# RUSSELL HANSON, DAVID BOHM AND OTHERS ON THE SEMANTICS OF DISCOVERY

## 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
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