Contextuality and entanglement are valuable resources for quantum computing and quantum information. Bell inequalities are used to certify entanglement; thus, it is important to understand why and how they are violated. Quantum mechanics and behavioural sciences teach us that random variables ‘measuring’ the same content (the answer to the same Yes or No question) may vary, if ‘measured’ jointly with other random variables. Alice’s and Bob’s raw data confirm Einsteinian non-signaling, but setting dependent experimental protocols are used to create samples (...) of coupled pairs of distant ±1 outcomes and to estimate correlations.Marginal expectations, estimated using these final samples, depend on distant settings. Therefore,a system of random variables ‘measured’ in Bell tests is inconsistently connected and it should be analyzed using a Contextuality- by-Default approach, what is done for the first time in this paper.The violation of Bell inequalities and inconsistent connectedness may be explained using a contextual locally causal probabilistic model in which setting dependent variables describing measuring instruments are correctly incorporated. We prove that this model does not restrict experimenters` freedom of choice which is a prerequisite of science. Contextuality seems to be the rule and not an exception; thus, it should be carefully tested. (shrink)

Bell-CHSH inequalities are trivial algebraic properties satisfied by each line of an Nx4 spreadsheet containing ±1 entries, thus it is surprising that their violation in some experiments allows us to speculate about the existence of non-local influences in nature and casts doubt on the existence of the objective external physical reality. Such speculations are rooted in incorrect interpretations of quantum mechanics and in a failure of local realistic hidden variable models to reproduce quantum predictions for spin polarization correlation experiments (SPCE). (...) In these models, one uses a counterfactual joint probability distribution of only pairwise measurable random variables (A, A′, B, B′) to prove Bell-CHSH inequalities. In SPCE, Alice and Bob, using 4 incompatible pairs of experimental settings, estimate imperfect correlations between clicks registered by their detectors. Clicks announce the detection of photons and are coded by ±1. Expectations of corresponding random variables—E (AB), E (AB′), E (A′B), and E (A′B′)—are estimated and compared with quantum predictions. These estimates significantly violate CHSH inequalities. Since variables (A, A′) and (B, B′) cannot be measured jointly, neither Nx4 spreadsheets nor a joint probability distribution of (A, A′, B, B′) exist, thus Bell-CHSH inequalities may not be derived. Nevertheless, imperfect correlations between clicks in SPCE may be explained in a locally causal way, if contextual setting-dependent parameters describing measuring instruments are correctly included in the description. The violation of Bell-CHSH inequalities may not therefore justify the existence of a spooky action at the distance, super-determinism, or speculations that an electron can be both here and a meter away at the same time. In this paper we review and rephrase several arguments proving that such conclusions are unfounded. Entangled photon pairs cannot be described as pairs of socks nor as pairs of fair dice producing in each trial perfectly correlated outcomes. Thus, the violation of inequalities confirms only that the measurement outcomes and ‘the fate of photons’ are not predetermined before the experiment is done. It does not allow for doubt regarding the objective existence of atoms, electrons, and other invisible elementary particles which are the building blocks of the visible world around us. (shrink)

Recent experiments allowed concluding that Bell-type inequalities are indeed violated thus it is important to understand what it means and how can we explain the existence of strong correlations between outcomes of distant measurements. Do we have to announce that: Einstein was wrong, Nature is nonlocal and nonlocal correlations are produced due to the quantum magic and emerge, somehow, from outside space-time? Fortunately such conclusions are unfounded because if supplementary parameters describing measuring instruments are correctly incorporated in a theoretical model (...) then Bell-type inequalities may not be proven .We construct a simple probabilistic model explaining these correlations in a locally causal way. In our model measurement outcomes are neither predetermined nor produced in irreducibly random way. We explain in detail why, contrary to the general belief; an introduction of setting dependent parameters does not restrict experimenters’ freedom of choice. Since the violation of Bell-type inequalities does not allow concluding that Nature is nonlocal and that quantum theory is complete thus the Bohr-Einstein quantum debate may not be closed. The continuation of this debate is not only important for a better understanding of Nature but also for various practical applications of quantum phenomena. (shrink)

Ilya Schmelzer wrote recently: Nieuwenhuizen argued that there exists some “contextuality loophole” in Bell’s theorem. This claim in unjustified. It is made clear that this arose from attaching a meaning to the title and the content of the paper different from the one intended by Nieuwenhuizen. “Contextual loophole” means only that if the supplementary parameters describing measuring instruments are correctly introduced, Bell and Bell-type inequalities may not be proven. It is also stressed that a hidden variable model suffers from a (...) “contextuality loophole” if it tries to describe different sets of incompatible experiments using a unique probability space and a unique joint probability distribution. (shrink)