Foundations of Physics 41 (3):466-491 (2011)
AbstractThe point of departure for this article is Werner Heisenberg’s remark, made in 1929: “It is not surprising that our language [or conceptuality] should be incapable of describing processes occurring within atoms, for … it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. … Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory [quantum mechanics]—which seems entirely adequate for the treatment of atomic processes.” The cost of this discovery, at least in Heisenberg’s and related interpretations of quantum mechanics, is that, in contrast to classical mechanics, the mathematical scheme in question no longer offers a description, even an idealized one, of quantum objects and processes. This scheme only enables predictions, in general, probabilistic in character, of the outcomes of quantum experiments. As a result, a new type of the relationships between mathematics and physics is established, which, in the language of Eugene Wigner adopted in my title, indeed makes the effectiveness of mathematics unreasonable in quantum but, as I shall explain, not in classical physics. The article discusses these new relationships between mathematics and physics in quantum theory and their implications for theoretical physics—past, present, and future
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References found in this work
Critique of Pure Reason.Immanuel Kant - 1781/1998 - In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Philosophy and Phenomenological Research. Blackwell. pp. 449-451.
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?Albert Einstein, Boris Podolsky & Nathan Rosen - 1935 - Physical Review (47):777-780.
Physics and Philosophy: The Revolution in Modern Science.Werner Heisenberg - 1958 - London, England: Prometheus Books.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.
Citations of this work
Thomistic Foundations for Moderate Realism About Mathematical Objects.Ryan Miller - 2021 - In Proceedings of the Eleventh International Thomistic Congress.
Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law.Masanari Asano, Irina Basieva, Andrei Khrennikov, Masanori Ohya & Ichiro Yamato - 2013 - Foundations of Physics 43 (7):895-911.
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