Tekhnema 5 / "Energy and Chance"/ Fall 1999

Techno-Atoms: The "Ultimate Constituents of Matter" and the Technological Constitution of Phenomena in Quantum Physics

Arkady Plotnitsky

…aiming to bring out the essential ambiguity involved in a reference to physical attributes of objects when dealing with phenomena where no sharp separation can be made between the behavior of the objects themselves and their interaction with the measuring instruments.
—Niels Bohr

Quantum physics was inaugurated in 1900 by Max Planck’s discovery of, under certain conditions, the quantum or, as the phenomenon was initially understood, the discontinuous (particle-like) character of radiation, previously believed to be a continuous (wave-like) phenomenon in all circumstances.1 Planck made his discovery in the course of his attempt to formulate and, then, interpret the radiation law for the so-called black body, whose model is a heated piece of metal with a cavity.2 The limit at which discontinuity appears is defined by the specific frequency of the radiation of the body and a universal constant of a very small magnitude, h, now known as Planck’s constant, which Planck himself termed "the quantum of action" and which turned out to be one of the most fundamental constants of all physics. The indivisible quantum (i.e. quantity) of radiation in each case is the product of h and the frequency v, E = hv.

Planck’s discovery is widely seen as the single greatest discovery in twentieth-century physics. According to Einstein, "this discovery set science a fresh task: that of finding a new conceptual basis for all physics"; according to Bohr, "a new epoch in physical science was inaugurated by Planck’s discovery of the elementary quantum of action, which revealed a new feature of wholeness [i.e. indivisibility] inherent in atomic processes, going far beyond the ancient idea of the limited divisibility of matter."3

Bohr’s addition of "elementary" to "quantum of action" is significant. It indicates that, at least in his view, not only is there a certain definite quantity at stake, but also a certain general quality of indivisibility, or atomicity proper. As will be seen, in Bohr’s view, this atomicity appears at the level of the interaction between quantum (micro) objects and classical measuring (macro) instruments, rather than that of quantum objects themselves. From this perspective, the only "atoms" that can be rigorously described by quantum theory are "techno-atoms"—certain indivisible configurations of experimental technology. Any attempt to subdivide such phenomena can only produce other indivisible phenomena of the same nature. This circumstance prevents any possibility for quantum objects to appear independently, outside of, in this sense, techno-phenomenological enclosures of specific experiments. We only have access to certain effects of quantum objects upon such enclosures, whose particular character is in turn determined by these effects. According to Bohr, quantum mechanics describes such "closed phenomena" and only them, rather than the behavior of quantum objects, the ultimate constituents of nature, themselves.

Planck indeed remarkably succeeded in deriving his law. Whether he equally succeeded in understanding and interpreting it is a far more complex issue. It may be, and has been, questioned whether he actually discovered, or at least initially accepted, that radiation or energy itself must be "quantized" (i.e. is seen as occurring in discontinuous and indivisible, "atomized" portions) in certain circumstances. The latter discovery may be more properly credited to Einstein and his, in Bohr’s words, "unfailing intuition" which, in 1905, led him to the invention of the photon, the "atom" of light, and, hence, of the particle-like, rather than only wave-like, character of radiation (PWNB 2:33). At least some of Planck’s reasoning was incompatible with his law itself, and it was Einstein who appears to have been the first to show this incompatibility rigorously in 1906.4 Einstein observed that "the imperfections of [Planck’s] derivation" and the fact that these imperfections "remained at first hidden" were "most fortunate for the development of physics." He added, however, "delighted as every physicist must be that Planck in so fortunate a manner disregarded the need [for properly justifying certain key physical aspects of his derivation], it would be out of place to forget that Planck’s radiation law is incompatible with the theoretical foundations which provide his point of departure."5

Planck’s reasoning was that of classical physics; Planck’s law was that of quantum physics. The two kinds of physics ultimately proved to be incompatible, indeed more incompatible than Einstein suspected at the time and than he ever wished them to be. Or rather, they cannot be brought together in the way Planck tried to do in explaining his law through the reasoning of classical physics. As will be seen, classical and quantum physics can (and perhaps must) coexist and function jointly in quantum theory in a very different way. In particular, in Bohr’s interpretation, one retains the applicability of classical physical attributes and behavior, and makes their application necessary, in describing measuring instruments, while this application is always prohibited in describing the quantum objects under investigation. Indeed, as will be seen, it appears that any description—mathematical, physical, or other—is rigorously inapplicable to "quantum objects," that is, what we refer to by this term.6

Planck’s discovery emerged from the investigation of the nature of energy, entropy, and chance at the level of the ultimate constituents of matter as modern physics defines these constituents now—that is, at the quantum level.7 The situation may have been imperfectly understood initially. Eventually, however, Planck’s law and related developments, and our attempts to interpret them radically transformed our understanding of physics and of the limits of our scientific and philosophical knowledge, and its claims upon nature, technology, and mind. The transformation took a while, as did a more adequate interpretation of quantum phenomena themselves—more or less, in the wake of quantum mechanics, introduced by Heisenberg and Schrödinger in 1925 and 1926, respectively. (These two formulations of quantum mechanics were quickly proven to be mathematically equivalent.) Indeed we are hardly finished with either even now, as the year 2000 approaches, at least insofar as the debate concerning quantum physics continues. No end appears to be in sight.8

