Original Source
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Comments on Bohr's Original Argument
The argument represented in the Como paper always remained Bohr's basic
approach to complementarity. He expanded on these concepts with two subsequent
essays in 1929, but neither contained any specific new points bearing on his
arguments. These papers along with the Como paper were published, with Bohr's
1925 paper on "Atomic Theory and Mechanics", as "Atomic Theory and the
Description of Nature", a slim volume of only 119 pages written without any
overall structure. This provides Bohr's fundamental statement of
complementarity.
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However, more than 25 articles bearing on complementarity were written by Bohr
between 1931 and his death in 1962, and there are included some substantial
changes in both the mode of expression and emphasis Bohr used, as well as
considerable comments on the application of complementarity to fields beyond
atomic physics. Here in Part 3 of this review, these important changes in
expression and emphasis will be explored in greater detail.
One of the biggest misconceptions about Bohr's framework of complementarity is
that it merely describes what is occurring at the quantum level. As I mention
in Part 4 of this review, Complementarity and the Uncertainty Principle, the
fact that Bohr did not stress this enough is very evident. Bohr believed the
framework of complementarity offered a more expanded view of what was
occurring in the atomic system because it used fundamental principles of
perception for its foundation.
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Complementarity, as conceived by Bohr, requires that both matter and radiation
be described through seemingly contradictory "pictures" of particles and
waves. This paradoxical nature of complementarity is due to the classical
tendency to regard these pictures as representations of objects having an
"independent reality", the properties of which correspond to the properties of
the "visualizable pictures". The justification of this approach lies in the
classical description of interaction as taking place continuously, which makes
it possible to define the state of the system at any point in its transition
from one state to another. The wave and particle pictures derived from the
classical definition thus enable us to "visualize" that system being observed
throughout the course of its interactions with observing instruments.
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Individuality
Once the change of state in an interaction is represented as taking place
discontinuously, it is not possible to provide a spatio-temporal picture of
the system changing from one state to another. Thus the state of the observed
system cannot be defined separately from that of the observing system. This
gives the interaction the feature of indivisibility, which Bohr calls
"individuality". Consequently it is impossible to visualize the interaction as
a "transition process". Bohr writes:
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Indeed only by a conscious resignation of our usual [i.e., classical] demands
for visualization and causality was it possible to make Planck's discovery
fruitful in explaining the properties of the elements on the basis of our
knowledge of the building stones of atoms. Taking the indivisibility of the
quantum of action as a starting-point, the author suggested that every change
in the state of the atom should be regarded as an individual process,
incapable of more detailed description, by which the atom goes over from one
so-called stationary state into another...On the whole, this point of view
offers a consistent way of ordering the experimental data, but the
consistency is admittedly only achieved by the renunciation of all attempts
to obtain a detailed description of the individual transition process. The
Philosophy of Niels Bohr Page 119
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This "individuality" of the interaction makes it impossible to define a
classical state for the atomic system as it is observed in an interaction,
and thus to uphold the classical justification for according an independent
reality to the objects visualized. But the tendency to accord an independent
reality to observed objects, even in theoretical quantum representation,
persists so long as we the observers see the description of nature from the
classical point of view.
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This is why it is imperative to realize that the framework of
complementarity, in order to be interpreted correctly, must start by making
us aware of how it is that we perceive our reality in the first place, and
then shifting the classical subject and object viewpoint into what may be
called a "two-position" complementary view. Ultimately I see this leading to
a actuality/ non-actuality, or static/Dynamic Quality view as Pirsig calls
it.
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Bohr never approached complementarity in such a fashion, that I am aware of
however. First of all, he was concerned mostly with atomic systems and so
that is where he focused. This is one of the least understood parts of
complementarity, in my opinion...just exactly why it was that Bohr refused to
consider where the observations originated. Yet taken in a larger context of
our awareness, we begin to see just why it was he was prohibited from
considering such a concept. You may begin that journey by reading my paper
Two Riders Approaching; Concepts of Good and Evil in the Metaphysics of
Quality which attempts to put the framework of complementarity into the
concepts of life and death, good and evil.
