Locality,reflection, and wave-particle duality

Bell's theorem is believed to establish that the quantum mechanical predictions do not generally admit a causal representation compatible with Einsten's principle of separability, thereby proving incompatibility between quantum mechanics and relativity. This interpretation is contested via two convergent approaches which lead to a sharp distinction between quantum nonseparability and violation of Einstein's theory of relativity.In a first approach we explicate from the quantum mechanical formalism a concept of reflected dependence. Founded on this concept, we produce a causal representation of the quantum mechanical probability measure involved in Bell's proof, which is clearly separable in Einstein's sense, i.e., it does not involve supraluminal velocities, and nevertheless is nonlocal in Bell's sense. So Bell locality and Einstein separability aredistinct qualifications, and Bell nonlocality (or Bell nonseparability) and Einstein separability arenot incompatible. It is then proved explicitly that with respect to the mentioned representation Bell's derivation does not hold. So Bell's derivation does notestablish thatany Einstein-separable representation is incompatible with quantum mechanics. This first—negative—conclusion is asyntactic fact.The characteristics of the representation and of the reasoning involved in the mentioned counterexample to the usual interpretation of Bell's theorem suggest that the representation used—notwithstanding its ability to bring forth the specified syntactic fact—isnot factually true. Factual truth and syntactic properties also have to be radically distinguished in their turn. So, in a second approach, starting from de Broglie's initial relativistic model of a microsystem, a deeper, factually acceptable representation is constructed. The analyses leading to this second representation show that quantum mechanics does indeed involve basically a certain sort of nonseparability, called here de Broglie-Bohr quantum nonseparability. But the de Broglie-Bohr quantum nonseparability is shown to stem directly from the relativistic character of the considerations which led Louis de Broglie to the fundamental relation p = h/,thereby being essentially consistent with relativity. As to Einstein separability, it appears to be a still insufficiently specified conceptof which a future, improved specification, will probably be explicitly harmonizable with the de Broglie-Bohr quantum nonseparability.The ensemble of the conclusions obtained here brings forth a new concept of causality, a concept offolded, zigzag, reflexive causality, with respect to which the type of causality conceived of up to now appears as aparticular case of outstretched, one-way causality. The reflexive causality is found compatible with the results of Aspect's experiment, and it suggests new experiments.Considered globally, the conclusions obtained in the present work might convert the conceptual situation created by Bell's proof into a process of unification of quantum mechanics and relativity.Dedicated to Prof. Bernard Grossetête.     

Bell’s Theorem Without Inequalities and Only Two Distant Observers

A proof of Bell's theorem without inequalities and involving only two observers is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's theorem for a set of n Bell states (with n odd) shared between two distant observers. A generalized CHSH inequality is formulated for n Bell states shared symmetrically between two observers and it is shown that quantum mechanics violates this inequality by an amount that grows exponentially with increasing n.     

Spin correlations in elastic e<Superscript>+</Superscript>e<Superscript>-</Superscript> scattering in QED

Spin correlations are carefully investigated in elastic e⁺e^- scattering in QED, for initially polarized as well as unpolarized particles, with emphasis placed on energy or speed of the underlying particles involved in the process. An explicit expression is derived for the corresponding transition probabilities in closed form to the leading order. These expressions differ from those obtained from simply combining the spins of the relevant particles, which are of kinematic nature. It is remarkable that these explicit results obtained from quantum field theory show a clear violation of Bell's inequality at all energies, in support of quantum theory in the relativistic regime. We hope that our explicit expression will lead to experiments, of the type described in the bulk of this paper, that monitor speed.     

The chaotic ball: An intuitive analogy for EPR experiments

Actual realisations of EPR experiments donot demonstrate non-locality. A model is presented that should enable non-specialists as well as specialists to understand how easy it is to find realistic explanations for the observations. The model also suggests new areas where realistic (hidden-variable) models can give valid predictions whilst quantum mechanics fails. It offers straightforward explanations for some anomalies that Aspect was unable to account for, providing perhaps the first experimental evidence that a hidden-variable theory can besuperior to quantum mechanics. The apparent success of quantum mechanics in predicting results is shown to be largely due to the use of unjustifiable and biased analysis of the data. Data that has been discarded because it did not lead to a valid Bell's test may give further evidence that hidden variables exist.     