1. Quantum Techno-Phenomenology

My argument here concerns some of the most radical and controversial aspects of quantum epistemology. Following Bohr’s interpretation of quantum mechanics, known as complementarity, I shall argue that the nature of the ultimate constituents of matter as quantum entails two interrelated features:
a) the irreducibly statistical character of quantum physics, not only in practice (as would be the case in classical statistical physics, or chaos theory) but also in principle; and
b) the equally irreducible, in practice and in principle, role of technology (specifically that of measuring instruments) in the constitution of the experimental data of quantum physics and, correlatively, in the interpretation of the mathematical formalism of quantum theory.
Thus, quantum physics entails a radical rethinking of the relationships among the data, the experimental technology, and the mathematical formalism of a physical theory, and of the concepts of data, experimental technology, and mathematical formalism themselves.9
Epistemologically, Bohr argues, the first feature described above entails "the necessity of a final renunciation of the classical ideal of causality" and the second "a radical revision of our attitude towards the problem of physical reality."10 This revision and, arguably, in turn a final renunciation of the classical ideal of reality are specifically necessary in view of, in Bohr’s words (recurring throughout his writings), "the impossibility of any sharp separation between the behavior of atomic [i.e. quantum] objects and the interaction with measuring instruments which serve to define the conditions under which the phenomena [i.e. what we actually observe] appear" (PWNB 2:39, Bohr’s emphasis). According to Bohr, this inseparability and, thus, a certain "indivisibility" or "wholeness" of all phenomena that can be rigorously considered in quantum physics are direct consequences of what he calls "the quantum postulate" (which I shall consider later). It is this interaction or, more rigorously, the effects of this interaction upon the character of the phenomena in question (rather than the behavior of quantum objects themselves), that is rigorously covered by the mathematical formalism of quantum mechanics. As Bohr says, "in accordance with this situation there can be no question of any unambiguous interpretation of the symbols of quantum mechanics other than that embodied in the well-known rules which allow [us] to predict the results to be obtained by a given experimental arrangement described in a totally classical way, and which have found their general expression through the transformation theorems" (Quantum Theory and Measurement [hereafter QTM], 150). The transformation theorems are part of the mathematical formalism of quantum mechanics, "which," Bohr observes, "perhaps more than any other feature of the [quantum-mechanical] formalism contribute to secure its mathematical completeness and its rational correspondence with classical mechanics" (QTM, 145, note). The quantum constitution of the measuring instruments themselves must, to some degree, be disregarded in quantum measurement, on which I shall comment later. Bohr maintains that "under these circumstances an essential element of ambiguity is [always] involved in ascribing conventional physical attributes to [quantum] objects [themselves]" (PWNB 2:40).

I shall argue here (against more conventional interpretations of quantum mechanics and, sometimes, of Bohr’s views) that this ascription is ultimately ambiguous in any and all circumstances, for example and in particular:
a) even when measurements upon quantum objects are performed (it is standard to see this ascription ambiguous in the absence of measurement); and
b) even in the case of any single such attribute, rather than only that of a simultaneous joint attribution of certain conjoined physical quantities (such as position and momentum, or time and energy), more immediately prohibited in view of Heisenberg’s uncertainty relations.

As a result, the elementary nature, strictly "atomicity," of quantum physics, initially understood as the limited divisibility of quantum objects themselves, is refigured as or translated into the indivisibility or wholeness of the (irreducibly) technological observable "phenomena" in Bohr’s special sense of the term. This new concept is, according to Bohr, necessary in the field of quantum theory. Phenomena are defined by "the impossibility of any sharp separation between the behavior of atomic [i.e. quantum] objects and the interaction with measuring instruments," mentioned above, and, hence, refer in each case to the overall experimental set-up at the macro-level. Accordingly, phenomena are no longer identified with (the representation of) quantum objects themselves, or even with their direct effects upon the measuring instruments, such as traces in cloud chambers or on photographic plates. Instead they are conceived of as (representing) the overall experimental arrangements, as affected by their interactions with quantum objects.11 The ultimate constituents of matter can only be approached through the indivisible technological-experimental phenomena in this sense, but never in themselves. Hence, these constituents cannot be (unambiguously) characterized either as indivisible or as divisible, or indeed in terms of any other physical attributes. At the limit, rarely accepted in the interpretations of quantum mechanics or in readings of Bohr, this is impossible even when the interaction with the measuring instruments takes place. (It is, as I said, a more or less accepted view within the orthodox interpretation to see a physical description of quantum objects as impossible outside this interaction.) The ultimate constituents of matter are, thus, seen as giving rise to indivisible macro-phenomena, while they remain in themselves rigorously inaccessible, unrepresentable, inconceivable, and so forth, including, naturally, as the "ultimate constituents of matter." (Hence, the structural quotation marks here and in my title, and, implicitly, whenever the expression occurs in this article.) Their constitution as "quantum objects" is unavailable, and any reference to their physical properties (be they conventional physical attributes, such as position or momentum, or qualities such as atomicity or/as discontinuity, or, conversely, continuity), independent of their interaction with the technology would always entail an essential ambiguity. For Bohr, this indivisibility gives the proper meaning to the quantum of action discovered by Planck, or, as he says, this indivisibility is "symbolized" by Planck’s quantum of action. On this view, the "techno-atomicity" becomes the proper and perhaps the only possible meaning of the "atomicity" in the field of quantum theory. So (re)interpreted, "Planck’s discovery," in Bohr’s radical formulation, indeed "reveal[s] a new feature of wholeness […], going far beyond the ancient idea of the limited divisibility of matter" (PWNB 3:2). By the same token, this feature is "quite foreign to the mechanical conception of nature" (PWNB 2:71), whereby the laws of physics would, on the model of classical mechanics, apply or would be assumed to apply to the ultimate constituents of nature themselves and their attributes.

In this interpretation, quantum mechanics provides no ontology of the quantum world and appears to tell us that no such ontology is possible. Thus, it prohibits doing in principle what it does not do in practice. At least, in Arthur Fine’s formulation, "the theory cannot provide, even in principle, what it does not provide [in practice]."12 This statement may be seen as a variation on Bohr’s: "we are not dealing with an arbitrary renunciation of a more detailed analysis of atomic phenomena but with a recognition that such an analysis is in principle excluded" (PWNB 2:62).13 Both propositions combined may be applied throughout the present argument.

