## 1. The Background



In 1900 Max Planck discovered that the radiation spectrum of black
bodies occurs only with discrete energies separated by the value
*hn*, where *n* is the frequency and *h* is
a new constant, the so-called Planck constant. According to classical
physics, the intensity of this continuous radiation would grow
unlimitedly with growing frequencies, resulting in what was called the
ultraviolet catastrophe. But Planck's suggestion was that if
black bodies only exchange energy with the radiation field in a
proportion equal to *hn* that problem would disappear. The
fact that the absorption and the emission of energy is discontinuous
is in conflict with the principles of classical physics. A few years
later Albert Einstein used this discovery in his explanation of the
photoelectric effect. He suggested that light waves were quantized,
and that the amount of energy which each quantum of light could
deliver to the electrons of the cathode, was exactly *hn*.
The next step came in 1911 when Ernest Rutherford performed some
experiments shooting alpha particles into a gold foil. Based on these
results he could set up a model of the atom in which the atom
consisted of a heavy nucleus with a positive charge surrounded by
negatively charged electrons like a small solar system. Also this
model was in conflict with the laws of classical physics. According to
classical mechanics and electrodynamics, one might expect that the
electrons orbiting around a positively charged nucleus would
continuously emit radiation so that the nucleus would quickly swallow
the electrons.



At this point Niels Bohr entered the scene and soon became the leading
physicist on atoms. In 1913 Bohr, visiting Rutherford in Manchester,
put forward a mathematical model of the atom which provided the first
theoretical support for Rutherford's model and could explain the
emission spectrum of the hydrogen atom (the Balmer series). The theory
was based on two postulates:


1. An atomic system is only stable in a certain set of states, called
stationary states, each state being associated with a discrete energy,
and every change of energy corresponds to a complete transition from
one state to another.
2. The possibility for the atom to absorb and emit radiation is
determined by a law according to which the energy of the radiation is
given by the energy difference between two stationary states being
equal to *hn*.



Some features of Bohr's semi-classical model were indeed very
strange compared to the principles of classical physics. It introduced
an element of discontinuity and indeterminism foreign to classical
mechanics:


1. Apparently not every point in space was accessible to an electron
moving around a hydrogen nucleus. An electron moved in classical
orbits, but during its transition from one orbit to another it was at
no definite place between these orbits. Thus, an electron could only
be in its ground state (the orbit of lowest energy) or an excited
state (if an impact of another particle had forced it to leave its
ground state.)
2. It was impossible to predict when the transition would take place
and how it would take place. Moreover, there were no external (or
internal) causes that determined the "jump" back again.
Any excited electron might in principle move spontaneously to either a
lower state or down to the ground state.
3. Rutherford pointed out that if, as Bohr did, one postulates that
the frequency of light *n*, which an electron emits in a
transition, depends on the difference between the initial energy level
and the final energy level, it appears as if the electron must
"know" to what final energy level it is heading in order
to emit light with the right frequency.
4. Einstein made another strange observation. He was curious to know
in which direction the photon decided to move off from the
electron.



Between 1913 and 1925 Bohr, Arnold Sommerfeld and others were able to
improve Bohr's model, and together with the introduction of spin
and Wolfgang Pauli's exclusion principle it gave a reasonably
good description of the basic chemical elements. The model ran into
problems, nonetheless, when one tried to apply it to spectra other
than that of hydrogen. So there was a general feeling among all
leading physicists that Bohr's model had to be replaced by a
more radical theory. In 1925 Werner Heisenberg, at that time
Bohr's assistant in Copenhagen, laid down the basic principles
of a complete quantum mechanics. In his new matrix theory he replaced
classical commuting variables with non-commuting ones. The following
year, Erwin Schrodinger gave a simpler formulation of the theory
in which he introduced a second-order differential equation for a wave
function. He himself attempted a largely classical interpretation of
the wave function. However, already the same year Max Born proposed a
consistent statistical interpretation in which the square of the
absolute value of this wave function expresses a probability amplitude
for the outcome of a measurement.


## 2. Classical Physics



Bohr saw quantum mechanics as a generalization of classical physics
although it violates some of the basic ontological principles on which
classical physics rests. Some of these principles are:


* *The principles of physical objects and their identity*:
	+ Physical objects (systems of objects) exist in space and time and
	physical processes take place in space and time, i.e., it is a
	fundamental feature of all changes and movements of physical objects
	(systems of objects) that they happen on a background of space and
	time;
	+ Physical objects (systems) are localizable, i.e., they do not
	exist everywhere in space and time; rather, they are confined to
	definite places and times;
	+ A particular place can only be occupied by one object of the same
	kind at a time;
	+ Two physical objects of the same kind exist separately; i.e., two
	objects that belong to the same kind cannot have identical location at
	an identical time and must therefore be separated in space and
	time;
	+ Physical objects are countable, i.e., two alluded objects of the
	same kind count numerically as one if both share identical location at
	a time and counts numerically as two if they occupy different
	locations at a time;
* *The principle of separated properties*, i.e., two objects
(systems) separated in space and time have each independent inherent
states or properties;
* *The principle of value determinateness*, i.e., all
inherent states or properties have a specific value or magnitude
independent of the value or magnitude of other properties;
* *The principle of causality*, i.e., every event, every
change of a system, has a cause;
* *The principle of determination*, i.e., every later state
of a system is uniquely determined by any earlier state;
* *The principle of continuity*, i.e., all processes
exhibiting a difference between the initial and the final state have
to go through every possible intervening state; in other words, the
evolution of a system is an unbroken path through its state space; and
finally
* *The principle of the conservation of energy*, i.e., the
energy of a closed system can be transformed into various forms but is
never gained, lost or destroyed.



Due to these principles it is possible within, say, classical
mechanics, to define a state of a system at any later time with
respect to a state at any earlier time. So whenever we know the
initial state consisting of the system's position and momentum,
and know all external forces acting on it, we also know what will be
its later states. The knowledge of the initial state is usually
acquired by observing the state properties of the system at the time
selected as the initial moment. Furthermore, the observation of a
system does not affect its later behavior or, if observation somehow
should influence this behavior, it is always possible to incorporate
the effect into the prediction of the system's later state.
Thus, in classical physics we can always draw a sharp distinction
between the state of the measuring instrument being used on a system
and the state of the physical system itself. It means that the
physical description of the system is objective because the definition
of any later state is not dependent on measuring conditions or other
observational conditions.



Much of Kant's philosophy can be seen as an attempt to provide
satisfactory philosophical grounds for the objective basis of
Newton's mechanics against Humean scepticism. Kant thus argued
that classical mechanics is in accordance with the transcendental
conditions for objective knowledge. Kant's philosophy
undoubtedly influenced Bohr in various ways, as many scholars in
recent years have noticed (Hooker 1972; Folse 1985; Honner 1987; Faye
1991; Kaiser 1992; and Chevalley 1994). Bohr was definitely neither a
subjectivist nor a positivist philosopher, as Karl Popper (1967) and
Mario Bunge (1967) have claimed. He explicitly rejected the idea that
the experimental outcome is due to the observer. As he said: "It
is certainly not possible for the observer to influence the events
which may appear under the conditions he has arranged"
(*APHK*, p.51). Not unlike Kant, Bohr thought that we could
have objective knowledge only in case we can distinguish between the
experiential subject and the experienced object. It is a precondition
for the knowledge of a phenomenon as being something distinct from the
sensorial subject, that we can refer to it as an object without
involving the subject's experience of the object. In order to
separate the object from the subject itself, the experiential subject
must be able to distinguish between the form and the content of his or
her experiences. This is possible only if the subject uses causal and
spatial-temporal concepts for describing the sensorial content,
placing phenomena in causal connection in space and time, since it is
the causal space-time description of our perceptions that constitutes
the criterion of reality for them. Bohr therefore believed that what
gives us the possibility of talking about an object and an objectively
existing reality is the application of those necessary concepts, and
that the physical equivalents of "space,"
"time," "causation," and
"continuity" were the concepts "position,"
"time," "momentum," and "energy,"
which he referred to as *the classical concepts*. He also
believed that the above basic concepts exist already as preconditions
of unambiguous and meaningful communication, built in as rules of our
ordinary language. So, in Bohr's opinion the conditions for an
objective description of nature given by the concepts of classical
physics were merely a refinement of the preconditions of human
knowledge.


## 3. The Correspondence Rule



The guiding principle behind Bohr's and later Heisenberg's
work in the development of a consistent theory of atoms was the
correspondence rule. The full rule states that a transition between
stationary states is allowed if, and only if, there is a corresponding
harmonic component in the classical motion (*CW Vol. 3*, p.
479). Bohr furthermore realized that according to his theory of the
hydrogen atom, the frequencies of radiation due to the
electron's transition between stationary states with high
quantum numbers, i.e. states far from the ground state, coincide
approximately with the results of classical electrodynamics. Hence in
the search for a theory of quantum mechanics it became a
methodological requirement to Bohr that any further theory of the atom
should predict values in domains of high quantum numbers that should
be a close approximation to the values of classical physics. The
correspondence rule was a heuristic principle meant to make sure that
in areas where the influence of Planck's constant could be
neglected the numerical values predicted by such a theory should be
the same as if they were predicted by classical radiation theory.