Bell's inequality for a single particle

Bell's inequality must be satisfied by a theory that can be based on local realistic variables. We derive such an inequality and show that it is violated by some quantum mechanical states. These states may be looked upon as pertaining to one particle.This paper is a contribution in honor of Prof. M. Jammer's 80th birthday April 13, 1995.     

Bell's theorem based on a generalized EPR criterion of reality

First, the demonstration of Bell's theorem, i.e., of the nonlocal character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedankenexperiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almostwith certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future.     

Has quantum nonlocality been experimentally verified?

Bell's theorem tells us that if we wish to preserve the results of quantum theory, then we cannot supplement the theory by any sort of locally determined hidden variables. The Aspect experiments tell us that the results of quantum theory, in certain relevant circumstances, are correct. Thus, some type of information about the result of an experiment must travel to other points of space. If we take a reasonable, simple, model of how a measurement actually produces a result, namely, the GRW collapse model, then the experiments that have so far been done, do not distinguish between instantaneous communication, which is required in the orthodox theory, and communication at the speed of light. We discuss how models which incorporate such communication might be constructed, and urge the need for experimental tests. Likely values of the relevant parameters suggest that these are possible. Finally, we note that, contrary to what is generally claimed, nonlocal collapse models which agree in all circumstances with quantum theory do permit instantaneous signals to be sent over arbitrarily large distances.Text of a talk given at the 1991 Cesena conference,Bell's Theorem and the Foundations of Modern Physics.     

The Einstein–Podolsky–Rosen Effect: Paradox or Gate?

The Einstein–Podolsky–Rosen (EPR) paradox represents one of the most controversial aspects of quantum mechanics (QM). In this paper, we suggest that it can be solved by taking into account the fact that physical quantum phenomena can be extended backward in time (i.e. we take into account two arrows of time instead of one). We derive such a strong statement as a consequence of symmetries and conservation laws implying field equations which are invariant under time reversal. Our approach, violating Einstein's locality postulate, confirms QM predictions and explains the failure of Bell's inequalities.     

Three-particle Einstein-Podolsky-Rosen correlations

It has been argued by Mermin that agedanken decay of a three-particle system gives a more powerful demonstration of quantum nonlocality than Bell's analysis. It is shown that this claim is premature. Anad hoc model based on local realism is constructed in order to reproduce the quantum mechanical prediction of the three-particlegedanken decay.     

Photon entanglement in the phase-space Q representation of quantum optics

Several examples of photon entanglement are studied in the Q representation of quantum optics. In particular, the entangled states produced in parametric downconversion are studied in detail, and we determine the conditions for the violation of Bell's inequality. Our approach shows that photon entanglement is related to the existence of correlations between the quantum fluctuations of the electromagnetic field associated to different modes. Received 10 August 2002 / Received in final form 7 November 2002 Published online 4 February 2003     

About a Generalization of Bell's Inequality

We make use of natural induction to propose, following John Ju Sakurai, a generalization of Bell's inequality for two spin s=n/2(n=1,2,...) particle systems in a singlet state. We have found that for any finite integer or half-integer spin Bell's inequality is violated when the terms in the inequality are calculated from a quantum mechanical point of view. In the final expression for this inequality the two members therein are expressed in terms of a single parameter . Violation occurs for in some interval of the form (,/2) where parameter becomes closer and closer to /2, as the spin grows, that is, the greater the spin number the size of the interval in which violation occurs diminishes to zero. Bell's inequality is a relationship among observables that discriminates between Einstein's locality principle and the non-local point of view of orthodox quantum mechanics. So our conclusion may also be stated by saying that for large spin numbers the non-local and local points of view agree.     

Existence of “free will” as a problem of physics

The proof of Bell's inequality is based on the assumption that distant observers can freely and independently choose their experiments. As Bell's inequality isexperimentally violated, it appears that distant physical systems may behave as a single, nonlocal, indivisible entity. This apparent contradiction is resolved. It is shown that the free will assumption is, under usual circumstances, an excellent approximation.I have set before you life and death, blessing and cursing: therefore choose life....

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Violation of bell's inequalities with a local theory of photons

We use a local theory of photons purely as particles to model the single-photon experiment proposed by Tan, Walls, and Collett. Like Tanet al. we are able to derive a violation of Bell's inequalities, but our local probabilistic theory does not use any specific quantum mechanical assumptions or calculations.     

