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.
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.
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.
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:
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
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.
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.
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.
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.
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".
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.
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
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.
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.
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.
This point is vital to the understanding of how Bohr presented his idea of complementarity. Schrödinger'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, Schrödinger'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:
...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
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".
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...
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.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.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.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.
"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."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.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.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."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."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 Schrödinger's famous wave equation and Dirac's relativistic
equation for the electron. The same format shows up across the
whole of physics.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
why.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.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.Beyond action
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.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.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.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.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.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.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 thatsystem, and thus of deriving the physical law that rules it.
(I is the Law, article by Robert Matthews)
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.
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".
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.
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.
Some Conclusions about Complementarity
Niels 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. |
Doug Renselle, Quantonics
Inc.
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. ) |
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. |
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.
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.
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.
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.
This ends part 3 of this review. Thank you for reading!
Part 1 - Overview
of Complementarity
Part 2 - Argument
for Complementarity
Part 4 - 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
Other Links
Perceptions of Quality Homepage