BOOK VII - Page 3

Bohm and Bell on the EPR Experiment and Nonlocality

In 1935 Einstein, Podolsky and Rosen (conventionally abbreviated as “EPR”) published an article in the Physical Review titled “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”  Their negative answer implies that the current statistical quantum theory is inadequate, and that further development is needed that would presumably involve identifying additional but presently undetected factors conventionally referred to as “hidden variables”. 

The authors firstly set forth a necessary condition for completeness, according to which every element of the physical reality must have a counterpart in the physical theory.  And they secondly set forth a sufficient condition for affirming the reality of a physical quantity, which consists in the possibility of predicting with certainty the physical quantity under investigation without disturbing the physical system. The three authors propose a hypothetical or gedanken experiment, now conventionally known as the “EPR thought experiment”, which concludes to a demonstration of the present quantum theory’s incompleteness.

There have been several versions of this now famous proposed experiment including one that has since actually been performed.  The authors postulate two particles initially interacting, such that their properties are correlated, and then subsequently separated spatially by being sent off in opposite directions, so that they can no longer interact but still retain their initially correlated properties independently of being measured, something that the Copenhagen interpretation cannot describe and is therefore deemed incomplete.  One of the implicit assumptions of the argument is that there is no instantaneous action at a distance, which Einstein called “spooky”, so that the spatial separation of the two particles precludes the measurement of one particle from disturbing the other separated particle in any way.  This assumption has been called either separability or locality. 

In the original version of the thought experiment the noteworthy properties are the noncommuting observables, position and momentum.  If the momentum of one of the particles is measured, then since its momentum is correlated to the momentum of the second particle, the momentum of the second is also known by the measurement of the first and without measurement of the second.  Or if the position of the first particle is measured, then since its position is correlated to the position of the second particle, the position of the second is also known by the measurement of the first and without measurement of the second. 

But according to Heisenberg’s indeterminacy relations no quantum wave/particle can simultaneously have both position and momentum as determinate properties.  The selection of which quantity is determinate is made by the measurement action, a selection that by design is the free and arbitrary choice of the experimenter.  The second particle has no interaction with the first at the time that the first particle is measured, so the second particle cannot know, as it were, which of the noncommuting properties the experimenter selected as the determinate property of the first particle.  Yet paradoxically the second particle’s determinate property is always correlated to that of the first.  Einstein, Podolsky and Rosen, conclude that the paradox can only be resolved by recognizing that in fact both particles always had both determinate position and determinate momentum from the instant of their separation, and that the current quantum theory fails to represent completely the physical reality of the situation.  The current quantum theory therefore is incomplete.

Bohr responded to this argument in an article with the same title appearing in a later issue of the same journal in the same year.  He takes issue with EPR’s criterion for physical reality, reaffirms his principle of complementarity, and maintains contrary to EPR that quantum theory is not incomplete.  He admits that because it is impossible to control the reaction of the object to the measuring instruments, the interaction between object and measuring devices conditioned by the very existence of the quantum of action entails the necessity of a final renunciation of the classical ideal of causality and a radical revision of our attitude towards the nature of physical reality. 

David Bohm has several views on quantum theory and on the EPR thought experiment.  Initially in a section titled “The Paradox of Einstein, Podolsky and Rosen” in his Quantum Theory Bohm says that the EPR criticism of quantum theory has been shown to be unjustified, and in a footnote to this statement he references Bohr’s critique of EPR published in Physical Review. At this time Bohm was sympathetic to the Copenhagen interpretation, and critical of Einstein’s views.  But later in addition to EPR’s necessary condition for a complete physical theory and their sufficient condition for recognizing an element of reality, Bohm says that there are two additional assumptions implicit in the EPR argument.  These assumptions are firstly that the world can be correctly analyzed in terms of distinct and separately existing elements of reality, and secondly that every one of these elements is a counterpart of a precisely defined mathematical quantity appearing in a complete theory.  Bohm attacks these two implicit assumptions.  He states that the one-to-one correspondence between mathematical theory and well defined elements of reality exists only at the classical level.  At the quantum level, on the other hand, the properties described by the wave function are not well defined properties, but are only potentialities that are more definitely realized in interaction with an appropriate classical system such as a measuring apparatus.

