Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics Today

Readers offer their own magic moments with John Bell

Michael Nauenberg

Published Nov 30, 2015• 3 citations
Publisher

Abstract

I read with pleasure Reinhold Bertlmann’s article about remembrances of John Bell and his contributions to physics. Bell is famous for establishing an inequality between the prediction of quantum mechanics and local hidden-variable theories, and Bertlmann wrote that “so far, all experiments looking for violations in Bell inequalities have found them, so we have to conclude, along with John, that nature contains a nonlocality in its structure.” But that conclusion is valid only in the context of Bell’s conviction that classical “realism is the proper position for a scientist.”Experiments have revealed that the nature of reality in the quantum world is different from our experience in the classical world.11. A. Aspect, Nature 446, 866 (2007). https://doi.org/10.1038/446866a Properties like the direction of an electron spin and its position and momentum remain undetermined until a measurement has been performed,22. W. Heisenberg, Physics and Philosophy: The Revolution in Modern Science, Prometheus Books (1999), p. 44. 9781573926942 but the colors of Bertlmann’s socks are fixed after he puts them on. Albert Einstein’s famous quotation, “spooky action at a distance,”33. A. Einstein, M. Born, H. Born, The Born–Einstein Letters: Correspondence Between Albert Einstein and Max and Hedwig Born from 1916–1955, I. Born, trans., MacMillan (1971), p. 159. that appears in Bertlmann’s amusing cartoon, is also misleading, because quantum correlations for entangled electron or photon pairs also occur at atomic distance of separation—for example, in the ground state of the helium atom. What would be spooky is if those correlations were altered when the entangled pair moved apart without further interactions, but experiments have shown that this is not the case.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. A. Aspect, Nature 446, 866 (2007). https://doi.org/10.1038/446866a, Google ScholarCrossref2. W. Heisenberg, Physics and Philosophy: The Revolution in Modern Science, Prometheus Books (1999), p. 44. 9781573926942, Google Scholar3. A. Einstein, M. Born, H. Born, The Born–Einstein Letters: Correspondence Between Albert Einstein and Max and Hedwig Born from 1916–1955, I. Born, trans., MacMillan (1971), p. 159. Google Scholar© 2015 American Institute of Physics.

DOI
10.1063/pt.3.2997

Related papers

Readers offer their own magic moments with John Bell

Robert B. Griffiths

Reinhold Bertlmann’s article “Magic moments with John Bell” was a pleasure to read. I add a note concerning some later developments that are significant for understanding the implications of Bell’s quantum foundations work.The crucial point is that under the Bell locality hypothesis for a joint measurement as given in the article,E(a,b)=∫dλρ(λ)A(a,λ)·B(b,λ)the quantity λ that represents the hidden variable(s) is a classical, not a quantum, object, and ρ(λ) is a classical probability distribution. Such expressions only make sense in the context of quantum theory when the operators of interest commute with each other, but that is not the case when this expression is used to derive a Bell inequality.Many years ago Arthur Fine pointed out that hidden variables and Bell inequalities were “imposing requirements to make well defined precisely those probability distributions for noncommuting observables whose rejection is the very essence of quantum mechanics.”11. A. Fine, Phys. Rev. Lett. 48, 291 (1982). https://doi.org/10.1103/PhysRevLett.48.291 Thus the real issue is not one of locality but, instead, the proper use of probabilities in quantum theory.Fine’s point has been confirmed by the later development of a fully consistent way of introducing probabilities in quantum mechanics.22. R. B. Griffiths, Stanford Encyclopedia of Philosophy (2014); http://plato.stanford.edu/entries/qm-consistent-histories. That approach has shown that when quantum mechanics is interpreted using subspaces of the Hilbert space rather than classical hidden variables to represent physical properties, it is local: There are no ghostly nonlocal influences.We cannot know how Bell would have responded to those new developments, which only came to full fruition after his untimely death. The reader willing to dig into my somewhat tedious discussion33. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press (2002), sec. 23.4. of the Einstein-Podolsky-Rosen and Bohm situation will find an explicit proof that a measurement by Alice has not the slightest effect on the spin on Bob’s side. More recent is a general argument that quantum mechanics satisfies a principle of Einstein locality: What is done to system A has no effect on system B as long as there is no interaction between the two.44. R. B. Griffiths, Found. Phys. 41, 705 (2011). https://doi.org/10.1007/s10701-010-9512-5Those proofs of quantum locality begin by taking very seriously John von Neumann’s proposal that quantum properties correspond to Hilbert subspaces, whose projectors do not, in general, commute with one another.55. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton U. Press (1955), sec. 3.5. Bell, though, assumed that such properties can be represented by classical hidden variables, which always commute. Thus Bell’s theorem teaches that if one uses classical hidden variables in place of quantum properties, the result will contradict quantum theory and disagree with experiment. Indeed, while Bell started off by pointing out deficiencies in von Neumann’s argument against hidden variables, the end result of his work is an even better and much more conclusive argument, backed by experiment, for rejecting classical hidden variables.REFERENCESSection:ChooseTop of pageREFERENCES <<1. A. Fine, Phys. Rev. Lett. 48, 291 (1982). https://doi.org/10.1103/PhysRevLett.48.291, Google ScholarCrossref2. R. B. Griffiths, Stanford Encyclopedia of Philosophy (2014); http://plato.stanford.edu/entries/qm-consistent-histories. Google Scholar3. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press (2002), sec. 23.4. Google Scholar4. R. B. Griffiths, Found. Phys. 41, 705 (2011). https://doi.org/10.1007/s10701-010-9512-5, Google ScholarCrossref5. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton U. Press (1955), sec. 3.5. Google Scholar© 2015 American Institute of Physics.

