A categorical framework for quantum theory

Authors

  • T. Filk,

    Corresponding author
    1. Institute for Physics, University of Freiburg, Hermann-Herder-Str. 3a, 79104 Freiburg, Germany
    2. Parmenides Center for the Study of Thinking, Kirchplatz 1, 82049 München, Germany
    • Institute for Physics, University of Freiburg, Hermann-Herder-Str. 3a, 79104 Freiburg, Germany
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  • A. von Müller

    1. Parmenides Center for the Study of Thinking, Kirchplatz 1, 82049 München, Germany
    2. Institute for Philosophy, University of Munich, Munich, Germany
    3. SISSA, Via Bonomea 265, 34136 Trieste, Italy
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Abstract

Underlying any physical theory is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with the phenomena, but they also constitute our fundamental assumptions about reality. Many of the discrepancies between quantum physics and classical physics (including Maxwell's electrodynamics and relativity) can be traced back to these categorical foundations. We argue that classical physics corresponds to the factual aspects of reality and requires a categorical framework which consists of four interdependent components: boolean logic, the linear-sequential notion of time, the principle of sufficient reason, and the dichotomy between observer and observed. None of these can be dropped without affecting the others. However, quantum theory also addresses the “status nascendi” of facts, i.e., their coming into being. Therefore, quantum physics requires a different conceptual framework which will be elaborated in this article. It is shown that many of its components are already present in the standard formalisms of quantum physics, but in most cases they are highlighted not so much from a conceptual perspective but more from their mathematical structures. The categorical frame underlying quantum physics includes a profoundly different notion of time which encompasses a crucial role for the present. The article introduces the concept of a categorical apparatus (a framework of interdependent categories), explores the appropriate apparatus for classical and quantum theory, and elaborates in particular on the category of non-sequential time and an extended present which seems to be relevant for a quantum theory of (space)-time.

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