On the relation between the Einstein-Podolsky-Rosen paradox and the problem of nonlocality in quantum mechanics

The EPR problem is studied both from an instrumentalistic and from a realistic point of view. Bohr's reply to the EPR paper is analyzed and demonstrated to be not completely representative of Bohr's general views on the possibility of defining properties of a microscopic object. A more faithful Bohrian answer would not have led Einstein to the conclusion that Bohr's completeness claim of quantum mechanics implies nonlocality. The projection postulate, already denounced in 1936 by Margenau as the source of the EPR paradox, is found to be also at the origin of the nonlocality conundrum. Its unobservability in EPR-like experiments is demonstrated, thus showing the redundancy of the idea of nonlocality in the instrumentalist interpretation of quantum mechanics. It is argued that also from a realist point of view there is no reason to assume nonlocality. The relevance of Bohm's quantum potential and of Bell's inequalities with respect to the (non)locality problem is discussed.     

On the possibility of measuring the electron spin in an inhomogeneous magnetic field

It is widely held that Bohr has shown that the spin of a free electron is not measurable. We point out that Bohr's argument has some important ifs and buts. A concrete configuration is calculated to produce a clear spin separation. This is then shown not to contradict Bohr's reasoning.     

Wave Node Dynamics and Revival Symmetry in Quantum Rotors

Symmetries and dynamics of wave nodes in space and time expose principles of quantum theory and its relativistic underpinning. Among these are key principles behind recently discovered dephasing and rephasing phenomena known as revivals. A reexamination of basic Eberly revivals, Berry “quantum fractal” landscapes, and the “quantum carpets” of Schleich and co-workers reveals a simple Farey arithmetic and C_n-group revival structure in one of the earliest quantum wave models, the Bohr rotor. These principles may be useful for interpreting modern time-dependent rovibrational spectra. The nodal dynamics of the Bohr rotor is seen to have a quasi-fractal structure similar to that of earlier systems involving chaotic circle maps. The fractal structure is an overlay of discrete versions of Bohr's rotor model. Each N-point Bohr rotor acts like a base-N quantum “odometer” which performs rational fraction arithmetic. Such systems may have applications for optical information technology and quantum computing.     

关于玻尔理论的几点注记

根据玻尔的两个基本假设、里德伯公式与经典力学的有关结果,可以导出玻尔半径,里德伯常数的表达式与简化有关椭圆轨道的计算。并说明玻尔理是一种唯象理论,且含有波动性的内涵。     

Bell’s inequality, Einstein, Podolsky, Rosen arguments and von Neumann’s projection postulate

This paper is devoted to analysis of the role of projection postulate in Einstein, Podolsky, and Rosen-EPR [1] argument against completeness of QM. It will be shown that the EPR considerations do not match with von Neumann’s quantum measurement theory (QMT). The root of EPR’s conclusion on incompleteness of QM is the misuse of von Neumann’s projection postulate. EPR applied this postulate to observables with degenerate spectra (which is totally forbidden by von Neumann’s axiomatics of QM). Consequences for Bell’s inequality and quantum information theory are analyzed. This paper might stimulate discussion on the role of projection postulate in quantum information theory, especially quantum cryptography and teleportation.     

