Studies in History and Philosophy of Science Part A 87 (C):28-43 (2021)
AbstractThe 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.
Similar books and articles
Ehrenfest's theorem reinterpreted and extended with Wigner's function.Antoine Royer - 1992 - Foundations of Physics 22 (5):727-736.
Reeh-schlieder defeats Newton-Wigner: On alternative localization schemes in relativistic quantum field theory.Hans Halvorson - 2001 - Philosophy of Science 68 (1):111-133.
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.
Respecting One’s Fellow: QBism’s Analysis of Wigner’s Friend.John B. DeBrota, Christopher A. Fuchs & Rüdiger Schack - 2020 - Foundations of Physics 50 (12):1859-1874.
The Wigner phase-space description of collision processes.Hai-Woong Lee & Marlan O. Scully - 1983 - Foundations of Physics 13 (1):61-72.
Wigner’s “Unreasonable Effectiveness of Mathematics”, Revisited.Roland Omnès - 2011 - Foundations of Physics 41 (11):1729-1739.
A tomographic approach to Wigner's function.J. Bertrand & P. Bertrand - 1987 - Foundations of Physics 17 (4):397-405.
Local Hidden Variables Underpinning of Entanglement and Teleportation.A. Kalev, A. Mann & M. Revzen - 2007 - Foundations of Physics 37 (1):125-143.
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 the Natural Interpretation of QM Avoids the Recent No-Go Theorem.Anthony Rizzi - 2020 - Foundations of Physics 50 (3):204-215.
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.
Added to PP
Historical graph of downloads
Citations of this work
No citations found.
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 Dynamical Approach to Spacetime Theories.Harvey R. Brown & James Read - 2021 - In Eleanor Knox & Alistair Wilson (eds.), The Routledge Companion to Philosophy of Physics.
Representing and Explaining: The Eikonic Conception of Scientific Explanation.Alisa Bokulich - 2018 - Philosophy of Science (5):793-805.
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.