Measurement and “beables” in quantum mechanics

It is argued that the measurement problem reduces to the problem of modeling quasi-classical systems in a modified quantum mechanics with superselection rules. A measurement theorem is proved, demonstrating, on the basis of a principle for selecting the quantities of a system that are determinate (i.e., have values) in a given state, that after a suitable interaction between a systemS and a quasi-classical systemM, essentially only the quantity measured in the interaction and the indicator quantity ofM are determinate. The theorem justifies interpreting the noncommutative algebra of observables of a quantum mechanical system as an algebra of beables, in Bell's sense.     

Entanglement and nonlocality of one- and two-mode combination squeezed state

We investigate the entanglement and nonlocality properties of one- and two-mode combination squeezed vacuum state (OTCSS, with two-parameter λ and γ) by analyzing the logarithmic negativity and the Bell's inequality. It is found that this state exhibits larger entanglement than that of the usual two-mode squeezed vacuum state (TSVS), and that in a certain regime of λ, the violation of Bell's inequality becomes more obvious, which indicates that the nonlocality of OTCSS can be stronger than that of TSVS. As an application of OTCSS, the quantum teleportation is examined, which shows that there is a region spanned by λ and γin which the fidelity of OTCSS channel is larger than that of TSVS.     

Robustness of entanglement for Bell decomposable states

We propose a simple geometrical approach for finding robustness of entanglement for Bell decomposable states of two-qubit quantum systems. It is shown that for these states robustness is equal to the concurrence. We also present an analytical expression for two separable states that wipe out all entanglement of these states. Random robustness of these states is also obtained. We also obtain robustness of a class of states obtained from Bell decomposable states via some special local operations and classical communications (LOCC).Received: 28 October 2002, Published online: 5 August 2003PACS: 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)     

A remark on Bell's inequality and decomposable normal states

Bell's correlation inequality is considered in the algebraic framework as discussed by Baez. It is shown that all normal states of the tensor product of two W ^*-algebras satisfy Bell's inequality, if and only if every normal state lies in the closure of the convex hull of the normal product states, if and only if one of the algebras is commutative.     

Empirical consequences of the scientific construction: The program of local hidden-variables theories in quantum mechanics

We claim that physics has been constructed because three “philosophical” principles have been respected, namely, realism, locality, and consistency. These principles lead to an interpretation of quantum mechanics (QM) in terms of local hidden-variables theories (LHV). In order to prove that LHV have not been refuted, we analyze the empirical proofs of Bell's inequalities and we argue that none is loophole-free. Then we propose a restricted QM that does not contain measurement postulates and that does not claim that all state vectors (self-adjoint operators) are states (observables). The contradiction of such restricted QM with Bell's inequality cannot be shown as a theorem, but only by the design of a loophole-free experiment. Finally, we argue that noise has been underestimated in quantum theory. It does not appear in QM, but it is essential in quantum field theory. We conjecture that noise will prevent the violation of Bell's inequality.     

Bell's theorem,inference, and quantum transactions

Bell's theorem is expounded as an analysis in Bayesian inference. Assuming the result of a spin measurement on a particle is governed by a causal variable internal (hidden, local) to the particle, one learns about it by making a spin measurement; thence about the internal variable of a second particle correlated with the first; and from there predicts the probabilistic result of spin measurements on the second particle. Such predictions are violated by experiment: locality/causality fails. The statistical nature of the observations rules out signalling; acausal, superluminal, or otherwise. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of experiment imply that it has a nonlocal/acausal interpretation. Cramer's newtransactional interpretation, which incorporates this feature by adapting the Wheeler-Feynman idea of advanced and retarded processes to the quantum laws, is advocated. It leads to an invaluable way of envisaging quantum processes. The usual paradoxes melt before this, and one, the delayed choice experiment, is chosen for detailed inspection. Nonlocality implies practical difficulties in influencing hidden variables, which provides a very plausible explanation for why they have not yet been found; from this standpoint, Bell's theoremreinforces arguments in favor of hidden variables.     

Criticizing Bell: Local realism and quantum physics reconciled

A typical sample of Bell's inequality is proved to require, besides the standard assumptions on realism and locality, the adoption of a metatheoretical classical principle for interpreting quantum laws. A new principle is proposed which is consistent with the operational philosophy of quantum physics; it is then shown that, whenever the latter principle is adopted in place of the former, realism (here intended in a purely semantical sense) and locality do not imply Bell's inequality in the form considered here, but a new inequality which is not violated in quantum physics. Thus an interpretation of quantum physics that is (semantically) realistic and local is suggested, which eliminates a number of seeming paradoxes.