An ambiguity is pointed out in J.S. Bell's argument that the distinction between quantum mechanics and hidden variable theories cannot be found in the behavior of single-particle beams. Within the context of theories for which states are unambiguously defined it is shown that the question of whether quantum mechanics or a locally realistic theory is valid may indeed be answered by single-particle beam measurements. It is argued that two-particle correlation experiments are required to answer the more fundamental question of whether or not the notion of a state can be unambiguously defined. As a byproduct of the discussion the general form of completely entangled states is deduced.
An ambiguity is pointed out in J.S. Bell's argument that the distinction between quantum mechanics and hidden variable theories cannot be found in the behavior of single-particle beams. Within the context of theories for which states are unambiguously defined it is shown that the question of whether quantum mechanics or a locally realistic theory is valid may indeed be answered by single-particle beam measurements. It is argued that two-particle correlation experiments are required to answer the more fundamental question of whether or not the notion of a state can be unambiguously defined. As a byproduct of the discussion the general form of completely entangled states is deduced.
The purpose of this article is to show that the introduction of hidden variables to describe individual events is fully consistent with the statistical predictions of quantum theory. We illustrate the validity of this assertion by discussing two fundamental experiments on correlated photons which are believed to behave ``violently non-classical''. Our considerations carry over to correlated pairs of neutral particles of spin one-half in a singlet state. Much in the spirit of Einstein's conviction we come to the conclusion that the state vector of a system does not provide an exhaustive description of the individual physical system. We also briefly discuss an experiment on ``quantum teleportation'' and demonstrate that our completely local approach leads to a full understanding of the experiment indicating the absence of any teleportation phenomenon. We caution that the indiscriminated use of the term ``Quantum Theory'' tends to obscure distinct differences between the quantum mechanics of massive particles and the propagation of photons. It is emphasized that the properties of polarizers, beam splitters, halfwave plates etc. used in photon-correlation experiments are defined by the laws of classical optics. Hence, understanding the outcome of those experiments requires a well-founded interconnection between classical and quantum electrodynamics free from unnecessary hypotheses.
Most physicists agree that the Einstein–Podolsky–Rosen–Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell’s inequality are locality and counterfactual definiteness but not scientific realism, determinism, or hidden variables as are often suggested. We further examine the resulting constraints on physical theory with an illustration from the many-worlds interpretation of quantum mechanics—an interpretation that we argue is deterministic, local, and realist but that nonetheless violates the Bell inequality.
The long-standing puzzle of the nonlocal Einstein-Podolsky-Rosen correlations is resolved. The correct quantum mechanical correlations arise for the case of entangled particles when strict locality is assumed for the probability amplitudes instead of locality for probabilities. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Sixty five years ago, the most significant paper questioning a fundamental aspect of quantum phenomena was written by Einstein, Podolsky and Rosen (EPR) [1]. They addressed the question whether the wave-function represented a complete description of reality in quantum mechanics, and argued that it didn’t. Bohr’s reply to this paper [2] was not sufficient to resolve the fundamental issues raised by EPR. Decades later, Bohm rephrased the EPR problem [3] in terms of particles correlated in their spin and this helped enormously in analyzing the problem with clarity. John Bell analyzed the EPR problem in the early sixties and established the Bell’s inequalities obeyed by
Introduction The paradox of Einstein, Podolsky and Rosen was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty. There have been attempts to show that even without such a separability or locality requirement no ‘hidden variable’ interpretation of quantum mechanics is possible. These attempts have been examined elsewhere and found wanting. Moreover, a hidden variable interpretation of elementary quantum theory has been explicitly constructed. That particular interpretation has indeed a grossly non-local structure. This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions. Formulation With the example advocated by Bohm and Aharonov, the EPR argument is the following. Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite directions. Measurements can be made, say by Stern–Gerlach magnets, on selected components of the spins σ 1 and σ 2 .
It is shown that when properly analyzed using principles consistent with the use of a Hilbert space to describe microscopic properties, quantum mechanics is a local theory: one system cannot influence another system with which it does not interact. Claims to the contrary based on quantum violations of Bell inequalities are argued to be incorrect. A specific example traces a violation of the CHSH Bell inequality in the case of a spin-3/2 particle to the noncommutation of certain quantum operators in a situation where (non)locality is not an issue. A consistent histories analysis of what quantum measurements measure, in terms of quantum properties, is used to identify the basic problem with derivations of Bell inequalities: the use of classical concepts (hidden variables) rather than a probabilistic structure appropriate to the quantum domain. A difficulty with the original Einstein-Podolsky-Rosen (EPR) argument for the incompleteness of quantum mechanics is the use of a counterfactual argument which is not valid if one assumes that Hilbert-space quantum mechanics is complete; locality is not an issue. The quantum correlations that violate Bell inequalities can be understood using local quantum common causes. Wave-function collapse and Schr\"odinger steering are calculational procedures, not physical processes. A general Principle of Einstein Locality rules out nonlocal influences between noninteracting quantum systems. Some suggestions are made for changes in terminology that could clarify discussions of quantum foundations and be less confusing to students.
Einstein, Podolsky, and Rosen pointed out that the quantum-mechanical description of “physical reality” implies an unphysical, instantaneous action between distant measurements. To avoid such an action at a distance, these three concluded that quantum mechanics had to be incomplete. However, its extensions involving additional “hidden variables,” allowing for the recovery of determinism and locality, have been disproved experimentally (Bell’s theorem). In this paper, an opposite solution of the paradox is presented, based on the greater indeterminism of the modern quantum field theory (QFT) description of particle physics, which prevents the preparation of any state having a definite number of particles. The resulting uncertainty in photon radiation has interesting consequences in quantum information theory (e.g., cryptography and teleportation). Moreover, since it allows for fewer elements of Einstein-Podolsky-Rosen (EPR) physical reality than the old non-relativistic quantum mechanics, QFT satisfies the EPR condition of completeness without the need for hidden variables. The residual physical reality never violates locality; thus, the unique objective proof of “quantum nonlocality” is removed in an interpretation-independent way. At the same time, the supposed nonlocality of the EPR correlations turns out to be a problem in interpretation of the measurement process. If we do not rely on hidden variables or new physics beyond QFT, the viable interpretation is a minimal statistical one, which preserves locality and Lorentz symmetry.