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American Journal of Physics

How bell reasoned: A reply to Griffiths

Tim Maudlin

Published Aug 19, 2011• 13 citations
Publisher

Abstract

Robert Griffiths claims that the consistent histories approach to quantum theory recovers all of the predictions of standard quantum theory and retains the principle of locality, contrary to Bell’s theorem. Griffiths locates the flaw in Bell’s reasoning in his use of standard logic. According to Griffiths, quantum theory requires us to adopt new rules for reasoning, which he calls quantum reasoning. I review the structure of the standard logical connectives and the proof that reasoning by standard logic is always valid. Griffiths’s novel logical “rule,” which is claimed to expose Bell’s error, serves rather only to obscure the fact that the theory Griffiths proposes is inconsistent and hence cannot be correct.

DOI
10.1119/1.3606476

Related papers

The Logic of Consistent Histories: A Reply to Maudlin

Robert B. Griffiths

The relationship between quantum logic, standard propositional logic, and the (consistent) histories rules for quantum reasoning is discussed. It is shown that Maudlin's claim [Am. J. Phys. 79 (2011) 954] that the histories approach is inconsistent, is incorrect. The histories approach is both internally consistent and adequate for discussing the physical situations considered by Maudlin.

arXiv:1110.0974•Oct 5, 2011•3 citations

Comment on "Nonlocality claims are inconsistent with Hilbert-space quantum mechanics"

Justo Pastor Lambare

The view exists that the Bell inequality is a mere inconsistent application of classical concepts to a well-established quantum world. In the article, ``Nonlocality claims are inconsistent with Hilbert-space quantum mechanics'' [Phys. Rev. A, 101, 022117, (2020)], Robert B. Griffiths advocates for quantum theory's locality. Although R. B. Griffiths presents valuable insights in favor of quantum mechanics' local character, he argues the Bell inequality is an inconsistent application of classical physics to quantum mechanics. We explain why a correct assessment of the Bell inequality does not in fact conflict with Griffiths's views of quantum locality and, on the contrary, it already contemplates them. Hence, Bell inequality inconsistency is not necessary for Griffiths's quantum locality to hold.

arXiv:2102.07524•Feb 15, 2021•5 citations

Consistent Histories and the Bohm Approach

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In a recent paper Griffiths claims that the consistent histories interpretation of quantum mechanics gives rise to results that contradict those obtained from the Bohm interpretation. This is in spite of the fact that both claim to provide a realist interpretation of the formalism without the need to add any new mathematical content and both always produce exactly the same probability predictions of the outcome of experiments. In constrasting the differences Griffiths argues that the consistent histories interpretation provides a more physically reasonable account of quantum phenomena. We examine this claim and show that the consistent histories approach is not without its difficulties.

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Some mostly recent theoretical and mathematical advances can be linked together to yield a new consistent interpretation of quantum mechanics. It relies upon a unique and universal interpretative rule of a logical character which is based upon Griffiths consistent historie. Some new results in semi-classical physics allow to derive classical physics from this rule, including its logical aspects, and to prove accordingly the existence of determinism within the quantum framework. Together with decoherence, this can be used to retrieve the existence of facts, despite the probabilistic character of the theory. Measurement theory can then be made entirely deductive. It is accordingly found that wave packet reduction is a logical property, whereas one can always choose to avoid using it. The practical consequences of this interpretation are most often in agreement with the Copenhagen formulation but they can be proved never to give rise to any logical inconsistency or paradox.

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The consistent histories approach was initially proposed by Robert Griffiths in 1984. Roland Omnes then developed a more mathematically rigorous version based on the rules of classical probability and logic. In the consistent histories terminology, each projective decomposition defines a framework, which is, in essence, a context for discussing the system. As Griffith describes it: In quantum mechanics, each Boolean event algebra constitutes what is in effect a “language” out of which one can construct a quantum description of some physical system. A crucial and distinctive feature of the consistent histories approach is the single framework rule , which provides guidance for quantum reasoning. From the perspective of consistent histories, the emergence of classical physics from the quantum level is linked to the suppression of interference, so that the normal rules of probability apply.

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Classicality and Bell’s theorem

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Abstract A widespread view among physicists is that Bell’s theorem rests on an implicit assumption of “classicality,” in addition to locality. According to this understanding, the violation of Bell’s inequalities poses no challenge to locality, but simply reinforces the fact that quantum mechanics is not classical. The paper provides a critical analysis of this view. First we characterize the notion of classicality in probabilistic terms. We argue that classicality thus construed has nothing to do with the validity of classical physics, nor of classical probability theory, contrary to what many believe. At the same time, we show that the probabilistic notion of classicality is not an additional premise of Bell’s theorem, but a mathematical corollary of locality in conjunction with the standard auxiliary assumptions of Bell. Accordingly, any theory that claims to get around the derivation of Bell’s inequalities by giving up classicality, in fact has to give up one of those standard assumptions. As an illustration of this, we look at two recent interpretations of quantum mechanics, Reinhard Werner’s operational quantum mechanics and Robert Griffiths’ consistent histories approach, that are claimed to be local and non-classical, and identify which of the standard assumptions of Bell’s theorem each of them is forced to give up. We claim that while in operational quantum mechanics the Common Cause Principle is violated, the consistent histories approach is conspiratorial. Finally, we relate these two options to the idea of realism, a notion that is also often identified as an implicit assumption of Bell’s theorem.

