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Helvetica Physica Acta (Switzerland)

A mechanistic classical laboratory situation violating the Bell inequalities with sqrt(2), exactly 'in the same way' as its violations by the EPR experiments

Diederik Aerts

Published Jan 1, 1991• 60 citations
OpenAlex

Abstract

We present a macroscopical mechanistic classical laboratory situation, and a classical macroscopical entity, and coincidence measurements on this entity, that lead to a violation of the Bell inequalities corresponding to these coincidence measurements. The violation that we obtain with these coincidence measurements is exactly the same as the violation of the Bell inequalities by the well known coincidence measurements of the quantum entity of two spin 1/2 particles in a singlet spin state. With this we mean that it gives rise to the same numerical values for the expectation values and the same numerical value 2•√2 for the expression used in the Bell inequalities.

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A macroscopic experiment capable of detecting a signature of spinorial sign changes is discussed. If realized, it would determine whether Bell inequalities are satisfied for a manifestly local, classical system. By providing an explicitly local-realistic derivation of the EPR-Bohm type spin correlations, it is demonstrated why Bell inequalities must be violated even in such a manifestly local, macroscopic domain, just as strongly as they are in the microscopic domain. The proposed experiment has the potential to transform our understanding of the relationship between classical and quantum physics.

•Jan 1, 2022•1 citation
We present a macroscopical mechanistic classical laboratory situation, and a classical macroscopical entity, and coincidence measurements on this entity, that lead to a violation of the Bell inequalities corresponding to these coincidence measurements. The violation that we obtain with these coincidence measurements is exactly the same as the violation of the Bell inequalities by the well known coincidence measurements of the quantum entity of two spin 1/2 particles in a singlet spin state. With this we mean that it gives rise to the same numerical values for the expectation values and the same numerical value 2•√2 for the expression used in the Bell inequalities.
Measuring processes of a single spin-1/2 object and of a pair of spin-1/2 objects in the EPR-Bohm state are modeled by systems of differential equations. These models are based on mainly the following two ideas: (i) as a result of the interaction with a measuring apparatus, the state of the object, changes and approaches an attractor, in which the object possesses the measured value in the phase space of states of objects; (ii) a quantum-mechanical state corresponds to an ensemble of states in the corresponding attractor in the phase space. The latter model is a local model with hidden variables of the EPR-Bohm gedanken experiment. Although there is no dynamical interaction between the pair of spin-1/2 objects, the model reproduces approximately the quantum-mechanical correlations by using coincidence counting. Hence the Bell inequality is violated. This result supports the idea that the coincidence counting is the source of the apparent nonlocality in the EPR-Bohm gedankenexperiment.
Measuring processes of a single spin-1/2 object and of a pair of spin-1/2 objects in the EPR-Bohm state are modeled by systems of differential equations. These models are based on mainly the following two ideas: (i) as a result of the interaction with a measuring apparatus, the state of the object, changes and approaches an attractor, in which the object possesses the measured value in the phase space of states of objects; (ii) a quantum-mechanical state corresponds to an ensemble of states in the corresponding attractor in the phase space. The latter model is a local model with hidden variables of the EPR-Bohm gedanken experiment. Although there is no dynamical interaction between the pair of spin-1/2 objects, the model reproduces approximately the quantum-mechanical correlations by using coincidence counting. Hence the Bell inequality is violated. This result supports the idea that the coincidence counting is the source of the apparent nonlocality in the EPR-Bohm gedankenexperiment.
Abstract One of the Bell’s assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell’s inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell’s inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality in canonical notatons reads 〈AB〉 + 〈A’B〉 + 〈AB’〉 − 〈A’B’〉 ⩽ 6.
Bell's inequality is applied to a gedanken experiment, where a spin singlet decays into two spin-sss particles. This is done by defining dichotomic observables depending on the spin components. The range of settings, for which the inequality is violated by quantum mechanics, is calculated for certain values of sss. The classical limit is taken and the results are compared to those obtained, by an alternative method, by Mermin.
An experiment is proposed to test Bell's theorem in a purely macroscopic domain. If realized, it would determine whether Bell inequalities are satisfied for a manifestly local, classical system. It is stressed why the inequalities should not be presumed to hold for such a macroscopic system without actual experimental evidence. In particular, by providing a purely classical, topological explanation for the EPR-Bohm type spin correlations, it is demonstrated why Bell inequalities must be violated in the manifestly local, macroscopic domain, just as strongly as they are in the microscopic domain.
A macroscopic experiment capable of detecting a signature of spinorial sign changes is discussed. If realized, it would determine whether Bell inequalities are satisfied for a manifestly local, classical system. By providing an explicitly local-realistic derivation of the EPR-Bohm type spin correlations, it is demonstrated why Bell inequalities must be violated even in such a manifestly local, macroscopic domain, just as strongly as they are in the microscopic domain. The proposed experiment has the potential to transform our understanding of the relationship between classical and quantum physics.