This is not to say that quantum objects do not exist. Indeed it is their existence that is responsible for the situation in question. Some information concerning quantum objects is obtainable and is comprehensively accounted for by quantum mechanics, which makes rigorous predictions concerning measurable quantities pertaining to phenomena. By so doing, it establishes continuity with and, as Bohr likes to point out, may even be seen as a rational generalization of classical physics. The question is what is the nature of this information, or what measurable quantities these predictions relate to. In Bohr’s view, all such information must be seen as manifesting itself in the properties of phenomena in Bohr’s sense, the phenomena resulting from the interaction between measuring instruments and quantum objects. That is, this information manifests itself as specific data emerging in the experimental arrangements involving the measuring instruments, whose own behavior is described by means of classical physics, while the character of the data itself is unaccountable by these means. All quantum-mechanical predictions can only concern phenomena in this sense and, hence, refer to outcomes of the interactions between quantum objects and measuring instruments, not to the behavior of quantum objects themselves. As will be seen, in part for this reason (and given the specific nature of these interactions), these predictions can only be of statistical nature.

There may be a kind of "indivisibility" or at least "individuality" at the level of quantum objects, insofar as we need to consider them as individuals and even as, in some respects, identical or indistinguishable individuals (electrons, photons, neutrinos, quarks, etc).14 From the present viewpoint, however, this can only mean that these objects must be seen as producing individual (and in certain respects identical) effects upon our measuring instruments, say, when we measure the mass or electrical charge of, or associated with, such elementary objects. The value measured will be the same for each particle denomination just mentioned. As will be seen, however, for any type of quantum object, the outcome of the repeated experiments concerning, as they are called, kinematic (such as position or time) and dynamical (such as momentum and energy) variables, defined by the same experimental setups, are never strictly identical, which, as will be seen, entail the irreducibly statistical character of quantum mechanics.

We appear to encounter problems whenever we try to establish an unambiguous reference to physical attributes of quantum objects or to explain what is going on with quantum objects themselves, for example, when "particles" pass through the slits in the famous double-slit experiment. The same happens in other more or less equivalent and more or less spectacular experiments, illustrating the famously strange behavior of quantum objects. There are numerous accounts of such experiments (including by Bohr in many works cited here), which need not be recounted in detail here. It may, however, be useful to recall the key features of the double-slit experiment—the "archetypal" quantum-mechanical experiment.

The arrangement consists of a diaphragm with a slit, (A) and, then, at a sufficient distance from it, a second diaphragm with two slits (B and C), widely separated, and, finally, also at a sufficient distance a screen (say, a silver bromide photographic plate), where we can register the interaction with particles hitting it. Provisionally speaking for the moment in terms of quantum objects themselves, let us allow a sufficient number (for a full effect it must be very large, say, a million) of elementary particles, such as electrons or photons, emitted from a source to pass through both diaphragms and leave their traces on the screen. A wave-like interference pattern will emerge on the screen, or more accurately, the pattern analogous to the traces that would be left by classical waves in the corresponding media, say, water waves in the sand. That is, it will emerge unless we install particle-counters or make other arrangements, which would allow us to check through which of the two slits the particles that hit the screen pass. This pattern is the actual manifestation and, according to the standard interpretation, the only possible manifestation of the "wave" character of the quantum world, whether we deal with what would be classically (prior to the advent of quantum physics) seen as wave-like phenomena, such as light, or as particle-like phenomena, such as electrons. In this interpretation at least, one can speak of "wave propagation" or of any attributes of the classical-like phenomenon of wave propagation (either associated with individual particles or with their behavior as a multiplicity) prior to the appearance of these registered marks only by convention or symbolically. (The same is true as concerns the attributes of classical particle motion, in particular trajectories).15 It is also worth keeping in mind that, in accordance with the overall scheme here presented, we see on the screen only classically manifest traces of quantum objects. The latter themselves are destroyed in the process of this, in Bohr’s terms, "irreversible amplification" of all our encounters with quantum objects to the classical level (PWNB 3:3). If, however, there are counters or other devices allowing us to check through which slit particles pass (we can also do it by closing one slit or the other), the interference pattern inevitably disappears. Its appearance entails the lack of knowledge as to through which slit particles pass. Thus, ironically (such ironies are typical of quantum mechanics), the irreducible lack of knowledge, the impossibility of knowing, is in fact associated with the appearance of a pattern and, hence, with a higher rather than lower degree of order, as would be the case in, say, classical statistical physics. (Chaos theory is something else again.) I shall return to this point below in discussing the nonclassical character of chance in quantum physics.

The behavior just described, sometimes also known as the quantum measurement paradox, is indeed remarkable. Other standard locutions include "strange," "puzzling," "mysterious" (and sometimes "mystical"), and "incomprehensible." The reason for this reaction is that, if one speaks in terms of particles themselves (this always appears to be the source of trouble), in the interference picture the behavior of each particle appears to be "influenced" by the location of the slits. Or, even more radically, the particle appears somehow to "know" whether both slits are open or not, or whether there are counting devices installed or not. The first possibility may appear to imply that each particle would spread into a volume larger than the slit separation or would somehow divide into two and then re-localize or re-unite so as to produce a single effect, a point-like trace on the plate. (The distance between slits can be very large relative to the "size" of the particles, thousands of times as large.)16 This view, or equivalent or analogous views are sometimes found in literature on the subject. However, whether one subscribes or not to the particular interpretation under discussion here, the standard view is more or less as follows. Although having both routes open always leads to the interference effect, any given particle passing through the slits should be seen as an indivisible whole (or, in present terms, the corresponding effects upon measuring devices are individualized accordingly). There is no evidence for it being anything else. Placing a detector in the experiment would always confirm this—at the cost of losing the interference pattern. In the so-called delayed choice experiment we can make alternative arrangements, revealing either the particle-like or the interference pattern, long after the event, while we can never observe either any "spreading" or any "division" of single particles (or, again, the corresponding effects).17

