We critically evaluate the treatment of the notion of measurement in the Consistent Histories approach to quantum mechanics. We find such a treatment unsatisfactory because it relies, often implicitly, on elements external to those provided by the formalism. In particular, we note that, in order for the formalism to be informative when dealing with measurement scenarios, one needs to assume that the appropriate choice of framework is such that apparatuses are always in states of well defined pointer positions after measurements. (...) The problem is that there is nothing in the formalism to justify this assumption. We conclude that the Consistent Histories approach, contrary to what is claimed by its proponents, fails to provide a truly satisfactory resolution for the measurement problem in quantum theory. (shrink)

Intuitively, an object is something that coheres internally and is largely independent of its environment. But what is the environment? Viewed at one scale, it surrounds and separates objects and differentiates them. Viewed at another scale, it is itself a collection of objects surrounded by environment. At all scales, we describe the world in terms of objects in an environment. I examine the nature of the environment and its role in mediating the object-subject relation. This dedicated analysis of the environment (...) provides a new perspective on the notion of objectivity. (shrink)

In spite of being a well articulated proposal, the theory of quantum histories, in its different versions, suffers from certain difficulties that have been pointed out in the literature. Nevertheless, two facets of the proposal have not been sufficiently stressed. On the one hand, it is a non-collapse formalism that should be technically appropriate to supply descriptions based on quantum properties at different times. On the other hand, it intends to provide an interpretation of quantum mechanics that solves the traditional (...) puzzles of the theory. In this article we spell out the main criticisms to TQH and classify them into two groups: theoretical and interpretive. Whereas the latter might be ignored if the TQH were considered as a quantum formalism with its minimum interpretation, the former seems to point toward technical difficulties that must be faced in a theoretically adequate proposal. Precisely with the purpose of solving these difficulties, we introduce a different perspective, called Formalism of Generalized Contexts or Formalism of Contextual Histories, which supplies a precise condition for consistently talking of quantum properties at different times without the theoretical shortcomings of the TQH. (shrink)

It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or decoherent histories interpretation of quantum mechanics by using a modified form of quantum logic to discuss quantum properties (subspaces of the quantum Hilbert space), and treating quantum time development as a stochastic process. The histories approach in turn gives rise to some conceptual difficulties, in particular the (...) correct choice of a framework (probabilistic sample space) or family of histories, and these are discussed. The central issue is that the principle of unicity, the idea that there is a unique single true description of the world, is incompatible with our current understanding of quantum mechanics. (shrink)

The Ollivier–Poulin–Zurek definition of objectivity provides a philosophical basis for the environment as witness formulation of decoherence theory and hence for quantum Darwinism. It is shown that no account of the reference of the key terms in this definition can be given that does not render the definition inapplicable within quantum theory. It is argued that this is not the fault of the language used, but of the assumption that the laws of physics are independent of Hilbert-space decomposition. All evidence (...) suggests that this latter assumption is true. If it is, decoherence cannot explain the emergence of classicality. (shrink)

It is standardly assumed in discussions of quantum theory that physical systems can be regarded as having well-defined Hilbert spaces. It is shown here that a Hilbert space can be consistently partitioned only if its components are assumed not to interact. The assumption that physical systems have well-defined Hilbert spaces is, therefore, physically unwarranted.

The use of probability theory is widespread in our daily life as well as in scientific theories. In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics, which gives rise to a new probability theory: quantum probability theory. This dissertation deals with the question of how this formalism can be understood from a philosophical and physical perspective. The dissertation is divided into three parts. In the first (...) part, the formalism of quantum probability theory and its relation to quantum mechanics is presented. The second part considers the possibility of reformulating quantum probability theory to embed it within classical probability. Mathematically, this possibility overlaps with the possibility of the existence of hidden variables theories of quantum mechanics: theories that attempt to solve fundamental problems in quantum mechanics by introducing additional physical properties of systems. The conclusion of this part is that, although classical reformulations of quantum probability theory are formally possible, they offer little insight into the formalism of quantum probability theory itself. The third part regards a more direct investigation of quantum probability theory. A reformulation of quantum probability theory is obtained by constructing a quantum logic on the basis of empirical non-probabilistic predictions of quantum mechanics. In this reformulation quantum probability functions are conditional probability functions on an algebra of propositions about measurements and measurement outcomes. (shrink)