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Interpreting the Wigner-Eckart Theorem
1Department of Philosophy, University of Michigan, Ann Arbor, MI, 48109, USA.
Studies in History and Philosophy of Science
|June 10, 2021
Summary
The Wigner-Eckart theorem, crucial for symmetry in physics, is surprisingly dispensable. This study argues its significance lies in how it conceptually restructures problem-solving, not in necessity.
Area of Science:
- Physics
- Quantum Mechanics
- Symmetry Principles
Background:
- The Wigner-Eckart theorem is fundamental in applying symmetry principles in atomic, molecular, and nuclear physics.
- Despite its centrality, the theorem is often considered dispensable as elementary methods can solve related problems.
Purpose of the Study:
- To analyze the significance of the Wigner-Eckart theorem.
- To explore different philosophical interpretations of the theorem's role and value.
Main Methods:
- Contrast the Wigner-Eckart theorem with elementary matrix element calculation methods.
- Evaluate three interpretive frameworks: conventionalism, fundamentalism, and conceptualism.
Main Results:
- Conventionalism is deemed too pragmatic; fundamentalism requires excessive ontological commitments.
- Conceptualism offers a superior framework by focusing on epistemic restructuring.
Conclusions:
- The Wigner-Eckart theorem's significance stems from its ability to modularize and unify matrix element calculations.
- It epistemically transforms problem-solving by altering the knowledge required to find solutions.
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