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Entanglement & MWI of Quantum Mechanics

Michele Caponigro

Published Nov 23, 2017• 0 citations
OpenAlex

Abstract

According to Many Worlds Interpretation (MWI, Everett, 1957), the terms of an entangled state describe something that really exist; the state does not just refer to the probabilities of results that would be obtained if measurement takes place. We argue in this essay from conceptual point of view the relationship between quantum entanglement and and MWI. The debate is still open and we suggest that the objective Bayesian interpretation of quantum probability could be an interesting approach to solve this fundamental question.

Related papers

Are there really many worlds in the "Many-worlds interpretation" of Quantum Mechanics?

Daniel Parrochia

Since the 1970s, the Everett-Wheeler many-worlds interpretation (MWI) of Quantum Mechanics (1955) has been much in the news. One wonders about the worlds in question, their branches, their splittings, their number. It is most often ignored that this language is not that of Everett, whom Wheeler very quickly stopped supporting. Moreover, for some interpreters, the real meaning of Everett ideas is not the coexistence of many worlds, but the existence of a single quantum one. In this context, what should we think of attempts to verify Everett thesis? What about the connexion between MWI and the cosmological multiverse? How to understand the links between the quantum world and the classical one? This article tries to answer some of these questions.

arXiv:2001.03771•Jan 11, 2020•0 citations

The Quantum Many-Worlds Interpretation, Simply Told

Brian C. Odom

The many-worlds interpretation (MWI) of quantum mechanics poses a simple question. What would reality look like if everything evolved in time according to the same quantum equations? There is an attractive consistency to treating microscopic objects, measuring devices, and observers all on the same footing, but do the predictions match our observations? Here, we build a model for a bolometer detector making a which-path measurement in an atom interferometer. We discuss the MWI claim that, while both measurement outcomes occur in each experimental iteration, an observer will experience only one outcome or the other, with a probability consistent with experiment. Finally, we discuss how MWI does not have action at a distance. This article is written to be accessible to anyone with an undergraduate course in quantum mechanics.

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Problems with Probability in Everett's Interpretation of Quantum Mechanics

Casey Blood

In the many-worlds interpretations (MWIs) of Everett and others, if I am the observer, there are several versions of me but no version is singled out as the one corresponding to my perceptions. However, it can be shown that the probability law implies one version must be singled out. Thus MWIs do not provide a sufficient basis for probability. If we are to have an acceptable description of the physical universe, MWIs must be supplemented by some mechanism, such as hidden variables or collapse, that singles out one version of the observer as the perceiving version.