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Wave and Particle Dualism
Back to the review...in light of Bohr's concern with this paradoxical
dualism, it is perhaps remarkable that the relationship between wave and
particle is NOT the basis for complementarity. It is clear from the Como
paper that Bohr uses complementarity to refer to the relationship of
space-time and causality. Nevertheless, in the Como paper and throughout his
other essays, Bohr refers to complementarity between particle and wave
"pictures". Complementarity was designed to remove the paradoxical quality
of this dualism by providing an alternative to the classical framework.
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Thus it was Bohr's opinion that "the well known dilemma between the
corpuscular and undulatory character of light and matter [is] avoidable only
by means of complementarity". In the Como paper, Bohr wrote that "we are not
dealing with contradictory but with complementary pictures of the phenomena,
which only together offer a natural generalization of the classical mode of
description".
Unfortunately, beyond these brief statements, Bohr never directly explains
the relationship between the complementarity of space-time and causal modes
of description and the complementarity between wave and particle pictures.
Nevertheless, it is possible to account for this relationship. Bohr cannot
mean to associate space-time description with "particle pictures" and causal
description with "wave pictures". The unambiguous use of the term "particle"
refers to that which exists in a classical mechanical state, and this
concept of the classical state requires determining BOTH the position and
the momentum of the particle. Thus any well-defined use of "particle" cannot
be the result of applying only the mode of space-time description. The same
holds true for the "wave picture".
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Each interaction must be "interpreted" in order to describe how the
measuring instruments determine the property of the observed object. With
such a theoretical interpretation of the observation, each system must be
unambiguously represented so that the interaction can be described in a way
which characterizes the observed object in terms of either spatio-temporal
concepts or the "dynamic" concepts of momentum and energy. At this point,
classical "wave" and "particle" pictures have their necessary uses.
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However, in order to apply the space-time mode of description, an
interaction with the system which is to be described MUST occur, which
physically precludes the necessary interaction to apply the conservation
principles in the causal mode, which determines the "dynamic behavior" of
the system. Bohr writes: ...since the discovery of the quantum of action, we
know that the classical ideal cannot be attained in the description of
atomic phenomena. In particular, any attempt at an ordering in space-time
leads to a break in the causal chain, since such an attempt is bound up with
an essential exchange of momentum and energy between the individuals and the
measuring rods and clocks used for observation; and just this exchange
cannot be taken into account if the measuring instruments are to fulfill
their purpose. Conversely, any conclusion, based in an unambiguous manner
upon the strict conservation of energy and momentum, with regards to the
dynamical behavior of the individual units obviously necessitates a complete
renunciation of following their courses in space and time. The Philosophy of
Niels Bohr Page 121
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Space-time Measurements
Making a space-time measurement requires describing a different interaction
from that required to determine energy or momentum. Since those interactions
which can be described as space-time observations will differ from those
which are described as momentum-energy observations, different pictures can
be used to describe the observed object in these different observations
without inconsistency or contradiction.
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In order to "interpret" an observation, the interacting systems must be
clearly distinguished by using the space-time mode of description. But to
describe the effect one system has on another, the causal mode is necessary.
This conclusion justifies regarding the two descriptions as "complementary"
rather than merely alternative ways of describing nature. It also implies
that neither mode of description can be abandoned, but neither can they be
used in conjunction with each other, as in the classical framework.
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Bohr points out that although we must use wave and particle pictures to
interpret observations, the classical expectation that we can visualize the
object of observation is no longer possible in quantum theoretical
descriptions. Once the quantum postulate is accepted, the state of the
system while observed cannot be defined separately from the instruments with
which it is interacting. The state of the system is isolated as an
"abstraction". Therefore, the classical expectation to visualize an
independent reality is neither reasonable nor necessary.
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This point is vital to the understanding of how Bohr presented his idea of
complementarity. Schr”dinger's famous cat was devised as a way to expose
this particular notion of complementarity as an absurdity, however, like so
many other thought-experiments dreamt up to discredit it, Schr”dinger's cat
merely confirmed that complementarity describes a fundamental way we observe
our reality.