The situation can also be given a statistical interpretation, equally manifesting this, apparently inescapable, strangeness of the quantum world. I here follow Anthony J. Leggett’s elegant exposition, describing a different but equivalent experiment, in which instead of slits we consider the initial state A, two intermediate states B and C, and then a final state E. (The latter would be analogous to the state of a given particle at the point of its interaction with the screen in the double slit experiment.) First, we arrange to block the path via state C, but leave the path via state B open. In a very large number (say, again, a million) of trials we record a number of particles reaching state E. Then we repeat the same number of runs of the experiment, this time blocking the path via B, and leaving the path via C open. Finally we repeat the experiment, again, with the same number of runs with both paths open. In Leggett’s words, "the striking feature of the experimentally observed results is, of course, summarized in the statement that […] the number reaching E via ‘either B or C’ appears to be unequal to the sum of the numbers reaching E ‘via B’ or ‘via C.’" The probabilities of the outcomes of individual experiments will be affected accordingly. (Quantum mechanics predicts these probabilities and only these probabilities, rather than accounting for the motion of quantum objects themselves in the way classical mechanics does for classical objects.) The situation is equivalent to the emergence of the interference pattern when both slits are open in the double slit experiment. In particular, in the absence of counters or, more generally, in any situation when the interference pattern is found one cannot assign probabilities to two alternative "histories" of a "particle" passing through either B or C on its way to the screen. If we do, the above probability sum law would not be obeyed and the conflict with the interference pattern will inevitably emerge, as Bohr stressed on many occasions (QTM, 146-47; PWNB 2:46-47). Leggett concludes:

In the light of this result, it is difficult to avoid the conclusion that each microsystem [i.e. particle] in some sense samples both intermediate states B and C. (The only obvious alternative would be to postulate that the ensemble as a whole possesses properties in this respect that are not possessed by its individual members—a postulate which would seem to require a radical revision of assumptions we are accustomed to regard as basic.)

On the other hand, it is perfectly possible to set up a "measurement apparatus" to detect which of the intermediate states (B or C) any particular microsystem [particle] passed through. If we do so, then as we know we will always find a definite result, i.e., each particular microsystem is found to have passed either B or C; we never find both possibilities simultaneously represented. (Needless to say, under these [different] physical conditions we no longer see any interference between the two processes.) […] (Clearly, we can read off the result of the measurement only when it has been amplified to a macroscopic [classical] level, e.g. in the form of a pointer position [of measuring instruments] [or traces on photographic plates].)18

The first possibility corresponds to more familiar questions, such as "how do particles know that both slits are open, or conversely that counters are installed, and modify their behavior accordingly?" The alternative proposed by Leggett would be as remarkable as any "explanation" of the mysterious behavior of quantum objects, if one tries to think of such objects and their behavior as independent of their interaction with the measuring devices. One may describe the situation as follows. We must take into account the possibility of a particle passing through both states B and C (and through both slits in the double slit experiments), when both are open to it, in calculating the probabilities of the outcomes of such experiments. This also explains, for example, Dirac’s (not altogether accurate) statement that "each photon interferes […] with itself." Indeed, each photon must be seen as interfering "only with itself." "Interference between two different photons never occurs" (The Principles of Quantum Mechanics, 9). If we assumed that photons in the double slit experiments did, we would not get the probabilities or the interference pattern right. (Keep in mind that, even if we shut out the next photon after the previous one has already left its trace and been destroyed in its collision with the screen, we will still observe the interference pattern, unless we install devices enabling us to establish through which slit each photon passes.) However, we cannot see such an event or self-interference as in fact physically occurring for any single particle. In sum, any attempt to picture or conceive of this behavior (leading to the effects in question) in the way we do it in classical physics would lead to a logical contradiction; or be incompatible with one aspect of experimental evidence or the other; or entails (by classical or any conceivable criteria) strange or mysterious behavior, as just described; or requires more or less difficult assumptions, as the one described by Leggett; or, as Einstein argued, implies nonlocality, forbidden by relativity, which one finds, for example, in David Bohm’s hidden variables interpretation.

Bohr, by contrast, sees the situation as revealing the essential ambiguity in ascribing the conventional (and perhaps any) physical attributes to quantum objects themselves or referring to their independent behavior. As he writes, "to my mind, there is no other alternative than to admit that, in this field of experience, we are dealing with individual phenomena and that our possibilities of handling the measuring instruments allow us only to make a choice between the different complementary types of phenomena we want to study" (PWNB 2:51).19 Elsewhere he elaborates as follows:

In this context, some sometimes speak of "disturbance of phenomena [object?] by observation" or "creation of physical attribute of atomic objects by measurements." Such phrases, however, are apt to cause confusion, since words like phenomena and observation, just as attributes and measurements, are here used in a way incompatible with common language and practical definition. On the lines of objective description, it is indeed more appropriate to use the word phenomenon to refer only to observations obtained under circumstances whose description includes an account of the whole experimental arrangements. In such terminology, the observational problem in quantum physics is deprived of any special intricacy and we are, moreover, directly reminded that every atomic phenomenon is closed in the sense that its observation is based on registration obtained by means of suitable amplification devices with irreversible functioning such as, for example, permanent marks on a photographic plate, caused by the penetration of electrons into the emulsion. In this connection, it is important to realize that the quantum-mechanical formalism permits well-defined applications referring only to such closed phenomenon. Also in this respect it represents a rational generalization of classical physics in which every stage of the course of events is described by measurable quantities.

