Related papers: An Introduction to Topos Physics
The main purpose of this paper is to present a new approach to logic or what we will call superlogic. This approach constitutes a new way of looking at the connection between quantum mechanics and logic. It is a {\it geometrisation} of the…
This paper deals with topos-theoretic truth-value valuations of quantum propositions. Concretely, a mathematical framework of a specific type of modal approach is extended to the topos theory, and further, structures of the obtained…
The job of a physicist is to describe Nature. General features, hypotheses and theories help to describe physics phenomena at a more abstract, fundamental level, and are sometimes tacitly assigned some sort of real existence; doing so…
The aim of this paper is to compare the two topos-theoretic approaches to quantum mechanics that may be found in the literature to date. The first approach, which we will call the contravariant approach, was originally proposed by Isham and…
There exist dozens of interpretations of quantum theory, but they do not seem to contribute much to understanding the theory. This paper attempts to clarify some issues that are discussed in those interpretations. The main keywords are:…
There is good evidence that quantum computers are more powerful than classical computers, and that various simple modifications of quantum theory yield computational power that is dramatically greater still. However, these modifications…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances…
In this paper, we first introduce a technique that we call "Yoneda representation of flat functors", based on ideas from indexed category theory; then we provide applications of this technique to the theory of classifying toposes.…
Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…
Essential elements of quantum theory are derived from an epistemic point of view, i.e., the viewpoint that thetheory has to do with what can be said about nature. This gives a relationship to statistical reasoning and to other areas of…
We suggest a generalization of \pi_0 for topological groupoids, which encodes incidence relations among the strata of the associated quotient object, and argue for its utility by example, starting from the orbit categories of the theory of…
An important step in learning to use math in science is learning to see physics equations as not just calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and…
Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines…
This paper introduces a theory about the role of language in learning physics. The theory is developed in the context of physics students' and physicists' talking and writing about the subject of quantum mechanics. We found that physicists'…
In this paper, I propose a project of enlisting quantum information science as a source of task-oriented axioms for use in the investigation of operational theories in a general framework capable of encompassing quantum mechanics, classical…
Quantum categories were introduced in [4] as generalizations of both bi(co)algebroids and small categories. We clarify details of that work. In particular, we show explicitly how the monadic definition of a quantum category unpacks to a set…
Recent critiques of the semantic conception of scientific theories suggest that a theory is not best formulated as a collection of models satisfying some set of kinematical or dynamical conditions. Thus it has been argued that additional…
Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…
Recently, we have endowed various categories of groups with topologies. The purpose of this paper is to introduce on these categories others topologies which are statistically more suitable to study well-known problems in groups theory. We…