It may seem as if the proper inference to draw from this is that these
classical modes of description need to be replaced with a new alternative
method which would eliminate wave-particle dualism and restore determinism.
However, Bohr rejects this search for any alternative mode of description:
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...the view has been expressed from various sides that some future more
radical departure in our mode of description from the concepts adapted to
our daily experience would perhaps make it possible to preserve the ideal of
causality also in the field of atomic physics. Such an opinion would,
however, seem due to the misapprehension of the situation. For the
requirement of communicability of the circumstances and results of
experiments implies that we can speak of well-defined experiences only
within the framework of ordinary concepts. In particular, it should not be
forgotten that the concept of causality underlies the very interpretation of
each result of experiment, and that even in the coordination of experience,
one can never, in the nature of things, have to do with well-defined breaks
in the causal chain. The renunciation of the ideal of causality in atomic
physics which has been forced on us is logically founded only on our not
being any longer in a position to speak of the autonomous behavior of a
physical object, due to the unavoidable interaction between the object and
the measuring instruments which in principle cannot be taken into account,
if these instruments according to their purpose shall allow the unambiguous
use of the concepts necessary for the description of experience. In the last
resort an artificial word like "complementarity" which does not belong to
our daily concepts serves only briefly to remind us of the epistemological
situation here encountered, which at least in physics is of an entirely
novel character. The Philosophy of Niels Bohr Page 123
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A Framework of Ordinary Concepts
Bohr's rejection of any new set of descriptive concepts which would avoid
wave-particle dualism and the limitations expressed by the uncertainty
principle is a consequence of his conviction "that we can speak of
well-defined experiences only within the framework of ordinary concepts". He
makes the same point elsewhere that the "basic concepts of mechanics" are
"indispensable...for the definition of fundamental properties of the
agencies with which they [the atomic systems] react".
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Lagrangians
Here again, we see that Bohr fails to stress exactly why it is that we
must use our basic concepts of mechanics in order to define the atomic
system. Perhaps this extract from New Scientist magazine dealing with
mathematical concepts known as Lagrangians will help shed some light on
just why our basic concepts cannot be abandoned...
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Where do the laws of physics come from? It's the sort of question
only children and geniuses ask--certainly most physicists are far too
busy putting the laws to work.
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Take quantum theory, the laws of the subatomic world. Over the past century it
has passed every single test with flying colours, with some predictions
vindicated to 10 places of decimals. Not surprisingly, physicists claim
quantum theory as one of their greatest triumphs. But behind their boasts lies
a guilty secret: they haven't the slightest idea why the laws work, or where
they come from. All their vaunted equations are just mathematical lash-ups,
made out of bits and pieces from other parts of physics whose main
justification is that they seem to work.
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Now one physicist thinks he knows where the laws of quantum theory come from.
More amazingly still, Roy Frieden thinks he can account for all the laws of
physics, governing everything from schoolroom solenoids to space and time.
Sounds incredible? You haven't heard the first of it. For Frieden believes he
has found the Law of Laws, the principle underpinning physics itself.
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The laws of electricity, magnetism, gases, fluids, even Newton's laws of
motion--all of these, Frieden believes, arise directly from the same basic
source: the information gap between what nature knows and what nature is
prepared to let us find out. Using sophisticated mathematics, Frieden has
shown that this notion of physics as a "quest for information" is no empty
philosophical pose. It can be made solid, and leads to a way of deriving all
the major laws of fundamental physics--along with some new ones.
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"I came across a 1959 paper by the Dutch mathematician A. J. Stam, who showed
that I could be used to derive Heisenberg's famous uncertainty principle,"
recalls Frieden. "And being a physicist, this set me thinking."
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Studying Stam's work, Frieden noticed that it made use of a result from
information theory called the Cramer-Rao inequality. This little-known
mathematical result shows, roughly speaking, that when the error in a
measurement is multiplied by the amount of Fisher information in the
measurement, the result is a number that is never less than one.