Bohm offers a modified version of the EPR experiment.  His version considers the spin properties of the two separated and correlated particles.  Bohm’s own proposed resolution to the EPR paradox involving his rejection of the two implicit assumptions he believed contained in the EPR argument resulted in his ontological thesis of potentialities based on his wholistic philosophy of nature, and his belief that mathematics is of limited value for physics.  Contrary to Einstein’s ontology, Bohm maintains the wholistic view that there are no distinct and separately existing elements of reality, and that the present form of the quantum theory implies that the world cannot be put into one-to-one correspondence with any conceivable kind of precisely defined mathematical quantities.  Therefore a complete theory will always require concepts that are more general than those for an analysis into precisely defined elements.  Thus to obtain a description of all aspects of the world, one must supplement the mathematical description with a physical interpretation in terms of incompletely defined potentialities.  He later refers to any such supplementary nonmathematical description as “informal language”. 

Bohm’s conclusion that mathematical physics must be supplemented with informal nonmathematical discourse, may be contrasted with the approach of Dirac, who never doubted the adequacy of mathematics for physics, and who instead admitted a new type of variable into mathematical physics, namely the quantum or “Q” variables, as he called them, as opposed to the traditionally classical or “C” variables.  Finally to cope mathematically with the indeterminacies in microphysics Bohm introduces in his Undivided Universe his thesis that quantum theory is an “implicate algebra”.

In his early statement of his hidden-variable thesis published in Physical Review in 1952 Bohm revised his view of Bohr’s thesis.  He says that Bohr’s interpretation of the quantum theory leaves unexplained the correlations between the two separated particles in the EPR experiment, and that the quantum theory needs to be completed by additional elements or parameters.  This is the hidden-variables thesis, but there is no mention of potentiality in noncommuting variables or ontological wholism, although there is recognition of the nonlocality implication (i.e., action at a distance) in his new thesis.  Bohm seems to have been one of the first to acknowledge nonlocality.  Later he states that on his new interpretation in his Undivided Universe, the EPR experiment is describable in terms of a combination of a six-dimensional wave field, the subquantum field, and a precisely definable trajectory in a six-dimensional space. 

Thus when the experimenter measures either the position or the momentum of the first particle, he introduces uncontrollable fluctuations in the wave function for the entire system, which through the quantum-mechanical forces bring about corresponding uncontrollable fluctuations in the position or momentum respectively of the other particle.  And he notes that these quantum-mechanical forces transmit the disturbances instantaneously from one particle to the other through the medium of the subquantum field.  But Bohm does not conclude that the instantaneously transmitted disturbances involve signals having velocities greater than that of light.  He says that where the quantum theory is correct, his interpretation cannot lead to inconsistencies with relativity theory, and that where the quantum theory may break down in cases of high velocities and short distances, Lorentz invariance may serve as a heuristic principle in the search for new physical laws.

Before examining Bohm’s later statements in his Undivided Universe, consider firstly Bell’s locality inequality and actual EPR experiments. John Stewart Bell (1928-1990), a theoretical physicist associated with CERN, the European Organization for Nuclear Research near Geneva, Switzerland, was an advocate of the hidden-variable interpretation of the quantum theory, who further developed Bohm’s design for the EPR experiment.  In 1987 Bell published his collected papers under the title Speakable and Unspeakable in Quantum Mechanics, in which each chapter is a previously published paper.  In the chapter titled “Six Possible Worlds of Quantum Mechanics” (1968) Bell distinguishes six interpretations of the quantum theory, which he divides into the “romantic” and the “unromantic” views.  The romantic views are those that are principally of interest to journalists, and the unromantic ones are those of interest to professional physicists.  The three romantic views are 1) Bohr’s complementarity thesis, 2) the mentalistic views of Wigner and Wheeler, and 3) the many-worlds thesis of Hugh Everett. 

The three unromantic views are 1) the pragmatic philosophy of physicists who work with the quantum theory, 2) a new and not-yet developed classical nonlinear Schrödinger wave equation that makes microscopic and macroscopic physics continuous, and 3) the pilot-wave thesis of de Broglie and Bohm. This last alternative, which is the hidden-variable interpretation, makes the whole physical universe classical, and the probability outcome is viewed as due entirely to the experimenter’s limited control over the initial conditions.  Bell says that the pilot wave thesis seems so natural and simple for resolving the wave-particle dilemma that it is a great mystery to him why it had been ignored. 

