Bell's Theorem demonstrates that factorizable theories for the EPR experiment (EPR) cannot reproduce the quantum correlations. Factorizability is motivated by various locality conditions. So to understand the nature of nonlocality in EPR, we first need to understand the conceptual relations between factorizability, these various locality conditions and the nature of the quantum correlations. That is the main focus of my thesis. My main conclusion is that these conceptual relations are more subtle than the literature has usually suggested. Chapter 1 is a general introduction. In Chapter 2, I review the general framework of factorizable stochastic theories for EPR. I argue that factorizability can be motivated by various locality conditions, even in theories that admit time-dependent states and take the measurement interactions to be neither instantaneous, nor simultaneous. In Chapter 3, I focus on Cartwright' s (1989) and Humphreys' (1989) theories of probabilistic causation for singular events, which are based on modifications of traditional causal linear modelling. I argue (against Cartwright) that local models for EPR in the framework of these theories are committed to factorizability; and so they cannot reproduce the EPR correlations. In Chapter 4, I turn to Stochastic-Einstein Locality (SEL). Hellman (1982) proposed that SEL with some provisos characterizes the No-Superluminal-Action (NSA) of the Special Theory of Relativity (STR), and he argued that SEL is not violated in EPR. Butterfield (1994) proposed that SEL (without Hellman's provisos) characterizes the lack of superluminal Lewisian causation, and he argued that SEL is violated in EPR. I argue that SEL (without Hellman's provisos) is motivated by NSA and spatiotemporal separability. Thus, the violation of SEL might arise from the failure of spatiotemporal separability. And this failure is compatible with NSA and superluminal Lewisian causation. Accordingly, Hellman's and Butterfield's views need not be in tension. In Chapter 5, I focus on the implications for nonlocality of Jarrett's (1984) analysis of factorizability into "locality" and "completeness". I argue that although this analysis cannot distinguish between failures of factorizability which are compatible with STR and those which are not, it is significant for clarifying the implications of Bell's theorem for nonlocality. In Chapter 6, I qmsider three arguments that are intended to deny superluminal causal propagation in EPR, and a fourth argument that is intended to establish the opposite conclusion. I argue that in various ways these arguments have gone wrong. Three of these argument rely on implicit assumptions that have been overlooked. Accordingly, two of them reached a reasonable conclusion, i.e. the failure of separability, for the wrong reasons; whereas the third reached a wrong conclusion, i.e. that the failure of the contiguity of causal processes explains the failure of factorizability in EPR. The fourth relies on a wrong assumption, and thus it reaches a too strong conclusion, that the EPR correlations require superluminal action. My main conclusion is that the quantum correlations require nonseparability . In Chapter 7, I focus on decision theory in the context of EPR. In both EPR and the famous Newcomb's problem (NewProb), there are unscreenable-off correlations. I argue that NewProb can be related to EPR, in the sense that a NewProb can be realized by that experiment.
By implicitly assuming that all possible Bell-measurements occur simultaneously, all proofs of Bell's Theorem violate Heisenberg's Uncertainty Principle. This assumption is made in the original form of Bell's inequality, in Wigner's probability inequalities, and in the ``nonlocality without inequalities'' arguments. The introduction of time into derivations of these variants of Bell's theorem results in extra terms related to the time order of the measurements used in constructing correlation coefficients. Since the same locality assumptions are made in the Heisenberg-compliant derivations of this paper, only time-independent classical local hidden variable theories are forbidden by violations of the original Bell inequalities; time-dependent quantum local hidden variable theories can satisfy this new bound and agree with experiment. We further point out that factorizable wavefunctions have been used to describe some EPR experiments and can be used to describe others. These will generate local de Broglie-Bohm trajectories in the description of the data. This second, independent, line of argument also shows that violation of Bell's inequality is only evidence that Heisenberg's Uncertainty Principle cannot be ignored.