The freedom of experimentation, presupposed in classical physics, is of course retained and corresponds to the free choice of experimental arrangements for which the mathematics structure of the quantum-mechanical formalism offers an appropriate latitude [i.e. that of the uncertainty relations]. The circumstances that, in general, one and the same experimental arrangement may yield different recording [the strict uniqueness of all individual quantum effects] is sometimes picturesquely described as a "choice of nature" between such possibilities. Needless to say, such a phrase implies no allusion to a personification of nature, but simply points out the impossibility of ascertaining on accustomed lines directives for the course of a closed individual phenomenon. (PWNB 2:73)20

At the (classical) level of the actually observed (macro) phenomena all proper references to the data become "objective," that is, unambiguously defined and unambiguously reportable, and hence not subjective. One may even use the concept of reality (although not causality) in relation to this data, since one deals with the classical physics of measuring instruments. It also follows that "in complementary description all subjectivity is avoided by proper attention to the circumstances [of complementary measurement] required for the well-defined use of elementary concepts" (PWNB 3:7). Due to complementarity (mutual exclusivity), however, "in this situation, there could be no question of attempting a causal analysis of [quantum] radiative phenomena [or any phenomena in question in quantum physics], but only, by a combined use of the contrasting pictures, to estimate probabilities for the occurrence of the individual radiation processes." (The contrasting pictures in question are defined by mutually exclusive or, in Bohr’s terms, complementary situations of measurement.) "However," Bohr adds, "it is most important to realize that the recourse to probability laws under such circumstances is essentially different in aim from the familiar application of statistical considerations as a practical means of accounting for the properties of mechanical systems of great structural complexity [as in classical statistical physics]. In fact, in quantum physics, we are presented not with intricacies of this kind, but with the inability of the classical frame of concepts to comprise the peculiar feature of indivisibility, or ‘individuality,’ characterizing the elementary processes" (PWNB 2:34).21

One might argue that the price one pays for avoiding ambiguity or "mystery"—the apparent impossibility of physics (in the usual sense) that would describe quantum objects themselves, or indeed their inaccessibility by any means—is too heavy. However, as I have noted, at least in Bohr’s interpretation, this impossibility is a rigorous consequence of the empirically well-established data and laws of quantum mechanics, such as the emergence of interference pattern, as described above, or quantum correlations, or the uncertainty relations.

I shall explain the uncertainty relations below. It may be observed here that they are equivalent to the fact that one can never establish through which slit particles pass (the "particle" picture) without destroying the interference pattern (the "wave" picture). The two situations are always mutually exclusive or (this is strictly Bohr’s definition) complementary. Each "corresponds" to an individual and/as unsubdividable phenomena in Bohr’s sense. The two types of phenomena can never combine or supplement each other to produce a more complete picture (in the classical sense), either by way of subdivision, say, by adding counters or mirrors to an arrangement within which an interference pattern would appear on the screen, or still otherwise. As Bohr says, "within the scope of classical physics, all characteristic properties of a given object can in principle be ascertained by a single experimental arrangement, although in practice various arrangements are often convenient for the study of different aspects of the phenomena. In fact data obtained in such a way simply supplement each other and can be combined into a consistent picture of the behavior of the object under investigation. In quantum physics, however, evidence about atomic objects obtained by different experimental arrangements exhibits a novel kind of complementary relationship. Indeed, it must be recognized that such evidence which appears contradictory when combination into a single picture is attempted, exhausts all conceivable knowledge about the objects" (PWNB 3:4).

Accordingly, in quantum physics, "the essential wholeness of a proper quantum phenomenon finds indeed logical expression in the circumstance that any attempt at its well-defined subdivision would require a change in the experimental arrangement incompatible with the appearance of the phenomenon itself" (PWNB 2:72). Or, "any attempt of subdividing the phenomena will demand a change in the experimental arrangement introducing new possibilities of interaction between [quantum] objects and measuring instrument which [interaction] in principle cannot be controlled" (PWNB 2:40). Such attempts would only produce another individual and indivisible phenomenon or phenomena. They can never make it possible to refer unambiguously to simultaneously both complementary effects of the interaction between quantum objects and the measuring instruments upon the latter, or to any physical property of quantum objects themselves under all conditions.

Thus, in order to avoid ambiguity (which we must do in scientific discourse and communication) it indeed appears necessary in all circumstances to speak of individual quantum effects, manifest in "closed" phenomena at the macro-level of the measuring instruments, treated in terms of classical physics. Quantum mechanics predicts numerical data pertaining to these closed phenomena and only this type of data, rather than any aspects of their constitution that can be "unclosed" by subdividing these phenomena. The latter are, once again, irreducibly unsubdividable. The effects in question are individual or single, or indeed singular, unique, in each case. They are individual, first, insofar as they are irreversible and insofar as "the repetition of the same experiment in general yields different recordings pertaining to the objects," which "implies that a comprehensive account of experience in this field must be expressed by statistical laws" (PWNB 3:4). Second, they are individual in the sense of being defined by the individual/indivisible phenomena in Bohr’s sense. By contrast, all references to quantum objects as individual particles of matter (or, conversely, as waves, or indeed as, in themselves, anything) must be seen as "abstractions, their properties on the quantum theory being definable and observable only through their interaction with other [macro] systems," however useful and even indispensable these abstractions may be (PWNB 1:57).

This interaction is itself at the limit a quantum process. Accordingly, it can manifest itself only in the same mode of interactive indivisibility and is subject to the same techno-epistemology and techno-phenomenology, and in each given case would indeed form "an integral part of the [wholeness of the] phenomena," and hence will be inseparable from it (PWNB 2:72). At the quantum level, it would remain unexplainable and inconceivable as such as well, since any meaningful investigation of it would require another set of measuring instruments. According to this view, the physics of transition from the quantum micro-level of objects to the classical macro-level of the data manifest in the measuring instruments not only remains unexplained (as some critics point out), but (the point sometimes missed by those critics) may have to be seen as, in its quantum constitution, unexplainable by virtue of the laws of quantum mechanics.

