A topos perspective on the Kochen-Specker theorem: II. Conceptual Aspects, and Classical Analogues:

In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; and in part mathematical---the valuation arises naturally in the topos theory of presheaves. This paper discusses the conceptual aspects of this proposal. We also undertake two other tasks. First, we explain how the proposed valuations could arise much more generally than just in quantum physics; in particular, they arise as naturally in classical physics. Second, we give another motivation for such valuations (that applies equally to classical and quantum physics). This arises from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition.Comment: Small changes and correction

On the Emergence of Time in Quantum Gravity

We discuss from a philosophical perspective the way in which the normal concept of time might be said to `emerge' in a quantum theory of gravity. After an introduction, we briefly discuss the notion of emergence, without regard to time (Section 2). We then introduce the search for a quantum theory of gravity (Section 3); and review some general interpretative issues about space, time and matter Section 4). We then discuss the emergence of time in simple quantum geometrodynamics, and in the Euclidean approach (Section 5). Section 6 concludes.Comment: To appear in ``The Arguments of Time'', ed. J. Butterfield, Oxford University Press, 199

A topos perspective on the Kochen-Specker theorem: I. Quantum States as Generalized Valuations

The Kochen-Specker theorem asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which respects an appropriate version of the functional composition principle. The truth-values assigned to propositions are (i) contextual; and (ii) multi-valued, where the space of contexts and the multi-valued logic for each context come naturally from the topos theory of presheaves. The first step in our theory is to demonstrate that the Kochen-Specker theorem is equivalent to the statement that a certain presheaf defined on the category of self-adjoint operators has no global elements. We then show how the use of ideas drawn from the theory of presheaves leads to the definition of a generalized valuation in quantum theory whose values are sieves of operators. In particular, we show how each quantum state leads to such a generalized valuation.Comment: Clarification of situation for situation for operators with continuous spectr

A Topos Perspective on State-Vector Reduction

A preliminary investigation is made of possible applications in quantum theory of the topos formed by the collection of all $M$-sets, where $M$ is a monoid. Earlier results on topos aspects of quantum theory can be rederived in this way. However, the formalism also suggests a new way of constructing a `neo-realist' interpretation of quantum theory in which the truth values of propositions are determined by the actions of the monoid of strings of finite projection operators. By these means, a novel topos perspective is gained on the concept of state-vector reduction

Alien Registration- Butterfield, Jessie C. (Farmington, Franklin County)

https://digitalmaine.com/alien_docs/19877/thumbnail.jp

SWECS tower dynamics analysis methods and results

Several different tower dynamics analysis methods and computer codes were used to determine the natural frequencies and mode shapes of both guyed and freestanding wind turbine towers. These analysis methods are described and the results for two types of towers, a guyed tower and a freestanding tower, are shown. The advantages and disadvantages in the use of and the accuracy of each method are also described