Special relativity demands a locality principle (no instantaneous action at a distance); locality implies Bell’s theorem; quantum mechanics violates Bell’s inequality, therefore, quantum mechanics contradicts relativity! Or so it would seem. It is shown, however, that the locality principle needed for Bell’s theorem is stronger than the simple locality that is needed to satisfy the demands of relativity and that quantum mechanics satisfies the latter. The stronger locality principle is equivalent to the conjunction of simple locality and predictive completeness, and it is the latter principle that fails. The notion of predictive completeness is weaker than, and is implied by, the completeness criterion of Einstein, Podolsky, and Rosen. But the quantum mechanical state description is not only incomplete but incompletable, for any local complete state description would satisfy Bell’s inequality and disagree with experiment.
Special relativity demands a locality principle (no instantaneous action at a distance); locality implies Bell’s theorem; quantum mechanics violates Bell’s inequality, therefore, quantum mechanics contradicts relativity! Or so it would seem. It is shown, however, that the locality principle needed for Bell’s theorem is stronger than the simple locality that is needed to satisfy the demands of relativity and that quantum mechanics satisfies the latter. The stronger locality principle is equivalent to the conjunction of simple locality and predictive completeness, and it is the latter principle that fails. The notion of predictive completeness is weaker than, and is implied by, the completeness criterion of Einstein, Podolsky, and Rosen. But the quantum mechanical state description is not only incomplete but incompletable, for any local complete state description would satisfy Bell’s inequality and disagree with experiment.
In the early stages of the famous debates between Einstein and Bohr on the foundations of quantum mechanics, Einstein attempted to devise thought experiments aiming at showing that arbitrarily accurate predictions of incompatible physical quantities was possible, in violation of Heisenberg's uncertainty principle. Bohr was able to defend quantum mechanics from those attacks by showing that a careful application of the uncertainty principle to the experimental apparata as well as the measured system lead to consistent results. Could Bohr have given an independent argument for the irreducible unpredictability implied by the uncertainty principle?
The celebrated 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the ontological concepts of locality and determinism. However, nothing can be concluded from Bell's theorem alone about locality by itself or determinism by itself--it is possible to reproduce quantum-mechanical predictions with deterministic models which violate locality as well as indeterministic models which satisfy locality. On the other hand, there's almost universal agreement that the epistemic form of locality--signal locality, or the impossibility of faster-than-light communication--must hold in a relativistic universe. By making a similar distinction between determinism and the epistemic concept of predictability, I show that signal locality plus the bare observed phenomena of Bell inequality violations lead to the remarkable conclusion that Nature is fundamentally unpredictable. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the principle of relativity, regardless of any postulates of quantum mechanics.
Introduction Fifty years after the publication of Bell's theorem, there remains some controversy regarding what the theorem is telling us about quantum mechanics, and what the experimental violations of Bell inequalities are telling us about the world. This chapter represents my best attempt to be clear about what I think the lessons are. In brief: There is some sort of nonlocality inherent in any quantum theory, and, moreover, in any theory that reproduces, even approximately, the quantum probabilities for the outcomes of experiments. But not all forms of nonlocality are the same; there is a distinction to be made between action at a distance and other forms of nonlocality, and I will argue that the nonlocality needed to violate the Bell inequalities need not involve action at a distance. Furthermore, the distinction between forms of nonlocality makes a difference when it comes to compatibility with relativistic causal structure. The Bell locality condition is a condition which, if satisfied, renders possible a completely local account of the correlations between outcomes of spatially separated experiments. Bell's theorem tells us that the probabilities that we compute from quantum mechanics do not admit of such an account. Modulo auxiliary assumptions that, in my opinion, should be noncontroversial, this yields the conclusion that there must be something nonlocal about any theory that yields the quantum mechanical probabilities or anything close to them. One way to violate the Bell locality condition – and this is the way that any deterministic theory must do it – is via straightforward action at a distance. However, we should also consider the possibility of a stochastic theorywith probabilistic laws that involve irreducible correlations. The sort of nonlocality inherent in such a theory involves relations between events that are significantly different from causal relations as usually conceived. Perhaps surprisingly, such a theory, unlike its deterministic cousins, need not invoke a distinguished relation of distant simultaneity. This makes a difference for the situation of the two sorts of theories vis-a-vis relativity. Though a deterministic theory can achieve the appearance of being relativistic, at the level of observable phenomena, it can do so only by introducing a preferred foliation and with it a causal structure at odds with relativistic causal structures. Things are otherwise with dynamical collapse theories.
In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however, many physicists and philosophers of science do harbor this belief. Experts in the field often use the term `nonlocality' to designate particular non-classical aspects of quantum entanglement and do not confuse the term with superluminal interactions. However, many physicists seem to take the term more literally. I endeavor to disabuse the latter of this notion by emphasizing that the correlations of Bell-type entanglement are a result of ordinary quantum superposition with no need to introduce nonlocality. The conclusion of the EPR paper wasn't that quantum mechanics is nonlocal but rather that it is an incomplete description of reality. For different reasons, many physicists, including me, agree with Einstein that quantum mechanics is necessarily an incomplete description of reality.
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
It is known that "quantum non locality", leading to the violation of Bell's inequality and more generally of classical local realism, can be attributed to the conjunction of two properties, which we call here elementary locality and predictive completeness. Taking this point of view, we show again that quantum mechanics violates predictive completeness, allowing the making of contextual inferences, which can, in turn, explain why quantum non locality does not contradict relativistic causality. An important question remains: if the usual quantum state ψ is predictively incomplete, how do we complete it? We give here a set of new arguments to show that ψ should be completed indeed, not by looking for any "hidden variables", but rather by specifying the measurement context, which is required to define actual probabilities over a set of mutually exclusive physical events.
In the Einstein-Bohr debate, Einstein considered quantum mechanics incomplete and disagreed with Born’s probabilistic interpretation of wave-functions. Observers in the axioms of quantum mechanics also bothered Einstein. Inspired by Einstein, Bell and his followers intended to complete quantum mechanics within the framework of local realism. Regrettably, the deterministic correlation between distant components of a separable system in Einstein’s local-realist description of the world is mistaken for non-locality in the world described by Bell’s theorem, leading to incorrect interpretations of experimental results obtained by testing Bell inequalities. This article introduces a new principle, the general principle of measurements, which is proved as a mathematical theorem and allows quantum mechanics to be completed within the framework of local realism while keeping the formal axiomatic definition of a general Hilbert space unchanged. The completed theory can provide the same probabilistic predictions of empirical results as those provided by the current theory. Using disjunction (“or”) as the logical relation between superposed orthonormal vectors, the completed theory precludes observers in the axioms of the current theory and inexplicable collapses of wave-functions, thus it is intuitively comprehensible and alleviates much difficulty in understanding quantum mechanics. Among various world views, Einstein’s local-realist world view is correct.