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The Argument for Complementarity

Bohr presented his entire argument in six paragraphs which comprise the first section of his Como papers. He begins by calling attention to the "peculiar" difficulties which result from the quantum postulate:

The quantum theory is characterized by the acknowledgment of a fundamental limitation in the classical physical ideas when applied to atomic phenomena. The situation thus created is of a peculiar nature, since our interpretation of the experimental material rests essentially on the classical concepts. Notwithstanding the difficulties which, hence, are involved in the formulation of the quantum theory, it seems, as we shall see, that its essence may be expressed in the so-called quantum postulate, which attributes to any atomic process an essential discontinuity, or rather individuality, completely foreign to the classical theories and symbolized by Planck's quantum of action. The Philosophy of Niels Bohr Page 109

In this opening statement several important ideas are already noted. First, Bohr is clearly looking for a "fundamental limitation" which would restrict the application of "the classical physical ideas when applied to atomic phenomena". Once he realized that wave-particle dualism was inescapable, he concentrated not on over-throwing these paradoxical representations, but rather on removing the paradox by limiting their use. Second, Bohr claims these classical concepts MUST be retained because without them, it would be impossible to provide what he calls an "interpretation of the experimental material".

This has deep philosophical ramifications that I am not sure Bohr was completely aware of, otherwise he would have certainly stressed it more. In essence, what Bohr is telling us in this paragraph is that this "peculiar nature" is a fundamental way in which we conceive of our everyday classical reality. Complementarity does not spring from classical mechanics, but rather it is classical mechanics that spring from complementarity.

Bohr's reference to this discontinuity as an "individuality" is his way of expressing that because it has been discovered that it is necessary to describe interactions involving atomic systems with a theoretical formalism which represents them as taking place discontinuously, within that formalism it is impossible to define separately the classical state of each of the systems that interact. A state for the interacting whole system as an "individual" can be defined, but not for its separate components. Thus the acceptance of the quantum postulate implies the impossibility of describing the observations in a way which subdivides the whole phenomenon of interaction into a process taking place between systems for which classical mechanical states can be precisely defined throughout the interaction.

Here Bohr is identifying not only an individualistic atomic state, but also our individualist state of awareness, as the observers are indeed included in the framework of complementarity as essential components of the observation. Complementarity shifts the burden of proof away from an "independent" reality into a proof provided by unambiguous communication, in other words, our agreements (see Pragmatism, Precession and the Metaphysics of Quality) become all-important. This feature of "individuality" has major philosophical ramifications that cannot be stressed enough, something Bohr, in my opinion, failed to do time and again.

In the next paragraph, Bohr considers the consequences of this "individuality" on the use of the classical concepts in the description of such a discontinuous interaction:

This postulate implies a renunciation as regards the causal space-time co-ordination of atomic processes. Indeed, our usual description of physical phenomena is based on the idea that the phenomena may be observed without disturbing them appreciably. This appears, for example, clearly in the theory of relativity, which has been so fruitful for the elucidation of classical theories. As emphasized by Einstein, every observation or measurement ultimately rests on the coincidence of two independent events at the same space-time point. Just these coincidences will not be affected by any differences which the space-time co-ordination of different observers otherwise may exhibit. Now, the quantum postulate implies that any observation of atomic phenomena will involve an interaction with the agency of observation not to be neglected. Accordingly, an independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor to the agencies of observation. The Philosophy of Niels Bohr Page 110

Disturbing the Phenomena

In this early presentation of complementarity, Bohr is still confusing the observation as "disturbing" the observed phenomena. The fact that an observation requires a physical interaction between the observed object and the observing system implies that it "disturbs" it. This is already the case in classical mechanics. However, in that context, the presupposition that the observed and the observing system change state continuously in the interaction allows one to determine theoretically the nature and extent of the disturbance. Thus classically it was possible on the basis of an observation to define the state of the closed system isolated from interaction by correcting for the disturbance produced by observing it. In Bohr's words, "the interaction is controllable".

Unfortunately, Bohr's way of phrasing this tended to confuse his audiences into thinking he was claiming that in fact the systems described by quantum theory do exist in classical mechanical states while in an observational interaction, but because the observation "disturbs" those states it is impossible to determine empirically precisely what they are. In this interpretation, Bohr's talk of a "limitation" on the classical descriptive concepts would appear to be a limitation on knowledge of the classical mechanical state. This is clearly NOT what Bohr intended, seen by the fact that this is inconsistent with Bohr's primary conclusion, expressed in the last sentence.