arXiv:0901.0952•Jan 8, 2009•3 citations

Reviews of quantum foundations

L. E. Ballentine

I enjoyed the February 2019 issue of Physics Today on Reviews of Modern Physics at 90 but was disappointed with the article “Quantum foundations” by David DiVincenzo and Christopher Fuchs (page 50). The most useful part of that article was the reference list, which shows RMP’s diversity of papers on the subject. My 1970 article on the statistical-ensemble interpretation of quantum mechanics (QM),11. L. E. Ballentine, Rev. Mod. Phys. 42, 358 (1970). https://doi.org/10.1103/RevModPhys.42.358 which people tell me has encouraged them to continue research on quantum foundations (QF), was omitted from the list.Unfortunately, DiVincenzo and Fuchs continue to mystify measurement in QM, as if it were some deep philosophical concept that must be treated before QM has even been fully formulated. They assert that “physicists and philosophers are still debating what a ‘measurement’ really means.” What is important for QF is not the meaning of the word but an understanding of the physical process. The authors do not cite any of the published papers that provide such an understanding. And they give too much attention to two marginal interpretations: the many-worlds interpretation (MWI) and quantum Bayesianism (QBism).In QM, a measurement of an observable should yield an eigenvalue of the observable. If the initial state of the measured object is a superposition of eigenstates corresponding to different eigenvalues, then the interaction of the measurement apparatus with the object will lead to a final state of the whole system—measured object plus apparatus—that is a superposition of different measurement results. The squared amplitude of each term yields the probability of obtaining that result in an individual measurement. That statistical prediction, the Born rule, is common to the Copenhagen and statistical-ensemble interpretations. But the MWI takes a radically different turn. It postulates that the universe branches into several parallel worlds, with each term of the superposition corresponding to the unique result of the measurement in one branch world.The usual role of an interpretation of QM is to begin with the established mathematical formalism and provide an intuitively comprehensible idea of the physical process that the math describes. The MWI does not do that. Instead, it adds a mysterious process of world-splitting, a strange new cosmology that is alien to the mathematics of QM and not really an interpretation of QM at all. A typical QM measurement, such as that of a spin component in the Stern–Gerlach experiment, is a local and very low energy event. It is not credible that the measurement could have the huge cosmological effect of bifurcating the universe.When I first heard of the world-splitting assumed in the MWI, I went back to Hugh Everett’s paper22. H. Everett III, Rev. Mod. Phys. 29, 454 (1957). https://doi.org/10.1103/RevModPhys.29.454 to see if he had really said anything so absurd. I found that he had not said so explicitly, but he sometimes used words that could be interpreted in more than one way. The MWI is a possible interpretation of them, but not the most natural one, so I thought. And Everett’s framework still has value even without resorting to the MWI’s world-splitting. His concept of a “relative state” is useful, for instance, and he is correct in rejecting the notion of the quantum state “collapsing” after a measurement.QBism begins with the assumption that all kinds of probability can be regarded as subjective Bayesian probabilities. That assumption can be maintained only by ignoring the literature on interpretations of probability, from which it is clear that several different kinds—or interpretations—of probability exist. DiVincenzo and Fuchs may have ignored the classic philosophical writings on the subject because they were written by philosophers for philosophers and so do not address the needs of physicists.I have published a paper on the foundations of probability theory, written from the point of view of a quantum physicist.33. L. E. Ballentine, Found. Phys. 46, 973 (2016). https://doi.org/10.1007/s10701-016-9991-0 I classify the main kinds or interpretations of probability into three groups: inferential probability, of which Bayesian theory is an example; frequency or ensemble probability, commonly used in Gibbsian statistical mechanics and in QM; and propensity theory. Propensity, a degree of causality that is weaker than determinism, is not merely another interpretation of probability. Its mathematical theory must also differ from that of probability theory, as Paul Humphreys showed44. P. Humphreys, Philos. Rev. 94, 557 (1985). https://doi.org/10.2307/2185246 in 1985. Although the axioms of propensity33. L. E. Ballentine, Found. Phys. 46, 973 (2016). https://doi.org/10.1007/s10701-016-9991-0 differ from those of probability, the two axiom sets overlap. Both support the law of large numbers, so propensity theory is compatible with the most useful part of the frequency interpretation of probability.In general, QM states do not determine the results of a measurement, only the probabilities of the possible results. That a state’s influence on the results is not deterministic suggests strongly that the quantum probabilities given by the Born rule should be interpreted as propensities. They refer objectively to the physical system and its environment, not to any agent’s knowledge, so they are not naturally interpreted as subjective Bayesian probabilities.Interpretations of probability may differ not only in philosophy but also in substance. As I discuss in reference 33. L. E. Ballentine, Found. Phys. 46, 973 (2016). https://doi.org/10.1007/s10701-016-9991-0, John Bell’s theorem illustrates how local hidden-variable theories are incompatible with QM. E. T. Jaynes was a well-known supporter of the Bayesian theory of probability. In 1989 he repeated Bell’s derivation of inequality but carefully treated all instances of probability as Bayesian. He found that the derivation could not be completed without invoking an extra assumption that was not justifiable in the Bayesian theory. Bell’s theorem involves questions about causality, so it is natural to use propensity theory to treat it. That method is successful in deriving Bell’s inequality.33. L. E. Ballentine, Found. Phys. 46, 973 (2016). https://doi.org/10.1007/s10701-016-9991-0Not all probabilities occurring in QM can be treated as subjective Bayesian probabilities. That limitation disqualifies QBism, a Bayesian-based theory, as an interpretation of QM that can succeed in quantum foundations. The initial assumption of QBism is not valid.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. L. E. Ballentine, Rev. Mod. Phys. 42, 358 (1970). https://doi.org/10.1103/RevModPhys.42.358, Google ScholarCrossref2. H. Everett III, Rev. Mod. Phys. 29, 454 (1957). https://doi.org/10.1103/RevModPhys.29.454, Google ScholarCrossref3. L. E. Ballentine, Found. Phys. 46, 973 (2016). https://doi.org/10.1007/s10701-016-9991-0, Google ScholarCrossref4. P. Humphreys, Philos. Rev. 94, 557 (1985). https://doi.org/10.2307/2185246, Google ScholarCrossref© 2020 American Institute of Physics.