Generalization of the Greenberger-Horne-Zeilinger algebraic proof of nonlocality

We further develop a recent new proof (by Greenberger, Horne, and Zeilinger—GHZ) that local deterministic hidden-variable theories are inconsistent with certain strict correlations predicted by quantum mechanics. First, we generalize GHZ's proof so that it applies to factorable stochastic theories, theories in which apparatus hidden variables are causally relevant to measurement results, and theories in which the hidden variables evolve indeterministically prior to the particle-apparatus interactions. Then we adopt a more general measure-theoretic approach which requires that GHZ's argument be modified in order to produce a valid proof. Finally, we motivate our more general proof's assumptions in a somewhat different way from previous authors in order to strengthen the implications of our proof as much as possible. After developing GHZ's proof along these lines, we then consider the analogue, for our proof, of Bohr's reply to the EPR argument, and conclude (pace GHZ) that in at least one respect (viz. that of most concern to Bohr) the proof is no more powerful than Bell's. Nevertheless, we point out some new advantages of our proof over Bell's, and over other algebraic proofs of nonlocality. And we conclude by giving a modified version of our proof that, like Bell's, does not rely on experimentally unrealizable strict correlations, but still leads to a testable quasi-algebraic locality inequality.... to admit things not visible to the gross creatures that we are is, in my opinion, to show a decent humility, and not just a lamentable addiction to metaphysics.J. S. BellThis paper is dedicated to the memory of John Bell whose brilliant work has done so much to clarify the foundations of quantum mechanics.     

A new approach to the Einstein-Podolsky-Rosen paradox

Some new aspects of the EPR paradox are considered. We first show that the authors' argument, leading to the conclusion that quantum theory is incomplete, is based on a tacit assumption that may be questioned. We then investigate the non-local features of the EPR setup and point out an interesting connection between the nonlocality involved in the quantum correlations of pairs of particles and that of a single particle in quantum theory.     

A non-completeness argument for quantum mechanics (analysis of the EPR paper)

This paper aims at a clarification of the interrelations of the fundamental ideas in the EPR paper [2]. Through a logical analysis of the completeness condition and the physical reality criterion, we show how the premises of the EPR argument are obtained and explicate in what sense the conclusion that quantum mechanics is a non-complete theory follows.     

Reflections Concerning Niels Bohr's Refutation of the Einstein-Podolsky-Rosen-Paradox

The controverse discussion between Bohr and Einstein concerning the interpretation of quantum theory is resumed by a reappraisal of some arguments in the view of epistemological problems, which have come to the fore in recent times.     

Analysis of the role of von Neumann’s projection postulate in the canonical scheme of quantum teleportation

Modern development of quantum technologies based on quantum information theory (in particular, laser-based quantum-information technologies) stimulated the analysis of proposed computational, cryptographic, and teleportational schemes from the viewpoint of quantum foundations. It is evident that not all mathematical calculations performed in the complex Hilbert space can directly be realized in the physical space. Recently, analyzing the original EPR paper, we found that their argument was based on the misuse of von Neumann’s projection postulate. In contrast to von Neumann, Einstein, Podolsky, and Rosen (EPR) applied this postulate to the observables represented by the operators with degenerate spectra. It was completely forbidden by von Neumann’s axiomatics of quantum mechanics. It is impossible to repeat the EPR considerations within the von Neumann’s framework. We analyze here quantum teleportation by taking into account von Neumann’s projection postulate. Our analysis shows that the so-called quantum teleportation is impossible within the von Neumann’s framework.     

Nature Has No Elementary Particles and Makes No Measurements or Predictions: Quantum Measurement and Quantum Theory,from Bohr to Bell and from Bell to Bohr

This article reconsiders the concept of physical reality in quantum theory and the concept of quantum measurement, following Bohr, whose analysis of quantum measurement led him to his concept of a (quantum) “phenomenon,” referring to “the observations obtained under the specified circumstances,” in the interaction between quantum objects and measuring instruments. This situation makes the terms “observation” and “measurement,” as conventionally understood, inapplicable. These terms are remnants of classical physics or still earlier history, from which classical physics inherited it. As defined here, a quantum measurement does not measure any preexisting property of the ultimate constitution of the reality responsible for quantum phenomena. An act of measurement establishes a quantum phenomenon by an interaction between the instrument and the quantum object or in the present view the ultimate constitution of the reality responsible for quantum phenomena and, at the time of measurement, also quantum objects. In the view advanced in this article, in contrast to that of Bohr, quantum objects, such as electrons or photons, are assumed to exist only at the time of measurement and not independently, a view that redefines the concept of quantum object as well. This redefinition becomes especially important in high-energy quantum regimes and quantum field theory and allows this article to define a new concept of quantum field. The article also considers, now following Bohr, the quantum measurement as the entanglement between quantum objects and measurement instruments. The argument of the article is grounded in the concept “reality without realism” (RWR), as underlying quantum measurement thus understood, and the view, the RWR view, of quantum theory defined by this concept. The RWR view places a stratum of physical reality thus designated, here the reality ultimately responsible for quantum phenomena, beyond representation or knowledge, or even conception, and defines the corresponding set of interpretations quantum mechanics or quantum field theory, such as the one assumed in this article, in which, again, not only quantum phenomena but also quantum objects are (idealizations) defined by measurement. As such, the article also offers a broadly conceived response to J. Bell’s argument “against ‘measurement’”.     

