Bohmian mechanics is the most naively obvious embedding imaginable of Schrödinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically random, with probability density ρ given by |ψ | 2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of “measurements. ” This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas. Dedicated to Elliott Lieb on the occasion of his 70th birthday. Elliott will be (we fear unpleasantly) surprised to learn that he bears a greater responsibility for this paper than he could possibly imagine. We would of course like to think that our work addresses in some way the concern suggested by the title of his recent talks, The

The truth about physical objects must be strange. It may be unattainable, but if any philosopher believes that he has attained it, the fact that what he offers as the truth is strange ought not to be made a ground of objection to his opinion. – Bertrand Russell 1.

This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except the very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single realization of an experiment. For this purpose, orthodox quantum mechanics introduces a special postulate: the reduction of the state vector, which comes in addition to the Schrödinger evolution postulate. Nevertheless, the presence in parallel of two evolution processes of the same object (the state vector) may be a potential source for conflicts; various attitudes that are possible

I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch’s recent proof of the probability rule, but the proof is simpler and proceeds from weaker decisiontheoretic assumptions. This makes it easier to discuss the conceptual ideas involved in the proof, and to show that they are defensible. 1

This paper is a commentary on the foundational significance of the Clifton-Bub-Halvorson theorem characterizing quantum theory in terms of three information-theoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the information-theoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the information-theoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information.

Counterfactuals in quantum theory are briefly reviewed and it is argued that they are very different from counterfactuals considered in the general philosophical literature. The issue of time symmetry of quantum counterfactuals is considered and a novel time-symmetric definition of quantum counterfactuals is proposed. This definition is applied for analyzing several controversies related to quantum counterfactuals. 1 There are very many philosophical discussions on the concept of counterfactuals and especially on the time’s arrow in counterfactuals. There is also a considerable literature on counterfactual in quantum theory. In order to be a helpful tool in quantum theory counterfactuals have to be rigorously defined. Unfortunately, the concept of counterfactuals is vague 1 and this leads to several controversies. I, however, believe that since quantum counterfactuals appear in a much narrow context than in general discussions on counterfactuals, they can be defined unambiguously. I will briefly review counterfactuals in quantum theory and will propose a rigorous definition which can clarify several issues, in particular, those related to the time-symmetry of quantum counterfactuals.

Bohmian mechanics and the Ghirardi–Rimini–Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger’s equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about “matter” moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of space-time points. The role of the wave function then is to govern the motion of the matter.

I address the problem of indefiniteness in quantum mechanics: the problem that the theory, without changes to its formalism, seems to predict that macroscopic quantities have no definite values. The Everett interpretation is often criticised along these lines and I shall argue that much of this criticism rests on a false dichotomy: that the macroworld must either be written directly into the formalism or be regarded as somehow illusory. By means of analogy with other areas of physics, I develop the view that the macroworld is instead to be understood in terms of certain structures and patterns which emerge from quantum theory (given appropriate dynamics, in particular decoherence). I extend this view to the observer, and in doing so make contact with functionalist theories of mind.

call it, following Everett, the “relative state ” interpretation of quantum mechanics. It was rejected by one journal in 1990, primarily on the (I think incorrect) grounds that it was too similar to the Albert and Loewer “many minds ” version. It has seen limited circulation since then. My views are quite similar to ones since put forth by Simon Saunders, and subscribed to by David Wallace, among others. I believe that, within the relative state interpretation, when an observer interacts with a system in a measurement process in such a way that the combination of the two evolves into a superposition of the observer seeing macroscopically different apparatus pointer readings (or other macroscopic states), the observer’s consciousness “forks ” or “splits, ” because only those subspaces of Hilbert space describing definite macroscopic measurement results satisfy psychological/philosophical conditions for supporting a unified consciousness persisting through time. These conditions probably include things like the persistence of memory, and are probably closely linked to the “decoherence ” of certain subspace decompositions or approximate decompositions, corresponding to persisting macroscopic “classical ” structures that can support such persisting memories—relating the approach to the decoherence-based ones of, for example, Zurek, and Zeh, though this relation was not much stressed in the paper.

Whilst a straightforward consequence of the formalism of non-relativistic quantum mechanics, the phenomenon of quantum teleportation has given rise to considerable puzzlement. In this paper, the teleportation protocol is reviewed and these puzzles dispelled. It is suggested that they arise from two primary sources: (1) the familiar error of hypostatizing an abstract noun (in this case, ‘information’) and (2) failure to differentiate interpretation dependent from interpretation independent features of quantum mechanics. A subsidiary source of error, the simulation fallacy, is also identified. The resolution presented of the puzzles of teleportation illustrates the benefits of paying due attention to the logical status of ‘information ’ as an abstract noun.