Physics Today•Jun 1, 2020•1 citation

QUANTUM ENTANGLED STATES

Zheng Y. Zhou

Entanglement is one of the intriguing characteristics of quantum mechanics. We review the history of quantum entangled states and the main advances in the measure of entanglement, the distinguishing of entangled states from separable states and the classification of entangled states.

•Jan 1, 2000•2 citations

Many Worlds?

Simon W. Saunders

Abstract What does realism about the quantum state imply? What follows when quantum theory is applied without restriction, if need be, to the whole universe? These are the questions which are debated in this book. All the chapters start from the point of realism, and based on the need, or the aspiration, for a theory that unites micro- and macroworlds, at least in principle. But the further claim argued by some is that if you allow the Schrödinger equation unrestricted application, supposing the quantum state to be something physically real, then this universe is one of countlessly many others, constantly branching in time, all of which are real. The result is the many worlds theory, also known as the Everett interpretation of quantum mechanics. The contrary claim sees this picture of many worlds as in no sense inherent in quantum mechanics, even when the latter is allowed unrestricted scope and even given that the quantum state itself is something physically real. For this picture of branching worlds fails to make physical sense, let alone common sense, even on its own terms. The status of these worlds, what they are made of, is never adequately explained. Ordinary ideas about time and identity over time become hopelessly compromised. The concept of probability itself is brought into question. This picture of many branching worlds is inchoate, it is a vision, an error. There are realist alternatives to many worlds, some even that preserve the Schrödinger equation unchanged. Twenty chapters, accompanied by commentaries and discussions, examine these claims and counterclaims in depth. They focus first on the question of ontology, the existence of worlds, second on the interpretation of probability, and third on alternatives or additions to many worlds. The introduction offers a helpful guide to the arguments for the Everett interpretation, particularly as they have been formulated in the last two decades.