Rejection of the Light Quantum: The Dark Side of Niels Bohr

Evidence is recalled of the strong opposition of Niels Bohr, at the time of the Old Quantum Theory 1913–1925, to the Lichtquanten hypothesis of Einstein. Some episodes with H. A. Kramers, J. C. Slater, and W. Heisenberg are recollected; Bohr's changing point of view is traced back to some philosophical antecedents and to his endeavor to deduce quantum results from the Correspondence Principle. Some consequences for the future interpretation of Quantum Mechanics, specially to the Complementarity Principle, are considered.     

A critical analysis of N. Bohr's reply to the EPR argument

N. Bohr's counter-argument to EPR assumes that the complementarity principle imposes a limitation on the types of predictions permissible in quantum theory, similar to the limitation imposed on the types of measurements by the Heisenberg uncertainty relation. Since this assumption has no quantum-theoretical justification, the EPR argument cannot be refuted on the basis of the complementarity principle.     

On Bohr's response to EPR: II

In my reconstruction of Bohr's reply to the Einstein-Podolsky-Rosen argument, I pointed out that Bohr showed explicitly, within the framework of the complementarity interpretation, how a locally maximal measurement on a subsystem S₂ of a composite system S₁+S₂, consisting of two spatially separated subsystems, can make determinate both a locally maximal Boolean subalgebra for S₂ and a locally maximal Boolean subalgebra for S₁. As it stands, this response is open to an objection. In this note, I show that meeting the objection requires a modification of the complementarity thesis concerning what propositions can be taken as determinate, or what observables can be raken to have values, in a given measurement context.     

Quantum Theory and the Limits of Objectivity

Three recent arguments seek to show that the universal applicability of unitary quantum theory is inconsistent with the assumption that a well-conducted measurement always has a definite physical outcome. In this paper I restate and analyze these arguments. The import of the first two is diminished by their dependence on assumptions about the outcomes of counterfactual measurements. But the third argument establishes its intended conclusion. Even if every well-conducted quantum measurement we ever make will have a definite physical outcome, this argument should make us reconsider the objectivity of that outcome.     

Quantum cellular automata and free quantum field theory

In a series of recent papers [1–4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors.     

The Einstein–Podolsky–Rosen State Maximally Violates Bell's Inequalities

In their well-known argument against the completeness of quantum theory, Einstein, Podolsky, and Rosen (EPR) made use of a state that strictly correlates the positions and momenta of two particles. We prove the existence and uniqueness of the EPR state as a normalized, positive linear functional of the Weyl algebra for two degrees of freedom. We then show that the EPR state maximally violates Bell's inequalities.     

Solving the Measurement Problem: De Broglie--Bohm Loses Out to Everett

The quantum theory of de Broglie and Bohm solves the measurement problem, but the hypothetical corpuscles play no role in the argument. The solution finds a more natural home in the Everett interpretation.     

Improved Epstein–Glaser Renormalization in Coordinate Space I. Euclidean Framework

In a series of papers, we investigate the reformulation of Epstein–Glaser renormalization in coordinate space, both in analytic and (Hopf) algebraic terms. This first article deals with analytical aspects. Some of the (historically good) reasons for the divorces of the Epstein–Glaser method, both from mainstream quantum field theory and the mathematical literature on distributions, are made plain; and overcome.