satisfacción de dichos requisitos depende de la interpretación de la teoría considerada, defendemos que en mecánica bohmiana la cuestión de la interpretación es tan relevante como lo es en mecánica cuántica. (shrink)

This essay is a discussion of the philosophical and foundational issues that arise in non-relativistic quantum theory. After introducing the formalism of the theory, I consider: characterizations of the quantum formalism, empirical content, uncertainty, the measurement problem, and non-locality. In each case, the main point is to give the reader some introductory understanding of some of the major issues and recent ideas.

In 2002 the readers of the scientific magazine 'Physics World' voted Young's double-slit experiment applied to the interference of single electrons to be 'the most beautiful experiment in physics'; this experiment, in truth, had already been carried out 30 years beforehand. The present article aims to re-examine the latter real experiment and put it into its proper historical perspective. Even though the experiment was not afforded the importance it perhaps deserved among philosophers, its philosophical mplications add new arguments to the (...) already far-reaching debate triggered off by the ideal experiment. Within the context of quantum mechanics in particular, the experiment revealed for the first time the importance that ought to be attributed at the empirical level to single-case probability, that is, to the probability of a single electron's reaching the screen. I investigate how the empirical significance of the experimental results comes within the framework of the debate over the propensity interpretation of probability in quantum mechanics. I argue that the experiment, when examined in all its technical details does in fact throw light on the evidence for the propensity, as a physical property, of micro-objects. (shrink)

The paper presents an argument for the incompleteness in principle of quantum mechanics. I introduce four principles (P0–P3) concerning the interpretation of probability, in general and in quantum mechanics, and argue that the defender of completeness must reject either P0 or all of P1–P3, which options both seem unacceptable. The problem is shown to be more fundamental than the measurement problem and to have implications for our understanding of quantum-mechanical contextuality.

This article focuses on two of the main problems raising interpretational issues in quantum mechanics, namely the notorious measurement problem and the equally important but not quite as widely discussed problem of the classical regime. The two problems are distinct, but they are both intimately related to some of the issues arising from entanglement and density operators. The article aims to be fairly non-technical in language, but modern in outlook and covering the chosen topics in more depth than most introductory (...) treatments. (shrink)

We propose the conjecture according to which the fact that quantum mechanics does not admit sharp value attributions to both members of a complementary pair of observables can be understood in the light of the symplectic reduction of phase space in constrained Hamiltonian systems. In order to unpack this claim, we propose a quantum ontology based on two independent postulates, namely the phase postulate and the quantum postulate. The phase postulate generalizes the gauge correspondence between first-class constraints and gauge transformations (...) to the observables of unconstrained Hamiltonian systems. The quantum postulate specifies the relationship between the numerical values of the observables that permit us to individualize a physical system and the symmetry transformations generated by the operators associated to these observables. We argue that the quantum postulate and the phase postulate are formally implemented by the two independent stages of the geometric quantization of a symplectic manifold, namely the prequantization formalism and the election of a polarization of pre-quantum states respectively. (shrink)