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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

Bell’s inequalities from the field concept in general relativity

Mendel Sachs

Published Jul 1, 1980• 3 citations
Publisher
DOI
10.1007/bf02730216

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This paper is the philosopher-friendly version of our more technical work (Hofer-Szabó and Vecsernyés, 2014). It aims to give a clear-cut definition of Bell's notion of local causality. Having provided a framework, called local physical theory, which integrates probabilistic and spatiotemporal concepts, we formulate the notion of local causality and relate it to other locality and causality concepts. Then we compare Bell's local causality with Reichenbach's Common Cause Principle and relate both to the Bell inequalities. We find a nice parallelism: both local causality and the Common Cause Principle are more general notions than captured by the Bell inequalities. Namely, Bell inequalities cannot be derived neither from local causality nor from a common cause unless the local physical theory is classical or the common cause is commuting, respectively.

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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 Physics•Oct 1, 1987•237 citations
This paper examines the history of Bell’s inequality from EPR argument to Bell’s papers, and the influence of Bell’s inequality on the frontier exploration of quantum mechanics. It is found that Bell’s inequality has some hidden assumptions that are different from EPR argument. Along Schrodinger’s idea that the measurement process of the EPR experiment requires time, Karl Hess and his follows treat time as a time order parameter, by extending the method of space-time geometry analysis of relativity to the localized geometry analysis of quantum states, it is believed that the reasoning of Bell’s inequality does not meet the requirements of the completeness of EPR argument. Analyzing the non locality of gravitational energy in general relativity makes it necessary for us to seek a more localized expression of relativistic gravitational theory. Based on local realism, exploring new interpretations and expressions of quantum mechanics may open up new avenues for studying quantum gravity. We found that Lorentz almost discovered the incompleteness of general relativity but erroneously insisted on the concepts of ether and absolute space, just as Einstein correctly discovered the flaws in the non local representation of quantum mechanics based on outdated determinism.
This paper is the philosopher-friendly version of our more technical work (Hofer-Szabó and Vecsernyés, 2014). It aims to give a clear-cut definition of Bell's notion of local causality. Having provided a framework, called local physical theory, which integrates probabilistic and spatiotemporal concepts, we formulate the notion of local causality and relate it to other locality and causality concepts. Then we compare Bell's local causality with Reichenbach's Common Cause Principle and relate both to the Bell inequalities. We find a nice parallelism: both local causality and the Common Cause Principle are more general notions than captured by the Bell inequalities. Namely, Bell inequalities cannot be derived neither from local causality nor from a common cause unless the local physical theory is classical or the common cause is commuting, respectively.
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.