Original Source
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The Refinement of Complementarity
Bohr's Como paper made very little impact upon its audience. It was not a
paper on physics and presented no new empirically testable consequences for
quantum theory. However, the Como paper did make it clear that Bohr now
regarded quantum theory in a certain sense as complete. This surprised,
puzzled and left unimpressed a great many of Bohr's colleagues.
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Bohr had intended his Como paper as a general outline of his new framework to
be worked out in greater detail, and in the years following 1927 his attention
turned to refining his concepts of complementarity. The application to quantum
physics was always uppermost in Bohr's mind, but as early as 1929 it was
obvious that he had a strong interest in carrying complementarity as an
epistemological lesson to other fields, eventually developing it as a
generalization of the classical framework over all empirical knowledge.
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His thoughts did not develop as he had originally planned, however. Instead,
they were sharply influenced by the criticisms of Einstein, and a great deal
of his thoughts were manifested in specific reply to challenges put forward by
Einstein. Although the differences between Bohr and Einstein reflected a real
disagreement about the nature of scientifically describing physical reality,
there were also some very serious misunderstandings on both sides. Bohr
probably weakened his own cause by not stating at the beginning that what was
at stake was no less than a proposed revision of our understanding of our
relationship between physical reality and the concepts we use to describe it.
In a way, Einstein realized this more clearly than Bohr himself.
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The Bohr-Einstein Debates
About one month after Bohr's presentation of his Como paper, he met Albert
Einstein at the Solvay Congress in Brussels. Einstein opposed Bohr's
complementarity view and proposed the first of a series of thought experiments
designed to get around the uncertainty principle so that the classical notion
of the state of system could be retained. In 1927, Bohr had little difficulty
in showing that Einstein's experiment failed to provide more empirical
information about the system than permitted by the quantum postulate. But at
the Solvay Congress of 1930, Einstein presented a particularly difficult
thought experiment.
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Bohr spent a sleepless night pondering it, then demonstrated that Einstein had
failed to take into consideration the effects of his own general relativity
theory, which when considered, gave the exact degree of uncertainty that was
compatible with Heisenberg's principle. Then, in 1935, in conjunction with B.
Podolsky and N. Rosen, Einstein made his final attempt at a
Gedanken-Experiment to show that the physical system had simultaneous
properties that quantum theory could not explain, demonstrating that the
theory was incomplete. This become commonly known as the EPR experiment, or
paradox.
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This experiment brought to light the opposition between two conceptions of
physical reality. Bohr concluded that complementarity is a "new feature of
natural philosophy [which] means a radical revision of our attitude as regards
physical reality...". Bohr felt that the difference between complementarity
and the classical framework was such that there cannot be an "experimentum
crucis" demonstrating the correctness of one view or another. In other words,
from the point of view of complementarity, Bohr's answer was completely
consistent, while from the point of view of the classical framework,
Einstein's objections were equally consistent. Of course, Einstein's rejection
allowed him to continue to use the classical framework, while Bohr's
acceptance of complementarity forced him to adopt a new framework.
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I am not interested in exploring the actual experiments themselves. If the
reader wishes, they may purchase "Atomic Theory and the Description of Nature;
Philosophical Writings of Niels Bohr Series, Vol. 1" and read Bohr's comments
personally. But I do want to stress that most of Bohr's writings after 1927
were designed primarily to win Einstein over to the framework of
complementarity. This changed Bohr's original focus on complementarity as a
"description of nature" into a use as a "conceptual framework" for a detailed
analysis of the "physical" situation in numerous imaginary experiments. This
application to quantum theory gave way to the "Copenhagen Interpretation" and
Bohr's original concern with a fundamental revision of the framework of
science was largely lost from sight.
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In his last interview, Bohr was asked, "Einstein was always apparently asking
for a definition or a clarification, a precise formulation of what is the
principle complementarity. Could you give that?" Bohr replied, "He also got
it, but he did not like it." [2] Einstein seemed to
think of complementarity as a principle in a physical sense, and so was
frustrated by Bohr's failure (from Einstein's viewpoint) to provide a clear
formulation which would have testable consequences, like Einstein's own
principle of relativity.
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Einstein argued that properties corresponding to classical parameters belong
to physical entities independent of observation, which he considered justified
because such parameters have empirical reference to observed phenomenal
properties which are used to confirm theory. Einstein felt that since, with
the classical framework, it is always possible in principle to define
precisely the mechanical state of the system even as it is being observed, it
then follows that if these parameters used to define the state are interpreted
as corresponding to properties possessed by the system, these systems must
"really" always have simultaneousness of such properties as position and
momentum.
