Grinbaum, Alexei
(2017)
The Effectiveness of Mathematics in Physics of the Unknown.
[Preprint]
Abstract
If physics is a science that unveils the fundamental laws of nature, then the appearance of mathematical formulae 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 by employing fundamental principles as constraints within a general mathematical framework. Such studies of the unknown, or blackbox models, demonstrate the unsurprising effectiveness of mathematics on the example of Einstein's principle theories, the Smatrix approach in quantum field theory, effective field theories, and deviceindependent approaches in quantum information.
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