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CRC Press eBooks

The “Hidden Variables” Approach

Bernard d’Espagnat

Published Mar 5, 2018• 1 citation
Publisher

Abstract

Any theory whatsoever which, in all circumstances, attributes definite properties to non-interacting physical objects necessarily violates some of the predictions of quantum mechanics. The very existence of the hidden variables theories should, however, prompt to have a second look at the problem. The theory necessarily implies the existence of a violent nonlocality effect which, as a matter of fact, may reasonably be considered as similar to—and even more surprising than—the nonseparability of the orthodox theory. The simultaneous existence of non-separability effects and of the principle that the velocity of propagation of interactions is finite raises nontrivial conceptual problems. One possible way to study these problems is to make use of the fact that hidden variables theories exist which reproduce correctly the verifiable predictions of quantum mechanics. For the ensembles the expectation values coincide, of course, with the observed value.

DOI
10.1201/9780429501449-14

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Comments

Bernard d’Espagnat

A view most physicists adhere to is that scientific research should keep aloof from implicit metaphysical hypotheses. This prompts most of them to make it a principle that the only "existing" physical entities are those that could somehow be observed, directly or indirectly. In quantum mechanics the assumption is made, that, with the exception of nondynamical quantities such as masses and electric charges as well as of time. All these observable quantities are described by Hermitean operators, with the help of which the quantum rules tell us all that can, or could, be observed, in any circumstances whatsoever. One basic feature of the pilot-wave theory is that the quantum mechanical predictions are exactly reproduced for any ensemble E in which the hidden variables are distributed at random. This suffices to show how difficult it is to build up tests to discriminate the two theories on the basis of their observational predictions.

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The experimentally verified violation of Bell's inequalities apparently implies that at least one of two intuitive beliefs must be false: that effects propagating at infinite velocity do not exist, and that natural phenomena occur independently of being observed. Giving up any one of these two beliefs (usually known together as Local Realism) is controversial. Many theories have been proposed to reconcile the violation of Bell's inequalities with Local Realism, but none has been fully successful. In this paper, it is recalled that any theory aimed to violate Bell's inequalities must start by giving up Boolean logic. The problem is split in two: the "soft" problem is to explain the violation of Bell's inequalities within (non-Boolean) Local Realism. The "hard" problem is to predict the time values when single particles are detected. A simple hidden variables model is introduced, which solves the soft problem. This is possible thanks to the use of vectors as the hidden variables and the operation projection, which do not hold to Boolean logic. This model reconciles the violation of Bell's inequalities with Local Realism and should end decades of controversy. Regarding the hard problem, the introduced model is as incomplete as Quantum Mechanics is. It is argued that solving the hard problem involves devising a new kind of quantum computer, which should be able to accept (non-Boolean) hidden variables as input data and replace the statistical Born's rule with a deterministic threshold condition.

arXiv:2005.10367•May 20, 2020•1 citation
Any theory whatsoever which, in all circumstances, attributes definite properties to non-interacting physical objects necessarily violates some of the predictions of quantum mechanics. The very existence of the hidden variables theories should, however, prompt to have a second look at the problem. The theory necessarily implies the existence of a violent nonlocality effect which, as a matter of fact, may reasonably be considered as similar to—and even more surprising than—the nonseparability of the orthodox theory. The simultaneous existence of non-separability effects and of the principle that the velocity of propagation of interactions is finite raises nontrivial conceptual problems. One possible way to study these problems is to make use of the fact that hidden variables theories exist which reproduce correctly the verifiable predictions of quantum mechanics. For the ensembles the expectation values coincide, of course, with the observed value.
Abstract The experimentally verified violation of Bell’s inequalities apparently implies that at least one of two beliefs, which are accepted as true in almost all scientific practice, must be false. These beliefs are: that effects propagating at infinite velocity do not exist, and that natural phenomena occur independently of being observed. Giving up any one of these two beliefs (usually known together as Local Realism) is controversial. For many years, many theories have been proposed to reconcile the violation of Bell’s inequalities with Local Realism, but none has been fully successful. In this paper, it is recalled that Bell’s inequalities are equivalent to the conditions to decide the completeness of a theory according to Boolean logic. Therefore, any theory aimed to violate Bell’s inequalities must start by giving up Boolean logic. Two problems are therefore defined: the “soft” one is to explain the violation of Bell’s inequalities without violating (non-Boolean) Local Realism; the “hard” one is to predict the time values when single particles are detected, in such a way that the resulting number of coincidences violates Bell’s inequalities. A simple hidden variables model is introduced, which solves the “soft” problem even in an ideal setup. This is possible thanks to the use of vectors in real space as the hidden variables and the corresponding operation (projection), which do not hold to Boolean logic. This model reconciles the violation of Bell’s inequalities with Local Realism and should end a controversy that has lasted for decades. Regarding the “hard” problem, the introduced model is as incomplete as Quantum Mechanics is. It is claimed that solving the “hard” problem requires devising a new kind of quantum computer, which should be able to accept (non-Boolean) hidden variable values as input data and to replace the statistical Born’s rule of Quantum Mechanics with a deterministic threshold condition.
A view most physicists adhere to is that scientific research should keep aloof from implicit metaphysical hypotheses. This prompts most of them to make it a principle that the only "existing" physical entities are those that could somehow be observed, directly or indirectly. In quantum mechanics the assumption is made, that, with the exception of nondynamical quantities such as masses and electric charges as well as of time. All these observable quantities are described by Hermitean operators, with the help of which the quantum rules tell us all that can, or could, be observed, in any circumstances whatsoever. One basic feature of the pilot-wave theory is that the quantum mechanical predictions are exactly reproduced for any ensemble E in which the hidden variables are distributed at random. This suffices to show how difficult it is to build up tests to discriminate the two theories on the basis of their observational predictions.
The experimentally verified violation of Bell's inequalities apparently implies that at least one of two intuitive beliefs must be false: that effects propagating at infinite velocity do not exist, and that natural phenomena occur independently of being observed. Giving up any one of these two beliefs (usually known together as Local Realism) is controversial. Many theories have been proposed to reconcile the violation of Bell's inequalities with Local Realism, but none has been fully successful. In this paper, it is recalled that any theory aimed to violate Bell's inequalities must start by giving up Boolean logic. The problem is split in two: the "soft" problem is to explain the violation of Bell's inequalities within (non-Boolean) Local Realism. The "hard" problem is to predict the time values when single particles are detected. A simple hidden variables model is introduced, which solves the soft problem. This is possible thanks to the use of vectors as the hidden variables and the operation projection, which do not hold to Boolean logic. This model reconciles the violation of Bell's inequalities with Local Realism and should end decades of controversy. Regarding the hard problem, the introduced model is as incomplete as Quantum Mechanics is. It is argued that solving the hard problem involves devising a new kind of quantum computer, which should be able to accept (non-Boolean) hidden variables as input data and replace the statistical Born's rule with a deterministic threshold condition.