There he concludes that we cannot describe an observation in a way that treats the observed object and the observing instrument as having "an independent reality in the ordinary physical sense." If the objects described by quantum mechanics, such as waves and particles, did in fact have "independent reality in the ordinary physical sense" it would be possible to define classical mechanical states for them.

Since by the quantum theory this is not possible, if the theory provides a complete description, these objects cannot be regarded as existing in classical mechanical states whether or not it would be possible for us to determine these states. If Bohr had believed that the observed object does indeed exist in a well-defined mechanical state, though we cannot determine it because of the disturbance, there would be no reason why we could not continue to regard the observed object as having "independent reality in the ordinary physical sense". But the fact that we can no longer regard the observed object as really "existing" represents the most dramatic break with the classical framework.

The disturbance language Bohr uses at the beginning of the second paragraph tends to lead the reader away from this important conclusion. However, the second line of argument derived from the "individuality" of the observational interaction does not lend itself to this misinterpretation. This argument is more apparent in later essays and is evident in the following sentences that were appended to the second paragraph only in later versions:

After all, the concept of observation is in so far arbitrary as it depends upon which objects are included in the system to be observed. Ultimately, every observation can, of course, be reduced to our sense perceptions. The circumstance, however, that in interpreting observations use has always to be made of theoretical notions entails that for every particular case it is a question of convenience at which point the concept of observation involving the quantum postulate with its inherent "irrationality" is brought in. The Philosophy of Niels Bohr Page 112

This passage presents a way of regarding the observational interaction not liable to be misunderstood involving the "disturbance" interpretation. Bohr explicitly repudiated the "disturbance" way of speaking. He emphasized even more the fact that the process of interaction could not be non arbitrarily subdivided. Because of the individuality of the interaction described as an observation, any distinction between observed object and agency of observation is arbitrary. Since it is arbitrary in any interaction which we wish to consider an object and an observation system, it is merely a question of convenience at which point we wish to make the discontinuity of change of state required by the quantum postulate.

Interpreting the Observation

Bohr's talk of "interpreting observations" refers to the need to describe the observation as an interaction between physical systems. Hence, such an "interpretation" must make use of "theoretical notions". Since the discontinuity in change of state occurs in the description of the interaction between observed object and the observing system, where ever we decide to make that distinction in the whole interaction is the point at which the discontinuity will enter the picture.

In no case did Bohr mean that "reason" was to be abandoned in describing quantum processes, as has been frequently misunderstood. In the third paragraph, Bohr turns to consider the consequence of this individuality of quantum processes on the classical ideal of description: This situation has far-reaching consequences. On the one hand, the definition of the state of a physical system, as ordinarily understood, claims the elimination of all external disturbances. But in this case, according to the quantum postulate, any observation will be impossible, and above all, the concepts of space and time will lose their immediate sense. On the other hand, if in order to make an observation possible we permit certain interactions with suitable agencies of measurement, not belonging to the system, an unambiguous definition of the state of the system is naturally no longer possible, and there can be no question of causality in the ordinary sense of the word. The Philosophy of Niels Bohr Page 112

Here Bohr uses "definition" to refer to the classical goal of defining the state of an isolated system from which all "external disturbances" and been "eliminated". He points out that this goal, necessary for applying the conservation principles to determine the causal development of the state of the system is impossible to achieve simultaneously with giving the space and time concepts empirical reference ("immediate sense") in an observation.

If an observation is made, the observed system is in an interaction and in the quantum representation the individuality of this interaction means that any division made between observing system and observed object is an arbitrary one made within the description of that interaction. Thus it is impossible to formulate an "unambiguous" definition of the system's classical mechanical state. Without such a definition of the closed system's state, it is impossible to apply the conservation principles (the claim of causality) to the state of the isolated system to provide a causal description of the temporal development of that state.

