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A Proposal for Testing Local Realism Without Using Assumptions Related to Hidden Variable States

Luiz Carlos Ryff

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

A feasible experiment is discussed which allows us to prove a Bell's theorem for two particles without using an inequality. The experiment could be used to test local realism against quantum mechanics without the introduction of additional assumptions related to hidden variables states. Only assumptions based on direct experimental observation are needed.

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•Nov 28, 2023•0 citations
A feasible experiment is discussed which allows us to prove a Bell's theorem for two particles without using an inequality. The experiment could be used to test local realism against quantum mechanics without the introduction of additional assumptions related to hidden variables states. Only assumptions based on direct experimental observation are needed.
Bell's theorem, and inequalities that stem from it, address the conflict between the explanation of key experimental observations by quantum mechanics (QM) and by models expressing Locally Realistic (LR) properties, regardless of their inclusion or exclusion of hidden variables. To demonstrate the conflict between experimental results described by QM and LR models, a physical realization of the quantum state must be chosen. Entangled photons or electrons provide the most viable choices. In this work we consider a simplified version of a Bell inequality (BI) that focuses entirely on the physical state properties of photons in order to demonstrate the difference between QM and LR correlations. While the experiment we propose is in principle similar in intent to prior Bell inequality experiments, our version requires fewer measurements, and is more advantageous in its conceptual clarity.
Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics.
We shortly review a couple of proposals of Bell inequality tests with entangled pairs of neutral kaons from φ resonance decays.The suggested experiments are discussed in the light of the essential requirements for a genuine discrimination between local hidden-variable theories (i.e., local realism) and quantum mechanics.We clarify the logical limitations of these tests in refuting the whole class of local realistic models.Detailed analyses imply that a Bell-type test with neutral kaons free from the detection loophole requires a few % strangeness detection efficiencies and very high efficiencies for the detection of the kaon decay products.
I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.