The Bohr-Sommerfeld core model of the atomic structure came into
trouble in the beginning of the 1920s due to the fact that it
couldn't handle an increasing number of spectroscopic phenomena.
In 1924 Wolfgang Pauli introduced a new degree of freedom according to
which two electrons with the same known quantum numbers could not be
in the same state. A year later, in 1925, Ralph Kronig, Georg
Uhlenbeck and Samuel Goudsmit explained this new degree of freedom by
introducing the non-classical concept of electron spin. It has been
suggested, however, that Pauli's proposal meant a lethal blow
not only to the Bohr-Sommerfeld model, but also to the correspondence
principle because "how to reconcile the classical periodic
motions presupposed by the correspondence principle with the
classically non-describable *Zweideutigkeit* of the
electron's angular momentum?" (Massimi 2005, p. 73)



Although the exclusion rule and the introduction of spin broke with
the attempt to explain the structure of the basic elements along the
lines of the correspondence argument (as Pauli pointed out in a letter
to Bohr) Bohr continued to think of it as an important methodological
principle in the attempt to establish a coherent quantum theory. In
fact, he repeatedly expressed the opinion that Heisenberg's
matrix mechanics came to light under the guidance of this very
principle. In his Faraday Lectures from 1932, for instance, Bohr
emphasizes: "A fundamental step towards the establishing of a
proper quantum mechanics was taken in 1925 by Heisenberg who showed
how to replace the ordinary kinematical concepts, in the spirit of the
correspondence argument, by symbols referring to the elementary
processes and the probability of their occurrence" (*CC*,
p. 48). Bohr acknowledged, however, that the correspondence argument
failed too in those cases where particular non-classical concepts have
to be introduced into the description of atoms. But he still thought
that the correspondence argument was indispensable for both structural
and semantic reasons in constructing a proper quantum theory as a
generalised theory from classical mechanics.



Indeed, spin is a quantum property of the electrons which cannot be
understood as a classical angular momentum. Needless to say, Bohr
fully understood that. But he didn't think that this discovery
ruled out the use of the correspondence rule as guidance to finding a
satisfactory quantum theory. A lengthy quotation from Bohr's
paper "The Causality Problem in Atomic Physics" (1938)
gives evidence for this:



> 
> Indeed, as adequate as the quantum postulates are in the
> phenomenological description of the atomic reactions, as indispensable
> are the basic concepts of mechanics and electrodynamics for the
> specification of atomic structures and for the definition of
> fundamental properties of the agencies with which they react. Far from
> being a temporary compromise in this dilemma, the recourse to
> essentially statistical considerations is our only conceivable means
> of arriving at a generalization of the customary way of description
> sufficiently wide to account for the features of individuality
> expressed by the quantum postulates and reducing to classical theory
> in the limiting case where all actions involved in the analysis of the
> phenomena are large compared with a single quantum. In the search for
> the formulation of such a generalization, our only guide has just been
> the so called correspondence argument, which gives expression for the
> exigency of upholding the use of classical concepts to the largest
> possible extent compatible with the quantum postulates. (*CC*,
> p.96)
> 



This shows that, according to Bohr, quantum mechanics, as formulated
by Heisenberg, was a rational generalization of classical mechanics
when the quantum of action and the spin property were taken into
account.



The correspondence rule was an important methodological principle. In
the beginning it had a clear technical meaning for Bohr. It is
obvious, however, that it makes no sense to compare the numerical
values of the theory of atoms with those of classical physics unless
the meaning of the physical terms in both theories is commensurable.
The correspondence rule was based on the epistemological idea that
classical concepts were indispensable for our understanding of
physical reality, and it is only when classical phenomena and quantum
phenomena are described in terms of the same classical concepts that
we can compare different physical experiences. It was this broader
sense of the correspondence rule that Bohr often had in mind later on.
He directly mentioned the relationship between the use of classical
concepts and the correspondence principle in 1934 when he wrote in the
Introduction to *Atomic Theory and the Description of
Nature*:



> 
> [T]he necessity of making an extensive use ... of the classical
> concepts, upon which depends ultimately the interpretation of all
> experience, gave rise to the formulation of the so-called
> correspondence principle which expresses our endeavours to utilize all
> the classical concepts by giving them a suitable quantum-theoretical
> re-interpretation (*ATDN*, p. 8)
> 



Bohr's practical methodology stands therefore in direct
opposition to Thomas Kuhn and Paul Feyerabend's historical view
that succeeding theories, like classical mechanics and quantum
mechanics, are incommensurable. In contrast to their philosophical
claims of meaning gaps and partial lack of rationality in the choice
between incommensurable theories, Bohr believed not just
retrospectively that quantum mechanics was a natural generalization of
classical physics, but he and Heisenberg followed in practice the
requirements of the correspondence rule. Thus, in the mind of Bohr,
the meaning of the classical concepts did not change but their
application was restricted. This was the lesson of
complementarity.


## 4. Complementarity



After Heisenberg had managed to formulate a consistent quantum
mechanics in 1925, both he and Bohr began their struggle to find a
coherent interpretation for the mathematical formalism. Heisenberg and
Bohr followed somewhat different approaches. Where Heisenberg looked
to the formalism and developed his famous uncertainty principle or
indeterminacy relation, Bohr chose to analyze concrete experimental
arrangements, especially the double-slit experiment. In a way Bohr
merely regarded Heisenberg's relation as an expression of his
general notion that our understanding of atomic phenomena builds on
complementary descriptions. At Como in 1927 he presented for the first
time his ideas according to which certain different descriptions are
said to be complementary.



Bohr pointed to two sets of descriptions which he took to be
complementary. On the one hand, there are those that attribute either
kinematic or dynamic properties to the atom; that is,
"space-time descriptions" are complementary to
"claims of causality", where Bohr interpreted the causal
claims in physics in terms of the conservation of energy and momentum.
On the other hand, there are those descriptions that ascribe either
wave or particle properties to a single object. How these two kinds of
complementary sets of descriptions are related is something Bohr never
indicated (Murdoch 1987). Even among people, like Rosenfeld and Pais,
who claimed to speak on behalf of Bohr, there is no agreement. The
fact is that the description of light as either particles or waves was
already a classical dilemma, which not even Einstein's
definition of a photon really solved since the momentum of the photon
as a particle depends on the frequency of the light as a wave.
Furthermore, Bohr eventually realized that the attribution of
kinematic and dynamic properties to an object is complementary because
the ascription of both of these conjugate variables rests on mutually
exclusive experiments. The attribution of particle and wave properties
to an object may, however, occur in a single experiment; for instance,
in the double-slit experiment where the interference pattern consists
of single dots. So within less than ten years after his Como lecture
Bohr tacitly abandoned "wave-particle complementarity" in
favor of the exclusivity of "kinematic-dynamic
complementarity" (Held 1994).



It was clear to Bohr that any interpretation of the atomic world had
to take into account an important empirical fact. The discovery of the
quantization of action meant that quantum mechanics could not fulfill
the above principles of classical physics. Every time we measure, say,
an electron's position, the apparatus and the electron interact
in an uncontrollable way, so that we are unable to measure the
electron's momentum at the same time. Until the mid-1930s when
Einstein, Podolsky and Rosen published their famous thought-experiment
with the intention of showing that quantum mechanics was incomplete,
Bohr spoke as if the measurement apparatus disturbed the electron.
This paper had a significant influence on Bohr's line of
thought. Apparently, Bohr realized that speaking of disturbance seemed
to indicate--as some of his opponents may have understood
him--that atomic objects were classical particles with definite
inherent kinematic and dynamic properties. After the EPR paper he
stated quite clearly: "the whole situation in atomic physics
deprives of all meaning such inherent attributes as the idealization
of classical physics would ascribe to such objects."



Hence, according to Bohr, the state of the measuring device and the
state of the object cannot be separated from each other during a
measurement but they form a dynamical whole. Bohr called this form of
holism "the individuality" of the atomic process. Thereby,
he had in mind not only that the interaction is uncontrollable but
also that the system-cum-measurement forms an inseparable unity due to
the entanglement - although Bohr's did not use this term
(Faye 1991, 1994; Howard 1994, 2004).



Also after the EPR paper Bohr spoke about Heisenberg's
"indeterminacy relation" as indicating the ontological
consequences of his claim that kinematic and dynamic variables are
ill-defined unless they refer to an experimental outcome. Earlier he
had often called it Heisenberg's "uncertainty
relation", as if it were a question of a merely epistemological
limitation. Furthermore, Bohr no longer mentioned descriptions as
being complementary, but rather phenomena or information. He
introduced the definition of a "phenomenon" as requiring a
complete description of the entire experimental arrangement, and he
took a phenomenon to be a measurement of the values of either
kinematic or dynamic properties.



