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arXiv:1306.1383

Time weakens the Bell's inequalities

Alejandro Andrés Hnilo

Published Jun 6, 2013• 2 citations
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Abstract

By taking into account that all real measurements are performed successively, during time, it is concluded that the violation of the Bell's inequalities in the Nature does not refute (even in an ideally perfect experiment) the theories holding to Local Realism, for an unavoidable additional assumption is involved. Yet, in order to be acceptable, such theories must predict different values for the factual and counterfactual time averages of probabilities or observables.

DOI
10.48550/arxiv.1306.1383

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By taking into account that all real measurements are performed successively, during time, it is concluded that the violation of the Bell's inequalities in the Nature does not refute (even in an ideally perfect experiment) the theories holding to Local Realism, for an unavoidable additional assumption is involved. Yet, in order to be acceptable, such theories must predict different values for the factual and counterfactual time averages of probabilities or observables.
The Bell's inequalities are derived from the hypotheses of Locality, Realism and (what is lesser known) the equality between the factual and the counterfactual time averages of the expectation values of observables. The necessity of a hypothesis additional to Local Realism opens a promising way out to the old controversy between Quantum Mechanics and Local Realism. For, it is possible to speculate that it is this additional hypothesis, and not Local Realism, what is disproved in the experiments reporting the violation of the Bell's inequalities. Yet, there are doubts on how the additional hypothesis may be violated in a physically reasonable process. A simple example showing that this is possible, the relationship between the validity of the additional hypothesis and the validity of the Bell's inequalities, and considerations on its physical meaning, are presented.
The recent loophole-free experiments have confirmed the violation of Bell’s inequalities in nature. Yet, in order to insert measured values in Bell’s inequalities, it is unavoidable to make a hypothesis similar to “ergodicity at the hidden variables level”. This possibility opens a promising way out from the old controversy between quantum mechanics and local realism. Here, I review the reason why such a hypothesis (actually, it is one of a set of related hypotheses) in addition to local realism is necessary, and present a simple example, related to Bell’s inequalities, where the hypothesis is violated. This example shows that the violation of the additional hypothesis is necessary, but not sufficient, to violate Bell’s inequalities without violating local realism. The example also provides some clues that may reveal the violation of the additional hypothesis in an experiment.
With Bell's inequalities one has a formal expression to show how essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a simple experimental arrangement. For the case of entangled pairs of spin-1/2 particles we propose an alternative measurement setup which is consistent to the necessary assumptions corresponding to the derivation of the Bell inequalities. We find that the Bell inequalities are never violated with respect to our suggested measurement process.
We give a counter example to show that determinism as such is in contradiction to quantum mechanics. More precisely, we consider a simple quantum system and its environment, including the measurement device, and make the assumption that the time evolution of the global system, the quantum system plus this environment, is deterministic, i. e., the time evolution is given by a dynamical trajectory from some initial conditions. From this, we prove a type of Bell inequalities which are violated by quantum mechanics, reaching the conclusion that our quantum system evolves in a non deterministic way. In order to seize the interest of this conclusion, one must realize that it cannot be reached from the present experimental violation of Bell inequalities predicted by quantum mechanics, since this violation is compatible with non-local realism.
Bell’s theorem founded on Bell’s inequalities asserts that no local realistic theories can reproduce all quantum mechanical predictions for spin correlation of particle pairs. It is pointed out that the assumption of setting-independent probability makes Bell’s inequalities not impose constraint on all local realistic models and thus constitutes a theoretical loophole of Bell’s theorem. A counterexample is presented by showing that a local realistic model with appropriate probability density reproduces all quantum mechanical predictions. It becomes clear that experiments violate Bell’s inequalities because the real correlation functions are not constrained by these inequalities. It is also exposed that, rigorous logical reasoning of counter factual deduction does not permit to exclude any premises of Bell’s inequalities by a certain amount of experimental violations of these inequalities.
Bell inequalities applicable to non-ideal EPRB experiments are critical to the interpretation of experimental Bell tests. In this article it is shown that previous treatments of this subject are incorrect due to an implicit assumption and new inequalities are derived under general conditions. Published experimental evidence is reinterpreted under these results and found to be entirely compatible with local-realism, both, when experiments involve inefficient detection, if fair-sampling detection is assumed, as well as when experiments have nearly ideal detection and measurement crosstalk is taken into account.