In a chapter titled “Introduction to the Hidden-Variable Question” (1971) Bell discusses his motivations for defending and developing the hidden-variable thesis.  His first reason, and the one that he finds most compelling, is the possibility of a homogeneous account of the physical world, which is to say, a single uniform ontology for microphysical and macrophysical domains based on classical concepts.  Bell denies that there is a boundary between classical and quantum worlds, the boundary that Heisenberg had called the “schism” in physics, and Bell agrees with Einstein that the wave function is an incomplete and provisional microphysical theory.  This is a coherence agenda for the aim of science. 

His second motivation concerns the statistical character of quantum mechanical predictions.  Once the incompleteness of the wave function is suspected, then the seemingly random statistical fluctuations may be viewed as determined by additional realities or “hidden variables”, which are hidden because at the present time physicists can only conjecture their existence. 

His third motivation is the peculiar character of some quantum-mechanical predictions considered in the famous gedanken experiment formulated by EPR, and a refinement proposed by Bohm in 1951, in which Stern-Gerlach magnets are used as spin detectors to measure selected components of spin revealed by the deflections of particles moving simultaneously away from each other in opposite directions from a source.  The experiment permits the observer to know in advance the result of measuring one particle’s deflection by observing the other’s deflection even at great distance.  The implication intended by Einstein is that the outcomes of such measurements are actually determined in advance by variables over which the physicist has no control, but which are sufficiently revealed by the first measurement that he can anticipate the result of the second.  Therefore, contrary to the Copenhagen view there is no need to regard the performance of one measurement as a causal influence on the result of the second distant measurement, and the situation can be described as “local”.

In a paper titled “On the Einstein-Podolsky-Rosen Paradox” (1964) Bell set forth his famous locality inequality known as Bell’s theorem, the theoretical accomplishment for which he is best known. Bohm had developed a simpler version of the original EPR experiment.  Einstein, Podolsky and Rosen had proposed two properties of a particle, position and momentum.  Bohm proposed only one, namely spin.  An electron has only two spin states, spin-up and spin-down.  In Bohm’s version a spin-zero particle disintegrates and produces two electrons with one having spin-up and the other having spin-down.  When they are separated so that no interaction between them is possible, the quantum spin of each is measured at exactly the same time by a spin detector.  As soon as the spin of one electron is measured as spin-up, the spin of the other in the same direction will be simultaneously measured as spin-down.  The EPR thesis implies that the spins are determined at the time of separation.  The Copenhagen advocates believed that the correlated spins are not determined until the time of the two simultaneous measurements, even though the two separated electrons cannot interact, such that the perfect correlation is due to nonlocal “entanglement” of the two separated electrons.  But Bohm’s simple version of the EPR experiment cannot decide which view is correct.

Bell enabled a crucial experiment by modifying Bohm’s version of the EPR experiment by changing the relative orientation of the two spin detectors.  If the spin detectors are aligned, there will be perfect correlation.  But if one is rotated through successive executions of the experiment, the more it is rotated the less the correlation.  At ninety degrees the correlation will be fifty percent, and at one hundred-eighty degrees the spin directions will be the same.  Bell’s theorem said that no hidden-variables theory could reproduce the same set of correlations as quantum mechanics.  He could then calculate the limits on the degree of spin correlation between pairs of entangled electrons.

Several years after Bell’s 1964 paper physicists began to design and perform actual EPR experiments to test Bell’s locality inequality.  The first proposed EPR experimental design was published under the title “Proposed Experiment to Test Local Hidden-Variable Theories” in Physical Review Letters by J.F. Clauser, M.A. Horne, A. Shimony, and R.A. Holt.  These experiments examined the statistical behavior of separated photons with polarization analyzers to detect up or down polarization.  The most reliable experiments of the several actually performed have outcomes violating Bell’s locality inequality thus supporting the Copenhagen interpretation of quantum mechanics. 