Bohr's more mature view, i.e., his view after the EPR paper, on
complementarity and the interpretation of quantum mechanics may be
summarized in the following points:


1. The interpretation of a physical theory has to rely on an
experimental practice.
2. The experimental practice presupposes a certain pre-scientific
practice of description, which establishes the norm for experimental
measurement apparatus, and consequently what counts as scientific
experience.
3. Our pre-scientific practice of understanding our environment is an
adaptation to the sense experience of separation, orientation,
identification and reidentification over time of physical
objects.
4. This pre-scientific experience is grasped in terms of common
categories like thing's position and change of position,
duration and change of duration, and the relation of cause and effect,
terms and principles that are now parts of our common language.
5. These common categories yield the preconditions for objective
knowledge, and any description of nature has to use these concepts to
be objective.
6. The concepts of classical physics are merely exact specifications
of the above categories.
7. The classical concepts--and not classical physics
itself--are therefore necessary in any description of physical
experience in order to understand what we are doing and to be able to
communicate our results to others, in particular in the description of
quantum phenomena as they present themselves in experiments;
8. Planck's empirical discovery of the quantization of action
requires a revision of the foundation for the use of classical
concepts, because they are not all applicable at the same time. Their
use is well defined only if they apply to experimental interactions in
which the quantization of action can be regarded as negligible.
9. In experimental cases where the quantization of action plays a
significant role, the application of a classical concept does not
refer to independent properties of the object; rather the ascription
of either kinematic or dynamic properties to the object as it exists
independently of a specific experimental interaction is
ill-defined.
10. The quantization of action demands a limitation of the use of
classical concepts so that these concepts apply only to a phenomenon,
which Bohr understood as the macroscopic manifestation of a
measurement on the object, i.e. the uncontrollable interaction between
the object and the apparatus.
11. The quantum mechanical description of the object differs from the
classical description of the measuring apparatus, and this requires
that the object and the measuring device should be separated in the
description, but the line of separation is not the one between
macroscopic instruments and microscopic objects. It has been argued in
detail (Howard 1994) that Bohr pointed out that parts of the measuring
device may sometimes be treated as parts of the object in the quantum
mechanical description.
12. The quantum mechanical formalism does not provide physicists with
a 'pictorial' representation: the *ps*-function
does not, as Schrodinger had hoped, represent a new kind of
reality. Instead, as Born suggested, the square of the absolute value
of the *ps*-function expresses a probability amplitude for
the outcome of a measurement. Due to the fact that the wave equation
involves an imaginary quantity this equation can have only a symbolic
character, but the formalism may be used to predict the outcome of a
measurement that establishes the conditions under which concepts like
position, momentum, time and energy apply to the phenomena.
13. The ascription of these classical concepts to the phenomena of
measurements rely on the experimental context of the phenomena, so
that the entire setup provides us with the defining conditions for the
application of kinematic and dynamic concepts in the domain of quantum
physics.
14. Such phenomena are complementary in the sense that their
manifestations depend on mutually exclusive measurements, but that the
information gained through these various experiments exhausts all
possible objective knowledge of the object.



Bohr thought of the atom as real. Atoms are neither heuristic nor
logical constructions. A couple of times he emphasized this directly
using arguments from experiments in a very similar way to Ian Hacking
and Nancy Cartwright much later. What he did not believe was that the
quantum mechanical formalism was true in the sense that it gave us a
literal ('pictorial') rather than a symbolic
representation of the quantum world. It makes much sense to
characterize Bohr in modern terms as an entity realist who opposes
theory realism (Folse 1986; Faye 1991). 



It is because of the imaginary quantities in quantum mechanics (where
the commutation rule for canonically conjugate variable, *p*
and *q*, introduces Planck's constant into the formalism
by *qp* [?] *pq* = *ih*/2p that quantum
mechanics does not give us a 'pictorial' representation of
the world. Neither does the theory of relativity, Bohr argued, provide
us with a literal representation, since the velocity of light is
introduced with a factor of *i* in the definition of the fourth
coordinate in a four-dimensional manifold (*CC*, p. 86 and p.
105). Instead these theories can only be used symbolically to predict
observations under well-defined conditions. Therefore, many
philosophers have interpreted Bohr as an antirealist or an
instrumentalist when it comes to theories. However, Bohr's
reference to the use of imaginary number in quantum mechanics as an
argument for his rejection of a pictoral representation may seem
misplaced. The use of imaginary numbers is more a question about the
conventional choice of scale whether measurements should be
represented in terms of imaginary or real number than an indication of
a certain magnitude expressed in terms of these numbers is not real.
Dieks (2017) gives a nuanced discussion of Bohr's argument, and
he concludes that in the context of quantrum mechanics Bohr saw
imaginary numbers to be associated with incompatible physical
quantities. 



In general, Bohr considered the demands of complementarity in quantum
mechanics to be logically on a par with the requirements of relativity
in the theory of relativity. He believed that both theories were a
result of novel aspects of the observation problem, namely the fact
that observation in physics is context-dependent. This again is due to
the existence of a maximum velocity of propagation of all actions in
the domain of relativity and a minimum of any action in the domain of
quantum mechanics. And it is because of these universal limits that it
is impossible in the theory of relativity to make an unambiguous
separation between time and space without reference to the observer
(the context) and impossible in quantum mechanics to make a sharp
distinction between the behavior of the object and its interaction
with the means of observation (*CC*, p. 105).



Complementarity is first and foremost a semantic and epistemological
reading of quantum mechanics that carries certain ontological
implications. Bohr's view was, to phrase it in a modern
philosophical jargon, that the truth conditions of sentences ascribing
a certain kinematic or dynamic value to an atomic object are dependent
on the apparatus involved, in such a way that these truth conditions
have to include reference to the experimental setup as well as the
actual outcome of the experiment. This claim is called Bohr's
*indefinability thesis* (Murdoch 1987; Faye 1991). Hence, those
physicists who accuse this interpretation of operating with a
mysterious collapse of the wave function during measurements
haven't got it right. Bohr accepted the Born statistical
interpretation because he believed that the *ps*-function
has only a symbolic meaning and does not represent anything real. It
makes sense to talk about a collapse of the wave function only if, as
Bohr put it, the *ps*-function can be given a pictorial
representation, something he strongly denied.



Indeed, Bohr, Heisenberg, and many other physicists considered
complementarity to be the only rational interpretation of the quantum
world. They thought that it gave us the understanding of atomic
phenomena in accordance with the conditions for any physical
description and the possible objective knowledge of the world. Bohr
believed that atoms are real, but it remains a much debated point in
recent literature what sort of reality he believed them to have,
whether or not they are something beyond and different from what they
are observed to be. Henry Folse argues that Bohr must operate with a
distinction between a phenomenal and a transcendental object. The
reason is that this is the only way it makes sense to talk about the
physical disturbance of the atomic object by the measuring instrument
as Bohr did for a while (Folse 1985, 1994). But Jan Faye has replied
that Bohr gave up the disturbance metaphor in connection with his
discussion of the EPR thought-experiment because he realized that it
was misleading. Moreover, there is no further evidence in Bohr's
writings indicating that Bohr would attribute intrinsic and
measurement-independent state properties to atomic objects (though
quite unintelligible and inaccessible to us) in addition to the
classical ones being manifested in measurement (Faye 1991).


## 5. The Use of Classical Concepts



A central element in the Copenhagen Interpretation is Bohr's
insistence on the use of classical concepts both with respect to
describing experimental results and endowing quantum formalism with an
empirical interpretation. The special cognitive status ascribed to the
classical concepts is something Bohr stressed from the very beginning.
Here is a quotation from 1934: 



> 
> 
> No more is it likely that the fundamental concepts of the classical
> theories will ever become superfluous for the description of physical
> experience. ... It continues to be the application of these
> concepts alone that makes it possible to relate the symbolism of the
> quantum theory to the data of experience (*ATDN*, p.16).
> 
> 
> 

 Later he expressed the same view in an often quoted
passage:


> 
> 
> It is decisive to recognize that, however far the phenomena transcend
> the scope of classical physical explanation, the account of all
> evidence must be expressed in classical terms. The argument is simply
> that by the word 'experiment' we refer to a situation
> where we can tell to others what we have done and what we have learned
> and that, therefore, the account of the experimental arrangement and
> of the results of the observations must be expressed in unambiguous
> language with suitable application of the terminology of classical
> physics (*APHK*, p. 39). 
> 
> 
> 



Bohr saw the classical concepts as necessary for procuring unambiguous
communication about what happens in the laboratory. Classical concepts
are indispensable, because they enable physicists to describe
observations in a clear common language, and because they are the ones
by which the physicists connect the mathematical formalism with
observational content.



