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  1. Intuitionistic Quantum Logic of an N-Level System.Martijn Caspers, Chris Heunen, Nicolaas P. Landsman & Bas Spitters - 2009 - Foundations of Physics 39 (7):731-759.
    A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in arXiv:0709.4364). The goal of the present paper is to illustrate our abstract setup through the (...)
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  • The Principle of General Tovariance.Chris Heunen, Klaas Landsman & Bas Spitters - unknown
    We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical language for combining (...)
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  • A Topos Perspective on the Kochen-Specker Theorem: II. Conceptual Aspects, and Classical Analogues.Jeremy Butterfield & Chris Isham - unknown
    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 (...)
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  • The Logos Categorical Approach to Quantum Mechanics: I. Kochen-Specker Contextuality and Global Intensive Valuations.Christian de Ronde & Cesar Massri - unknown
    In this paper we present a new categorical approach which attempts to provide an original understanding of QM. Our logos categorical approach attempts to consider the main features of the quantum formalism as the standpoint to develop a conceptual representation that explains what the theory is really talking about —rather than as problems that need to be bypassed in order to allow a restoration of a classical “common sense” understanding of what there is. In particular, we discuss a solution to (...)
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  • Chasing Individuation: Mathematical Description of Physical Systems.Zalamea Federico - 2016 - Dissertation, Paris Diderot University
    This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the set of observables of a physical system, be it classical or quantum, is described by a Jordan-Lie algebra. From the geometric point of view, the space of states of any system is described by a uniform Poisson space with transition probability. Both these structures (...)
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  • Spacetime and the Philosophical Challenge of Quantum Gravity.Jeremy Butterfield & Chris Isham - 2001 - In Physics Meets Philosophy at the Panck Scale. Cambridge University Press.
    We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction (Section 1), we briefly review the conceptual problems of the ingredient theories (Section 2) and introduce the enterprise of quantum gravity (Section 3). We then describe how three main research programmes in quantum (...)
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  • Double-Slit Interference and Temporal Topos.Goro Kato & Tsunefumi Tanaka - 2006 - Foundations of Physics 36 (11):1681-1700.
    The electron double-slit interference is re-examined from the point of view of temporal topos. Temporal topos (or t-topos) is an abstract algebraic (categorical) method using the theory of sheaves. A brief introduction to t-topos is given. When the structural foundation for describing particles is based on t-topos, the particle-wave duality of electron is a natural consequence. A presheaf associated with the electron represents both particle-like and wave-like properties depending upon whether an object in the site (t-site) is specified (particle-like) or (...)
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  • Conceptual Mathematics: A First Introduction to Categories.David Corfield - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33 (2):359-366.
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  • Book Review. [REVIEW]Chris Heunen - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 48 (2):99-100.
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  • Conceptual Mathematics: A First Introduction to Categories.David Corfield - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33 (2):359-366.
  • A Model for Spacetime: The Role of Interpretation in Some Grothendieck Topoi. [REVIEW]Jerzy Król - 2006 - Foundations of Physics 36 (7):1070-1098.
    We analyse the proposition that the spacetime structure is modified at short distances or at high energies due to weakening of classical logic. The logic assigned to the regions of spacetime is intuitionistic logic of some topoi. Several cases of special topoi are considered. The quantum mechanical effects can be generated by such semi-classical spacetimes. The issues of: background independence and general relativity covariance, field theoretic renormalization of divergent expressions, the existence and definition of path integral measures, are briefly discussed (...)
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