J. S. Bell’s well-known proofs of inequalities (and related work) are shown to be invalidated by two counter-arguments (-examples) that are based on Einstein-local propositions: Bell-type inequalities of Einstein-Podolsky-Rosen experiments must include, as virtually all physical theories do, elements of physical reality and their mathematical representations that relate to continua as opposed to exclusively finite numbers. Furthermore, Bell-type inequalities must be valid for all possible experimental geometries that lead to the quantum result. Based on these propositions, violations of Bell-type inequalities are demonstrated without violating Einstein locality, without conspiracy type theories and even for the case that all known “loopholes” are closed.
J. S. Bell’s well-known proofs of inequalities (and related work) are shown to be invalidated by two counter-arguments (-examples) that are based on Einstein-local propositions: Bell-type inequalities of Einstein-Podolsky-Rosen experiments must include, as virtually all physical theories do, elements of physical reality and their mathematical representations that relate to continua as opposed to exclusively finite numbers. Furthermore, Bell-type inequalities must be valid for all possible experimental geometries that lead to the quantum result. Based on these propositions, violations of Bell-type inequalities are demonstrated without violating Einstein locality, without conspiracy type theories and even for the case that all known “loopholes” are closed.
An overview of the history of Bell’s inequality is given, beginning with the so-called EPR paradox originally put forward by Einstein, Podolsky and Rosen and the impossibility proof of von Neumann. Bell’s inequality, which ultimately shifted the discussion from arguments based on philosophically introduced postulates to the domain of experimental physics, is presented together with experimental attempts from the early 1970s to 2010s to violate this inequality. We introduce three historical loopholes in the experimental schemes which have prevented experimentalists from being able to fully disprove the possibility of a hidden-variables description of nature. Recent experimental data indicate that all the main loopholes are now closed for photons (albeit not simultaneously in one experiment). Besides the class of stochastic local realism that have been tested experimentally, some other possible classical interpretations are mentioned.
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.
Bell inequalities are intended to formulate mathematically the argument of the thought-experiment proposed by Einstein, Podolsky and Rosen (EPR) in the Einstein-Bohr Debate. Devised to test Bell inequalities against quantum mechanics for resolving the Einstein-Bohr debate, Bell experiments are purportedly modern versions of the EPR experiment. However, there exists a fatal logical flaw in Bell experiments. Because of the logical flaw, Bell experiments differ essentially from the EPR experiment, and quantum correlation in the EPR experiment is not "quantum entanglement" in Bell experiments; the latter is not physically meaningful. In addition to the logical flaw in Bell experiments, a physical constraint imposed on measuring individual quantum objects is violated by all Bell inequalities, which makes Bell inequalities physically meaningless. Unlike Bell experiments, the EPR experiment will not violate any physical constraint, and the EPR argument has no logical flaw. Consequently, the experimental invalidation of Bell inequalities is not evidence for falsifying the two fundamental hypotheses for scientific research, i.e., locality and realism, underlying the EPR experiment, and by no means can Bell experiments resolve the Einstein-Bohr debate. Stemming from abandoning either locality or realism or both, the so-called new applications of quantum mechanics, including various quantum information technologies, are all ineligible and doomed to failure, for they attempt to exploit physically meaningless "quantum superposition" or "quantum entanglement", treating them as physical resources "out there" in the real world.
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.
This review is related to the Einstein-Bohr debate and to Einstein–Podolsky–Rosen’s (EPR) and Bohm’s (EPRB) Gedanken-experiments as well as their realization in actual experiments. I examine a significant number of papers, from my minority point of view and conclude that the well-known theorems of Bell and Clauser, Horne, Shimony and Holt (CHSH) deal with mathematical abstractions that have only a tenuous relation to quantum theory and the actual EPRB experiments. It is also shown that, therefore, Bell-CHSH cannot be used to assess the nature of quantum entanglement, nor can physical features of entanglement be used to prove Bell-CHSH. Their proofs are, among other factors, based on a statistical sampling argument that is invalid for general physical entities and processes and only applicable for finite “populations”; not for elements of physical reality that are linked, for example, to a time-like continuum. Bell-CHSH have, furthermore, neglected the subtleties of the theorem of Vorob’ev that includes their theorems as special cases. Vorob’ev found that certain combinatorial-topological cyclicities of classical random variables form a necessary and sufficient condition for the constraints that are now known as Bell-CHSH inequalities. These constraints, however, must not be linked to the observables of quantum theory nor to the actual EPRB experiments for a variety of reasons, including the existence of continuum-related variables and appropriate considerations of symmetry.
In 1935, Einstein, Podolsky, and Rosen (EPR) argued that (then new) quantum mechanics was incomplete. At the heart of EPR’s paradox was the strange non-local nature of an entangled state which allowed EPR to simultaneously assign local values for position and momentum of a particle. In 1964, John Bell proposed an inequality (Bell’s inequality) that must be satisfied by any local realistic theory. The experimental confirmation of quantum physics, i.e., the experimental test of Bell’s inequality, required a pair of particles in an entangled state. The experiments first performed in the early 1970s, followed by a series of experiments until now, have confirmed the violation of Bell’s inequality, strongly implying that local realistic descriptions of nature are not consistent with experimental observations. The early simplistic view of entanglement has now been significantly expanded to include mixed states and multiple particles. Moreover, theoretical and experimental studies on the nature of entanglement have led to quantum information science where entanglement is an essential resource. In this article, we briefly review the early experiments on Bell’s inequality and experimental attempts to close “loopholes” as well as some key experiments on quantum information.