This article summarizes the Quantum Bayesian point of view of quantum mechanics, with special emphasis on the view's outer edges---dubbed QBism. QBism has its roots in personalist Bayesian probability theory, is crucially dependent upon the tools of quantum information theory, and most recently, has set out to investigate whether the physical world might be of a type sketched by some false-started philosophies of 100 years ago (pragmatism, pluralism, nonreductionism, and meliorism). Beyond conceptual issues, work at Perimeter Institute is focused on (...) the hard technical problem of finding a good representation of quantum mechanics purely in terms of probabilities, without amplitudes or Hilbert-space operators. The best candidate representation involves a mysterious entity called a symmetric informationally complete quantum measurement. Contemplation of it gives a way of thinking of the Born Rule as an addition to the rules of probability theory, applicable when an agent considers gambling on the consequences of his interactions with a newly recognized universal capacity: dimension (formerly Hilbert-space dimension). (The word "capacity" should conjure up an image of something like gravitational mass---a body's mass measures its capacity to attract other bodies. With hindsight one can say that the founders of quantum mechanics discovered another universal capacity, "dimension.") The article ends by showing that the egocentric elements in QBism represent no impediment to pursuing quantum cosmology and outlining some directions for future work. (shrink)

Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain (...) kinds of 'time observables' to find a representation within quantum theory, including clock operators and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on reflection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack. (shrink)

Schrödinger averred that entanglement is the characteristic trait of quantum mechanics. The first part of this paper is simultaneously an exploration of Schrödinger’s claim and an investigation into the distinction between mere entanglement and genuine quantum entanglement. The typical discussion of these matters in the philosophical literature neglects the structure of the algebra of observables, implicitly assuming a tensor product structure of the simple Type I factor algebras used in ordinary Quantum Mechanics . This limitation is overcome by adopting the (...) algebraic approach to quantum physics, which allows a uniform treatment of ordinary QM, relativistic quantum field theory, and quantum statistical mechanics. The algebraic apparatus helps to distinguish several different criteria of quantum entanglement and to prove results about the relation of quantum entanglement to two additional ways of characterizing the classical versus quantum divide, viz. abelian versus non-abelian algebras of observables, and the ability versus inability to interrogate the system without disturbing it. Schrödinger’s claim is reassessed in the light of this discussion. The second part of the paper deals with the relativity-to-ambiguity threat: the entanglement of a state on a system algebra is entanglement of the state relative to a decomposition of the system algebra into subsystem algebras; a state may be entangled with respect to one decomposition but not another; hence, unless there is some principled way to choose a decomposition, entanglement is a radically ambiguous notion. The problem is illustrated in terms a Realist versus Pragmatist debate, the former claiming that the decomposition must correspond to real as opposed to virtual subsystems, while the latter claims that the real versus virtual distinction is bogus and that practical considerations can steer the choice of decomposition. This debate is applied to the fraught problem of measuring entanglement for indistinguishable particles. The paper ends with some remarks about claims in the philosophical literature that entanglement undermines the separability or independence of subsystems while promoting holism. (shrink)

A normal state on a von Neumann algebra defines a countably additive probability measure over its projection lattice. The von Neumann algebras familiar from ordinary QM are algebras of all the bounded operators on a Hilbert space H, aka Type I factor von Neumann algebras. Their normal states are density operator states, and can be pure or mixed. In QFT and the thermodynamic limit of QSM, von Neumann algebras of more exotic types abound. Type III von Neumann algebras, for instance, (...) have no pure normal states; the pure states they do have fail to be countably additive. I will catalog a number of temptations to accord physical significance to non-normal states, and then give some reasons to resist these temptations: pure though they may be, non-normal states on non-Type I factor von Neumann algebras can't do the interpretive work we've come to expect from pure states on Type I factors; our best accounts of state preparation don't work for the preparation of non-normal states; there is a sense in which non-normal states fail to instantiate the laws of quantum mechanics. (shrink)

In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent’s degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim that probabilities (...) always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent’s prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent’s prior beliefs. Quantum certainty is therefore always some agent’s certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [(1983). Quantum logic, realism, and value-definiteness. Philosophy of Science, 50, 578], which applies the Kochen–Specker theorem to an entangled bipartite system. (shrink)

The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from common objections: that it is solipsist; that it is too instrumentalist; that it cannot deal with Wigner's friend scenarios. Three more substantive problems are raised: Can a reasonable ontology be found for the approach? Can it account for explanation in quantum theory? Are subjective (...) probabilities on their own adequate in the quantum domain? The first question is answered in the affirmative, drawing on elements from Nancy Cartwright's philosophy of science. The second two are not: it is argued that these present outstanding difficulties for the project. A quantum Bayesian version of Moore's paradox is developed to illustrate difficulties with the subjectivist account of pure state assignments. (shrink)

The Many-Worlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.