Physics Today•Nov 30, 2015•0 citations

Readers offer their own magic moments with John Bell

Reinhold A. Bertlmann

Bertlmann replies: I am pleased at the positive response of readers to my “Magic moments with John Bell.”I enjoyed very much the contributions of Charles Clement and Kerson Huang, who reported about their own “magic moments” with Bell. Their amusing anecdotes help complete the portrait of Bell, who was an outstanding personality indeed.I found the comments of Nicholas Bykovetz very interesting. I remember that Bell strongly sympathized with Lorentzian relativity and Fitzgerald contraction. In my opinion, the ether-based Lorentzian view of relativity is just closer to the heart of the realist that Bell was. I think it was the acceptance of Lorentz’s conception on relativity rather than Einstein’s that led Bell to the correct answer that a string between two equally accelerated spaceships will break, what is known as Bell’s spaceship paradox.11. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd ed., Cambridge U. Press (2004), p. 67. In Bell’s quote “An ‘ether’ would be the cheapest solution. But the unobservability of this ether would be disturbing,” he did not mean for the “cheapest solution” to be a derogatory phrase, but rather to mean “simple.” The “unobservability of this ether” disturbed Bell, since why should the laws of physics conspire to prevent us from identifying the ether experimentally.Regarding Robert Griffiths’s arguments, I agree with some parts but strongly disagree with others. Griffiths remarks that the specific form of the expectation value used by Bell for the joint measurement of Alice and Bob in the EPR-Bohm-Bell experiment does not make sense in the context of quantum theory with noncommuting operators. That is not the point Bell wanted to make. In his formalism, the quantum states are supplemented by hidden variables, which are governed by a classical probability distribution, in order to predetermine the measurement results.The expectation value, assigned to the local hidden-variable theory, is not applied to quantum mechanics but compared with the corresponding quantum mechanical result. Its specific form is excluded via a Bell inequality, in which a certain combination of expectation values is needed. Concentrating on the expectation value alone is not enough to distinguish local hidden variable theories from quantum mechanics; for example, the predictions of quantum mechanics can also be achieved by working with a local hidden variable theory. See reference 22. R. A. Bertlmann, J. Phys. A 47, 424007 (2014). https://doi.org/10.1088/1751-8113/47/42/424007 for a more explicit discussion.Quantum mechanics as a mathematical formalism is a theory on (mathematical) Hilbert spaces, no matter whether the quantities associated with those spaces correspond to internal degrees of freedom, like spin, or external ones, like the position. In the EPR-Bohm-Bell context, the quantum formalism contains no reference to our three-dimensional space. Nevertheless, experiments are carried out in 3D space. Alice and Bob perform joint measurements of their particles at different, very remote locations. Then this nonlocal feature turns up: A measurement by Alice on the spin of her particle does have an effect— instantaneously—on Bob’s result, in contrast to what Griffiths claims in his comments. Therefore, quantum correlations are locally inexplicable.I sympathize with some of the comments by Michael Nauenberg, who collaborated with Bell long ago on “The moral aspect of quantum mechanics.”33. J. S. Bell, M. Nauenberg, in Preludes in Theoretical Physics in Honor of V. F. Weisskopf, A. De-Shalit, H. Feshbach, L. Van Hove, eds., North-Holland (1966), p. 279. In particular, Nauenberg’s comment that “experiments have revealed that the nature of reality in the quantum world is different from our experience in the classical world” is, in my opinion, the lesson we have to learn from Bell inequalities.I do not appreciate so much Nauenberg’s example of the helium atom since it distracts from the issue of nonlocality. In fact, it is at macroscopic distances where the “puzzle” arises and not at atomic distances of separation.I have a confession: I am not the realist one might expect after reading Bell’s article “Bertlmann’s socks and the nature of reality”; the world in its very foundations is much more abstract than we think with our ”anschauliche” (intuitive) concepts, to borrow Werner Heisenberg’s term. My personal feeling is that Bell’s theorem, which reveals an apparent nonlocality in nature, points to a more radical conception whose onset we do not yet have.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd ed., Cambridge U. Press (2004), p. 67. Google ScholarCrossref2. R. A. Bertlmann, J. Phys. A 47, 424007 (2014). https://doi.org/10.1088/1751-8113/47/42/424007, Google ScholarCrossref3. J. S. Bell, M. Nauenberg, in Preludes in Theoretical Physics in Honor of V. F. Weisskopf, A. De-Shalit, H. Feshbach, L. Van Hove, eds., North-Holland (1966), p. 279. Google Scholar© 2015 American Institute of Physics.