Bell’s [Physics 1 (1964) 195–200] theorem is popularly supposed to establish the nonlocality of quantum physics. Violation of Bell’s inequality in experiments such as that of Aspect, Dalibard and Roger [Phys. Rev. Lett. 49 (1982) 1804–1807] provides empirical proof of nonlocality in the real world. This paper reviews recent work on Bell’s theorem, linking it to issues in causality as understood by statisticians. The paper starts with a proof of a strong, finite sample, version of Bell’s inequality and thereby also of Bell’s theorem, which states that quantum theory is incompatible with the conjunction of three formerly uncontroversial physical principles, here referred to as locality, realism and freedom. Locality is the principle that the direction of causality matches the direction of time, and that causal influences need time to propagate spatially. Realism and freedom are directly connected to statistical thinking on causality: they relate to counterfactual reasoning, and to randomisation, respectively. Experimental loopholes in state-of-the-art Bell type experiments are related to statistical issues of post-selection in observational studies, and the missing at random assumption. They can be avoided by properly matching the statistical analysis to the actual experimental design, instead of by making untestable assumptions of independence between observed and unobserved variables. Methodological and statistical issues in the design of quantum Randi challenges (QRC) are discussed. The paper argues that Bell’s theorem (and its experimental confirmation) should lead us to relinquish not locality, but realism.
Abstract One of the Bell’s assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell’s inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell’s inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality in canonical notatons reads 〈AB〉 + 〈A’B〉 + 〈AB’〉 − 〈A’B’〉 ⩽ 6.
Bell's theorem is a conditional statement about theoretical models specified by a complete physical state
λ. It shows that models satisfying measurement independence and a stochastic Bell-locality (factorizability) condition obey Bell inequalities. Bell experiments, however, do not directly observe
λ or the
λ-conditioned probabilities appearing in that condition. They record analyzer settings, detector outcomes, and experimental metadata, from which they estimate operational joint distributions, marginals, correlations, and Bell statistics. We clarify the logical relationship between these two levels. The
λ-conditioned factorization identity cannot be directly evaluated at fixed
λ from the operational record alone. Nevertheless, by marginalizing over
λ under measurement independence, the model class implies observable inequalities that can be empirically violated. A Bell-inequality violation therefore excludes the corresponding Bell-local model class under the assumptions required for the inequality, but it does not by itself identify which latent assumption---measurement independence, parameter independence, or outcome independence---failed, nor does it uniquely determine an ontological interpretation. To illustrate this distinction concretely, we employ the Unified Quantum Mechanics formulation, in which the physical state is real, and the complex wavefunction is representational. We show that all four formulations of the dynamics---Schr\"odinger, Hilbert-transform, complex second-order, and real second-order---require the same two real initial functions
u0=u(0) and
u1=∂tu(0); the complex initial state is merely a repackaging of them, not additional physical information. We formulate the distinction as a three-level hierarchy: operational data, model-class exclusion, and ontological interpretation. The hierarchy separates experimental loopholes, which concern assumptions linking an actual experiment to an ideal Bell model, from the conceptual underdetermination of latent-variable conditional probabilities, which remains even in a loophole-free experiment. The result clarifies what Bell experiments establish without claiming that Bell-local models are empirically untestable. A Monte Carlo simulation illustrates the distinction between operational Bell-test results and latent-state factorization.
The EPR paradox was caused by the provision that quantum variables must have pre-existing values. This type of "hidden property realism" was later falsified by Bell's Theorem. Accordingly, the physical basis for action-at-a-distance between entangled quanta was removed. Yet, modern interpretations present Bell's inequality as a Locality Criterion, as if Bell violations can only happen at the quantum level, and only with remote interactions. This is a questionable practice, considering that classical joint measurements also violate such inequalities for mutually exclusive wave properties. In particular, consecutive measurements of polarization produce the same coefficients of correlation as parallel measurements with entangled quanta, yet they are explicitly local. Furthermore, it is possible to combine parallel and consecutive measurements of Type I polarization-entangled photons in a single experiment, conclusively showing that quantum Bell violations can be local. Surprisingly, classical phenomena also require nonlocal interpretations if pre-existing properties are taken for granted. Hence, the solution is to reject the models with pre-existing properties for both classical and quantum wave-like phenomena.