As I said, these considerations do not imply that we can obtain no information about quantum objects, nor that they do not exist, nor that we cannot make predictions concerning their behavior, that is (which is the point), their specific and unique effects upon the measuring instruments or other macro-objects. Nor, as Bohr said in 1958, "of course [does] such argumentation […] imply that, in atomic physics we have no more to learn as regards experimental evidence and the mathematical tools appropriate to its comprehension. In fact it seems likely that the introduction of still further abstractions into the formalism will be required to account for the novel features revealed by the explorations of atomic processes of very high energy" (PWNB 3:6). The latter prediction proved true, as, so far, did Bohr’s comment in the same paragraph that in spite of these circumstances "there is no question of reverting [in quantum physics] to a mode of description which fulfills" the ideals of classical physics (PWNB 3:6). A similar set of points can be made concerning the physics of transition from the quantum to the classical world, a significant issue in recent investigations, in which a number of interesting new ideas have emerged.22

Bohr is reported to have said that "there is no quantum world."23 One must, of course, approach such reported statements with caution. I would argue, however, that it would be difficult to conclude on the basis of Bohr’s works that we would deny the existence of that to which the expression "the quantum world" refers. Accordingly, the statement may be read, especially given the context (the question whether quantum mechanics represents the quantum world), by putting the emphasis on "quantum," without in any way indicating the nonexistence of "quantum" objects. Instead it indicates the inapplicability, to the latter, of conventional "quantum" attributes—such as discontinuity (of radiation), invisibility (of quanta themselves), and so forth, or any other physical or conceivably any attributes, even "objects," "constituents," and so forth. This attribution, moreover, is impossible not only independently of their interaction with the measuring instruments (a more standard view of the situation and, sometimes, of Bohr’s position), but even when this interaction actually takes place.

Quantum mechanics itself is interpreted as accounting for this indivisibility of the observable techno-phenomena, while under the condition of the irreducible "distinction between the objects under investigation and the measuring instruments which serve to define, in classical terms, the conditions under which the phenomena appear" (PWNB 2:50). Moreover, it accounts (statistically) only for the classical effects of this interaction (manifesting themselves in experimental arrangements), rather than the (quantum) character of this interaction, even though the latter and hence, the existence of quantum objects may ultimately be responsible for these effects.24 As Bohr writes:

This necessity of discriminating in each experimental arrangement between those parts of the physical system considered which are to be treated as measuring instruments and those which constitute the objects under investigation may indeed be said to form a principle distinction between classical and quantum mechanical description of physical phenomena. It is true that the place within each measuring procedure where this discrimination is made is in both cases largely a matter of convenience. While, however, in classical physics the distinction between object and measuring agencies does not entail any difference in the character of the description of the phenomena concerned, its fundamental importance in quantum theory […] has its root in the indispensable use of classical concepts in the interpretation of all proper measurements, even though the classical theories do not suffice in accounting for the new types of regularities with which we are concerned in atomic physics. (QTM, 150)25

This and related statements by Bohr are sometimes taken to mean that the measuring instruments are described by means of classical theory while the (quantum) objects are described by means of quantum theory. Bohr obviously says the first, but he clearly does not say and, I would argue, does not mean the second.26 To begin with, Bohr only speaks of the "necessity of discriminating in each experimental arrangement between those parts of the physical system considered which are to be treated as measuring instruments and those which constitute the objects under investigation." He does not say that these two parts are to be treated respectively by means of classical and quantum theory. The difference between the two descriptions is clearly that classical theory describes the classical world, specifically the measuring instruments, while quantum theory describes the interaction between the measuring instruments (described classically) and quantum objects, indescribable by means of either classical or quantum theory. The two types of formalism themselves remain incompatible, of course, even though they must, on this view, coexist in quantum theory.27

The degree of arbitrariness in the place where the discrimination in question is made, or the arbitrariness of the so-called "cut," is a logical feature of this interpretation, rather than the kind of problem it would be, and has been, if we assumed that quantum mechanics describes the quantum world itself.28 This is the case even though one can, in principle, speak of the cut made at the level of perception and consciousness, which may be in part responsible for Bohr’s "phenomenon" (rather than "noumenon") terminology. As Bohr observes, "after all, the concept of observation is arbitrary in so far as it depends upon which objects are included into the system to be observed. Ultimately every observation can of course be reduced to our sense perception" which is seen as classical (PWNB 1:54). It scarcely needs to be added that our sense perception is technological, indeed, in the case of the human eye, even quantum-technological. Hence, the techno-atomic phenomena in question can be retained at this level as well. However, it is crucial that, "by securing its proper correspondence with the classical theory the [transformation] theorems [of quantum mechanics] exclude in particular any imaginable inconsistency in the quantum-mechanical description, connected with a change of the place where the discrimination is made between object and measuring agencies. In fact it is an obvious consequence of [Bohr’s] argumentation that in each experimental arrangement and measuring procedure we have only a free choice of this place within a region where the quantum-mechanical description of the process concerned is effectively equivalent with the classical description" (QTM, 150). It follows that the ultimate constituents of matter are always on the quantum side of the "cut" and may indeed be defined (as quantum) accordingly.

The prediction of quantum mechanics refers strictly to classically manifest effects upon the measuring instruments, for example, the positional displacement of certain parts of the apparatus or the change in their momentum, which can be rigorously correlated with specific configurations involving quantum objects. It is only this correlation that enables any possible identification of such a measurement with the position or momentum of a quantum object. The correlation is, according to Bohr, real, or rigorous, while the identification can only be, in his words, "symbolic" (one is almost tempted to say "allegorical," especially with Paul de Man’s theory of allegory in mind). Bohr does say that "to measure the position of [a] particle can mean nothing else than to establish a correlation between its behavior and some instrument rigidly fixed to the support which defines the space frame of reference [or some equivalent classical-like configuration]" (QTM, 149-48, in this order). He is, however, careful to say "behavior," which is quite different from saying "position." The sentence also clearly allows one to argue that in Bohr’s scheme this "behavior" itself, too, cannot be described but only correlated with the behavior of the measuring instruments, the behavior describable by means of classical physics.29 The sum total of such correlated effects is, however, unaccountable by means of classical physics. This circumstance leads us, first, to infer the existence of quantum objects and, second, to a different, quantum-mechanical, account of the situation, since "the classical theories do not suffice in accounting for the new types of regularities with which we are concerned in quantum physics."