Physics Today•Nov 30, 2015•1 citation

Strengthening Bell's Theorem: Removing the Hidden-Variable Assumption

Henry Pierce Stapp

Spooky Action at a Distance In the context of correlation experiments involving pairs of experiments performed at very nearly the same time in very far-apart experimental regions, Einstein famously said [1], But on one supposition we should in my opinion hold absolutely fast: “The real factual situation of the system S2 is independent of what is done with system S1 which is spatially separated from the former.” This demand is incompatible with the basic ideas of standard (Copenhagen/orthodox) quantum mechanics, which makes two relevant claims: (1) Experimenters in the two labs make “local free choices” that determine which experiments will be performed in their respective labs. These choices are free in the sense of not being predetermined by the prior history of the physically described aspects of the universe, and they are localized in the sense that the physical effects of these free choices are inserted into the physically described aspects of the universe only within the laboratory in which the associated experiment is being performed. (2) These choices of what is done with the system being measured in one lab can (because of a measurement-induced global collapse of the quantum state) influence the outcome of the experiment performed at very close to the same time in the very faraway lab. This influence of what is done with the system being measured in one region upon the outcome appearing at very nearly the same time in a very faraway lab was called “spooky action at a distance” by Einstein, and was rejected by him as a possible feature of “reality.” John Bell's Quasi-classical Statistical Theory Responding to the seeming existence in the quantum world of “spooky actions,” John Bell [2] proposed a possible alternative to the standard approach that might conceivably be able to reconcile quantum spookiness with “reality.” This alternative approach rests on the fact that quantum mechanics is a statistical theory.We already have in physics a statistical theory called “classical statistical mechanics.”