Modes of Space and Time

The modes of space and time are necessary to describe what is determined by an observation, and it has also been empirically determined that conservation principles DO apply to each atomic process. Hence, although the two classical modes of description cannot be applied at the same time, neither can they be abandoned. In the fourth paragraph, Bohr concludes that space-time co-ordination and causal description are "complementary":

The very nature of quantum theory thus forces us to regard the space-time co-ordination and the claim of causality, the union of which characterizes the classical theories, as complementary but exclusive features, of the description, symbolizing the idealization of observation and definition respectively. Just as the relativity theory has taught us that the convenience of distinguishing sharply between space and time rests solely on the smallness of the velocities ordinarily met with compared to the velocity of light, we learn from the quantum theory that the appropriateness of our usual space-time descriptions depends entirely on the small value of the quantum of action compared to the actions involved in ordinary sense perceptions. Indeed, in the description of atomic phenomena, the quantum postulate presents us with the task of developing a "complementarity" theory the consistency of which can only be judged by weighing the possibilities of definition and observation. The Philosophy of Niels Bohr Page 114

The complementary relationship holds between space-time co-ordination and the claim of causality, both of which were combined in the classical framework. Only later does Bohr speak of complementarity between wave and particle "pictures". Bohr's initial concern is to explain why these two modes of description could have been united classically and why they no longer can be so combined when describing atomic systems. The reason he gives is because the processes in the classical framework normally can be described using "ordinary sense perceptions", which require interactions so huge relative to that measured by Planck's quantum constant, that for all practical purposes the discontinuity in the interaction could be ignored. This reasoning is an instance of Bohr's correspondence principle at work. It provides his reasoning for regarding the classical framework as a special case of which complementarity is a generalization.

In the next paragraph, Bohr calls to mind both the phenomena that requires wave description and those which require particle descriptions: This situation would seem clearly to indicate the impossibility of a causal space-time description of the light phenomena. On the one hand, in attempting to trace the laws of the time-spatial propagation of light according to the quantum postulate, we are confined to statistical considerations. On the other hand, the fulfillment of the claim of causality for the individual light processes, characterized by the quantum of action, entails a renunciation as regards space-time description. Of course, there can be no question of a quite independent application of the ideas of space-time and causality. The two views of the nature of light are rather to be considered as different attempts at an interpretation of the experimental evidence in which the limitation of the classical concepts is expressed in complementary ways. The Philosophy of Niels Bohr Page 115

Bohr argues that "we are confined to statistical considerations" when attempting a space-time description of light propagation because the quantum formalism does not permit determining the state of the observed radiation in an observational interaction with any greater precision than that expressed by Heisenberg's uncertainty principle. If an observation of a phenomenon which is interpreted by representing radiation as a photon at a precise point in space and time, the energy of that photon cannot be defined, for it requires determining the frequency of the radiation and that in turn requires a wave description which represents the radiation as spread out through a region of space.

Wave and Particle "Pictures"

Thus Bohr concludes the sixth paragraph with the important claim that while the use of wave and particle pictures to represent the quantum mechanical object apart from the observational system is necessary for a theoretical representation, these pictures refer to "abstractions":

In the discussions of these questions, it must be kept in mind that, according to the view taken above, radiation in free space as well as isolated material particles are abstractions, their properties on the quantum theory being definable and observable only through their interactions with other systems. Nevertheless, these abstractions are, as we shall see, indispensable for a description of experience in connection with our ordinary space-time view. The Philosophy of Niels Bohr Page 117

Using wave and particle "pictures" we can formulate theoretical representations of the objects of quantum mechanical descriptions as independent from an observational interaction, i.e., as "radiation in free space" or as "isolated material particles. Bohr makes it clear that a "description of experience", i.e., interpreting an observational event, makes such a representation indispensable. And the apparent contradiction of using wave representations in some situations and particle representations in others is dispelled once it is understood they are both abstractions or idealizations, and not the actual property of independently existing entities.

This conclusion is the very core of the difference between how the description of nature is understood within the classical framework and how it is understood within complementarity. This is clearly one of the reasons Bohr refuses to speculate in any manner as to where the observation being focused on originated. This marks a break with classical epistemology and our normal way of thinking, and seems to have deep philosophical ramifications on what it is that we are capable of knowing at all.

Conclusions

Niels Bohr

PDR (Doug Renselle)

Dan Glover

[The Quantum] postulate implies a renunciation as regards the causal space-time co-ordination of atomic processes.

I.e., there is no y = f(t) analytic function which can describe space-time coordination of atomic processes.

This is what bothered Einstein about complementarity and triggered his famous saying 'God doesn't play dice with the universe', or words to that effect.

The quantum postulate implies that observation of atomic phenomena will involve an interaction with the agency of observation not to be neglected.

The quantum postulate implies that any observation of atomic phenomena will involve an interaction with the agency of observation not to be neglected. Accordingly, an independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor to the agencies of observation.

Nor can there be an independent observer apart from the observed phenomenon.