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It's a relationship strikingly similar to the uncertainty principle. Multiply
together the uncertainties in your knowledge of a particle's position and its
momentum, and the result is never less than a certain value. The more
precisely you know the position, the less precisely you can know the momentum.
Or put another way, the act of measuring the position influences the measured
value of the momentum--and vice versa.
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The similarity between the Cramer-Rao inequality and the uncertainty principle
started Frieden wondering whether information--and Fisher information in
particular--had a much deeper role in physics. "Since Heisenberg's principle is
so basic, it occurredto me that perhaps every physical phenomenon occurs in
reaction to measurement--that measurement acts as a kind of catalyst for the
effect," says Frieden. "And the possibility that physical laws occur as answers
to questions excited my curiosity."
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Digging into this possibility, Frieden soon found another mathematical
"coincidence". Whenever he did calculations using the Fisher information, the
final results were differential equations. "What struck me," he recalls, "is
that virtually all of physics can also be expressed in terms of differential
equations."
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Differential equations are formulae showing how the rate of change of a certain
quantity changes under outside influences. For instance, Newton's second law
of motion relates the acceleration of an object to the force applied: F = ma.
The acceleration in this formula is the rate of change of velocity, which in
turn is the rate of change of distance. Quantum theory has its own, more
abstract, examples, such as Schr”dinger's famous wave equation and Dirac's
relativistic equation for the electron. The same format shows up across the
whole of physics.
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Again, it's the kind of observation that is apt to provoke a shrug of the
shoulders. But now Frieden was sure he was on to something really deep. The
ubiquity of these types of equation, he believed, is intimately linked to one
of the most profound mysteries in science: despite the vast range of phenomena
covered by the fundamental laws of physics, all of those laws can be made to
drop out of mathematical objects known as Lagrangians. And no one knows
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Put simply, Lagrangians are made up of the difference between two quantities
which together form something called the "action". For reasons as yet utterly
mysterious, this quantity stays as small as possible under all circumstances.
This curiosity--known as the principle of least action--is reflected in the
fact that the fundamental laws of physics are differential equations, since
that's what you need to minimise the action.
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In Newton's laws of motion, for example, the relevant action turns out to be
the difference between the kinetic energy and the potential energy of a body.
Kinetic energy is the energy associated with how fast something is moving, and
potential energy with its location. It turns out that to keep the difference
between these two to a minimum, the object's mass times its acceleration always
has to equal the force applied. Minimising this particular action leads to
Newton's second law of motion.
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Beyond action
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Theorists are convinced that action must be incredibly important--so much so
that the discovery of any new fundamental law prompts a race to work out the
particular action needed to produce it. The trouble is that no one understands
the principles behind nature's infatuation with action, and so no one can
calculate it directly. Instead, they have to reverse-engineer it, working
backwards from the newly discovered law.
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It is the puzzle of action--and thus the origin of the laws of physics--that
Frieden now reckons he has solved. And, he says, it all comes down to
information--the information we try to prise from nature by making observations
and the information nature has, but is reluctant to part with.
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If you look at Lagrangians for gravity or electromagnetism, says Frieden, they
all have more or less the same mathematical form. They are all made up of the
difference between I, the Fisher information from observing the phenomenon, and
another statistical quantity, J, which is the amount of information bound up in
the phenomenon you're trying to measure.
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It is from this that Frieden has built his radically new vision of physics
based not on the mysterious "action", but on something more intuitive: our
attempt to come up with the best possible description of phenomena. All the
information needed for such a description exists, in the form of J, and we want
as much of it as possible to be extracted by our measurements, in the form of
I. In other words, we want the information difference--I minus J--to be as
small as possible. And it turns out that for this difference to be as small as
possible, the phenomenon must obey a differential equation.
