Geurdes (2014) outlines a probabilistic construction of a counterexample to Bell’s theorem. He gives a procedure to repeatedly sample from a specially constructed “pool” of local hidden variable models (depending on a table of numerically calculated parameters) and select from the results one LHV model, determining a random value S of the usual CHSH combination S of four (theoretical) correlation values. He claims Prob ( | S | > 2 ) > 0 . We expose a fatal flaw in the analysis: the procedure generates a non-local hidden variable model. To disprove this claim, Geurdes should program his procedure and generate random LHV’s till he finds one violating the CHSH inequality.
Geurdes (2014) outlines a probabilistic construction of a counterexample to Bell’s theorem. He gives a procedure to repeatedly sample from a specially constructed “pool” of local hidden variable models (depending on a table of numerically calculated parameters) and select from the results one LHV model, determining a random value S of the usual CHSH combination S of four (theoretical) correlation values. He claims Prob ( | S | > 2 ) > 0 . We expose a fatal flaw in the analysis: the procedure generates a non-local hidden variable model. To disprove this claim, Geurdes should program his procedure and generate random LHV’s till he finds one violating the CHSH inequality.
Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. However, the hypothesis from which Bell's inequalities are derived differ according to the probability space used to write them. The violation of Bell's inequalities can, alternatively, be explained by assuming that the hidden variables do not exist at all, that they exist but their values cannot be simultaneously assigned, that the values can be assigned but joint probabilities cannot be properly defined, or that averages taken in different contexts cannot be combined. All of the above are valid options, selected by different communities to provide support to their particular research program.
Bell--CHSH is frequently paraphrased as ``local realism is impossible'' after experimentalviolations of CHSH. The theorem is correct, but the paraphrase hides a structural assumption:\emph{selection centrality} (fair sampling), i.e.\ that the detected sample is not asetting- and hidden-variable--dependent reweighting of the hidden prior.We give a precise measure-theoretic separation between (i) the \emph{central} sector, whereEobs=Efull and CHSH≤2 holds under measurement independence and locality,and (ii) the \emph{noncentral} sector, where the observed correlations are computed under areweighted measure dνa,b=w(a,b,λ)dρ.We prove a sharp CHSH inflation boundSobs≤2+4δ,δ:=supa,b∫∣w(a,b,λ)−1∣ρ(dλ),so reproducing Tsirelson's 22 by strictly local measurement-independent models via selectionrequires δ≥(22−2)/4≈0.2071.We provide (A) a canonical Radon--Nikod\'ym construction (piecewise constants on sign regions plusa small positive remainder), (B) an explicit local factorized detection-loophole construction thatreproduces arbitrary finite correlation tables, and (C) an implementable optics protocol to estimateor upper-bound δ from time-tag data via window dithering, threshold and spectral sweeps, andauxiliary-tag binning.This paper critiques not the validity of Bell's theorem, but the common overstatement of what CHSHviolations imply without an explicit, quantitative centrality audit.
Today, quantum-mechanical concepts i.e. such as non-locality refer to some mathematical foundations, especially to Bell’s inequality and the Chsh inequality. Experimental data, analyzed while using Bell’s inequality or the Chsh inequality, favor a quantum mechanical description of nature over local hidden variable theories (often referred to as local realism). In general, the use of mathematically inconsistent methods can imply a waste of money, time and effort on this account. Under some certain conditions (the assumption of independence) Bell’s theorem and the Chsh inequality are already refuted. The purpose of this publication is to explore the terra incognita, the interior logic that may lie beyond Bell’s original theorem and the Chsh inequality and to refute both Bell’s original theorem and the Chsh inequality under any circumstances by the proof that we can derive a logical contradiction out of Bell’s inequalities. Thus far, if you accept Bell’s theorem or the Chsh inequality as correct, then you must accept too that +0 = +1, which is a logical contradiction. Bell’s theorem and the Chsh inequality are refuted in general. In this insight, it appears to be necessary to revisit the very foundations of quantum theory and of physics as such.
In a sequence of papers, Marian Kupczynski has argued that Bell’s theorem can be circumvented if one takes correct account of contextual setting-dependent parameters describing measuring instruments. We show that this is not true. Despite first appearances, Kupczynksi’s concept of a contextual locally causal probabilistic model is mathematically a special case of a Bell local hidden variables model. Thus, even if one takes account of contextuality in the way he suggests, the Bell–CHSH inequality can still be derived. Violation thereof by quantum mechanics cannot be easily explained away: quantum mechanics and local realism (including Kupczynski’s claimed enlargement of the concept) are not compatible with one another. Further inspection shows that Kupczynski is actually falling back on the detection loophole. Since 2015, numerous loophole-free experiments have been performed, in which the Bell–CHSH inequality is violated, so, despite any other possible imperfections of such experiments, Kupczynski’s escape route for local realism is not available.