The quantum strata of the phenomena in question, including quantum aspects of the interaction between the objects and the measuring instruments are both ineliminable and (in themselves) ineliminably indescribable. We cannot free the experimental data in question in quantum theory from technology or tekhné and reduce, or indeed connect, these data to the specific properties of quantum objects themselves.30 The phenomena in question in quantum physics are indivisible, even though and because these phenomena, as phenomena (not objects), are constituted by two fundamentally and irreducibly different types of physical components, the classical measuring instruments and the quantum objects.

2. Nonrealism, Acausality, and the Uncertainty Relations

The circumstances of quantum measurement here considered make it extremely difficult to maintain in the field of quantum theory either causal or realist physical description, which, jointly, define classical physics. Once, however, these circumstances are taken into account, quantum mechanics offers an unambiguous, rigorous and comprehensive (complete, within its limits) description of the physical phenomena it claims to account for, just as classical physics does within its limits. In this sense, this account is (while not realist) "objective," that is, as objective as any physical account can be. At the very least, in Bohr’s words, "in complementarity all subjectivity is avoided by proper attention to the circumstances required for a well-defined use of elementary physical concepts" (PWNB 3:7).31 Accordingly, the difference between classical and quantum theory may be defined in terms of physics itself (that is, in terms of the constitution of the data in question and the structure of the theories accounting for these data) rather than on the basis of a priori ontological and epistemological claims upon the object of investigation or the nature of theory. Classical physics is causal and realist, or at least it may be interpreted as such consistently with its data and its mathematical formalism. Quantum physics is neither, and, crucially (at least in the present interpretation), it cannot be claimed to be either on the basis of the rigorous examination of all the circumstances of quantum experiments and measurements.32

Classical physics, such as Newtonian mechanics, is or again can be interpreted as ontologically realist because it fully describes the (independent) physical properties of its objects necessary to explain their behavior, and it is, ontologically, causal because the state of the systems it considers at any given point is assumed to determine its behavior at all other points. It is also, epistemologically, deterministic insofar as our knowledge of the state of a classical system at any point allows us to know its state at any other point. Indeed, as Bohr pointed out, "the principles of Newtonian mechanics meant a far-reaching clarification of the problem of cause and effect by permitting, from the state of a physical system defined at a given instant by measurable quantities, the prediction of its state at any subsequent time" (PWNB 2:69). Not all causal theories are deterministic in this sense. Classical statistical physics or, differently, chaos theory (which is, in most of its forms, classical and sometimes is a direct extension of Newtonian mechanics) are, or are at least usually assumed to be (in all rigor, neither case is altogether clear cut), causal. They are, however, not deterministic even in ideal cases, in view of the great structural complexity of the physical systems involved. This complexity blocks our ability to predict the behavior of such systems, even though we can write equations that describe them and assume their behavior to be causal. (Indeed the latter assumption is often necessary in these cases.) For similar reasons, it would be difficult to speak of Newtonian mechanics as truly deterministic (or even realist) in most actual cases. In principle, however, as an idealization, it is a causal and deterministic theory, or can be rigorously interpreted as such, while classical statistical physics or chaos theory are (while causal) not deterministic even as idealizations. In general, it does not follow that either causal or deterministic theories are realist, since the actual behavior of a system may not be mapped by our description of it, even though we can make exact predictions concerning that behavior. Classical mechanics or chaos theory is, however, also realist insofar as such a mapping is assumed to take place, at least as a good theoretical approximation, however unachievable in practice. By contrast, classical statistical physics, or at least that part of it that enables statistical predictions concerning the behavior of the systems it describes, is not realist insofar as its equations do not describe any physical reality as such. It is, however, usually based on the realist assumption of the underlying non-statistical multiplicity, whose members in principle conform to strictly causal laws of Newtonian physics. We may expand the denomination "realist" to theories which are approximate in this sense, or even to theories that presuppose an independent reality that cannot be mapped or even approximated but that possess a structure and attributes, or properties, in the usual sense. Indeed, realist theories may be described most generally by the presupposition that their objects in principle possess independently existing structures and attributes, whether we can or cannot, in practice or in principle, describe or approximate them. It is this presupposition that, historically, defines classical theories most fundamentally (arguably more fundamentally than causality), while it (strongly) appears inapplicable in quantum physics.

By contrast, quantum theory, again, at the very least, in the interpretation here considered, is neither causal (or deterministic) nor realist in any of the senses just described. It is not only that the state of the system at a given point gives us no help in predicting its behavior at later points (noncausality and indeterminism), but even this state itself, at any point, cannot be unambiguously defined on the model of classical physics (nonrealism). In other words, the classical concept of physical state cannot unambiguously apply in the field of quantum theory.33

This is not possible because of the uncertainty relations, which, accordingly, have as much to do with the lack of realism as with the lack of causality. It may be helpful to recall what uncertainty relations are and what they mean, at least in the present interpretation.34 In classical physics the determination of the state of the system at any point on the basis of our knowledge of it at a given point is possible because we always can at least in principle, determine both the location and the velocity or momentum (including its direction) for objects comprising this system at this point. The equations of classical physics allow us to do the rest. By contrast, in quantum physics, in view of the uncertainty relations, we can at any given point only measure, determine, or indeed unambiguously define either the position or the momentum of an object, or more accurately those of a particular measuring instrument properly correlated with the object in question. We can never simultaneously determine both of these, as they are called, conjugate or complementary variables. The term "conjugate" is retained from classical physics. (It indicates that the respective evolutions in time of both variables are related, "conjugated," within the classical formalism in its so-called Hamiltonian form.) The term "complementary" refers to the mutually exclusive nature of their respective determination in quantum physics due to the uncertainty relations. It is in part for that reason that Bohr’s overall interpretation of quantum mechanics was developed under the rubric of complementarity.