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The EPR Experiment
Einstein finally gave up trying to disprove quantum mechanics by finding a way
to simultaneously make observational determinations, and instead focused on
demonstrating the incompleteness of quantum theory. And to argue that a theory
is incomplete makes it necessary to stipulate what constitutes completeness.
As a criterion of completeness, Einstein suggested "every element of physical
reality must have a counterpart in physical theory. If without in any way
disturbing a system, we can predict with certainty (i.e., with probability
equal to unity) the value of a physical quantity, then there exists an element
of physical reality corresponding to this physical quantity."
[3]
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In the EPR experiment, the authors propose a situation in which two physical
systems, the initial states of which are known, are allowed to interact for a
finite period of time. As noted already, quantum theory says that once the
systems interact, it becomes theoretically impossible to define the states of
each system separately. However, given the representations of the initial
states as defined in quantum formalism, it is possible to define the state of
the systems combined, treated in this sense as an individual interacting
whole. What cannot be defined by quantum theory is the state of each system
considered separately either during the interaction or after that interaction.
For that, another observation is needed. As the uncertainty principle demands,
observation cannot determine both parameters necessary to define precisely the
state of either system. However, from the observation of the first system and
theoretical definition of the combined states of the two systems, by means of
unambiguous communication, it is possible to theoretically predict the
interaction of the second system without in any way interacting with that
system.
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Bohr did not dispute this conclusion. And indeed, using the assumption that
"position" and "momentum" refer to properties possessed by systems independent
of an observational interaction, then what the observing system records is the
causal effects of said properties. The claim that measuring the value of a
phenomenal observable which is in no way physically interacting with the
observer would seem to demand a mysterious, non-physical communication between
the two systems. This claim does indeed seem unreasonable, as the EPR
experiment was designed to show.
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However, from Bohr's point of view, these same theoretical parameters do not
refer to properties of an independent reality, but instead refer to
phenomenal
properties. From this point of view, if there is no interaction to observe,
say the position of the system, there is no phenomenal property to which the
position parameter can refer. From this point of view, Einstein's conclusion
seems equally unreasonable.
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Bohr believed that although we have "free choice"
of which experiment to observe, that freedom merely indicated a freedom in
which phenomenon we choose to bring about. Bohr writes:
...in the phenomena concerned we are not dealing with an incomplete
description characterized by the arbitrary picking out of different elements
of physical reality at the cost of sacrificing other such elements, but with a
rational discrimination between essentially different experimental
arrangements and procedures which are suited either for an unambiguous use of
the idea of space location, or for a legitimate application of the
conservation theorem of momentum. Any remaining appearance of arbitrariness
concerns merely our freedom of handling the measuring instruments,
characteristic of the very idea of experiment.
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In fact, the renunciation in each experimental arrangement of the one or the
other of two aspects of the description of physical phenomena - the combination
of which characterizes the method of classical physics, and which therefore in
this sense may be considered complementary to one another - depends
essentially on the impossibility, in the field of quantum theory, of accurately
controlling the reaction of the object on the measuring instruments, i.e., the
transfer of momentum in the case of position measurements and the displacement
in case of momentum measurements...we are, in the "freedom of choice" offered
by the...[EPR] arrangement, just concerned with a discrimination between
different experimental procedures which allow of the unambiguous use of
complementary classical concepts. [4]
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Bohr's alternative interpretation of the EPR experiment revealed the
difference between two conceptions of physical reality. The ambiguity that
Bohr focused on was hidden in Einstein's use of "state of the system". Bohr
believed that when we determine the state of the system, the "system" to which
we refer is necessarily a phenomenal object. Einstein, on the other hand,
believed that observable properties of the state of the system is presumed to
be existing independent from the observation.
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In a paper written in 1939, four
years after the EPR experiment was proposed, Bohr writes:
...the very fact that in quantum phenomena no sharp separation can be made
between an independent behavior of the objects and their interaction with the
measurement instruments, lends indeed to any such phenomena a novel feature of
individuality which evades all attempts at analysis on classical lines,
because every imaginable experimental arrangement aiming at a subdivision of
the phenomena will be incompatible with its appearance and give rise, within
the latitude indicated by the uncertainty relations, to other phenomena of
similar individual character.
