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Interpreting Quantum Theories$
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Laura Ruetsche

Print publication date: 2011

Print ISBN-13: 9780199535408

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199535408.001.0001

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Interpreting QM∞

Interpreting QM∞

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(p.117) 6 Interpreting QM
Interpreting Quantum Theories

Laura Ruetsche

Oxford University Press

This chapter catalogs interpretative responses to the breakdown of unitary equivalence in QM. These range from ‘Hilbert Space Conservatism’ to ‘Algebraic Imperialism’. Maintaining the ordinary quantum mechanics account of physical equivalence in terms of unitary equivalence, the Hilbert Space Conservative takes unitarily inequivalent representations of the CCRs/CARs for a theory of QM to be rivals, at most one of which could convey the content of that theory. Asserting the physics of a theory of QM to reside in the abstract algebraic structure all its representations share, the Algebraic Imperialist announces criteria for the physical equivalence of quantum theories — including the criterion of ‘weak equivalence’ — at odds with the traditional criterion of unitary equivalence.

Keywords:   interpretation, quantum field theory, thermodynamic limit, semi-classical quantum gravity, symmetry, algebraic quantum theory, weak equivalence, physical equivalence, unitary equivalence, DHR selection theory

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