Over the years, different authors have come up with different
explanations of why Bohr thought that classical concepts were
unavoidable for the description of quantum phenomena. Here we
shall group those explanations in relation to five different
philosophical frameworks: 1) Empiricism, 2) Kantianism, 3) Pragmatism,
4) Darwinianism, and 5) Experimentalism.



*Empiricism*. This view is represented by the logical
positivists. They believed that the interpretation of any scientific
theory should be grounded in empirical observations. No theory,
according the positivists, is cognitively meaningful unless its terms
can be connected to terms that are able to express results that would
verify that theory. Observational terms refer directly to observable
things or observable properties of physical objects, whereas
theoretical terms are explicitly defined by correspondence rules
connecting them with the observational terms. Hence classical terms,
like position and momentum, are exactly such terms that enable
physicist to ascribe a physical meaning to quantum mechanics.



*Kantianism*. Many philosophers and physicists have recognized
a strong kinship between Kant and Bohr's thinking or a direct
Kantian influence on Bohr. In the thirties C.F. von Weizsacker
and Grete Hermann attempt to understand complementarity in the light
of neo-Kantian ideas. As von Weizsacker puts it many years later,
"The alliance between Kantians and physicists was premature in
Kant's time, and still is; in Bohr, we begin to perceive its
possibility". A series of modern scholars (Folse 1985; Honner
1982, 1987; Faye 1991; Kaiser 1992; Chevalley 1994; Pringe 2009;
Cuffaro 2010; Bitbol 2013, 2017; and Kauark-Leite 2017) has also
emphasized the Kantian parallels. Although these scholars find common
themes, they also disagree to what extent Kantian or neo-Kantian ideas
can be used as spectacles through which we may vision Bohr's
understanding of quantum mechanics. On the other hand, Cuffaro (2010)
holds that any proper "interpretation of Bohr should
*start* with Kant", and that "complementarity
follows naturally from a broadly Kantian epistemological
framework." Kant's assumption was that our forms of
intuition and our categories of thoughts constitute the transcendental
conditions for the possibility of any objective experience. Thus,
space and time are referred to as the forms of intuition, and the
categories of understanding such as causation, unity, plurality, and
totality are the a priori concepts which the mind imposes on the sense
impressions that appear in our intuition. In a similar way, it is
argued that Bohr saw concepts like space, time, causation, unity, and
totality as a priori categories that was necessary for any objective
description of quantum phenomena, and that classical physics was an
explication and operationalization of these a priori concepts. 



 *Pragmatism*. Some scholars have advocated for a more
pragmatic explanation of Bohr's thesis concerning the
indispensability of classical concepts. Here the interpretation
focuses on how we experimentally get to know something about atoms. We
find out about atoms by interacting with atomic systems, not by
picturing them, and the interaction are accounted for in terms of
experiential categories. The pragmatists typically reject the a priori
status of the mind's categories as they take them to be
contingent. From a physical perspective it is a simple matter of facts
that we need classical language to understand our scientific practise;
it does not require any philosophical justification (Dieks 2017).
Likewise, Dorato (2017) compares Bohr's indispensable thesis to
Peter Strawson's descriptive metaphysics according to which we
all share a common conceptual scheme about the experiential world which
cannot be given a further justification. Also Folse notes, in a
comparison between Bohr and I.C. Lewis, that classical concepts reflect
our empirical needs and shared interests and may eventually change if
these needs and interests change (Folse 2017). The common language
together with the development of a physical clarification of some
basic empirical concepts gave us the classical physics because such an
improved language enables us to communicate in an unambiguous and
objective manner about our observations. As Bohr puts it: "...
even when the phenomena transcend the scope of classical physical
theories, the account of the experimental arrangement and the
recording of observations must be given in plain language, suitably
supplemented by technical physical terminology. This is a clear
logical demand, since the very word "experiment" refers to
a situation where we can tell others what we have done and what we
have learned." (*APHK*, p. 71). The use of classical
concepts to grasp the world is beneficial for understanding each
other. Such empirical concepts provide us with an objective
description of the function and outcome of physical experiments.



*Darwinism*. In several places Bohr speaks about the classical
concepts as embodied in our common language, which is *adapted
to* account for our physical experiences. The selection of the
word "adapted to" seems to indicate that Bohr relied on
Darwin's theory of natural selection in his search for an
explanation. The classical concepts are indispensable for the
description of our experience because we are forced by nature to use a
common language that is *adapted to* reporting our visual
experiences, which again is a result of humans' adaptation to
their physical environment (Faye, 2017). Apart from Bohr's use
of the word "adapted to", Bohr's former assistant
Leon Rosenfelt, who was an ardent defender of Bohr's
complementarity, explicitly suggests that "the complementary
logic" is due to human evolution: "I suspect the
development of a computing and communication system like our brain
demands about that complexity of organization which has been reached
by our own species in the course of evolution" (Rosenfeld,
(1961 [1979]), p.515). Natural selection installs certain permanent
visual cognitive schemes in our predecessors, and this cognitive
adaptation explains why these schemes, later reflected in our common
language, gain a privileged epistemic status, and keep this status in
physics in terms of refined classical concepts.



*Experimentalism*. Camilleri (2017) calls Bohr the philosopher
of experiment. Others such as Perovic (2013) have also suggested that
Bohr was more occupied by understanding the outcome of quantum
experiments than by interpreting the quantum formalism. In his paper
Camilleri proposes that the challenge Bohr was facing was that, on the
one hand, experimental observation requires a sharp separation of the
experiment and the observed object, and, on the other hand, because of
what we today call entanglement, "it is no longer possible
sharply to distinguish between the autonomous behaviour of a physical
object and its inevitable interaction with other bodies serving as
measuring instruments" (*CC*, p.84). So, according to
Camilleri, Bohr solved this challenge by making a distinguish between
the function and the structure of an experiment. 



> 
> 
> Bohr's central insight was that if a measuring instrument is to
> serve its *purpose of furnishing us with knowledge of an
> object* - that is to say, if it is to be described
> functionally - it must be described classically. Of course, it
> is always possible to represent the experimental apparatus from a
> purely structural point of view as a quantum-mechanical system without
> any reference to its function. However, any functional description of
> the experimental apparatus, in which it is treated as a means to an
> end, and not merely as a dynamical system, must make use of the
> concepts of classical physics (Camilleri, 2017, pp.30-31).
> 
> 
> 



This analysis explains not only why Bohr thought that classical
concepts were indispensable for interpretational purposes, but also
indicates why he thought that properties like momentum, position, and
duration could be attributed only to an atom object in relation to a
specific experimental arrangement. As Dieks (2017) mentions while
denying any deeper philosophical motivation on Bohr's part: the
use of classical concepts is part of the laboratory life. "This
classical description is basically just the description in terms of
everyday language, generalized by the addition of physics terminology,
and it is the one we *de facto* use to describe our
environment" (Dieks 2017). But because of quantum of action,
symbolized by Planck's constant, the function of experiments
that supply the physicists with exact information about space-time
coordinations is incompatible with experiments whose function it is to
supply them with exact information about energy and momentum.



Indeed, there are both similarities and overlaps between some of the
proposed explanations concerning the indispensability of classical
concepts. Yet, not all of the suggested explanations can be true. Even
though the aim of Bohr's effort is to give an empirical
interpretation of the quantum formalism, his empiricism is different
from that of the logical positivists. He does not seek to reduce terms
concerning theoretical entities to terms about sense-data or purely
perceptual phenomena. He insists only that the empirical evidence
physicists collect from their experiments on atomic objects has to be
described in terms of the same concepts which were developed in
classical mechanics in order for them to understand what the quantum
theory is all about.



Nevertheless, the various explanations all give us some hints into the
complexity of Bohr's thinking concerning the description of
physical experiments. At different times, he seems to put emphasis on
one aspect rather than another, depending on the specific context of
discussion. Sometimes he was occupied with the interpretation of
experiments, sometimes with the relationship between actual
experiments and the formulation of quantum mechanics. In emphasizing
the necessity of classical concepts for the description of quantum
phenomena, Bohr might have been influenced by Kantian-like ideas or
neo-Kantianism (Hooker, 1994). But if so, he was a naturalized or a
pragmatized Kantian. The classical concepts are merely explications of
common-sense concepts that are already a result of our perceptual
adaptation to the world. These concepts and the conditions of their
application determine the conditions for objective knowledge. The
discovery of the quantization of action has revealed to us, however,
that we cannot apply these concepts to quantum objects as we did in
classical physics. The use of classical concepts in the domain of
quantum mechanics has to be restricted with respect to their use in
classical mechanics. Now kinematic and dynamic properties (represented
by conjugate variables) can be meaningfully ascribed to the object
only in relation to some actual experimental results, whereas
classical physics attributes such properties to the object regardless
of whether we actually observe them or not. In other words, Bohr
denied that classical concepts could be used to attribute properties
to a physical world in-itself behind the perceptual phenomena, i.e.
properties different from those being observed. In contrast, classical
physics rests on an idealization, he said, in the sense that it
assumes that the physical world has these properties in-itself, i.e.
as inherent properties, independent of their actual observation.