Cambridge University Press eBooks•Aug 31, 2016•1 citation

Readers offer their own magic moments with John Bell

N. Bykovetz

I greatly enjoyed reading Reinhold Bertlmann’s article “Magic moments with John Bell.” Sprinkled with levity, it discussed Bell’s life, work, and outstanding insights and achievements in the foundations of quantum mechanics (QM). In my view, the reading should also make one acutely aware that scientists, despite our expectations of them, are sometimes still prone to the same failings that beset the rest of humanity.Bertlmann outlines very nicely Bell’s theorem and inequalities and the consequences of their violation; that work led to the subsequent startling experimental results on “entangled” quantum mechanical states, which, Bertlmann writes, showed “that nature contains a nonlocality in its structure.” Nonlocality, in Bell’s conception of it, is clearly a violation of special relativity (SR), so we have a problem. The startling thing for me is that Bell actually does appear to solve the problem, at least in principle, but at the same time he seems afraid to say so and, in fact, distances himself from the proposed solution.The essence of his ambivalence is conveyed in the following paragraph, quoted by Bertlmann:It may be that we have to admit that causal influences do go faster than light. The role of Lorentz invariance in the completed theory would then be very problematic. An “ether” would be the cheapest solution. But the unobservability of this ether would be disturbing. So would be the impossibility of “messages” faster than light.Clearly, faster-than-light propagation is not possible in SR. But it is permissible in the approximately 100-year-old ether-based Lorentzian theory of relativity (LR), developed by Joseph Larmor, Hendrik Lorentz, Henri Poincaré, and others. Bell was explicitly cognizant of LR and discussed it in his book Speakable and Unspeakable in Quantum Mechanics (2nd edition, Cambridge University Press, 2004). It is well known that LR and SR are totally congruent in their kinematics and dynamics, for speeds equal to or less than c. All predictions are identical. However—though one cannot find this in any standard textbooks—the LR ether theory differs from SR by allowing, without contradiction, speeds greater than c.Historically, Einstein’s SR gained ascendancy, and LR was relegated to the scrap heap of history for many reasons, but I think predominantly for the following. SR was viewed as being far more elegant and simple to develop—from the perspective of theory formation—because it followed deductively from Einstein’s two simple axioms. On the other hand, LR theory was developed from a realism perspective, where waves were thought to need a medium to wave in (the luminiferous ether).Considering that Bell was clearly aware of LR and was entertaining the idea, albeit reluctantly, of “causal influences [going] faster than light”—that is, being consonant with LR—I find it difficult to understand his expressions in the quote above about cheap solutions and disturbing features. It seems to be part of human psychology that once a set of ideas or a theory is accepted as valid for a long enough time by a community of people, as has been the case for SR, it gets transformed into belief, psychologically not unlike religious belief. Once that happens, those who would question the established dogma are treated as if the questioning was ill-intentioned, if not downright sacrilegious.© 2015 American Institute of Physics.

Physics Today•Nov 30, 2015•0 citations

There Is No Action at a Distance in Quantum Mechanics, Spooky or Otherwise

S. P. Boughn

I feel compelled to respond to the frequent references to spooky action at a distance that often accompany reports of experiments investigating entangled quantum mechanical states. Most, but not all, of these articles have appeared in the popular press. As an experimentalist I have great admiration for such experiments and the concomitant advances in quantum information and quantum computing, but accompanying claims of action at a distance are quite simply nonsense. Some physicists and philosophers of science have bought into the story by promoting the nonlocal nature of quantum mechanics. In 1964, John Bell proved that classical hidden variable theories cannot reproduce the predictions of quantum mechanics unless they employ some type of action at a distance. I have no problem with this conclusion. Unfortunately, Bell later expanded his analysis and mistakenly deduced that quantum mechanics and by implication nature herself are nonlocal. In addition, some of these articles present Einstein in caricature, a tragic figure who neither understood quantum mechanics nor believed it to be an accurate theory of nature. Consequently, the current experiments have proven him wrong. This is also nonsense.

