Interpreting the Wigner–Eckart Theorem

Studies in History and Philosophy of Science Part A 87 (C):28-43 (2021)
  Copy   BIBTEX

Abstract

The Wigner--Eckart theorem is central to the application of symmetry principles throughout atomic, molecular, and nuclear physics. Nevertheless, the theorem has a puzzling feature: it is dispensable for solving problems within these domains, since elementary methods suffice. To account for the significance of the theorem, I first contrast it with an elementary approach to calculating matrix elements. Next, I consider three broad strategies for interpreting the theorem: conventionalism, fundamentalism, and conceptualism. I argue that the conventionalist framework is unnecessarily pragmatic, while the fundamentalist framework requires more ontological commitments than necessary. Conceptualism avoids both defects, accounting for the theorem's significance in terms of how it epistemically restructures the calculation of matrix elements. Specifically, the Wigner--Eckart theorem modularizes and unifies matrix element problems, thereby changing what we need to know to solve them.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,346

External links

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

Through your library

Similar books and articles

Study of Wigner's theorem on joint probabilities.M. Mugur-Schächter - 1979 - Foundations of Physics 9 (5-6):389-404.
An Axiomatic Basis for Quantum Mechanics.Gianni Cassinelli & Pekka Lahti - 2016 - Foundations of Physics 46 (10):1341-1373.
Reeh-schlieder meets Newton-Wigner.Gordon N. Fleming - 2000 - Philosophy of Science 67 (3):515.
A tomographic approach to Wigner's function.J. Bertrand & P. Bertrand - 1987 - Foundations of Physics 17 (4):397-405.
Classic texts: extracts from Wigner.Eugene P. Wigner - 2003 - In Katherine A. Brading & Elena Castellani (eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press. pp. 367.
Quantum mechanics in Galilean space-time.Ray E. Artz - 1981 - Foundations of Physics 11 (11-12):839-862.
How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence.David John Baker & Hans Halvorson - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (4):464-469.

Analytics

Added to PP
2021-03-12

Downloads
23 (#502,103)

6 months
6 (#133,276)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Josh Hunt
University of Michigan, Ann Arbor

Citations of this work

No citations found.

Add more citations

References found in this work

New work for a theory of universals.David K. Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
The problem of variable choice.James Woodward - 2016 - Synthese 193 (4):1047-1072.
Laws and meta-laws of nature: Conservation laws and symmetries.Marc Lange - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (3):457-481.

View all 13 references / Add more references