On the Reasonable and Unreasonable Effectiveness of Mathematics in Classical and Quantum Physics

Foundations of Physics 41 (3):466-491 (2011)

Abstract

The 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

Download options

PhilArchive



    Upload a copy of this work     Papers currently archived: 72,879

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2013-11-22

Downloads
53 (#218,152)

6 months
2 (#257,917)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Critique of Pure Reason.I. Kant - 1787/1998 - Philosophy 59 (230):555-557.
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.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.

View all 13 references / Add more references

Similar books and articles

Niels Bohr’s Generalization of Classical Mechanics.Peter Bokulich - 2005 - Foundations of Physics 35 (3):347-371.
Theoretical Physics: A Primer for Philosophers of Science.Francisco Antonio Doria - 2009 - Principia: An International Journal of Epistemology 13 (2):195-232.
On the Classical Limit of Quantum Mechanics.Valia Allori & Nino Zanghi - 2008 - Foundations of Physics 10.1007/S10701-008-9259-4 39 (1):20-32.
Time Asymmetry and Quantum Equations of Motion.T. E. Phipps - 1973 - Foundations of Physics 3 (4):435-455.