arXiv:1806.07925•Jan 1, 2018•0 citations

A Modest View of Bell's Theorem

S. P. Boughn

In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however, many physicists and philosophers of science do harbor this belief. Experts in the field often use the term `nonlocality' to designate particular non-classical aspects of quantum entanglement and do not confuse the term with superluminal interactions. However, many physicists seem to take the term more literally. I endeavor to disabuse the latter of this notion by emphasizing that the correlations of Bell-type entanglement are a result of ordinary quantum superposition with no need to introduce nonlocality. The conclusion of the EPR paper wasn't that quantum mechanics is nonlocal but rather that it is an incomplete description of reality. For different reasons, many physicists, including me, agree with Einstein that quantum mechanics is necessarily an incomplete description of reality.

arXiv:1604.08529•Apr 28, 2016•3 citations
I read with pleasure Reinhold Bertlmann’s article about remembrances of John Bell and his contributions to physics. Bell is famous for establishing an inequality between the prediction of quantum mechanics and local hidden-variable theories, and Bertlmann wrote that “so far, all experiments looking for violations in Bell inequalities have found them, so we have to conclude, along with John, that nature contains a nonlocality in its structure.” But that conclusion is valid only in the context of Bell’s conviction that classical “realism is the proper position for a scientist.”Experiments have revealed that the nature of reality in the quantum world is different from our experience in the classical world.11. A. Aspect, Nature 446, 866 (2007). https://doi.org/10.1038/446866a Properties like the direction of an electron spin and its position and momentum remain undetermined until a measurement has been performed,22. W. Heisenberg, Physics and Philosophy: The Revolution in Modern Science, Prometheus Books (1999), p. 44. 9781573926942 but the colors of Bertlmann’s socks are fixed after he puts them on. Albert Einstein’s famous quotation, “spooky action at a distance,”33. A. Einstein, M. Born, H. Born, The Born–Einstein Letters: Correspondence Between Albert Einstein and Max and Hedwig Born from 1916–1955, I. Born, trans., MacMillan (1971), p. 159. that appears in Bertlmann’s amusing cartoon, is also misleading, because quantum correlations for entangled electron or photon pairs also occur at atomic distance of separation—for example, in the ground state of the helium atom. What would be spooky is if those correlations were altered when the entangled pair moved apart without further interactions, but experiments have shown that this is not the case.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. A. Aspect, Nature 446, 866 (2007). https://doi.org/10.1038/446866a, Google ScholarCrossref2. W. Heisenberg, Physics and Philosophy: The Revolution in Modern Science, Prometheus Books (1999), p. 44. 9781573926942, Google Scholar3. A. Einstein, M. Born, H. Born, The Born–Einstein Letters: Correspondence Between Albert Einstein and Max and Hedwig Born from 1916–1955, I. Born, trans., MacMillan (1971), p. 159. Google Scholar© 2015 American Institute of Physics.
Reinhold Bertlmann’s article “Magic moments with John Bell” was a pleasure to read. I add a note concerning some later developments that are significant for understanding the implications of Bell’s quantum foundations work.The crucial point is that under the Bell locality hypothesis for a joint measurement as given in the article,E(a,b)=∫dλρ(λ)A(a,λ)·B(b,λ)the quantity λ that represents the hidden variable(s) is a classical, not a quantum, object, and ρ(λ) is a classical probability distribution. Such expressions only make sense in the context of quantum theory when the operators of interest commute with each other, but that is not the case when this expression is used to derive a Bell inequality.Many years ago Arthur Fine pointed out that hidden variables and Bell inequalities were “imposing requirements to make well defined precisely those probability distributions for noncommuting observables whose rejection is the very essence of quantum mechanics.”11. A. Fine, Phys. Rev. Lett. 48, 291 (1982). https://doi.org/10.1103/PhysRevLett.48.291 Thus the real issue is not one of locality but, instead, the proper use of probabilities in quantum theory.Fine’s point has been confirmed by the later development of a fully consistent way of introducing probabilities in quantum mechanics.22. R. B. Griffiths, Stanford Encyclopedia of Philosophy (2014); http://plato.stanford.edu/entries/qm-consistent-histories. That approach has shown that when quantum mechanics is interpreted using subspaces of the Hilbert space rather than classical hidden variables to represent physical properties, it is local: There are no ghostly nonlocal influences.We cannot know how Bell would have responded to those new developments, which only came to full fruition after his untimely death. The reader willing to dig into my somewhat tedious discussion33. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press (2002), sec. 23.4. of the Einstein-Podolsky-Rosen and Bohm situation will find an explicit proof that a measurement by Alice has not the slightest effect on the spin on Bob’s side. More recent is a general argument that quantum mechanics satisfies a principle of Einstein locality: What is done to system A has no effect on system B as long as there is no interaction between the two.44. R. B. Griffiths, Found. Phys. 41, 705 (2011). https://doi.org/10.1007/s10701-010-9512-5Those proofs of quantum locality begin by taking very seriously John von Neumann’s proposal that quantum properties correspond to Hilbert subspaces, whose projectors do not, in general, commute with one another.55. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton U. Press (1955), sec. 3.5. Bell, though, assumed that such properties can be represented by classical hidden variables, which always commute. Thus Bell’s theorem teaches that if one uses classical hidden variables in place of quantum properties, the result will contradict quantum theory and disagree with experiment. Indeed, while Bell started off by pointing out deficiencies in von Neumann’s argument against hidden variables, the end result of his work is an even better and much more conclusive argument, backed by experiment, for rejecting classical hidden variables.REFERENCESSection:ChooseTop of pageREFERENCES <<1. A. Fine, Phys. Rev. Lett. 48, 291 (1982). https://doi.org/10.1103/PhysRevLett.48.291, Google ScholarCrossref2. R. B. Griffiths, Stanford Encyclopedia of Philosophy (2014); http://plato.stanford.edu/entries/qm-consistent-histories. Google Scholar3. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press (2002), sec. 23.4. Google Scholar4. R. B. Griffiths, Found. Phys. 41, 705 (2011). https://doi.org/10.1007/s10701-010-9512-5, Google ScholarCrossref5. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton U. Press (1955), sec. 3.5. Google Scholar© 2015 American Institute of Physics.
Bertlmann replies: I am pleased at the positive response of readers to my “Magic moments with John Bell.”I enjoyed very much the contributions of Charles Clement and Kerson Huang, who reported about their own “magic moments” with Bell. Their amusing anecdotes help complete the portrait of Bell, who was an outstanding personality indeed.I found the comments of Nicholas Bykovetz very interesting. I remember that Bell strongly sympathized with Lorentzian relativity and Fitzgerald contraction. In my opinion, the ether-based Lorentzian view of relativity is just closer to the heart of the realist that Bell was. I think it was the acceptance of Lorentz’s conception on relativity rather than Einstein’s that led Bell to the correct answer that a string between two equally accelerated spaceships will break, what is known as Bell’s spaceship paradox.11. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd ed., Cambridge U. Press (2004), p. 67. In Bell’s quote “An ‘ether’ would be the cheapest solution. But the unobservability of this ether would be disturbing,” he did not mean for the “cheapest solution” to be a derogatory phrase, but rather to mean “simple.” The “unobservability of this ether” disturbed Bell, since why should the laws of physics conspire to prevent us from identifying the ether experimentally.Regarding Robert Griffiths’s arguments, I agree with some parts but strongly disagree with others. Griffiths remarks that the specific form of the expectation value used by Bell for the joint measurement of Alice and Bob in the EPR-Bohm-Bell experiment does not make sense in the context of quantum theory with noncommuting operators. That is not the point Bell wanted to make. In his formalism, the quantum states are supplemented by hidden variables, which are governed by a classical probability distribution, in order to predetermine the measurement results.The expectation value, assigned to the local hidden-variable theory, is not applied to quantum mechanics but compared with the corresponding quantum mechanical result. Its specific form is excluded via a Bell inequality, in which a certain combination of expectation values is needed. Concentrating on the expectation value alone is not enough to distinguish local hidden variable theories from quantum mechanics; for example, the predictions of quantum mechanics can also be achieved by working with a local hidden variable theory. See reference 22. R. A. Bertlmann, J. Phys. A 47, 424007 (2014). https://doi.org/10.1088/1751-8113/47/42/424007 for a more explicit discussion.Quantum mechanics as a mathematical formalism is a theory on (mathematical) Hilbert spaces, no matter whether the