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The Effectiveness of Mathematics in Physics of the Unknown

Grinbaum, Alexei (2017) The Effectiveness of Mathematics in Physics of the Unknown. [Preprint]

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If physics is a science that unveils the fundamental laws of nature, then the appearance of mathematical concepts in its language can be surprising or even mysterious. This was Eugene Wigner's argument in 1960. I show that another approach to physical theory accommodates mathematics in a perfectly reasonable way. To explore unknown processes or phenomena, one builds a theory from fundamental principles, employing them as constraints within a general mathematical framework. The rise of such theories of the unknown, which I call blackbox models, drives home the unsurprising effectiveness of mathematics. I illustrate it on the examples of Einstein's principle theories, the $S$-matrix approach in quantum field theory, effective field theories, and device-independent approaches in quantum information.

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Item Type: Preprint
Grinbaum, Alexeialexei.grinbaum@cea.fr0000-0002-7484-1553
Keywords: Mathematics; physics; Wigner; Einstein; principle theory; S-matrix; effective field theory; device-independence
Subjects: Specific Sciences > Physics
Depositing User: Alexei Grinbaum
Date Deposited: 04 Jul 2017 20:32
Last Modified: 04 Jul 2017 20:32
Item ID: 13179
Subjects: Specific Sciences > Physics
Date: 2017

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