•Jun 24, 2010•352 citations
According to Many Worlds Interpretation (MWI, Everett, 1957), the terms of an entangled state describe something that really exist; the state does not just refer to the probabilities of results that would be obtained if measurement takes place. We argue in this essay from conceptual point of view the relationship between quantum entanglement and and MWI. The debate is still open and we suggest that the objective Bayesian interpretation of quantum probability could be an interesting approach to solve this fundamental question.
Since the 1970s, the Everett-Wheeler many-worlds interpretation (MWI) of Quantum Mechanics (1955) has been much in the news. One wonders about the worlds in question, their branches, their splittings, their number. It is most often ignored that this language is not that of Everett, whom Wheeler very quickly stopped supporting. Moreover, for some interpreters, the real meaning of Everett ideas is not the coexistence of many worlds, but the existence of a single quantum one. In this context, what should we think of attempts to verify Everett thesis? What about the connexion between MWI and the cosmological multiverse? How to understand the links between the quantum world and the classical one? This article tries to answer some of these questions.
The many-worlds interpretation (MWI) of quantum mechanics poses a simple question. What would reality look like if everything evolved in time according to the same quantum equations? There is an attractive consistency to treating microscopic objects, measuring devices, and observers all on the same footing, but do the predictions match our observations? Here, we build a model for a bolometer detector making a which-path measurement in an atom interferometer. We discuss the MWI claim that, while both measurement outcomes occur in each experimental iteration, an observer will experience only one outcome or the other, with a probability consistent with experiment. Finally, we discuss how MWI does not have action at a distance. This article is written to be accessible to anyone with an undergraduate course in quantum mechanics.
In the many-worlds interpretations (MWIs) of Everett and others, if I am the observer, there are several versions of me but no version is singled out as the one corresponding to my perceptions. However, it can be shown that the probability law implies one version must be singled out. Thus MWIs do not provide a sufficient basis for probability. If we are to have an acceptable description of the physical universe, MWIs must be supplemented by some mechanism, such as hidden variables or collapse, that singles out one version of the observer as the perceiving version.
I enjoyed the February 2019 issue of Physics Today on Reviews of Modern Physics at 90 but was disappointed with the article “Quantum foundations” by David DiVincenzo and Christopher Fuchs (page 50). The most useful part of that article was the reference list, which shows RMP’s diversity of papers on the subject. My 1970 article on the statistical-ensemble interpretation of quantum mechanics (QM),11. L. E. Ballentine, Rev. Mod. Phys. 42, 358 (1970). https://doi.org/10.1103/RevModPhys.42.358 which people tell me has encouraged them to continue research on quantum foundations (QF), was omitted from the list.Unfortunately, DiVincenzo and Fuchs continue to mystify measurement in QM, as if it were some deep philosophical concept that must be treated before QM has even been fully formulated. They assert that “physicists and philosophers are still debating what a ‘measurement’ really means.” What is important for QF is not the meaning of the word but an understanding of the physical process. The authors do not cite any of the published papers that provide such an understanding. And they give too much attention to two marginal interpretations: the many-worlds interpretation (MWI) and quantum Bayesianism (QBism).In QM, a measurement of an observable should yield an eigenvalue of the observable. If the initial state of the measured object is a superposition of eigenstates corresponding to different eigenvalues, then the interaction of the measurement apparatus with the object will lead to a final state of the whole system—measured object plus apparatus—that is a superposition of different measurement results. The squared amplitude of each term yields the probability of obtaining that result in an individual measurement. That statistical prediction, the Born rule, is common to the Copenhagen and statistical-ensemble interpretations. But the MWI takes a radically different turn. It postulates that the universe branches into several parallel worlds, with each term of the superposition corresponding to the unique result of the measurement in one branch world.The usual role of an interpretation of QM is to begin with the established mathematical formalism and provide an intuitively comprehensible idea of the physical process that the math describes. The MWI does not do that. Instead, it adds a mysterious process of world-splitting, a strange new cosmology that is alien to the mathematics of QM and not really an interpretation of QM at all. A typical QM measurement, such as that of a spin component in the Stern–Gerlach experiment, is a local and very low energy event. It is not credible that the measurement could have the huge cosmological effect of bifurcating the universe.When I first heard of the world-splitting assumed in the MWI, I went back to Hugh Everett’s paper22. H. Everett III, Rev. Mod. Phys. 29, 454 (1957). https://doi.org/10.1103/RevModPhys.29.454 to see if he had really said anything so absurd. I found that he had not said so explicitly, but he sometimes used words that could be interpreted in more than one way. The MWI is a possible interpretation of them, but not the most natural one, so I thought. And Everett’s framework still has value