On the Tension Between Physics and Mathematics
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On the Tension Between Physics and Mathematics Miklós Rédei1
© The Author(s) 2020
Abstract Because of the complex interdependence of physics and mathematics their relation is not free of tensions. The paper looks at how the tension has been perceived and articulated by some physicists, mathematicians and mathematical physicists. Some sources of the tension are identified and it is claimed that the tension is both natural and fruitful for both physics and mathematics. An attempt is made to explain why mathematical precision is typically not welcome in physics. Keywords Mathematics and physics · Mathematical precision · Mathematical physics · Quantum theory
1 The “Supermarket Picture” of the Relation of Physics and Mathematics, and Tension of Type I According to what can be called the standard picture of the relation of physics and mathematics, physics is a science in the modern sense because it is systematically mathematical, which means two things: (a) Physics carries out precision measurements aiming at determining values of operationally defined physical quantities. This is what quantitative experimental physics does, and this ensures descriptive accuracy of physics. (b) Physics sets up mathematical models of physical phenomena that make explicit the functional relationships among the measured quantities; i.e. physics formulates gen-
This paper is a slightly expanded version of the plenary talk delivered at the 2019 Frühjahrstagung (München, March 17–22, 2019) of the Deutsche Physikalische Gesellschaft (DPG) on the invitation of the Arbeitsgruppe Philosophie der Physik of DPG. I wish to thank the representatives of the Arbeitsgruppe Philosophie der Physik, R. Dardashti, M. Kuhlman and C. Wüthrich, for the invitation. Written while staying at the Munich Center for Mathematical Philosophy, Ludwig Maximilians University, supported by the Alexander von Humboldt Foundation and by the National Research, Development and Innovation Office, Hungary, K115593. * Miklós Rédei [email protected] 1
Department of Philosophy, Logic and Scientific Method, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK
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eral quantitative physical laws. This is the main activity in theoretical physics and this enables physics to be predictively successful. Both descriptive accuracy and predictive success should be understood here with a number of qualifications: the descriptive accuracy is never perfect (experimental errors); the operationally defined quantities are not purely empirical (theory-ladenness of observations), natural laws may also refer to entities that are not observable strictly speaking, etc. While the standard picture of the relation of mathematics and physics as characterized by (a) and (b) captures crucial properties of the role of mathematics in physics, it is somewhat naive because it is (tacitly) based on what I call here the ‘supermarket picture’ of the relation of mathematics and physics: that mathematics is like a supermarket and physics is
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