11 found
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  1.  97
    Between Classical and Quantum.Nicolaas P. Landsman - unknown
    The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...)
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  2.  72
    Spontaneous Symmetry Breaking in Quantum Systems: Emergence or Reduction?Nicolaas P. Landsman - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (4):379-394.
    Beginning with Anderson, spontaneous symmetry breaking in infinite quantum systems is often put forward as an example of emergence in physics, since in theory no finite system should display it. Even the correspondence between theory and reality is at stake here, since numerous real materials show ssb in their ground states, although they are finite. Thus against what is sometimes called ‘Earman's Principle’, a genuine physical effect seems theoretically recovered only in some idealisation, disappearing as soon as the idealisation is (...)
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  3. When Champions Meet: Rethinking the Bohr–Einstein Debate.Nicolaas P. Landsman - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (1):212-242.
    Einstein's philosophy of physics (as clarified by Fine, Howard, and Held) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy (as elucidated by Hooker, Scheibe, Folse, Howard, Held, and others), on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic (...)
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  4.  74
    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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  5.  71
    Macroscopic Observables and the Born Rule. I. Long Run Frequencies.Nicolaas P. Landsman - unknown
    We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a noncommutative C*-algebra of observables is empirically accessible only through associated commutative C*-algebras. The Born probabilities emerge as the relative frequencies of outcomes in long runs of measurements on a quantum system; it is not necessary to adopt the frequency interpretation of single-case probabilities (which will (...)
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  6.  93
    Bohrification of Operator Algebras and Quantum Logic.Chris Heunen, Nicolaas P. Landsman & Bas Spitters - 2012 - Synthese 186 (3):719 - 752.
    Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...)
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  7.  18
    When Champions Meet: Rethinking the Bohr–Einstein Debate.Nicolaas P. Landsman - 2006 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (1):212-242.
    Einstein's philosophy of physics was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy, on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic quantum theory that - within an appropriate class of physical theories - suitable mathematical translations of the (...)
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  8.  6
    Bohrification of Operator Algebras and Quantum Logic.Chris Heunen, Nicolaas P. Landsman & Bas Spitters - 2012 - Synthese 186 (3):719-752.
    Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...)
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  9.  25
    Essay Review: P. L. Rose, Heisenberg and the Nazi Atomic Bomb Project: A Study in German Culture. [REVIEW]Nicolaas P. Landsman - unknown
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  10.  20
    Essay Review Of: Maximilian Schlosshauer, Decoherence and the Quantum-To-Classical Transition.Nicolaas P. Landsman - unknown
  11.  6
    2010 North American Annual Meeting of the Association for Symbolic Logic.Alexander Razborov, Bob Coecke, Zoé Chatzidakis, Bjørn Kjos, Nicolaas P. Landsman, Lawrence S. Moss, Dilip Raghavan, Tom Scanlon, Ernest Schimmerling & Henry Towsner - 2011 - Bulletin of Symbolic Logic 17 (1):127-154.