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Interpretation of Quantum Theory: The Quantum "Grue-Bleen" Problem
Benjamin Schumacher1, Michael D Westmoreland2
1Department of Physics, Kenyon College, Gambier, OH 43022, USA.
Entropy (Basel, Switzerland)
|September 23, 2022
Summary
The many-world interpretation of quantum mechanics requires external frames for meaningful statements, similar to induction problems. Without this structure, isolated systems lack interpretation in quantum and classical mechanics.
Area of Science:
- Quantum Mechanics
- Philosophy of Science
- Theoretical Physics
Background:
- The many-world interpretation (MWI) offers a perspective on quantum mechanics.
- Dynamical theories describe the time evolution of systems.
- The 'grue-bleen' problem highlights issues in induction and language.
Purpose of the Study:
- To critique the many-world interpretation of quantum mechanics.
- To identify necessary structures for meaningful theoretical interpretation.
- To explore the scope of interpretational challenges in dynamical theories.
Main Methods:
- Analysis of quantum system time evolution using different 'pictures'.
- Application of a general framework to various dynamical theories.
- Analogy drawn to Goodman's 'grue-bleen' problem.
Main Results:
- The MWI, without external frames, fails to provide non-trivial interpretational statements.
- The 'grue-bleen' problem extends beyond quantum mechanics.
- Classical Hamiltonian mechanics also faces similar interpretational issues.
Conclusions:
- External frame information is crucial for interpreting isolated systems.
- The problem of interpretation is not unique to quantum mechanics.
- Meaningful interpretation of dynamical theories requires specific additional structures.
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