quantities associated with those spaces correspond to internal degrees of freedom, like spin, or external ones, like the position. In the EPR-Bohm-Bell context, the quantum formalism contains no reference to our three-dimensional space. Nevertheless, experiments are carried out in 3D space. Alice and Bob perform joint measurements of their particles at different, very remote locations. Then this nonlocal feature turns up: A measurement by Alice on the spin of her particle does have an effect— instantaneously—on Bob’s result, in contrast to what Griffiths claims in his comments. Therefore, quantum correlations are locally inexplicable.I sympathize with some of the comments by Michael Nauenberg, who collaborated with Bell long ago on “The moral aspect of quantum mechanics.”33. J. S. Bell, M. Nauenberg, in Preludes in Theoretical Physics in Honor of V. F. Weisskopf, A. De-Shalit, H. Feshbach, L. Van Hove, eds., North-Holland (1966), p. 279. In particular, Nauenberg’s comment that “experiments have revealed that the nature of reality in the quantum world is different from our experience in the classical world” is, in my opinion, the lesson we have to learn from Bell inequalities.I do not appreciate so much Nauenberg’s example of the helium atom since it distracts from the issue of nonlocality. In fact, it is at macroscopic distances where the “puzzle” arises and not at atomic distances of separation.I have a confession: I am not the realist one might expect after reading Bell’s article “Bertlmann’s socks and the nature of reality”; the world in its very foundations is much more abstract than we think with our ”anschauliche” (intuitive) concepts, to borrow Werner Heisenberg’s term. My personal feeling is that Bell’s theorem, which reveals an apparent nonlocality in nature, points to a more radical conception whose onset we do not yet have.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd ed., Cambridge U. Press (2004), p. 67. Google ScholarCrossref2. R. A. Bertlmann, J. Phys. A 47, 424007 (2014). https://doi.org/10.1088/1751-8113/47/42/424007, Google ScholarCrossref3. J. S. Bell, M. Nauenberg, in Preludes in Theoretical Physics in Honor of V. F. Weisskopf, A. De-Shalit, H. Feshbach, L. Van Hove, eds., North-Holland (1966), p. 279. Google Scholar© 2015 American Institute of Physics.
Spooky Action at a Distance In the context of correlation experiments involving pairs of experiments performed at very nearly the same time in very far-apart experimental regions, Einstein famously said [1], But on one supposition we should in my opinion hold absolutely fast: “The real factual situation of the system S2 is independent of what is done with system S1 which is spatially separated from the former.” This demand is incompatible with the basic ideas of standard (Copenhagen/orthodox) quantum mechanics, which makes two relevant claims: (1) Experimenters in the two labs make “local free choices” that determine which experiments will be performed in their respective labs. These choices are free in the sense of not being predetermined by the prior history of the physically described aspects of the universe, and they are localized in the sense that the physical effects of these free choices are inserted into the physically described aspects of the universe only within the laboratory in which the associated experiment is being performed. (2) These choices of what is done with the system being measured in one lab can (because of a measurement-induced global collapse of the quantum state) influence the outcome of the experiment performed at very close to the same time in the very faraway lab. This influence of what is done with the system being measured in one region upon the outcome appearing at very nearly the same time in a very faraway lab was called “spooky action at a distance” by Einstein, and was rejected by him as a possible feature of “reality.” John Bell's Quasi-classical Statistical Theory Responding to the seeming existence in the quantum world of “spooky actions,” John Bell [2] proposed a possible alternative to the standard approach that might conceivably be able to reconcile quantum spookiness with “reality.” This alternative approach rests on the fact that quantum mechanics is a statistical theory.We already have in physics a statistical theory called “classical statistical mechanics.”
