arXiv:quant-ph/9802010

Unified Treatment of EPR and Bell Arguments in Algebraic Quantum Field Theory

Michael L. G. Redhead, Fabian Wagner

Published Feb 3, 1998• 1 citation

Abstract

A conjecture concerning vacuum correlations in axiomatic quantum field theory is proved. It is shown that this result can be applied both in the context of EPR-type experiments and Bell-type experiments.

DOI: 10.48550/arxiv.quant-ph/9802010

Related papers

Necessary and Sufficient Proof of Quantum Nonlocality from Vacuum Noncommutativity

Zhen Su

We present a rigorous necessary and sufficient proof of quantum nonlocality within algebraic quantum field theory (AQFT). Using only the standard axioms of AQFT and fundamental properties of the vacuum state, we establish a mathematical equivalence between quantum nonlocality and the vacuum’s inherent noncommutativity. The EPR–Bell contradiction is resolved from first principles within relativistic quantum field theory.

May 16, 20260 citations

EPR States and Bell Correlated States in Algebraic Quantum Field Theory

Yuichiro Kitajima

arXiv:1304.5261Foundations of PhysicsAug 20, 20136 citations

Bell’s inequalities and quantum field theory. I. General setting

Stephen J. Summers, Reinhard F. Werner

Bell’s inequalities are briefly presented in the context of order-unit spaces and then studied in some detail in the framework of C*-algebras. The discussion is then specialized to quantum field theory. Maximal Bell correlations β(φ,𝒜(𝒪1), 𝒜(𝒪2)) for two subsystems localized in regions 𝒪1 and 𝒪2 and constituting a system in the state φ are defined, along with the concept of maximal Bell violations. After a study of these ideas in general, properties of these correlations in vacuum states of arbitrary quantum field models are studied. For example, it is shown that in the vacuum state the maximal Bell correlations decay exponentially with the product of the lowest mass and the spacelike separation of 𝒪1 and 𝒪2. This paper is also preparation for the proof in Paper II [S. J. Summers and R. Werner, J. Math. Phys. 28, 2448 (1987)] that Bell’s inequalities are maximally violated in the vacuum state.

Journal of Mathematical PhysicsOct 1, 1987237 citations

Generic Bell correlation between arbitrary local algebras in quantum field theory

Rob Clifton

Abstract There are many senses in which the phenomenon of Bell correlation, originally discovered and investigated in the context of elementary nonrelativistic quantum mechanics (Bell 1987, Clauser et al. 1969), is ‘generic’ in quantum field theory models. For example, it has been shown that every pair of commuting nonabelian von Neumann algebras possesses some normal state with maximal Bell correlation (Summers 1990; see also Landau 1987b). Moreover, in most standard quantum field models, all normal states are maximally Bell correlated across spacelike separated tangent wedges

Sep 23, 20091 citation

Bell theorem

Franck Laloë

The Bell theorem [103] can be seen in several different ways, as the EPR argument. Initially, Bell invented it as a direct logical continuation of the EPR theorem: the idea is to take the existence of the EPR elements of reality seriously, and to push it further by introducing them explicitly into the mathematics with the notation λ; one then proceeds to study all possible kinds of correlations that can be obtained from the fluctuations of one or several variables λ, making the condition of locality explicit in the mathematics (locality was already useful in the EPR theorem, but not used in equations). The reasoning develops within determinism (considered as proved by the EPR reasoning) and classical probabilities; it studies in a completely general way all kinds of correlations that can be predicted from the fluctuations of some classical common cause in the past – if one prefers, from some random choice concerning the initial state of the system. This leads to the famous inequalities. But subsequent studies have shown that the scope of the Bell theorem is not limited to determinism; for instance, the λ variables may determine the probabilities of the results of future experiments, instead of the results themselves (see Appendix B), without canceling the theorem. We postpone the discussion of the various possible generalizations to §4.2.3. For the moment, we just emphasize that the essential condition for the validity of the Bell theorem is locality: all kinds of fluctuations can be assumed, but their effect must affect physics only locally.

Cambridge University Press eBooksAug 30, 20120 citations

The EPR-Bell Experiments: The Role of Counterfactuality and Probability in the Context of Actually Conducted Experiments

Anthony J. Leggett

Some aspects of the concepts of counterfactuality and probability are explored as they apply to the specific example of the famous “EPR-Bell” experiments realized by physicists over the last half-century. In particular the question is raised: what hypotheses about actually conducted experiments do the results exclude? It is argued that the answer depends on both whether these hypotheses are deterministic or stochastic, and on the “cardinality” of the experiment relative to the theory.

PhilosophiesAug 27, 20241 citation