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Frieden's information-based methods provide a stunningly clear interpretation
of the laws of physics: they represent the best we can possibly do in our quest
to extract information using our inevitably error-prone methods. "Through the
very act of observing, we thus actually define the physics of the thing
measured," says Frieden. He adds that while unfamiliar, the idea that
"reality"--or, at least, the laws of physics--are created by observation is not
new. During the 18th century, empiricist philosophers such as Bishop Berkeley
were raising similar ideas. Much more recently, John Wheeler, a physicist at
Princeton University who is widely regarded as one of the deepest thinkers on
the foundations of physics, has championed remarkably similar views. "Observer
participancy gives rise to information and information gives rise to physics,"
he says.
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That's not to say Frieden's approach implies that the laws of physics are "all
in the mind". Rather, it means that any physical attempt to extract
information about nature determines the answer we obtain--and the best
information we can ever extract is what we call the laws of physics.
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So Frieden's achievement is to give a philosophical view of physics a solid
mathematical foundation. For any given system, I and J are statistical
quantities which can be calculated using Frieden's methods.And the payoff is
spectacular: with these two quantities, you can fulfil the 200-year-old dream
of deriving the Lagrangian for that system, and thus of deriving the physical
law that rules it.
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(I is the Law, article by Robert Matthews)
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The Significance of Complementarity
It is clear to me that Bohr knew of the significance of what complementarity
says about the way we observe reality, yet he failed to stress that enough. In
Bohr's later essays, the need for classical concepts to communicate
unambiguously the results of experiments becomes the basis for his claim that
complementarity provides an "objective" description of the phenomena with
which atomic physics is concerned. The experiences on the basis of which the
experimenter describes the observing instruments are experiences of everyday
objects in space and time, thus space-time concepts refer directly to the
experience of the observing instruments. However, the use of the classical
concept of causality is also essential. Without the concept of causality it
would be impossible to consider the state of the observing systems as an
affect of its interaction with the observed object.
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The fact that a measurement must be described through the classical mechanical
concepts joined with the fact that formalism does not permit a well-defined
classical state for the observed object implies that if causality is
identified with determinism, then "the invocation of the classical ideas,
necessitated by the very nature of measurement, is, beforehand, tantamount to
a renunciation of a strict causal description". However, the loss of
determinism in quantum physics "does not imply that the laws of conservation
of momentum and energy lose their validity, but only that their application
stands in an exclusive, so-called 'complementarity', relationship to the
analysis of the motion of the particles".
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Therefore, the talk of renunciation of causality in quantum physics should not
mislead anyone into thinking that the classical account of causal reactions
between systems is abandoned. Bohr's point is that this means of describing
interactions is complementary to giving a space-time description of the
quantum system. Although this is not a typical way to present complementarity,
Bohr's remarks that space-time coordination and dynamical conservation laws
may be considered two complementary aspects of ordinary causality, which in
quantum mechanics exclude one another to a certain extent, although neither
has lost their intrinsic value.
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Bohr's recurrent claims that we must "renounce the customary demand for
visualization" in describing quantum theory may seem inconsistent with his
view that in complementarity observed phenomena must be described in terms of
ordinary space-time concepts working with the classical framework. Bohr had no
objection to the heuristic value of visualization. Nevertheless, from the very
beginning he was somewhat upset over the tendency of many physicists to take
his model too concretely, and occasionally he himself was drawn into taking it
more literally than he intended.
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Some Conclusions about Complementarity
Neils Bohr
Indeed only by a conscious resignation of our usual [i.e., classical] demands
for visualization and causality was it possible to make Planck's discovery
fruitful in explaining the properties of the elements on the basis of our
knowledge of the building stones of atoms. Taking the indivisibility of the
quantum of action as a starting-point, the author suggested that every change
in the state of the atom should be regarded as an individual process,
incapable of more detailed description, by which the atom goes over from one
so-called stationary state into another...On the whole, this point of view
offers a consistent way of ordering the experimental data, but the consistency
is admittedly only achieved by the renunciation of all attempts to obtain a
detailed description of the individual transition process.
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Doug Renselle, Quantonics Inc.
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Now we know Bohr's process description in the blue highlight above is not an
individual process. We know individuistic classical state change is
impossible. DQ is always imposing its flux on all of actuality. ( And all of
actuality is resisting DQ's flux affects. ) Very recent experiments show this.