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In fact the [EPR] paradox finds its complete solution within the framework of
the quantum mechanical formalism, according to which no well-defined use of
the concept of "state" can be made as referring to the object separate from
the body with which it has been in contact, until the external conditions
involved in the definition of this concept are unambiguously fixed by a
further suitable control of the auxiliary body.
[5]
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Bohr's point is that there can be no empirical reason for assuming classical
parameters as referring to an "independent reality", and if one does make such
an assumption, quantum theory becomes involved in the contradiction of
asserting the atomic domain system as having incompatible properties of both
particles and waves. As Bohr saw it, these descriptive concepts are
well-defined only in reference to observed phenomenal objects, or
abstractions.
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From Einstein's point of view, it seemed the "free choice" we have of which of
the two possible measurements to make involves one and the same system. But
from Bohr's point of view, in order to give terms like "position" and
"momentum" empirical significance, "system" must be interpreted in the sense
of that which is observed. And since the experimental arrangement necessary
for alternative observations of position and momentum are mutually exclusive,
he concluded that the two observations refer to the properties of two distinct
phenomenal objects. There was simply no "same system" in a sense that both
position and momentum could be observed.
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In short, the EPR experiment, as advanced by Einstein, assumes that in the
interaction necessary to determine the parameter representing the phenomenal
observation, it remains possible to describe the system independently of the
observational interaction. And if the observing apparatus is changed, for
example, if measurement involves momentum instead of position, Einstein
assumed that it will not influence the "property" of the "system". In fact,
Bohr was disheartened by Einstein's reasoning, for he felt it missed the core
of his framework of complementarity and the quantum postulate. And
unfortunately, since all Bohr's arguments were erected on the quantum
postulate, it all by-passed Einstein.
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Bohr's Concept of "Phenomenon"
Following 1935, Bohr distinguished his view by emphasizing that the
description of nature is free from ambiguity and metaphysical dogma only if it
is realized that the observational basis of science depends on devising ways
to describe unambiguously an individual interaction between systems. This
point of view was already implicit in his Como paper, however after 1935 there
was a real change in Bohr's emphasis and manner of speaking. In his first
philosophical writing after the EPR experiment, in 1937, Bohr is careful to
point out that what we must renounce is the classical attempt to "visualize"
objects of quantum description as possessing "such inherent attributes as the
idealizations of classical physics [i.e., "waves" and "particles"] would
ascribe to the object.
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...the fundamental postulate of the indivisibility of the quantum of action is
itself, from the classical point of view, an irrational element which
inevitably requires us to forgo a causal mode of description and which,
because of the coupling between phenomena and their observation, forces us to
adopt a new mode of description designated as complementary in the sense that
any given application of classical concepts precludes the simultaneous use of
other classical concepts which in a different connection are equally necessary
for the elucidation of the phenomena...
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...the finite magnitude of the quantum of action prevents altogether a sharp
distinction being made between a phenomenon and the agency by which it is
observed, a distinction which underlies the customary concept of observation
and, therefore, forms the basis of the classical ideas of motion.
[6]
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From 1939 on, Bohr always used the word "phenomenon" to refer to the whole
observational interaction. Bohr emphasized that the two complementary
measurements of position and momentum are different phenomena and hence
determine the properties of different phenomenal objects. Eventually he
adopted a way of speaking which referred to the complementarity of different
phenomena or complementary evidence from different observations.
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For this reason, some physicists have seen Bohr's complementarity as having
undergone a radical change during this time and that therefore there are
really two distinct notions of complementarity. Bohr agreed that
complementarity presents a many faceted viewpoint, yet he resolutely
maintained that the complementarity of modes of description and the
complementarity of phenomena are simply two consequences of the quantum
postulate. The first indication of a change in Bohr's way of describing
complementarity came in 1938 when he wrote:
Information regarding the behavior of an atomic object obtained under definite
experimental conditions may...be adequately characterized as complementary to
any information about the same object by some other experimental arrangement
excluding the fulfillment of the first conditions.