even without resorting to the MWI’s world-splitting. His concept of a “relative state” is useful, for instance, and he is correct in rejecting the notion of the quantum state “collapsing” after a measurement.QBism begins with the assumption that all kinds of probability can be regarded as subjective Bayesian probabilities. That assumption can be maintained only by ignoring the literature on interpretations of probability, from which it is clear that several different kinds—or interpretations—of probability exist. DiVincenzo and Fuchs may have ignored the classic philosophical writings on the subject because they were written by philosophers for philosophers and so do not address the needs of physicists.I have published a paper on the foundations of probability theory, written from the point of view of a quantum physicist.33. L. E. Ballentine, Found. Phys. 46, 973 (2016). https://doi.org/10.1007/s10701-016-9991-0 I classify the main kinds or interpretations of probability into three groups: inferential probability, of which Bayesian theory is an example; frequency or ensemble probability, commonly used in Gibbsian statistical mechanics and in QM; and propensity theory. Propensity, a degree of causality that is weaker than determinism, is not merely another interpretation of probability. Its mathematical theory must also differ from that of probability theory, as Paul Humphreys showed44. P. Humphreys, Philos. Rev. 94, 557 (1985). https://doi.org/10.2307/2185246 in 1985. Although the axioms of propensity33. L. E. Ballentine, Found. Phys. 46, 973 (2016). https://doi.org/10.1007/s10701-016-9991-0 differ from those of probability, the two axiom sets overlap. Both support the law of large numbers, so propensity theory is compatible with the most useful part of the frequency interpretation of probability.In general, QM states do not determine the results of a measurement, only the probabilities of the possible results. That a state’s influence on the results is not deterministic suggests strongly that the quantum probabilities given by the Born rule should be interpreted as propensities. They refer objectively to the physical system and its environment, not to any agent’s knowledge, so they are not naturally interpreted as subjective Bayesian probabilities.Interpretations of probability may differ not only in philosophy but also in substance. As I discuss in reference 33. L. E. Ballentine, Found. Phys. 46, 973 (2016). https://doi.org/10.1007/s10701-016-9991-0, John Bell’s theorem illustrates how local hidden-variable theories are incompatible with QM. E. T. Jaynes was a well-known supporter of the Bayesian theory of probability. In 1989 he repeated Bell’s derivation of inequality but carefully treated all instances of probability as Bayesian. He found that the derivation could not be completed without invoking an extra assumption that was not justifiable in the Bayesian theory. Bell’s theorem involves questions about causality, so it is natural to use propensity theory to treat it. That method is successful in deriving Bell’s inequality.33. L. E. Ballentine, Found. Phys. 46, 973 (2016). https://doi.org/10.1007/s10701-016-9991-0Not all probabilities occurring in QM can be treated as subjective Bayesian probabilities. That limitation disqualifies QBism, a Bayesian-based theory, as an interpretation of QM that can succeed in quantum foundations. The initial assumption of QBism is not valid.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. L. E. Ballentine, Rev. Mod. Phys. 42, 358 (1970). https://doi.org/10.1103/RevModPhys.42.358, Google ScholarCrossref2. H. Everett III, Rev. Mod. Phys. 29, 454 (1957). https://doi.org/10.1103/RevModPhys.29.454, Google ScholarCrossref3. L. E. Ballentine, Found. Phys. 46, 973 (2016). https://doi.org/10.1007/s10701-016-9991-0, Google ScholarCrossref4. P. Humphreys, Philos. Rev. 94, 557 (1985). https://doi.org/10.2307/2185246, Google ScholarCrossref© 2020 American Institute of Physics.
Abstract What does realism about the quantum state imply? What follows when quantum theory is applied without restriction, if need be, to the whole universe? These are the questions which are debated in this book. All the chapters start from the point of realism, and based on the need, or the aspiration, for a theory that unites micro- and macroworlds, at least in principle. But the further claim argued by some is that if you allow the Schrödinger equation unrestricted application, supposing the quantum state to be something physically real, then this universe is one of countlessly many others, constantly branching in time, all of which are real. The result is the many worlds theory, also known as the Everett interpretation of quantum mechanics. The contrary claim sees this picture of many worlds as in no sense inherent in quantum mechanics, even when the latter is allowed unrestricted scope and even given that the quantum state itself is something physically real. For this picture of branching worlds fails to make physical sense, let alone common sense, even on its own terms. The status of these worlds, what they are made of, is never adequately explained. Ordinary ideas about time and identity over time become hopelessly compromised. The concept of probability itself is brought into question. This picture of many branching worlds is inchoate, it is a vision, an error. There are realist alternatives to many worlds, some even that preserve the Schrödinger equation unchanged. Twenty chapters, accompanied by commentaries and discussions, examine these claims and counterclaims in depth. They focus first on the question of ontology, the existence of worlds, second on the interpretation of probability, and third on alternatives or additions to many worlds. The introduction offers a helpful guide to the arguments for the Everett interpretation, particularly as they have been formulated in the last two decades.