I greatly enjoyed reading Reinhold Bertlmann’s article “Magic moments with John Bell.” Sprinkled with levity, it discussed Bell’s life, work, and outstanding insights and achievements in the foundations of quantum mechanics (QM). In my view, the reading should also make one acutely aware that scientists, despite our expectations of them, are sometimes still prone to the same failings that beset the rest of humanity.Bertlmann outlines very nicely Bell’s theorem and inequalities and the consequences of their violation; that work led to the subsequent startling experimental results on “entangled” quantum mechanical states, which, Bertlmann writes, showed “that nature contains a nonlocality in its structure.” Nonlocality, in Bell’s conception of it, is clearly a violation of special relativity (SR), so we have a problem. The startling thing for me is that Bell actually does appear to solve the problem, at least in principle, but at the same time he seems afraid to say so and, in fact, distances himself from the proposed solution.The essence of his ambivalence is conveyed in the following paragraph, quoted by Bertlmann:It may be that we have to admit that causal influences do go faster than light. The role of Lorentz invariance in the completed theory would then be very problematic. An “ether” would be the cheapest solution. But the unobservability of this ether would be disturbing. So would be the impossibility of “messages” faster than light.Clearly, faster-than-light propagation is not possible in SR. But it is permissible in the approximately 100-year-old ether-based Lorentzian theory of relativity (LR), developed by Joseph Larmor, Hendrik Lorentz, Henri Poincaré, and others. Bell was explicitly cognizant of LR and discussed it in his book Speakable and Unspeakable in Quantum Mechanics (2nd edition, Cambridge University Press, 2004). It is well known that LR and SR are totally congruent in their kinematics and dynamics, for speeds equal to or less than c. All predictions are identical. However—though one cannot find this in any standard textbooks—the LR ether theory differs from SR by allowing, without contradiction, speeds greater than c.Historically, Einstein’s SR gained ascendancy, and LR was relegated to the scrap heap of history for many reasons, but I think predominantly for the following. SR was viewed as being far more elegant and simple to develop—from the perspective of theory formation—because it followed deductively from Einstein’s two simple axioms. On the other hand, LR theory was developed from a realism perspective, where waves were thought to need a medium to wave in (the luminiferous ether).Considering that Bell was clearly aware of LR and was entertaining the idea, albeit reluctantly, of “causal influences [going] faster than light”—that is, being consonant with LR—I find it difficult to understand his expressions in the quote above about cheap solutions and disturbing features. It seems to be part of human psychology that once a set of ideas or a theory is accepted as valid for a long enough time by a community of people, as has been the case for SR, it gets transformed into belief, psychologically not unlike religious belief. Once that happens, those who would question the established dogma are treated as if the questioning was ill-intentioned, if not downright sacrilegious.© 2015 American Institute of Physics.
I feel compelled to respond to the frequent references to spooky action at a distance that often accompany reports of experiments investigating entangled quantum mechanical states. Most, but not all, of these articles have appeared in the popular press. As an experimentalist I have great admiration for such experiments and the concomitant advances in quantum information and quantum computing, but accompanying claims of action at a distance are quite simply nonsense. Some physicists and philosophers of science have bought into the story by promoting the nonlocal nature of quantum mechanics. In 1964, John Bell proved that classical hidden variable theories cannot reproduce the predictions of quantum mechanics unless they employ some type of action at a distance. I have no problem with this conclusion. Unfortunately, Bell later expanded his analysis and mistakenly deduced that quantum mechanics and by implication nature herself are nonlocal. In addition, some of these articles present Einstein in caricature, a tragic figure who neither understood quantum mechanics nor believed it to be an accurate theory of nature. Consequently, the current experiments have proven him wrong. This is also nonsense.
In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however, many physicists and philosophers of science do harbor this belief. Experts in the field often use the term `nonlocality' to designate particular non-classical aspects of quantum entanglement and do not confuse the term with superluminal interactions. However, many physicists seem to take the term more literally. I endeavor to disabuse the latter of this notion by emphasizing that the correlations of Bell-type entanglement are a result of ordinary quantum superposition with no need to introduce nonlocality. The conclusion of the EPR paper wasn't that quantum mechanics is nonlocal but rather that it is an incomplete description of reality. For different reasons, many physicists, including me, agree with Einstein that quantum mechanics is necessarily an incomplete description of reality.