Bohmian mechanics, which is also called the de Broglie-Bohm theory, the pilot-wave model, and the causal interpretation of quantum mechanics, is a version of quantum theory discovered by Louis de Broglie in 1927 and rediscovered by David Bohm in 1952. It is the simplest example of what is often called a hidden variables interpretation of quantum mechanics. In Bohmian mechanics a system of particles is described in part by its wave function, evolving, as usual, according to Schrödinger's equation. However, the (...) wave function provides only a partial description of the system. This description is completed by the specification of the actual positions of the particles. The latter evolve according to the.. (shrink)

We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it. The construction proceeds in the following steps: (a) Axioms for the algebra of events are introduced following Birkhoff and von Neumann. All axioms, except the one that expresses the uncertainty principle, are shared with the classical event space. The only models for (...) the set of axioms are lattices of subspaces of inner product spaces over a field K. (b) Another axiom due to Soler forces K to be the field of real, or complex numbers, or the quaternions. We suggest a probabilistic reading of Soler's axiom. (c) Gleason's theorem fully characterizes the probability measures on the algebra of events, so that Born's rule is derived. (d) Gleason's theorem is equivalent to the existence of a certain finite set of rays, with a particular orthogonality graph (Wondergraph). Consequently, all aspects of quantum probability can be derived from rational probability assignments to finite "quantum gambles". (e) All experimental aspects of entanglement- the violation of Bell's inequality in particular- are explained as natural outcomes of the probabilistic structure. (f) We hypothesize that even in the absence of decoherence macroscopic entanglement can very rarely be observed, and provide a precise conjecture to that effect .We also discuss the relation of the present approach to quantum logic, realism and truth, and the measurement problem. (shrink)

Quantum mechanics, with its revolutionary implications, has posed innumerable problems to philosophers of science. In particular, it has suggested reconsidering basic concepts such as the existence of a world that is, at least to some extent, independent of the observer, the possibility of getting reliable and objective knowledge about it, and the possibility of taking (under appropriate circumstances) certain properties to be objectively possessed by physical systems. It has also raised many others questions which are well known to those involved (...) in the debate on the interpretation of this pillar of modern science. One can argue that most of the problems are not only due to the intrinsic revolutionary nature of the phenomena which have led to the development of the theory. They are also related to the fact that, in its standard formulation and interpretation, quantum mechanics is a theory which is excellent (in fact it has met with a success unprecedented in the history of science) in telling us everything about what we observe, but it meets with serious difficulties in telling us what is. We are making here specific reference to the central problem of the theory, usually referred to as the measurement problem, or, with a more appropriate term, as the macro-objectification problem. It is just one of the many attempts to overcome the difficulties posed by this problem that has led to the development of Collapse Theories, i.e., to the Dynamical Reduction Program (DRP). As we shall see, this approach consists in accepting that the dynamical equation of the standard theory should be modified by the addition of stochastic and nonlinear terms. The nice fact is that the resulting theory is capable, on the basis of a unique dynamics which is assumed to govern all natural processes, to account at the same time for all well-established.. (shrink)

This paper comments on a paper by Chris Fuchs. Both papers are to appear in "New Directions in the Philosophy of Science", eds. M. C. Galavotti, S. Hartmann, M. Weber, W. Gonzalez, D. Dieks and T. Uebel. This paper presents some mild criticisms of Fuchs's views, some based on the EPR and Wigner's friend scenarios, and some based on the quantum theory of measurement. A few alternative suggestions for implementing a subjectivist interpretation of probability in quantum mechanics conclude the paper.

The discussion of different principles of additivity for probability functions has been largely focused on the personalist interpretation of probability. Very little attention has been given to additivity principles for physical probabilities. The form of additivity for quantum probabilities is determined by the algebra of observables that characterize a physical system and the type of quantum state that is realizable and preparable for that system. We assess arguments designed to show that only normal quantum states are realizable and preparable and, (...) therefore, quantum probabilities satisfy the principle of complete additivity. We underscore the little remarked fact that unless the dimension of the Hilbert space is incredibly large, complete additivity in ordinary non-relativistic quantum mechanics reduces to countable additivity. We then turn to ways in which knowledge of quantum probabilities may constrain rational credence about quantum events and, thereby, constrain the additivity principle satisfied by rational credence functions. (shrink)

Debates about scientific realism are closely connected to almost everything else in the philosophy of science, for they concern the very nature of scientific knowledge. Scientific realism is a positive epistemic attitude toward the content of our best theories and models, recommending belief in both observable and unobservable aspects of the world described by the sciences. This epistemic attitude has important metaphysical and semantic dimensions, and these various commitments are contested by a number of rival epistemologies of science, known collectively (...) as forms of scientific antirealism. This article explains what scientific realism is, outlines its main variants, considers the most common arguments for and against the position, and contrasts it with its most important antirealist counterparts. (shrink)

Philosophical accounts of quantum theory commonly suppose that the observables of a quantum system form a Type-I factor von Neumann algebra. Such algebras always have atoms, which are minimal projection operators in the case of quantum mechanics. However, relativistic quantum field theory and the thermodynamic limit of quantum statistical mechanics make extensive use of von Neumann algebras of more general types. This chapter addresses the question whether interpretations of quantum probability devised in the usual manner continue to apply in the (...) more general setting. Features of non-type I factor von Neumann algebras are cataloged. It is shown that these novel features do not cause the familiar formalism of quantum probability to falter, since Gleason's Theorem and the Lüders Rule can be generalized. However, the features render the problem of the interpretation of quantum probability more intricate. (shrink)