In his “Metaphysical Problems in the Foundations of Quantum Mechanics” in the International Philosophical Quarterly (1978) one of these experimenters, Abner Shimony, affirms a realistic interpretation based on the idea that the measurement produces a transition from potentiality to an actuality in both the separated photons.  Shimony says that the only changes that have occurred concerning the second photon are a transition from indefiniteness of certain dynamical variables to definiteness and not from one definite value to another.  He adds that there seems to be no way of utilizing quantum nonseparability and action at a distance for the purpose of sending a message faster than the velocity of light.  He prefers the idea of wormholes previously proposed by J.A. Wheeler in 1962.  Shimony describes a wormhole as a topological modification of space-time whereby two points are close to each other by one route and remote by another.  Thus the two photons in the actual EPR experiment are not only distantly separated as ordinary observation shows, but may be closely connected through a wormhole.

In “Bertlmann’s Socks and the Nature of Reality” (1981) Bell considers four possible theses in connection with nonlocality.  The first is that Einstein was correct in rejecting action at a distance, because the apparatus in any EPR experiment attempted to date is too inefficient to offer conclusive results.  This amounts to attacking the test design.  But Bell says that the experimental evidence is not encouraging for such a view.  The second position is that the physicist’s selection of dynamical variables is not truly an independent variable in the EPR experiment, because the mind of the experimenter influences the test outcome. This is one of those “romantic” interpretations to which Bell is unsympathetic.  He merely comments that this way of arranging quantum mechanical correlations would be even more mind boggling than one in which causal chains go faster than the speed of light, and that it implies that separate parts of the world are deeply entangled including our apparent free will.  A third position that he considers is Bohr’s view that there does not exist any reality below some classical or macroscopic level.  He says that on Bohr’s thesis fundamental physical theory would be fundamentally vague until macroscopic concepts are made sharper than they are currently.  And in an “Appendix” to this article Bell adds that he does not understand the meaning of such statements in Bohr’s 1935 rebuttal to EPR.

Finally Bell considers the position that causal influences do in fact travel faster than light, and this is the position he prefers.  In “Speakable and Unspeakable in Quantum Mechanics” (1984) he says that the problem of quantum theory is not how the world can be divided into the speakable macrophysical apparatus, which we can talk about, and the unspeakable quantum system, which we cannot talk about. Bell’s inequality assumes firstly that the particle has a well defined property such as spin prior to measurement, and secondly that locality is preserved and that there is no superluminary velocity. 

In 1982 Alain Aspect and colleagues also tested Bell’s theorem for correlation of the polarization of entangled pairs of photons.   His confirming findings mean that one of these assumptions is incorrect.  Bell was willing to reject locality, because contrary to Bohr he wanted a realistic interpretation.  The problem is to explain how the consequences of events at one place propagate to other places faster than light, which is in gross violation of relativistic causality.  Most notably he says that Aspect, Dalibard, and Roger, who published the findings from their EPR experiments in 1982, have realized specific quantum phenomena which require such superluminal explanation in the laboratory.  Bell concludes that there exists an apparent incompatibility at the deepest level between the two fundamental pillars of contemporary physical theory, and that a real synthesis of quantum and classical theories requires not just technical developments but a radical conceptual renewal.

Consider next Bohm’s final statements of his views on nonlocality in his Undivided Universe.  Bohm had affirmed the nonlocality thesis even before he adopted the hidden-variable interpretation, and nonlocality remained a basic feature of his mature view.  While nonlocality and wholeness are often associated with Bohr’s Copenhagen interpretation, and are opposed to EPR’s criticism, Bohm’s ideas of nonlocality and wholeness are not the same as Bohr’s.  On Bohr’s view an attempt to analyze a quantum process in detail is not possible, because the experimental conditions and measurement of the experimental results are a whole that is not further analyzable.  Bohm on the other hand not only proposes his hidden-variable interpretation as an analysis of the individual quantum phenomenon, but he also offers a philosophically sophisticated critique of Bohr’s rebuttal to EPR in the seventh chapter titled “Nonlocality”. 

Bohm replies that on Bohr’s view it is not possible even to talk about nonlocality, because nothing can be said about the detailed behavior of individual systems at the quantum order of magnitude.  In his critique Bohm attacks Bohr’s philosophy of language, according to which physical phenomena must be described with concepts from classical physics.  Bohm references Einstein’s statements that concepts are a free creation of the human mind, and says that there is no problem in assuming the simultaneous reality of all properties of the separated particles in the EPR experiment, even though these properties cannot be simultaneously observed.