## 6. The Interpretation of the Quantum Formalism



Classical concepts serve the important function of connecting the
quantum mechanical symbolism with experimental observations. If one
accepts that Bohr's grasp of physics began with his
understanding of the role of physical experiments, this understanding
had strong implications for his empirical interpretation of the
quantum formalism. The modern scholarly debate has taken Bohr to be an
instrumentalist, an objective anti-realist (Faye 1991), a
phenomenological realist (Shomar 2008), or a realist of various sorts
(Folse 1985, 1994; Favrholdt 1994; MacKinnon 1994; Howard 1994, 2004;
Zinkernagel 2015, 2016). But very often the various participants do
not give an exact specification of how they understand these terms and
how these terms apply to Bohr's thinking. The whole discussion
becomes confused because different authors use terms like
"realism" and "antirealism" differently in
relation to Bohr. For instance, Faye (1991) holds that Bohr is an
entity realist but a non-representationalist concerning theories.
Therefore he calls Bohr an objective antirealist. In contrast, Folse
(1986) who also sees Bohr as both a entity realist and a theoretical
non-representationalist calls him a realist. Moreover, Bohr himself
would probably refuse to put any such labels on his own view.



It is certain that Bohr regarded atomic objects as real
(*ATDN*, p.93 and p.103). Their existence has been confirmed by
countless experiments. Hence, phrased in a modern terminology Bohr
might be classified as an *entity realist* in the sense that
experiments reveal their classical properties in relation to an
experimental set-up. Such a view does not fit traditional
instrumentalism where the introduction of unobservable entities is a
logical construction in order to classify various empirical
observations together. But entity realism corresponds with objective
anti-realism, phenomenological realist, and all other forms of realism
because it does not indicate anything about one's attitude
towards theories. A further issue is then how to interpret a physical
theory. Does or doesn't the quantum formalism, according to
Bohr, represent the world over and above being a tool for prediction?




Here are four statements which seem to show that Bohr was an
instrumentalist concerning scientific theories in general and the
quantum formalism in particular.


1. The purpose of scientific theories "is not to disclose the
real essence of phenomena but only to track down, so far as it is
possible, relations between the manifold aspects of experience"
(*APHK*, p.71).
2. "The ingenious formalism of quantum mechanics, which
abandons pictorial representation and aims directly at a statistical
account of quantum processes ..." (*CC*, p.
152).
3. "The formalism thus defies pictorial representation and aims
directly at prediction of observations appearing under well-defined
conditions" (CC, p. 172).
4. "The entire formalism is to be considered as a tool for
deriving predictions of definite and statistical character
..." (*CC*, p. 144).



In these four statements Bohr mentions the absence of "pictorial
representation" twice in relation to the quantum formalism. The
term "pictorial representation" stands for a
representation that helps us to visualize what it represents in
contrast to "symbolic representation". A pictorial
representation is a formalism that has an isomorphic relation to the
objects it represents such that the visualized structure of the
representation corresponds to a similar structure in nature.
Conversely, a symbolic representation does not stand for anything
visualizable. It is an abstract tool whose function it is to calculate
a result whenever this representation is applied to an experimental
situation. With respect to the formalism of quantum mechanics it is
particularly one's interpretation of the wave function that
determines whether one thinks of it symbolically as a tool for
calculation of statistical outcomes or thinks of is as representing a
real physical field.



In a close reading of the Como-paper, Dennis Dieks reaches the
conclusion that "The notion that the lecture is meant to
promulgate an instrumentalist interpretation of quantum theory
according to which the whole formalism possesses only mathematical and
no physical descriptive content is thus immediately seen to sit
uneasily with the textual evidence." (Dieks 2017, p.305). In
other words, Dieks goes against the more general interpretation of
Bohr according to which Bohr only believed that the wave function
formalism is a mere tool for prediction. Just because Bohr writes off
quantum formalism as a pictoral representation, it still gives us some
insight into physical reality. First, Dieks points to another of
Bohr's argument against seeing Schodinger's wave
function as representing anything real. This argument concerns the
fact that the wave function in quantum mechanics cannot represent a
three-dimensional entity.



> 
> 
> Bohr himself tells us that his second argument, about the
> dimensionality of configuration space, is the most important one:
> "*above all* there can be no question of an immediate
> connexion with our ordinary conceptions because... the wave equation
> is associated with the so-called co-ordinate space." In other
> words, the Schrodinger wave in the case of a many-particle system
> cannot be a physical wave in three-dimensional space (which would be
> an "ordinary conception") since it "lives" in
> a high-dimensional mathematical space (Dieks 2017, p.308).
> 
> 
> 



Then Dieks argues that even though this is an argument against wave
function realism, it is not an argument that excludes the wave
function from containing information about the quantum world. Dieks
compares this argument to the one that denies phase space realism.
"We can consistently deny the physical reality of phase space
and still be realists with respect to particles. So we should not
mistake Bohr's argument for the symbolic character of the wave
function for an argument in favor of instrumentalism *tout
court*" (Dieks 2017, p. 308). The difference between
classical many-particles system placed in a phase space and a system
of quantum objects placed in the configuration space is, however, that
the description of many particles in phase space can be decomposed
into a description of single particles in three-dimensional physical
space, whereas the sum of the quantum waves associated with many
particles in configuration space yields yet another superimposed
quantum wave, which cannot be decomposed into a description of single
particles in three-dimensional space. Dieks then continues to show how
the structural features of the quantum formalism guided Bohr in his
interpretation of quantum mechanism. Likewise, he argues that
Bohr's pronouncements on the meaning of quantum mechanics should
first of all be seen as responses to concrete physical problems,
rather than as expressions of a preconceived philosophical doctrine.
His analysis results in a finding that Bohr's qualitative
interpretation is in line with modern non-collapse theories.


## 7. Misunderstandings of Complementarity



Complementarity has been commonly misunderstood in several ways, some
of which shall be outlined in this section. First of all, earlier
generations of philosophers and scientists have often accused
Bohr's interpretation of being positivistic or subjectivistic.
Today philosophers have almost reached a consensus that it is neither.
There are, as many have noticed, both typically realist as well as
antirealist elements involved in it, and it has affinities with Kant
or neo-Kantianism. The influence of Kant or Kantian thinking on
Bohr's philosophy seems to have several sources. Some have
pointed to the tradition from Hermann von Helmholtz (Chevalley 1991,
1994; Brock 2003); others have considered the Danish philosopher
Harald Hoffding to be the missing link to Kantianism (Faye
1991; and Christiansen 2006).



But because Bohr's view on complementarity has wrongly been
associated with positivism and subjectivism, much confusion still
seems to stick to the Copenhagen interpretation. Don Howard (2004)
argues, however, that what is commonly known as the Copenhagen
interpretation of quantum mechanics, regarded as representing a
unitary Copenhagen point of view, differs significantly from
Bohr's complementarity interpretation. He holds that "the
Copenhagen interpretation is an invention of the mid-1950s, for which
Heisenberg is chiefly responsible, [and that] various other physicists
and philosophers, including Bohm, Feyerabend, Hanson, and Popper,
hav[e] further promoted the invention in the service of their own
philosophical agendas" (p. 669).



More recently, Mara Beller (1999) argued that Bohr's statements
are intelligible only if we presume that he was a radical
operationalist or a simple-minded positivist. In fact, complementarity
was established as the orthodox interpretation of quantum mechanics in
the 1930s, a time when positivism was prevalent in philosophy of
science, and some commentators have taken the two to be closely
associated. During the 1930s Bohr was also in touch with some of the
leading neopositivists or logical empiricists such as Otto Neurath,
Philip Frank, and the Danish philosopher Jorgen
Jorgensen. Although their anti-metaphysical approach to science
may have had some influence on Bohr (especially around 1935 during his
final discussion with Einstein about the completeness of quantum
mechanics), one must recall that Bohr always saw complementarity as a
necessary response to the indeterministic description of quantum
mechanics due to the quantum of action. The quantum of action was an
empirical discovery, not a consequence of a certain epistemological
theory, and Bohr thought that indeterminism was the price to pay to
avoid paradoxes. Never did Bohr appeal to a verificationist theory of
meaning; nor did he claim classical concepts to be operationally
defined. But it cannot be denied that some of the logical empiricists
rightly or wrongly found support for their own philosophy in
Bohr's interpretation and that Bohr sometimes confirmed them in
their impressions (Faye 2008).



