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In response to recent criticisms by Okon and Sudarsky, various aspects of the consistent histories (CH) resolution of the quantum measurement problem(s) are discussed using a simple Stern-Gerlach device, and compared with the alternative approaches to the measurement problem provided by spontaneous localization (GRW), Bohmian mechanics, many worlds, and standard (textbook) quantum mechanics. Among these CH is unique in solving the second measurement problem: inferring from the measurement outcome a property of the measured system at a time before the measurement took place, as is done routinely by experimental physicists. The main respect in which CH differs from other quantum interpretations is in allowing multiple stochastic descriptions of a given measurement situation, from which one (or more) can be selected on the basis of its utility. This requires abandoning a principle (termed unicity), central to classical physics, that at any instant of time there is only a single correct description of the world., Version 2 has very minor changes. 17 pages

The (consistent or decoherent) histories interpretation provides a consistent realistic ontology for quantum mechanics, based on two main ideas. First, a logic (system of reasoning) is employed which is compatible with the Hilbert-space structure of quantum mechanics as understood by von Neumann: quantum properties and their negations correspond to subspaces and their orthogonal complements. It employs a special (single framework) syntactical rule to construct meaningful quantum expressions, quite different from the quantum logic of Birkhoff and von Neumann. Second, quantum time development is treated as an inherently stochastic process under all circumstances, not just when measurements take place. The time-dependent Schr\"odinger equation provides probabilities, not a deterministic time development of the world. The resulting interpretive framework has no measurement problem and can be used to analyze in quantum terms what is going on before, after, and during physical preparation and measurement processes. In particular, appropriate measurements can reveal quantum properties possessed by the measured system before the measurement took place. There are no mysterious superluminal influences: quantum systems satisfy an appropriate form of Einstein locality. This ontology provides a satisfactory foundation for quantum information theory, since it supplies definite answers as to what the information is about. The formalism of classical (Shannon) information theory applies without change in suitable quantum contexts, and this suggests the way in which quantum information theory extends beyond its classical counterpart., Comment: Very minor revisions to previous version

A consistent history analysis of a gedanken experiment proposed by Hardy to demonstrate the physical effect of an “empty wave” in a quantum interferometer shows that the particle actually passes through the arm of the interferometer where the effect is produced, rather than the other arm as claimed by Hardy, and thus there is no effect of an empty wave.

Renormalization-group transformations of the type introduced into statistical physics by K. G. Wilson have been widely used with great success for a variety of many-body calculations. The basic approach consists in integrating out certain degrees of freedom and using a new “image” Hamiltonian to describe the statistical properties of those that remain. The mathematical foundations of the procedure, however, remain somewhat obscure. P.A. Pearce and the author have pointed out that there are serious questions about the existence and properties of a thermodynamic limit for renormalization-group transformations. In particular, certain real-space transformations show peculiarities in this limit. These suggest that there may be serious mathematical problems with renormalization-group procedures, despite their considerable practical sucess.

The correlation inequalities of Fortuin, Kasteleyn, and Ginibre (FKG) are used in conjunction with those of Griffiths, Kelly, and Sherman (GKS) to demonstrate the existence of a ferromagnetic phase transition in a continuum fluid of classical particles carrying Ising-like spins and having suitable magnetic and non-magnetic interactions. The procedure involves finding a lower bound on the magnetization of the fluid in terms of that of a suitable spin system on a lattice.

The phase diagram for a lattice-gas model of physical adsorption on a homogeneous substrate has been calculated in a mean-field approximation. The first-order phase transitions corresponding to the addition of successive layers terminate in individual critical points as the temperature increases. The critical temperatures of successive layers increase, monotonically with layer number, from the critical temperature of the two-dimensional lattice gas to that of the bulk three-dimensional lattice gas. This last feature is probably an artifact of the mean-field approximation.