Contemporary philosophers of science refer to these different semantical views expressed by Bohr and Einstein and discussed by Bohm as the naturalistic and the artifactual theses of the semantics of language respectively.  Notwithstanding Bohm’s minority status among physicists, his philosophy of language is not only as sophisticated as may be found in the views of any contemporary academic philosopher of science, but it had also been developed independently by Heisenberg in response to his reflections on quantum mechanics.

Bohm’s adoption of the hidden-variable interpretation led him to modify his original explanation of nonlocality.  Thus in his Undivided Universe he says that the nonlocal connection between the separated particles which causes the correlation in the EPR experiment is the quantum potential in the subquantum field.  And he also maintains that the nonlocal quantum potential cannot be used to carry a signal.  By signal he means a controllable influence, and he says that there is no way to control the behavior of the remote second particle by anything that might be done to the first particle.  This is because any attempt to send a signal by influencing one of the pair of particles under EPR correlations will encounter difficulties arising from the irreducibly participatory nature of all quantum processes due to their wholistic nature.  To clarify his view on signals, he says that if an attempt were made in some way to modulate the wave function in a way similar to what is done to make a radio wave signal, and the whole pattern of this quantum wave would change radically in a chaotic and complex way, because it is so “fragile”.

Bohm takes up the relation between nonlocality and special relativity in “On the Relativistic Invariance of Our Ontological Interpretation”, the twelfth chapter of Undivided Universe.  He says that since a particle guided in a nonlocal way is not Lorentz invariant, physicists must either accept nonlocality, in which case relativity is not fully adequate in the quantum domain, or they must reject nonlocality, in which case quantum theory is not fully adequate in the relativistic domain.  Bohm does not renounce nonlocality, but instead concludes that physicists must assume the existence of a unique frame in which the nonlocal connections are instantaneous.  He says that he does not regard this unique frame to be intrinsically unobservable, but that these new properties cannot be observed presently in the statistical and manifest domains in which the current quantum theory and relativity theory are valid.  Just as the observations of atoms became possible where continuity of matter broke down, so the observation of the new properties will become possible where quantum theory and relativity theory break down.  He says that the idea of a unique frame fits in with an important historical tradition regarding the way in which new levels of reality, e.g., the atoms, are introduced into physics to explain older levels, e.g., continuous matter, on a qualitatively new basis. 

Bohm admits it will take time to demonstrate experimentally the existence of the subquantum fields and the unique frame of reference implied by nonlocality.  He also considers that the speed of the quantum connection is not actually instantaneous, but is nonetheless much faster than the speed of light, and he proposes the development of the EPR experiment reminiscent of the Michelson-Morley experiment to measure the superluminary velocity of the quantum connection between distant particles.  He says such a test might demonstrate the existence of the unique frame, indicate a failure of both quantum and relativity theories, eliminate quantum nonlocality, and indicate a deeper level of reality in which the basic laws are neither those of quantum theory nor relativity theory.  The modern quantum theory brought down the positivist philosophy by occasioning the rejection of the naturalistic thesis of the semantics of descriptive language including notably those terms that the positivists called “observation terms”.  This was analogous to rejecting the parallel postulate in Euclidian geometry, and has brought in its train the development of the contemporary pragmatist philosophy of science based on the thesis that the semantics of descriptive language is artifactual.  For the contemporary pragmatist, the EPR experimental findings may be viewed as business as usual for science.  The hidden-variables thesis has no monopoly on realism.  Heisenberg’s practice of ontological relativity enabled his Copenhagen interpretation to be more recognizably realist, while the experiments based on Bell’s theorem have diminished the hidden-variables’ realist claim.

In his “Essential quantum entanglement” in The New Physics for the Twenty-First Century (Ed. Fraser, 2006) Anton Zeilinger reports that several more recent three-particle experiments that have overcome previous detector inefficiencies have continued to display violation of Bell’s inequality, and thus reinforcement of the physics profession’s acceptance of the Copenhagen interpretation.

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NOTE: Pages do not corresponds with the actual pages from the book