Second, many physicists and philosophers see the reduction of the wave
function as an important part of the Copenhagen interpretation. This
may be true for people like Heisenberg. But Bohr never talked about
the collapse of the wave packet. Nor did it make sense for him to do
so because this would mean that one must understand the wave function
as referring to something physically real. Only if one can interpret a
quantum measurement as an interaction between an instrument and an
object, whose state is literally represented by
Schrodinger's wave function, and therefore taken to contain
all potential values of observation, does it make sense to claim that
the measurement forces the object to manifest one of these potential
vales. Indeed, such a literal interpretation of the state vector
implies that these values are somehow intrinsically present in the
object with a certain probability all at once. In contrast, Bohr
believed that particular kinematical and dynamical properties are
relational because their attribution to a quantum system makes sense
only in relation to a particular experimental set-up and therefore
that these numerical properties could have a specific value only
during a measurement.



Third, Bohr flatly denied the ontological thesis that the subject has
any direct impact on the outcome of a measurement. Hence, when he
occasionally mentioned the subjective character of quantum phenomena
and the difficulties of distinguishing the object from the subject in
quantum mechanics, he did not think of it as a problem confined to the
observation of atoms alone. For instance, he stated that already
"the theory of relativity reminds us of the subjective character
of all physical phenomena" (*ATDN*, p. 116). Rather, by
referring to the subjective character of quantum phenomena he was
expressing the epistemological thesis that all observations in physics
are in fact context-dependent. There exists, according to Bohr, no
view from nowhere in virtue of which quantum objects can be
described.



Fourth, although Bohr had spoken about "disturbing the phenomena
by observation," in some of his earliest papers on
complementarity, he never had in mind the observer-induced collapse of
the wave packet. Later he always talked about the interaction between
the object and the measurement apparatus which was taken to be
completely objective. Thus, Schrodinger's Cat did not pose
any riddle to Bohr. The cat would be dead or alive long before we open
the box to find out. What Bohr claimed was, however, that the state of
the object and the state of the instrument are dynamically inseparable
during the interaction. Moreover, the atomic object does not posses
any state separate from the one it manifests at the end of the
interaction because the measuring instrument establishes the necessary
conditions under which it makes sense to use the state concept.



It was the same analysis that Bohr applied in answering the challenge
of the EPR-paper. Bohr's reply was that we cannot separate the
dynamical and kinematical properties of a joint system of two
particles until we actually have made a measurement and thereby set
the experimental conditions for the ascription of a certain state
value (*CC*, p. 80). Bohr's way of addressing the puzzle
was to point out that individual states of a pair of coupled particles
cannot be considered in isolation, in the same way as the state of the
object and the state of the instrument are dynamically inseparable
during measurements. Thus, based on our knowledge of a particular
state value of the auxiliary body A, being an atomic object or an
instrument, we may then infer the state value of the object B with
which A once interacted (Faye 1991, pp. 182-183). It therefore
makes sense when Howard (2004, p.671) holds that Bohr considered the
post-measurement joint state of the object and the measuring apparatus
to be entangled as in any other quantum interaction involving an
entangled pair.



Finally, when Bohr insisted on the use of classical concepts for
understanding quantum phenomena, he did not believe, as it is
sometimes suggested, that macroscopic objects or the measuring
apparatus always have to be described in terms of the dynamical laws
of classical physics. The use of the classical concepts is necessary,
according to Bohr, because by these we have learned to communicate to
others about our physical experience. The classical concepts are
merely a refinement of everyday concepts of position and action in
space and time. However, the use of the classical concepts is not the
same in quantum mechanics as in classical physics. Bohr was well aware
of the fact that, on pains of inconsistency, the classical concepts
must be given "a suitable quantum-theoretical
re-interpretation," before they could be employed to describe
quantum phenomena (*ATDN*, p. 8).


## 8. The Divergent Views



The Copenhagen interpretation is not a homogenous view. This insight
has begun to emerge among historians and philosophers of science over
the last ten to fifteen years. Both James Cushing (1994) and Mara
Beller (1999) take for granted the existence of a unitary Copenhagen
interpretation in their social and institutional explanation of the
once total dominance of the Copenhagen orthodoxy; a view they
personally find unconvincing and outdated partly because they read
Bohr's view on quantum mechanics through Heisenberg's
exposition. But historians and philosophers of science have gradually
realized that Bohr's and Heisenberg's pictures of
complementarity on the surface may appear similar but beneath the
surface diverge significantly. Don Howard (2004, p. 680) goes as far
as concluding that "until Heisenberg coined the term in 1955,
there was no unitary Copenhagen interpretation of quantum
mechanics." The term apparently occurs for the first time in
Heisenberg (1955). In addition, Howard also argues that it was
Heisenberg's exposition of complementarity, and not
Bohr's, with its emphasis on a privileged role for the observer
and observer-induced wave packet collapse that became identical with
that interpretation. Says he: "Whatever Heisenberg's
motivation, his invention of a unitary Copenhagen view on
interpretation, at the center of which was his own, distinctively
subjectivist view of the role of the observer, quickly found an
audience" (p. 677). This audience included people like David
Bohm, Paul Feyerabend, Norwood Russell Hanson, and Karl Popper who
used Heisenberg's presentation of complementarity as the target
for their criticism of the orthodox view. However, it should also be
mentioned that in later work, Feyerabend (1968, 1969) was one of the
first philosophers who gave a painstaking analysis of complementarity
in order to clear up the myth of it being unintelligible. Feyerabend
urged philosophers and physicists to go back to Bohr and read him
carefully.



Following up on Don Howard's research, Kristian Camilleri (2006,
2007) points to the fact that complementarity was originally thought
by Bohr (in his Como-paper) to exist between the space-time
description and the causal description of the stationary states of
atoms -- and not between different experimental outcomes of the
free electron. So the formulation of complementarity was restricted to
the concept of stationary states because only there does the system
have a well-defined energy state independent of any measurement. This
observation deserves general recognition. But when Bohr rather soon
thereafter began analysing the double slit experiment in his
discussion with Einstein (1930), he had to extend his interpretation
to cover the electron in interaction with the measuring apparatus.



Camilleri then shows how Heisenberg's view of complementarity,
in spite of Heisenberg's own testimony, radically differs from
Bohr's. As Heisenberg understood complementarity between the
space-time description and causal description, it holds between the
classical description of experimental phenomena and the description of
the state of the system in terms of the wave function. A quotation
from Heisenberg (1958, p. 50) shows how much he misunderstood Bohr in
spite of their previously close working relationship.



> 
> Bohr uses the concept of 'complementarity' at several
> places in the interpretation of quantum theory ... The space-time
> description of the atomic events is complementary to their
> deterministic description. The probability function obeys an equation
> of motion as did the co-ordinates in Newtonian mechanics; its change
> in the course of time is completely determined by the quantum
> mechanical equation; it does not allow a description in space and time
> but breaks the determined continuity of the probability function by
> changing our knowledge of the system.
> 



So, where Bohr identified the causal description with the conservation
of energy, Heisenberg saw it as the deterministic evolution of
Schrodinger's *ps*-function. In other words,
Heisenberg, in contrast to Bohr, believed that the wave equation gave
a causal, albeit probabilistic description of the free electron in
configuration space. It also explains why so many philosophers and
physicists have identified the Copenhagen interpretation with the
mysterious collapse of the wave packet. The transition from a causal
description in terms of the evolution of the *ps*-function
to a classical space-time description is characterized by the
discontinuous change that occurs by the act of measurement. According
to Heisenberg, these two modes of description are complementary.



In another study Ravi Gomatam (2007) agrees with Howard's
exposition in arguing that Bohr's interpretation of
complementarity and the textbook Copenhagen interpretation (i.e.
wave-particle duality and wave packet collapse) are incompatible. More
recently, Henderson (2010) has come to a similar conclusion. He makes
a distinction between different versions of Copenhagen interpretations
based on statements from some of the main characters. On one side of
the spectrum there is Bohr who did not think of quantum measurement in
terms of a collapse of the wave function (for a contrasting view see
Jens Hebor 2005; and partly Zinkernagel 2016); in the middle we find
Heisenberg talking about the collapse as an objective physical process
but thinking that this couldn't be analyzed any further because
of its indeterministic nature, and at the opposite side Johann von
Neumann and Eugene Wigner argued that the human mind has a direct
influence on the reduction of the wave packet. Unfortunately, von
Neumann's dualistic view has become part of the Copenhagen
methodology by people opposing this interpretation.


## 9. The Measurement Problem and the Classical-Quantum Distinction



Apparently, we are living in a quantum world since everything is
constituted by atomic and subatomic particles. Hence classical physics
seems merely to be a useful approximation to a world which is quantum
mechanical on all scales. Such a view, which many modern physicists
support, can be called quantum fundamentalism (Zinkernagel 2015,
2016). It can be defined as a position containing two components: (1)
everything in the Universe is fundamentally of quantum nature (the
ontological component); and (2) everything in the Universe is
ultimately describable in quantum mechanical terms (the
epistemological component). Thus, we may define quantum fundamentalism
to be the position holding that everything in the world is essentially
quantized and that the quantum theory gives us a literal description
of this nature. The basic assumption behind quantum fundamentalism is
that the structure of the formalism, in this case the wave function,
corresponds to how the world is structured. For instance, according to
the wave function description every quantum system may be in a
superposition of different states because a combination of state
vectors is also a state vector. Now, assuming that both the quantum
object and the measuring apparatus are quantum systems that each can
be described by a wave function, it follows that their entangled state
would likewise be represented by a state vector. Then the challenge
is, of course, how we can explain why the pointer of a measuring
instrument enters a definite (and not a superposition) position, as
experience tells us, whenever the apparatus interacts with the object.
In a nutshell this is the measurement problem.



