Abstract:
An explicit model-example is presented to simulate Einstein-Podolsky-Rosen (EPR) experiments without invoking instantaneous influences at a distance. The model-example, together with the interpretation of past experiments by Kwiat and coworkers, uncovers logical inconsistencies in the application of Bell’s theorem to actual EPR experiments. The inconsistencies originate from topological-combinatorial assumptions that are both necessary and sufficient to derive all Bell-type inequalities including those of Wigner-d’Espagnat and Clauser-Horne-Shimony-Holt. The model-example circumvents these inconsistencies.

Abstract:
Bell's theorem contains the proposition that the Einstein-Podolsky-Rosen (EPR) theory (hypothesis) of the existence of elements of reality together with Einstein locality permits a mathematical description of EPR experiments by functions that are all defined on one common probability space. This proposition leads in turn to restrictions for possible experimental outcomes that Bell expressed in terms of his well known inequalities and that Vorob'ev and others had investigated before Bell. Summarizing several previous publications and adding new material, the above proposition is refuted by Einstein-local counterexamples from classical physics and shown to involve additional assumptions that can not be justified for mutually exclusive (incompatible) measurements and experiments. Moreover, criticism of our work by Mermin who invoked "standard sampling arguments" is shown to be false.

Abstract:
Counterfactual definiteness must be used as at least one of the postulates or axioms that are necessary to derive Bell-type inequalities. It is considered by many to be a postulate that not only is commensurate with classical physics (as for example Einstein’s special relativity), but also separates and distinguishes classical physics from quantum mechanics. It is the purpose of this paper to show that Bell’s choice of mathematical functions and independent variables implicitly includes counterfactual definiteness. However, his particular choice of variables reduces the generality of his theory, as well as the physics of all Bell-type theories, so significantly that no meaningful comparison of these theories with actual Einstein-Podolsky-Rosen experiments can be made.

Abstract:
We present a detailed analysis of the set theoretical proof of Wigner for Bell type inequalities with the following result. Wigner introduced a crucial assumption that is not related to Einstein’s local realism, but instead, without justification, to the existence of certain joint probability measures for possible and actual measurement outcomes of Einstein-Podolsky-Rosen (EPR) experiments. His conclusions about Einstein’s local realism are, therefore, not applicable to EPR experiments and the contradiction of the experimental outcomes to Wigner’s results has no bearing on the validity of Einstein’s local realism.

Abstract:
Most of the standard proofs of the Bell theorem are based on the Kolmogorov axioms of probability theory. We show that these proofs contain mathematical steps that cannot be reconciled with the Kolmogorov axioms. Specifically we demonstrate that these proofs ignore the conclusion of a theorem of Vorob'ev on the consistency of joint distributions. As a consequence Bell's theorem stated in its full generality remains unproven, in particular, for extended parameter spaces that are still objective local and that include instrument parameters that are correlated by both time and instrument settings. Although the Bell theorem correctly rules out certain small classes of hidden variables, for these extended parameter spaces the standard proofs come to a halt. The Greenberger-Horne-Zeilinger (GHZ) approach is based on similar fallacious arguments. For this case we are able to present an objective local computer experiment that simulates the experimental test of GHZ performed by Pan, Bouwmeester, Daniell, Weinfurter and Zeilinger and that directly contradicts their claim that Einstein-local elements of reality can neither explain the results of quantum mechanical theory nor their experimental results.

Abstract:
Mermin states in a recent paper that his nontechnical version of Bell's theorem stands and is not invalidated by time and setting dependent instrument parameters as claimed in one of our previous papers. We identify a number of misinterpretations (of our definitions) and mathematical inconsistencies in Mermin's paper and show that Mermin's conclusions are therefore not valid: his proof does not go forward if certain possible time dependencies are taken into account.

Abstract:
We discuss a class of proofs of Bell-type inequalities that are based on tables of potential outcomes. These proofs state in essence: if one can only imagine (or write down in a table) the potential outcome of a hidden parameter model for EPR experiments then a contradiction to experiment and quantum mechanics follows. We show that these proofs do not contain hidden variables that relate to time or, if they do, lead to logical contradictions that render them invalid.

Abstract:
We analyze the assumptions that are made in the proofs of Bell-type inequalities for the results of Einstein-Podolsky-Rosen type of experiments. We find that the introduction of time-like random variables permits the construction of a broader mathematical model which accounts for all correlations of variables that are contained in the time dependent parameter set of the backward light cone. It also permits to obtain the quantum result for the spin pair correlation, a result that contradicts Bell's inequality. Two key features of our mathematical model are (i) the introduction of time operators that are indexed by the measurement settings and appear in addition to Bell's source parameters and (ii) the related introduction of a probability measure for all parameters that does depend on the analyzer settings. Using the theory of B-splines, we then show that this probability measure can be constructed as a linear combination of setting dependent subspace product measures and that the construction guarantees Einstein-separability.

Abstract:
We show that Mermin's reasoning against our refutation of his non-technical proof for Bell-type inequalities is of limited significance or contains mathematical inconsistencies that, when taken into account, do not permit his proof to go forward. Our refutation therefore stands.

Abstract:
We show that the proofs of Gill as well as of Gill, Weihs, Zeilinger and Zukowski contain serious mathematical and physical deficiencies which render them invalid.