[7]
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Later, Bohr began to de-emphasize the complementarity between space-time
description and applying the conservation principle in favor of defining the
complementary relationship as holding between phenomena. He writes:
Although the phenomena in quantum physics can no longer be combined in the
customary manner, they can be said to be complementary in a sense that only
together do they exhaust the evidence regarding the objects, which is
unambiguously definable. [8]
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This sentence, or variations of it, became a standard formula for Bohr's
later work and is repeated over and over again in later essays. He does
continue to use other formulations as well however, for example:
...we are faced with the contrast revealed by the comparison between
observations regarding an atomic system, obtained by means of different
experimental arrangements. Such empirical evidence exhibits a novel
relationship, which has no analogue in classical physics and which may be
conveniently termed "complementarity" in order to stress that in the
contrasting phenomena we have to do with equally essential aspects of all
well-defined knowledge about the objects. [9]
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Once it is recognized that Bohr's talk of complementarity phenomena refers to
the effects observed under different experimental conditions, then the
confusion between complementary aspects of nature and complementary
descriptive modes disappears. All of Bohr's analyses of experiments in his
debates with Einstein were intended to show that determining the
spatio-temporal properties of the observed object is possible only in
experimental interactions which preclude any interaction determining momentum
or energy properties of the object. Thus, to give empirical reference to terms
like spatio-temporal co-ordination and causal descriptions require physical
interactions, "phenomena" in Bohr's later usage, which exclude each other but
are complementary.
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The Object of Description
His debate with Einstein forced Bohr to realize that there was a fundamental
ambiguity hidden in the notion of "physical reality" as that which is
described in natural science. In order for observation to determine
unambiguously the values of phenomenal objects, the description of the
observation must indicate exactly what part of the whole interaction is
considered observing instruments and what part is considered phenomenal object
being observed. For this reason, Bohr introduced an "inherent arbitrariness"
into the description of any phenomenal object, making what is now part of the
observing system part of the observed or visa versa. Only by making such an
arbitrary separation between what is treated as the means of observation and
what the phenomenal object is can an unambiguous description of what is
observed be communicated.
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"Observing system" and "observed object" are terms which are well defined only
in the context of a particular description of interaction. They must be
regarded as descriptive categories invoked for an unambiguous communication of
the results of an observation rather than as referring to different
constituents of nature. The requirement that descriptive terms must have some
empirical reference if they are to describe phenomenal objects make their
attempted use to describe an atomic system apart from its phenomenal
appearances in observational interactions descriptively ambiguous.
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Bohr never argued that the notion of object as an independent reality is
"meaningless", but he did argue that because of a certain physical fact, the
individuality of atomic interactions, the classical description of particles
and waves become restricted in their reference to the phenomenal object.
Therefore, the use of these concepts to picture the state of an isolated
system does not refer to an independent reality but to an abstraction. Bohr's
point is that we cannot describe an independent reality in the manner which
was thought possible in the classical framework, because that framework makes
different presuppositions about the nature of observation.
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An example involving the concept of temperature may help clarify Bohr's
position here. Since it has been empirically discovered that material bodies
can be represented as composed of many molecules, and that the property of
temperature observed in many-molecule bodies can be represented as the causal
effects of the motion of these molecules, these physical facts make the
concept of temperature inapplicable below the molecular level.
In Bohr's epistemological lesson we are taught that at the atomic level,
spatio-temporal concepts are not defined in an unambiguous sense for an
objective description of an independent physical reality.
This ends Part 5 of this review. Thanks for reading!
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Footnotes
[1] Niels Bohr, Can Quantum Mechanical Description of Reality Be Considered
Complete?
Review 47
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[2] AHQP, Bohr, Last Interview, page 4
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[3] A. Einstein, B. Podolsky, N. Rosen, Can Quantum Mechanical Description of
Reality Be Considered Complete? Review 48
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[4] Niels Bohr, Can Quantum Mechanical Description of Reality Be Considered
Complete?
Review 48
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[5] Niels Bohr, The Causality Problem in Atomic Physics
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[6] Niels Bohr, Atomic Theory and the Description of Nature
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[7] Niels Bohr, Natural Philosophy and Human Culture
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[8] Niels Bohr, Newton's Principles and Modern Atomic Physics
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[9] Niels Bohr, On the Notions of Causality and Complementarity
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The Framework of Complementarity
Part 1 - Overview Early Years Bohr Formulates Complementarity
Part 2 - Argument for Complementarity
Part 3 - Comments on Complementarity
Part 4 - Complementarity and the Uncertainty Principle
Part 5 - Refinement of Complementarity
Part 6 - Extension of Complementarity
Part 7 - The Nature of Empirical Knowledge
Part 8 - Complementarity and the Metaphysics of Quality