The Copenhagen interpretation is often taken to subscribe to a
solution to the measurement problem that has been offered in terms of
John von Neumann's projection postulate. In 1932 [1996], von
Neumann suggested that the entangled state of the object and the
instrument collapses to a determinate state whenever a measurement
takes place. This measurement process (a type 1-process as he called
it) could not be described by quantum mechanics; quantum mechanics can
only described type-2 processes (i.e., the development of a quantum
system in terms of Schrodinger's equation). In his
discussion of the measurement problem, von Neumann then distinguished
between (i) the system actually observed; (ii) the measuring
instrument; and (iii) the actual observer. He argues that during a
measurement the actual observer gets a subjective perception of what
is going on that has a non-physical nature, which distinguishes it
from the observed object and the measuring instrument. However, he
holds on to psycho-physical parallelism as a scientific principle,
which he interprets such that there exists a physical correlate to any
extra-physical process of the subjective experience. So in every case
where we have a subjective perception we must divide the world into
the observed system and the observer. But where the division takes
place is partly arbitrary. According von Neumann, it is contextual
whether the dividing line is drawn between the description of the
observed object (i) and the measuring instrument together with the
observer (ii) + (iii), or it is drawn between the description of the
observed object together with the measuring instrument, i.e., (i) +
(ii), and the observer (iii). In other words, von Neumann argues that
the observer can never be included in a type 2-process description,
but the measuring instrument may sometime be part of a type 2-process,
although it gives the same result with respect to the observed object
(i). An important consequence of von Neumann's solution to the
measurement problem is that a type 1-process takes place only in the
presence of the observer's consciousness. Furthermore, even when
von Neumann considers the situation in which the descriptions of (i)
and (ii) are combined, he talks about the interaction between the
physical system (i) + (ii) and an abstract *ego* (iii) (Neumann
1932 [1996], Ch VI). Therefore, the mind seems to play an active role
in forming a type 1-process, which would be incompatible with
psycho-physical parallelism.



Indeed, within philosophy of mind one cannot consistently maintain
both psycho-physical parallelism and the existence of an interaction
between the brain and the mind. So it is no wonder that Eugene Wigner
(1967) followed up on the suggestion of the mind's interaction
by proposing that what causes a collapse of the wave function is the
mind of the observer. But Wigner never explained how it was possible
for something mental to produce a material effect like the collapse of
a quantum system. The measuring problem led to the famous paradox of
Schrodinger's cat and later to the one of Wigner's
friend. Although von Neumann's and Wigner's positions are
usually associated with the Copenhagen Interpretation, such views were
definitely not Bohr's as we shall see in a moment.



Quantum fundamentalists must indeed be ready to explain why the
macroscopic world appears classical. An alternative to von
Neumann's projection postulate is the claim that the formalism
should be read literally and that measurements (classical outcomes) do
not describe the world as it really is. But there are ontological
cost, which is significant to some. In one interpretation the world
divides into as many worlds as there are possible measurement outcomes
each time a system is observed or interacts with another system. Other
fundamentalists had hoped that the decoherence program might come up
with an appropriate explanation. The decoherence theory sees
entanglement to exist not only between object and the measurement but
also as something which includes the environment. If Bohr had known
the idea of decoherence, he would probably have had no objection to
it, as several authors have pointed to decoherence as a natural
dynamical extension of his view that measurements is an irreversible
amplification process (Schlosshauer and Camilleri 2015, 2017;
Bachtold 2017, Tanona 2017; and Dieks 2017). However, it is
generally agreed that decoherence does not solve the measurement
problem (Bacciagaluppi 2016; Zinkernagel 2011). This might seems as if
von Neumann's projection postulate has to be reintroduced as a
dynamical factor to explain why one and only one measurement result
appears. However, as Dieks (2017) argues, Bohr's interpretation
could be understood as a non-collapse interpretation, since "the
superposition does not have an empirical meaning independently of its
interpretation via classically described experiments, so no
replacement by another mathematical state is needed. We just have to
interpret the formulas correctly." In spite of that there is no
general agreement to what extent Bohr opposed quantum
fundamentalism.



Time and again Bohr emphasized that the epistemological distinction
between the instrument and the object is necessary because this is the
only way one can functionally make sense of a measurement. The
epistemic purpose of a measuring instrument is to yield information
about an object separated from the instrument itself. It is also
generally agreed that Bohr didn't treat the classical world of
the measuring instrument as epistemically separated from quantum
object along the line of a microscopic and macroscopic division. He
sometimes included parts of the measuring instrument to which the
quantum mechanical description should be applied. Don Howard (1994)
therefore concludes that Bohr was not only an ontological quantum
fundamentalist but in fact also a sort of an epistemological one. He
believes that one can make Bohr's requirement that measuring
apparatus and the experimental results have to be described in
ordinary language supplemented with the terminology of classical
physics consistent with ontological quantum fundamentalism. According
to him, Bohr never considered the measuring instrument as a classical
object. Moreover, he thinks that this implies that Bohr had to
understand the use of classical concepts differently from what
scholars usually think. He reinterprets Bohr in terms of quantum
states called "mixtures". Howard believes that with
respect to an experimental context in which an instrument interacts
with an object, Bohr didn't understand them as being in an
entangled state but being separated in a mixture state. The
consequence would be that the instrument and the object exist in a
definite quantum state since such a state could be represented as a
product of the wave function for the instrument and for the
object.



But, as Maximilian Schlosshauer and Kristian Camilleri (2008 (Other
Internet Resources), 2011) have pointed out, this does not solve the
measurement problem. Howard does not explain under which circumstances
one can move from a quantum system-cum-measuring apparatus being in a
non-separable state to a mixture of separated states. Therefore one
cannot be sure that the measuring apparatus is in a definite state and
its pointer in a definite place. Some philosophers seem to argue that
Bohr was an ontological but not an epistemological quantum
fundamentalist. For instance, "Bohr believed in the fundamental
and universal nature of quantum mechanics, and saw the classical
description of the apparatus as a purely epistemological move, which
expressed the fact that a given quantum system is being used as a
measuring device" (Landsman 2007); and in a similar vein:
"One is left with the impression from Bohr's writings that
the quantum-classical divide is a necessary part of the
epistemological structure of quantum mechanics" (Schlosshauer
and Camilleri 2008 (Other Internet Resources), 2015). So Klaas
Landsman (2006, 2007) accepts Howard's suggestion that Bohr is
an ontological quantum fundamentalist but he rejects that Bohr should
be considered an epistemological quantum fundamentalist. Landsman
argues that Bohr held that the measuring instrument should be
described in classical terms since the results of any measurement like
in classical physics would always have a definite value. However,
Landsman agrees that Bohr understood all objects as essentially
quantum mechanical objects.



However, it may seem as if both Howard and Landsman miss the pragmatic
nature of Bohr's view on ontological issues. Bohr mentioned more
than once that physics was not about finding the essence of nature but
about describing the phenomena in an unambiguous way. In the
foreground of Bohr's thinking was the (1) the need of classical
concepts for the description of measuring results; (2)
non-separability due to the entanglement of the system and the
measuring instrument; (3) the contextual nature of the measurements of
complementary properties; and (4) the symbolic character of the
quantum formalism. One has to take all four components into
consideration if one wants to understand Bohr's solution to the
classical-quantum problem. According to Bohr, we are in quantum
mechanics confronted with the "impossibility of any sharp
separation between the behavior of atomic objects and the interaction
with the measuring instruments which serve to define the very
conditions under which the phenomena appear" (*APHK*, p.
210). This is definitely a non-classical feature which is described by
quantum mechanics alone. In his response to the EPR-paper, Bohr
strongly rejected that this form of interaction could be regarded as a
mechanical influence. The influence was on the conditions of
description, i.e. the experimental conditions under which it makes
sense to apply classical concepts. But during a measurement we need to
separate the system from the measuring instrument and the environment
for pragmatic reasons. The pragmatic reasons seem to be reasonably
clear. The outcomes of whatever experiment always yield a definite
value, so the entanglement of object and the measurement instrument
described by the quantum formalism only lasts until the interaction
between object and instrument stops. The quantum formalism can predict
the statistical outcome of these interactions but it cannot say
anything about the trajectory of objects.