Classically it was possible on the basis of an observation to define the state of the closed system isolated from interaction by correcting for the disturbance produced by observing it. In Bohr's words, "the interaction is controllable"

PDR believes this hints at the concept of local context. PDR believes all Quantonic interrelationships experience different levels of (statistical or stochastic) stability which may be measured in terms of their latch duration. The Quantonic interrelationships for any Quality Event may be ordered by stability, and for quasi-classical observations measurement may converge (adaptively) on selectable stable interrelationships. Imagine, for example, the integral of selected nodes of the 'ket.'

I think part of the misunderstanding revolving around complementarity involves the term "controllable interaction", by which Bohr seemed to mean that by which we communicate unambiguously, and thereby turn into a local context that our awareness can then deal with. Bohr's insistence on the need for using classical concepts arose from this conviction that complementarity is fundamental to how we perceive reality.

Given Stein's work and my comments above, I think Bohr is mistaken here. Classically space and time were different concepts until Einstein's theories of relativity united them. Now we know space-time is an identity, not a complementary interrelationship. Causality is produce of analyticity, determinism, and inductivism, all of which are well-refuted in any physical realm (all seem perfectly acceptable in any pure conceptual realm of mathematics -- which I see as a blissfully ignorant but pedagogic path of SOM philosophy). See Pirsig, Stein, Popper, et al.

I am as yet unconvinced that Bohr was mistaken, yet at the same time I am not able to offer a convincing reason why.

Just as the relativity theory has taught us that the convenience of distinguishing sharply between space and time rests solely on the smallness of the velocities ordinarily met with compared to the velocity of light, we learn from the quantum theory that the appropriateness of our usual space-time descriptions depends entirely on the small value of the quantum of action compared to the actions involved in ordinary sense perceptions.

To all of this I would simply respond, "Reality scales!"
It is important to understand what Bohr is saying about the complementarity twixt space-time and causality. Classically, as you noted, separate space and time concepts were analytic and causal. In other words classical science unified both concepts of time and analyticity, and, in addition, both concepts space and analyticity. In Einsteinian relativity space-time became unified and classical analyticity of its unification retained. In quantum science space-time has its own Steinian complement: nonspace-nontime, or what Stein calls nonspace, and I call nonactuality. We can represent these: Reality = quanton(nonactuality,actuality), or reality = quanton(nonspace,space). In quantum reality, nonspace is analytic and space is stochastic because of quantum reality's quantized and random nature of measurement events which allows nonspace to create, change, and discreate space.

This provides Bohr's reasoning for regarding the classical framework as a special case of which complementarity is a generalization. I tend to relate this to Stein's work relating space and time as special conditions of non space and imaginary time.

Of course, there can be no question of a quite independent application of the ideas of space-time and causality.

Absolutely! Stein's ontology approaches this idea. Pirsig's MoQ is a new philosophy which parents the new science.

And that independent application of ideas must be accomplished through unambiguous communication of these ideas.

In the new ontology, my conjecture is flux will be our one, general abstraction, and we will say Static Patterns of Value (both particles/substance and subjective phenomena) represent latched flux abstraction and all else represent unlatched flux abstraction. Flux-latched and flux-unlatched metaphors are something like this fluxL: SQ, mixed state, actuality, space, etc. And fluxU: DQ, pure state, nonactuality, nonspace, etc.

It is clear to me that both Bohr and Pirsig believe the subject and object dichotomy to be composed of only concepts, abstractions. Pirsig said that the intellect level was just such an abstraction and it appears that Bohr would agree with him on that count.

Complementarity, as Bohr understood it, was much more than only a quantum tool. Yet because he didn't really understand the philosophical significance of what that meant, due in part to his lack of a philosophical education, he discovered his framework of complementarity was too vague to be grasped, and instead of expanding his concepts of complementarity, he found himself embroiled in a life long battle to defend it.

This ends Part 2, The Argument for Complementarity.
The final paragraph in the first section the Como papers marks a transition to the remainder of the paper in which Bohr turns his attention to showing how the uncertainty relations express the complementary aspects of the description. This will be explored further in part 4 of this review. But first, Part 3 contains Comments on Complementarity. The reader is free to skip directly to Part 4 now, or continue sequentially with this review. And thank you for reading!

Framework of Complementarity

Part 1 - An Overview of Complementarity
Part 3 - Comments on Complementarity
Part 4 - The Uncertainty Principle and Complementarity
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

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The Argument for Complementarity

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