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arXiv:quant-ph/0405024

Some Comments on Entanglement and Local Thermofield Theory

Christian D. Jäkel

Published May 5, 2004• 1 citation
arXivHTMLPDF

Abstract

We combine recent results of Clifton and Halvorson [1] with structural results of the author [2--5] concerning the local observables in thermofield theory. An number of interesting consequences are discussed.
DOI
10.48550/arxiv.quant-ph/0405024

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This is the second of two papers responding (somewhat belatedly) to ‘recent’ commentary on various aspects of hyperplane dependence (HD) by several authors. In this paper I focus on the issues of the general need for HD dynamical variables, the identification of physically meaningful localizable properties, the basis vectors representing such properties and the relationship between the concepts of ‘localizable within’ and ‘measureable within’. The authors responded to here are de Koning, Halvorson, Clifton and Wallace. In the first paper of this set (Fleming 2003b) I focused on the issues of the relations of HD to state reduction and unitary evolution and addressed comments of Maudlin and Myrvold. The central conclusion argued for in this second paper (§§ 5, 7) is the non-existence of strictly localizable objects or measurement processes and the consequent undermining of the principle of universal microcausality. This contrasts with the existence of strictly localizable properties and results in the consequent priority of the concept of ‘localizable within’ over ‘measureable within’. The paper opens with discussions of the need for and status of HD dynamical variables which are responses to anonymous queries.
Some approaches which seek to make progress with the conceptual troubles of quantum theory using information-theoretic ideas are investigated. These include Zeilinger’s Foundational Principle and the information-theoretic characterization theorem of Clifton, Bub and Halvorson. It is shown that Zeilinger’s Foundational Principle does not provide a foundational principle for quantum mechanics and fails to underwrite explanations of the randomness of quantum measurement and the existence of entanglement. The Clifton- Bub-Halvorson theorem is more positively assessed: here an axiomatisation of quantum mechanics has been achieved. However some questions are raised concerning the C ∗-algebraic starting point of the theorem, which seems not a sufficiently neutral theoretical framework for the axiomatic project. Moreover, it is argued that rather than the Clifton-Bub-Halvorson result motivating an information-theoretic approach (principle theory approach) to understanding the quantum world which obviates our traditional concerns, such an approach simply fails to engage with the crucial interpretational issues.
Bell's inequalities in algebraic quantum field theory have been studied by Landau, Summers and Werner, and Halvorson and Clifton. Halvorson and Clifton showed that many normal states on local algebras associated with space-like separated bounded open regions violate Bell's inequalities under the the axioms of algebraic quantum field theory. In the present paper, I point out that many faithful normal states on local algebras associated with space-like separated bounded open regions violate Bell's inequalities under the axioms of algebraic quantum field theory.