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arXiv:quant-ph/0202151 · Journal of Optics B Quantum and Semiclassical Optics

A realistic view of the canonical Einstein$ndash$Podolsky$ndash$Rosen$ndash$Bohm experiment based on quantum theory and its consequences

Boon Leong Lan

Published Aug 1, 2002• 5 citations
arXivHTMLPDF

Abstract

A realistic view of the Einstein–Podolsky–Rosen–Bohm experiment with spins based on quantum theory is presented. This view implies that there is no action at a distance. It also implies that the measurement result A ( B ) for particle 1 (2) depends on both magnet angles, and hence the probability of obtaining the result A ( B ) also depends on both magnet angles. In the light of these realistic implications, it is clear that what is wrong at least with local realistic theory is not the locality or no-action-at-a-distance assumption itself but rather the formal implementation of that assumption.

DOI
10.1088/1464-4266/4/4/324

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A realistic view of the canonical EinsteinndashndashndashPodolskyndashndashndashRosenndashndashndashBohm experiment based on quantum theory and its consequences
A realistic view of the Einstein–Podolsky–Rosen–Bohm experiment with spins based on quantum theory is presented. This view implies that there is no action at a distance. It also implies that the measurement result A ( B ) for particle 1 (2) depends on both magnet angles, and hence the probability of obtaining the result A ( B ) also depends on both magnet angles. In the light of these realistic implications, it is clear that what is wrong at least with local realistic theory is not the locality or no-action-at-a-distance assumption itself but rather the formal implementation of that assumption.
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
According to the orthodox interpretation of quantum mechanics (Bohr being its leading voice), the attributes of a physical object (position, momentum, spin, etc.) can be assigned only when they have been measured. Einstein advocated the local realist viewpoint that an object had definite attributes whether they had been measured or not. The Copenhagen school view that measurement actually produces an object’s property would imply that the measurement of one part of an entangled quantum state can instantaneously fix the value of another part, no matter how far the two parts have been separated. Einstein, Podolsky, and Rosen devised a thought experiment to shine a light on this “spooky action-at-a-distance” feature; its discussion and debate have illuminated the meaning of quantum mechanics (QM). It led later to Bell’s theorem showing that these seemingly philosophical questions can lead to observable results. The experimental vindication of the orthodox theory has sharpened our appreciation of the nonlocal features of quantum mechanics. Nevertheless, the counter-intuitive QM picture of objective reality still troubles many, leaving one to wonder whether quantum mechanics is ultimately a complete theory.
It is shown that the quantum-theoretical descriptions of idealized Stern–Gerlach and Einstein–Podolsky–Rosen–Bohm experiments result from a logical inference treatment of robust experiments, without relying on concepts of quantum theory. For concreteness, the derivation is given for the case that the Stern–Gerlach magnet deflects the beam in three different directions, which in quantum theory corresponds to a description in terms of spin-1 particles. The logical inference description of the Einstein–Podolsky–Rosen–Bohm experiment is shown to contain the quantum theoretical description as a particular case.
In their celebrated paper titled Can quantum mechanical description of physical reality be considered complete?, Einstein, Podolsky and Rosen (EPR) showed for the first time the existence of `Spooky action-at-a-distance'. Though the result of their paper is unquestionable, but the conclusion of the same became sensational because of its challenge to quantum mechanical formalism whether it's complete or not in describing the physical reality of Nature. Bohr's physical and philosophical reply to that conclusion justified the completeness of quantum mechanics. Here, a simple algebraic way is presented for the results of these two classic papers in such a way that the actual reason behind why quantum world necessarily exhibits the action-at-a-distance and how Bohr defended against the incompleteness of the quantum formalism will become clear.This approach naturally reveals what physical assumption of EPR went wrong while considering the entangled quantum system and also provides the missing mathematical argument in Bohr's reply.
Abstract The Einstein‐Podolsky‐Rosen “gedanken‐experiment” does not imply non‐local interactions or an “action‐at‐a‐distance”. Contrary, the EPR proves the measurements at one particle does not have influences at canonical variables of the other particles if the quantum‐mechanical commutation relations are true. But, the EPR implices correlations between the particles which come in by “subjective knowledge”. These correlations are a priori informations about the relative motion or, complementarily, about the motion of the center of mass. The impression of an action‐at‐a‐distance is produced by the use of usual particle coordinates in the EPR‐arrangements. The discussion of the Einstein‐Podolsky‐Rosen “gedanken‐experiment” (EPR) has been going on over fifty years. EINSTEIN, PODOLSKY, and ROSEN formulated their famous paradox in 1935, and in the discussion between N. BOHR (1935, 1949) and A. EINSTEIN (1936, 1948); A. EINSTEIN (1948) made his point that the EPR implied an “action‐at‐a‐distance” for quantum‐mechanical particles (without obvious classical interactions). His argument is the starting point for the recent discussion about EPR and causality (see A. Aspect, 1981).