Bohr's firmness about the use of classical concepts for the
descriptions of measurement can be seen as his response to the
measurement problem. This problem arises from the fact that quantum
mechanics itself cannot account for why experiments on objects in a
state of superposition always produce a definite outcome. Hence if one
does not argue for spontaneous collapse of the wave function, hidden
variables, or many worlds, one needs to supplement quantum mechanics
with a classical description of measuring instruments in terms of
clocks and rods. Henrik Zinkernagel (2015, 2016) may seem to get close
to Bohr's view when he argues that Bohr not so much solved the
measuring problem as he dissolved it. According to his interpretation,
Bohr believed in a quantum world, but only relative to a particular
classical description and a certain classical world. The distinction
between classical and quantum (both ontic and epistemic) is
contextual. He thinks that the measurement problem is ultimately a
consequence of ontological quantum fundamentalism (that everything is
quantum). Because if everything is quantum - and correctly
described by quantum formalism (what else would it mean to call
everything quantum?) - then a measurement ends up in a
superposition whether we describe the apparatus classical or not. One
could say with Zinkernagel that Bohr believed all objects can be
treated as quantum objects, but they cannot all be treated as quantum
objects at the same time. Borrowing a conception from the two Russian
physicists, Landau and Lifshitz, Zinkernagel claims that only some
parts of the measuring device are entangled with the object in
question, but those parts which are not entangled exists as a
classical object. Depending on the context, objects cannot be treated
as quantum objects in those situations in which they acts as measuring
apparatuses. In these situations the classical treatment of the
measuring device provides us with a frame of reference of space and
time with respect to which an atomic object has a position, and,
mutatis mutandis, with respect to which it has energy and momentum.
Such a frame of reference is necessary for our ability to define and
measure a particular property. In Bohr's own words: "in
each case [of measurement] some ultimate measuring instruments, like
the scales and clocks which determine the frame of space-time
coordination on which, in the last resort, even the definitions of
momentum and energy quantities rest, must always be described entirely
on classical lines, and consequently kept outside the system subject
to quantum mechanical treatment" (*CC*, p. 104). What
characterizes a frame of reference is that it establishes the
conditions for the ascription of a well-defined position or a
well-defined momentum, and treated classically measuring instruments
act exactly as frames of reference. The implication is that Bohr did
not exclude the application of quantum theory to any system. Every
system can in principle be treated quantum mechanically, but since we
always need a frame of reference to describe experimental outcomes,
not all systems can be treated quantum mechanically at once.



In this debate Dorato (2017) stresses the fact that by making explicit
reference to Einstein's presentation of his special theory of
relativity, Bohr regarded quantum mechanics as a theory of principle.
This explains both Bohr's epistemic reliance on the domain of
classical physics and his ban of any attempt to construct classical
objects from quantum objects. Despite this position Dorato argues that
in order to justify his entity realism and anti-instrumentalist
interpretations, Bohr also needed to postulate something ontologically
distinct from the realm of quantum mechanics, a claim that creates the
well-known problem of defining in a non-ambiguous and exact way the
cut between the classical and the quantum realm. By following
Zinkernagel, he claims that this problem is somewhat softened by
Bohr's contextualist theory of measurement. However,
Bohr's holism, according to which the measuring device and
quantum object are in state of entanglement, is in objective tension
with Bohr's thesis of an ontological distinction, especially in
virtue of the fact that by referring to the interaction between the
quantum and the classical system as an irreversible physical process,
Bohr seems to need a constructive approach to quantum mechanics that
he wants to avoid.



Nonetheless, the question is to what extent Bohr really believed that
the classical world is not only epistemically but also ontologically
different from the quantum world? If he did not make an ontological
distinction, there would be no contradiction between his epistemic
view that the outcome of measurement needs to be described classically
but that the apparatus ontologically is just as much a quantum object
as the object under investigation. So when Bohr regarded quantum
mechanics as a rational generalization of classical physics, he always
thought of it as a way to secure the epistemic validity of quantum
mechanics and not a way to save a classical ontology. Directly
addressing Zinkernagel's analysis, Dieks (2017) strongly argues
that there can be little doubt that Bohr believed that quantum
mechanics is universal in the sense that Heisenberg's
indeterminacy relation applies to both micro- and macroscopic systems
due to the quantum of action. Classical mechanics is a mathematical
approximation. Moreover, Bohr believed for epistemic reasons that we
had to use classical language because this language is a refinement of
our everyday language, which is adapted to describe our sensory
experience and therefore the only language that can endow the quantum
formalism with an empirical content. Hence, according to Dieks, Bohr
assumed that it is only an epistemic necessity to describe
"*some* systems classically in order to have a pragmatic
starting point for the treatment of other systems." Bohr's
demand of using classical concepts for epistemic reasons has no
implications for his view that macroscopic objects are quantum
objects. Measuring devices are not classical objects even though we
need classical concepts to describe our general physical experiences
and the outcome of quantum experiments. So Dieks concludes that the
interaction between the measuring device and the quantum object
determines, in the classical textbook examples, whether position or
momentum talk can be carried over to the quantum object that is
measured. The measuring device itself, if macroscopic and under
ordinary circumstances (so that it really is a measuring device that
can be used by us) allows both position and momentum talk in its own
description. The measurement interaction determines which correlations
are forged with the micro-world.


## 10. New Perspectives



After the 1950s a number of alternative interpretations to
Bohr's complementarity were articulated and they all found their
proponents among physicists and philosophers of science. The
Copenhagen interpretation started to lose ground to other
interpretations such as Bohm's interpretation, the many worlds
interpretation, the modal interpretation and the decoherence
interpretation, which have been more in vogue the last couple of
decades. But parallel with the growing awareness of the essential
differences between Bohr's and Heisenberg's understanding
of quantum mechanics several philosophers of science have revitalised
Bohr's view on complementarity. Around the millennium a new
recognition of the Copenhagen interpretation has emerged.



Rob Clifton and Hans Halvorson (1999, 2002) argue that Bohm's
interpretation of quantum mechanics can be seen as a special case of
Bohr's complementarity interpretation if it is assumed that all
measurements ultimately reduce to positions measurement. Originally
Jeffrey Bub and Clifton (1996) were able to demonstrate (given some
idealized conditions) that Bohr's complementarity and
Bohm's mechanics fall under their uniqueness theorem for
no-collapse interpretations. Clifton and Halvorson improve this result
by showing that Bohr's idea of position and momentum
complementarity can be expressed in terms of inequivalent
representations in the C\*-algebraic formalism of quantum mechanics. It
turns out that either position or momentum are dynamically
significant, but it is not permissible to assume that position and
momentum are both dynamically significant in any single context. From
these assumptions they conclude that Bohm's hidden variables are
none other than the "value states" that the
complementarity interpretation postulates if position measurement were
always dynamically significant, but this metaphysical restriction is
not, as their results indicate, demanded by the physics. Rather,
Clifton and Halvorson (1999) and Halvorson (2004) believe that
complementarity may give us a realist interpretation of quantum field
theory.



Philosophers have also started to explore the idea of decoherence in
relation to Bohr's view about "the inseparability of the
behavior of the object and the interaction with the measuring
instrument" or "the uncontrollable interaction between the
atomic system and measurement apparatus." (Schlosshauer and
Camilleri 2011, 2017; Camilleri and Schlosshauer 2015; Bachtold
2017; and Tanona 2017). Although Bohr assumed that the measuring
apparatus is altogether a quantum mechanical system, he nevertheless
believed that the instrument could be approximately described by
classical *theory*. Among the scholars just mentioned there is
a general agreement that the notion of decoherent is coherent with
Bohr's view about the quantum-classical division and adds a
dynamical explanation of quantum-to-classical transition which
Bohr's own exposition lacked. Also attempts to clear up the
structural relationship between Bohr's view and Hugh
Everett's "relative state"-interpretation have been
carried out; a relationship which at some points is much closer than
usually thought (Bacciagaluppi 2017).



Another insight into Bohr's view of complementarity is due to
Michael Dickson (2001, 2002). By using the contemporary theory of
reference frames in quantum theory, he proves that Bohr's
response to the EPR thought-experiment was in fact the correct one.
Moreover, he also maintains that Bohr's discussions of spin, a
property much less frame dependent than position and momentum, were
very different from his discussions of the latter, and based on these
differences he offers a Bohrian account of Bell's theorem and
its significance.



A re-assessment of Bohr's philosophy of quantum mechanics is
made by Whitaker (2004) on the basis of Clifton and Halvorson's
and Dickson's works and in the light of quantum information
theory. Besides these attempts to apply Bohr's notion of
complementarity to the contemporary discussions of the interpretation
of quantum mechanics and quantum field theory there is an ongoing
attempt to understand Bohr's idea of symbolic representation
(Tanona, 2004a, 2004b) and his notion of complementarity with respect
to trends in post-modern philosophy and general epistemology such as
poststructuralism, deconstructivism, feminism and cultural studies
(Honner 1994; Plotnitsky 1994; Barad 2007; and Katsumori 2011).