Why Be regular?, part I |
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| Institution: | 1. Department of Philosophy, University of Washington, USA;2. Department of Logic and Philosophy of Science, University of California, Irvine, USA;1. College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba 275-8576, Japan;2. Department of Philosophy, Logic and Scientific Method, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, United Kingdom;3. Institute of Philosophy, Research Center for the Humanities of the Hungarian Academy of Sciences, Országház utca 30, 1014 Budapest, Hungary;1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, 316022, China;2. Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan, 316022, China |
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| Abstract: | We provide a novel perspective on “regularity” as a property of representations of the Weyl algebra. We first critique a proposal by Halvorson 2004, “Complementarity of representations in quantum mechanics”, Studies in History and Philosophy of Modern Physics 35 (1), pp. 45–56], who argues that the non-regular “position” and “momentum” representations of the Weyl algebra demonstrate that a quantum mechanical particle can have definite values for position or momentum, contrary to a widespread view. We show that there are obstacles to such an intepretation of non-regular representations. In Part II, we propose a justification for focusing on regular representations, pace Halvorson, by drawing on algebraic methods. |
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