Historically, evidence of vacuum energy arose in Casimir's test-for-VE-presence
experiment. Two plates separated by a small distance exhibit a measurable
external pressure pushing both plates together. Casimir's experiment was first
done, I believe, several decades ago. Very recently, though, someone asked the
question, "Would an atom spontaneously emit a photon in Casimir's plenum?" Test
results answer, "No!" Thus we see change of state in a classical system depends
on its interrelationship to VE/DQ to effect state change. This unambiguously
demonstrates an interrelationship between VE and a classically individuated
atom must be present for classical change of state to occur. (Consider a
possible implication: Does a Casimir plenum provide a way to classically
isolate an atom?) This makes it clear, at least to me, state change is a
classical concept. State change, as depicted by Bohr above, is a SOM
ontological, subject-object schismatic, single-ended perspective of a Quantonic
interrelationship twixt an atom and DQ. This is why I said we need to
symbolically change Dirac's bra-ket notation. We need to change his vertical
(SOM-dichotomous) bar (which separates complementary conjugates) to a Wingdings
lower case 'v' (Quantonic interrelationship). This is a very big deal and
another feather in the cap of both quantum science and Pirsig's MoQ. Your
review of Folse's work provides a venue of explanation for several rudimentary
Quantonic memes. Thanks! PDR 4Feb99. )
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Dan Glover
Doug, I am happy I can help! From what I gather, Bohr is not talking about
what actually occurs in the atomic system here, but rather how we are able to
turn it into something we can conceptualize into mathematical symbolism. I
agree with you that Bohr was trapped in the logical positivist atmosphere of
the times and his complementarity reflects that by focusing on only
individualistic events. However, it also seems to me that Bohr chose to use
Occam's Razor in the very same place that Pirsig uses it, between what it is
that we are aware of, and that which we are unaware of. I am pretty sure he
would be in agreement with what you say if he lived today and was aware of all
the new findings in quantum science.
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Additional Comments
Since we cannot use space-time concepts in their "usual" classical roles, and
if we accept the essential correctness of quantum mechanics, as Bohr certainly
did, then the classical ideal expressed in terms of visualization through
wave-particle "pictures" must be rejected in favor of complementarity. Bohr's
choice to revise our understanding of the use of these descriptive concepts
enabled complementarity to hold that a theoretical representation of an
isolated system is an abstraction from which one can make predictions
expressed in terms of space-time parameters which characterize the observed
object or in terms of defining its dynamic (momentum) behavior.
Complementarity does not assume that these phenomenal properties which confirm
the theoretical interactions are a causal effect of corresponding properties
possessed by an independent reality existing apart from the observed
interactions.
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Such a correspondence between phenomena and an alleged independent reality must
forever remain beyond the possibility of empirical investigation. We MUST
measure such empirical space-time observations in empirical science, but not
because there are corresponding properties possessed by independently real
entities, but according to complementarity, the reason we MUST use space-time
concepts is because the way in which the theoretical representation is
confirmed as adequate necessitates that at least some concepts find consistent
and unambiguous empirical reference in the description of the physical systems
used as observing instruments.
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The classical viewpoint justifies its application of space-time concepts to
both properties of observed phenomena AND the properties of an independently
existing physical reality by assuming that the classical state of the system is
NOT simply an abstraction, but pictures of the properties of an independent
reality. Once the quantum postulate is accepted however, the quantum
theoretical representation of an isolated system refers to an abstraction only,
and wave and particle pictures used to interpret observation can no longer be
regarded as describing an independent reality.
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This might be easier to see from the viewpoint of the Metaphysics of Quality.
The intellect level can be viewed as an abstraction as well, and it is there
that all our generalized notions of reality arise. The Metaphysics of Quality
tells us that these intellect level abstractions are every bit as "real" as the
"objects" they represent, but at the same time they are each governed by a
different set of moral codes, and are separated from each other by the
biological and social levels.
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This ends part 3 of this review. Thank you for reading!
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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