Article ID: CBB259885124

Interpreting the Wigner–Eckart Theorem (2021)

unapi

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.

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Authors & Contributors
Lara Piersanti
Marina Dalé
Molaro, Aurelio
Greco, Pietro
Silvio Bozzi
D'Agostino, Salvo
Concepts
Philosophy of science
Physics
Quantum mechanics
Mathematics
Epistemology
Symmetry
Time Periods
20th century
19th century
20th century, late
21st century
18th century
Places
Italy
Hungary
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