Bohm’s 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, 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 such supplementary 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 in his new thesis, and Bohm seems to have been one of the first to recognize it.  He states that on his new interpretation, 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 in Geneva, Switzerland, is an advocate of the hidden-variable interpretation of the quantum theory, who further developed Bohm’s analysis of 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 Everett.  The three unromantic views are 1) the pragmatic view that is the 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 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 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.  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 the extra 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 to measure selected components of spin revealed by the deflections of particles moving simultaneously away from each other in opposite trajectories 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.
          Heisenberg's indeterminacy principle says no quantum-mechanical state can be dispersion free for every variable.  On the other hand the hidden-variable theory says that all observations are fully determined, such that each quantum-mechanical state must correspond to an ensemble of states each with different values of the hidden variables with the component states dispersion free.  Therefore, one way to formulate the hidden-variable problem is to search for a formalism permitting such dispersion-free states.  Bell proposes such a formalism, a modification of the Schrödinger wave function with a set of hidden variables added, which he says provides an explicit causal mechanism by which operations on one of the two measuring devices in the apparatus can influence the response of the other distant device. However, this revision establishes that the measurement does not reveal some property previously possessed by the quantum system, but rather reveals something that comes into being in the combination of system and apparatus.  It is local in configuration space, but nonlocal in ordinary three-dimensional space thus providing an explicit causal mechanism by which one of the two measuring devices in the EPR experiment can influence the response of the distant device.  This is the opposite of the resolution hoped for by EPR, who had envisaged that the first device could serve only to reveal the character of the information already stored in space and propagating in an undisturbed way toward the other detecting equipment.
          In a paper titled “On the Einstein-Podolsky-Rosen Paradox” (1964) Bell set forth his locality inequality, the theoretical accomplishment for which he is best known.  This probabilistic expression assumes in agreement with EPR that the separated particles and thus their measured properties are statistically independent of one another.  The noteworthy consequence is that the values admitted by the inequality are inconsistent with the quantum theory.  Bell thus concludes that no local deterministic hidden-variable theory can reproduce all the experimental predictions of the quantum theory.  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.  The most reliable experiments of the several actually performed have outcomes favoring quantum mechanics, thus violating Bell’s locality inequality. 
          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.  Echoing Bohm’s early explanation Shimony adds 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 concludes 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 wormholes as topological modifications of space-time whereby two points are close to each other by one route and remote by another.  Thus the two photons in the EPR experiment are not only distantly separated as ordinary observation shows, but may also be more closely connected through a wormhole.
          In “Bertlmann’s Socks and the Nature of Reality” (1981) Bell considers four possible positions 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.  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. Bell seems unsympathetic to this position.  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 concepts like macroscopic 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.  Clearly Bell’s polite and reserved response is not intended as a confession of his ignorance, but rather as a criticism of Bohr’s obscurantism. 
          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.  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 (1993).  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 as sophisticated as may be found in the views of any contemporary academic philosopher of science.
          Bohm’s adoption of the hidden-variable interpretation led him to modify his original explanation of nonlocality.  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, 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 new EPR experiments using Bell’s locality inequality are empirical developments that have supplied ample grist for the philosophy dissertation mills.  Nonetheless, their interesting findings are of greater significance to physicists than to philosophers of science.  They may be the Michelson-Morley experiment for the contemporary physicists’ theory of relativity, but they present no anomalies for the contemporary philosopher’s Pragmatist philosophy of science.  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 it 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.  Following this development in philosophy of science, however, the new EPR experiments have not warranted any revision to the contemporary Pragmatist philosophy of science.  For the contemporary Pragmatist, the EPR experimental findings may be viewed as business as usual for science.  In view of Bell’s sympathy for Bohm’s hidden-variable thesis, it is ironic that the experiments performed using Bell’s inequality have yielded findings that contradict the expectations of Einstein, Podolsky and Rosen.

Pages [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
NOTE: Pages do not corresponds with the actual pages from the book