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.

In Bohmian mechanics elementary particles exist objectively, as point particles moving according to a law determined by a wavefunction. In this context, questions as to whether the particles of a certain species are real—questions such as, Do photons exist? Electrons? Or just the quarks?—have a clear meaning. We explain that, whatever the answer, there is a corresponding Bohm-type theory, and no experiment can ever decide between these theories. Another question that has a clear meaning is whether particles are intrinsically distinguishable, i.e., whether particle world lines have labels indicating the species. We discuss the intriguing possibility that the answer is no, and particles are points—just points. PACS number: 03.65.Ta (foundations of quantum mechanics)

We first introduce and discuss density operator interpretations of quantum theory as a special case of a more general class of interpretations, giving special attention to a version that we call the ‘atomic version’. We then review some crucial parts of the theory of stochastic processes (the proper context in which to discuss dynamics), and develop a general framework for specifying a dynamics for density operator interpretations. This framework admits infinitely many empirically equivalent dynamics. We give some examples, and discuss some of the properties of one of them. Dynamics for Density Operator Interpretations of Quantum Theory We first introduce and discuss density operator interpretations of quantum theory as a special case of a more general class of interpretations, giving special attention to a version that we call the ‘atomic version’. We then review some crucial parts of the theory of stochastic processes (the proper context in which to discuss dynamics), and develop a general framework for specifying a dynamics for density operator interpretations. This framework admits infinitely many empirically equivalent dynamics. We give some examples, and discuss some of the properties of one of them.

We analyze the origin of quantum randomness within the framework of a completely deterministic theory of particle motion—Bohmian mechanics. We show that a uni-verse governed by this mechanics evolves in such a way as to give rise to the appear-ance of randomness, with empirical distributions in agreement with the predictions of the quantum formalism. Crucial ingredients in our analysis are the concept of the effective wave function of a subsystem and that of a random system. The latter is a notion of interest in its own right and is relevant to any discussion of the role of probability in a deterministic universe. 1.

I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive—just as, following Einstein’s special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical primitive in its own right. 1

This Chapter deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, and concludes by considering whether a perspective in terms of quantum information

The meaning of superselection rules in Bohm–Bell theories (i.e., quantum theories with particle trajectories) is different from that in orthodox quantum theory. More precisely, there are two concepts of superselection rule, a weak and a strong one. Weak superselection rules exist both in orthodox quantum theory and in Bohm–Bell theories and represent the conventional understanding of superselection rules. We introduce the concept of strong superselection rule, which does not exist in orthodox quantum theory. It relies on the clear ontology of Bohm– Bell theories and is a sharper and, in the Bohm–Bell context, more fundamental notion. A strong superselection rule for the observable G asserts that one can replace every state vector by a suitable statistical mixture of eigenvectors of G without changing the particle trajectories or their probabilities. A weak superselection rule asserts that every state vector is empirically indistinguishable from a suitable statistical mixture of eigenvectors of G. We establish conditions on G for both kinds of superselection. For comparison, we also consider both kinds of superselection in theories of spontaneous wave function collapse. Key words: weak and strong superselection rules; Bohmian mechanics; Belltype quantum field theory; beables; number operators; Ghirardi–Rimini–Weber model of spontaneous wave function collapse. 1

I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive—just as, following Einstein’s special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical entity in its own right. KEY WORDS: quantum information; foundations of quantum mechanics; quantum measurement; entanglement. 1.

We develop an extension of Bohmian mechanics by defining Bohm-like trajectories for (one or more) quantum particles in a curved background space-time containing a singularity. Part one, the present paper, focuses on timelike singularities, part two will be devoted to spacelike singularities. We use the timelike singularity of the (super-critical) Reissner–Nordström geometry as an example. While one could impose boundary conditions at the singularity that would prevent the particles from falling into the singularity, in the case we are interested in here particles have positive probability to hit the singularity and get annihilated. The wish for reversibility, equivariance and the Markov property then dictate that particles must also be created by the singularity, and indeed dictate the rate at which this must occur. That is, a stochastic law prescribes what comes out of the singularity. We specify explicit model equations, involving a boundary condition on the wave function at the singularity, which is applicable also to other versions of quantum theory besides Bohmian mechanics. Key words: quantum theory in curved background space-time; Reissner–Nordstrom space-time geometry; timelike singularities; Bohmian trajectories; particle creation and annihilation; stochastic jump process. 1

In de Broglie and Bohm’s pilot-wave theory, as is well known, it is possible to consider alternative particle dynamics while still preserving the |ψ | 2 distribution. I present the analogous result for Nelson’s stochastic theory, thus characterising the most general diffusion processes that preserve the quantum equilibrium distribution, and discuss the analogy with the construction of the dynamics for Bell’s beable theories. I briefly comment on the problem of convergence to |ψ | 2 and on possible experimental constraints on the alternative dynamics. 1