European Journal for Philosophy of Science•Sep 1, 2023•0 citations
Robert Griffiths claims that the consistent histories approach to quantum theory recovers all of the predictions of standard quantum theory and retains the principle of locality, contrary to Bell’s theorem. Griffiths locates the flaw in Bell’s reasoning in his use of standard logic. According to Griffiths, quantum theory requires us to adopt new rules for reasoning, which he calls quantum reasoning. I review the structure of the standard logical connectives and the proof that reasoning by standard logic is always valid. Griffiths’s novel logical “rule,” which is claimed to expose Bell’s error, serves rather only to obscure the fact that the theory Griffiths proposes is inconsistent and hence cannot be correct.
The view exists that the Bell inequality is a mere inconsistent application of classical concepts to a well-established quantum world. In the article, ``Nonlocality claims are inconsistent with Hilbert-space quantum mechanics'' [Phys. Rev. A, 101, 022117, (2020)], Robert B. Griffiths advocates for quantum theory's locality. Although R. B. Griffiths presents valuable insights in favor of quantum mechanics' local character, he argues the Bell inequality is an inconsistent application of classical physics to quantum mechanics. We explain why a correct assessment of the Bell inequality does not in fact conflict with Griffiths's views of quantum locality and, on the contrary, it already contemplates them. Hence, Bell inequality inconsistency is not necessary for Griffiths's quantum locality to hold.
In a recent paper Griffiths claims that the consistent histories interpretation of quantum mechanics gives rise to results that contradict those obtained from the Bohm interpretation. This is in spite of the fact that both claim to provide a realist interpretation of the formalism without the need to add any new mathematical content and both always produce exactly the same probability predictions of the outcome of experiments. In constrasting the differences Griffiths argues that the consistent histories interpretation provides a more physically reasonable account of quantum phenomena. We examine this claim and show that the consistent histories approach is not without its difficulties.
Some mostly recent theoretical and mathematical advances can be linked together to yield a new consistent interpretation of quantum mechanics. It relies upon a unique and universal interpretative rule of a logical character which is based upon Griffiths consistent historie. Some new results in semi-classical physics allow to derive classical physics from this rule, including its logical aspects, and to prove accordingly the existence of determinism within the quantum framework. Together with decoherence, this can be used to retrieve the existence of facts, despite the probabilistic character of the theory. Measurement theory can then be made entirely deductive. It is accordingly found that wave packet reduction is a logical property, whereas one can always choose to avoid using it. The practical consequences of this interpretation are most often in agreement with the Copenhagen formulation but they can be proved never to give rise to any logical inconsistency or paradox.
The consistent histories approach was initially proposed by Robert Griffiths in 1984. Roland Omnes then developed a more mathematically rigorous version based on the rules of classical probability and logic. In the consistent histories terminology, each projective decomposition defines a framework, which is, in essence, a context for discussing the system. As Griffith describes it: In quantum mechanics, each Boolean event algebra constitutes what is in effect a “language” out of which one can construct a quantum description of some physical system. A crucial and distinctive feature of the consistent histories approach is the single framework rule , which provides guidance for quantum reasoning. From the perspective of consistent histories, the emergence of classical physics from the quantum level is linked to the suppression of interference, so that the normal rules of probability apply.
Abstract A widespread view among physicists is that Bell’s theorem rests on an implicit assumption of “classicality,” in addition to locality. According to this understanding, the violation of Bell’s inequalities poses no challenge to locality, but simply reinforces the fact that quantum mechanics is not classical. The paper provides a critical analysis of this view. First we characterize the notion of classicality in probabilistic terms. We argue that classicality thus construed has nothing to do with the validity of classical physics, nor of classical probability theory, contrary to what many believe. At the same time, we show that the probabilistic notion of classicality is not an additional premise of Bell’s theorem, but a mathematical corollary of locality in conjunction with the standard auxiliary assumptions of Bell. Accordingly, any theory that claims to get around the derivation of Bell’s inequalities by giving up classicality, in fact has to give up one of those standard assumptions. As an illustration of this, we look at two recent interpretations of quantum mechanics, Reinhard Werner’s operational quantum mechanics and Robert Griffiths’ consistent histories approach, that are claimed to be local and non-classical, and identify which of the standard assumptions of Bell’s theorem each of them is forced to give up. We claim that while in operational quantum mechanics the Common Cause Principle is violated, the consistent histories approach is conspiratorial. Finally, we relate these two options to the idea of realism, a notion that is also often identified as an implicit assumption of Bell’s theorem.