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Mysteries, Puzzles, and Paradoxes in Quantum Mechanics

A minimal local extension of the quantum formalism

Thomas D. Angelidis

Published Jan 1, 1999• 1 citation
Publisher

Abstract

We propose a consistent local theory Th(g) extending the quantum formalism. As a consequence, a realistic and local (“common cause”) interpretation of the Einstein-Podolsky-Rosen-Bohm ideal experiment can now be given. The extended local theory Th(g) satisfies the Bell inequality τ. We call for an experiment to test the validity of τ∈Th(g) and submit it as a crucial test against the apparently false conjecture of nonlocality.

DOI
10.1063/1.57874

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We propose a consistent local theory Th(g) extending the quantum formalism. As a consequence, a realistic and local (“common cause”) interpretation of the Einstein-Podolsky-Rosen-Bohm ideal experiment can now be given. The extended local theory Th(g) satisfies the Bell inequality τ. We call for an experiment to test the validity of τ∈Th(g) and submit it as a crucial test against the apparently false conjecture of nonlocality.
The suggested impossibility of a consistent local extension of the quantum formalism is reviewed in the context of the Einstein–Podolsky–Rosen–Bohm (EPRB) ideal experiment. A consistent local theory Th(𝒢) extending the quantum formalism is proposed. The postulates of Th(𝒢) stipulate a finer state specification than that given by the quantum state ‖γ1,γ2≳. This describes how the spontaneous annihilation process itself breaks the spherical symmetry of the singlet state ‖γ1,γ2≳ into a pair of back-to-back photons having only axial symmetry about the direction of their motion. The theory Th(𝒢) shows that local action suffices to explain all that the quantum formalism predicts for the EPRB ideal experiment as well as some other results.
By 1935, the Copenhagen interpretation had become the orthodoxy. Einstein needed to find a situation in which it is possible in principle to acquire knowledge of the state of a quantum system without disturbing it in any way. Working with two young theorists, Boris Podolsky and Nathan Rosen, Einstein devised an extraordinarily cunning challenge based on entangled particles. We can discover the state of one particle with certainty by making measurements on its entangled partner. All we have to assume is that the particles are local: any measurement we make on one in no way affects or disturbs the other. Through the work of David Bohm and John Bell, the challenge posed by EPR became accessible to experiment, and Bell devised a simple test for all locally realistic theories. All the experiments performed to date suggest that the standard quantum formalism is correct: in any realistic interpretation, quantum particles are non-local.
Starting from the late 60's many experiments have been performed to verify the violation Bell's inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell's inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical grounds (not discussed in the present paper) and the experiment discussed below has been devised to support these theoretical arguments. We emphasize that the goal of our experiment is not to reproduce classically the EPR correlations but to prove that there exist perfectly local classical dynamical systems violating Bell's inequality.
Starting from the late 60’s many experiments have been performed to verify the violation Bell’s inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell’s inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical grounds (not discussed in the present paper) and the experiment discussed below has been devised to support these theoretical arguments. We emphasize that the goal of our experiment is not to reproduce classically the EPR correlations but to prove that there exist perfectly local classical dynamical systems violating Bell’s inequality. The conclusions of the present experiment are: no contradiction between quantum theory and locality can be deduced from the violation of Bell’s inequality. The Copenhagen interpretation of quantum theory becomes quite reasonable and not metaphyisic if interpreted at the light of the chameleon effect. One can realize quantum entanglement by classical computers. In section (7) we prove that our experiment also provides a classical analogue of the type of logical (i.e. independent of statistics) incompatibilities pointed out by Greenberger, Home and Zeilinger. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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.
This chapter begins with a review of the ideas of locality and realism which provide the basis for the Einstein–Podolsky–Rosen paradox. The general conditions defining a local, realistic theory are stated, and then used to prove Bell's theorem, which yields — for any local, realistic theory — an inequality satisfied by certain linear combinations of correlations. It is shown that this inequality is violated by quantum theory and by experiment. The chapter ends with a discussion of possible experimental loopholes and the alternative Greenberger–Horne–Zeilinger (GHZ) state, which would, in principle, make the use of statistical correlations unnecessary.