Given the necessity of always considering the measuring instruments correlated with the quantum objects, in all rigor the situation is more complicated, even in the case of a single variable. For, according to Bohr, we cannot unambiguously ascribe independent classical-like, or perhaps any, physical attributes, either multiple or single, to quantum objects. Hence the uncertainty relations "cannot […] be interpreted in terms of attributes of objects referring to classical pictures" (PWNB 2:73). This impossibility does not make uncertainty relations meaningless, since they still apply, and indeed can rigorously only apply, to the data obtained in measurements resulting from the interactions between the quantum objects and the measuring instruments, within the indivisible phenomena in Bohr’s sense (the sense defined by these interactions). From this perspective, a more accurate way of seeing the uncertainty relations would be as follows. The data recorded in our measuring instruments as a result of their interactions with quantum objects is of the same type as the data resulting from measurements of classical objects in their interaction with the measuring devices (and in this sense, this macro-level data is also as "objective" and "realist" as that of classical physics). The difference is that in the latter case we always can, at least in principle, measure both the position and the momentum of the relevant part of the measuring instruments simultaneously. By contrast, in the case of the interaction between the quantum objects and the measuring instruments in quantum theory, we can, in principle, only measure and indeed unambiguously define, for the relevant parts of the measuring instruments, either one or the other variable of that type, but never both simultaneously. Hence, classical-like determinism is not possible even at the classical level, while the effects of the interactions between quantum objects and measuring instruments upon the latter can be described in the realist manner. (Any single variable by itself can always be predicted with the probability equal to unity, which led Einstein to think, and to argue, that something is amiss in quantum theory or that it is incomplete. Not so, Bohr countered.) In the present view, one can only speak of "variables of that type," rather than attributing them to the quantum object under investigation. Rigorously, such variables can only be seen as defining (in the classical manner) either the positional coordinates of the point registered in some part of the measuring instruments involved or, conversely, a change in momentum of some such part under the impact of its interaction with the object under investigation. Hence, Bohr argues, the interactions between quantum objects and the measuring instruments in quantum mechanics can never be neglected or compensated for in the way they, at least in principle, can be in classical physics. In this interpretation (in contrast, again, to those following the Von Neumann/Dirac view) there is, again, no presupposition that the quantum-mechanical formalism describes the ("undisturbed") quantum process before the measurement interference takes place, or between instances of such interference. Accordingly, rigorously speaking the formalism of quantum mechanics describes only these interactions and their impact on the measuring instruments, and only them, rather than the properties, even single properties (if one can still speak of properties here) or the behavior of quantum objects as such. Even in less radical interpretations, however, in view of the uncertainty relations we can never, in practice or in principle, determine or even define the state of the system in the way we do in and, hence, on the model of, classical physics.

Thus, in this interpretation, the meaning of the uncertainty relations is that we can never determine or even define the state of the system under investigation in the way we do in classical physics. The ultimate reasons for this is that in the classical or classical-like definition of the state of a physical system would entail the possibility of disregarding or compensating for the interaction between it and the measuring instruments. This can indeed be always done in classical but never in quantum physics, where these interactions irreducibly define the conditions under which all phenomena appear. As Bohr writes, "these circumstances find quantitative expression in Heisenberg’s indeterminacy relations which specify the reciprocal latitude for the fixation, in quantum mechanics, of kinematical [position] and dynamical [momentum] variables required for the definition of the state of a system in classical mechanics." He adds a rather striking sentence: "in this context, we are of course not concerned with a restriction as to the accuracy of measurement, but with a limitation of the well-defined application of space-time concepts and dynamical conservation laws, entailed by the necessary distinction between [classical] measuring instruments and atomic [quantum] objects" (PWNB 3:5).35

The uncertainty relations put uncircumventable limits upon our knowledge of the ultimate constituents of matter, at the limits, making it impossible to know and indeed assign any properties to such constituents at all. This fact, however, by no means limits our knowledge about quantum objects in terms of their effects upon the measuring instruments. Quantum mechanics has an extraordinarily predictive and explanatory power, and the effects in question cannot be explained otherwise. It is also worth recalling that quantum mechanics is not restricted to the uncertainty relations. It and its many extensions, such as quantum field theories, contain many formulae and equations, which extend their capacity very far indeed, and the uncertainty relations, too, can be used to make positive statements about the physical world, rather than only limit our knowledge about it. Indeed, if understood in terms of complementarity, even by virtue of limitation or, better, of restructuring of knowledge (techno-epistemology), the uncertainty relations "provide room for the new physical laws," the laws of quantum mechanics (QTM, 150). Complementarity allows us to see these laws as rigorous and unambiguous statements concerning nature at the quantum level, and indeed a complete set of such statements, making quantum mechanics a complete theory within its limits. We can do so precisely by virtue of interpreting these statements as referring only to certain effects of the interaction between the quantum objects and the measuring instruments. The understanding of the ultimate constituents of matter as quantum requires rigorously taking into account the irreducible role of technology in the physical description of the physical world. It is this situation, ultimately arising from Planck’s investigation, that defines the technological constitution of the phenomena in quantum physics. Technology is responsible for, correlatively, both the nonclassical (noncausal and nonrealist) nature of quantum epistemology and the fact that quantum mechanics is a fully rigorous and comprehensive physical theory, a theory of techno-atoms.

3. Complementarity and the Quantum Postulate

Complementarity was developed by Bohr in 1927 in the wake of Heisenberg’s and Schrödinger’s introduction of the quantum-mechanical formalism and, most immediately, in the wake of Heisenberg’s discovery of the uncertainty relations. It underwent considerable refinement and transformation from 1927, when it was introduced in a lecture at a conference in Como, Italy, (published, with considerable revisions, in 1928 as "The Quantum Postulate and the Recent Development of Atomic Theory") to "Discussion with Einstein Concerning the Epistemological Problems of Atomic Theory," published in 1949, to Bohr’s last essays on the subject. It may be argued that Bohr’s 1935 reply to the famous argument of Einstein, Podolsky, and Rosen (EPR) concerning the (in)completeness of quantum mechanics is the highest point of Bohr’s thought on complementarity, if not of all his specific formulations or ideas (both of which he refined subsequently). Both articles were published under the same title, "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?"36 Bohr’s argument was elicited by Einstein’s in turn most subtle questioning of quantum mechanics. Bohr’s subsequent writings, in particular "The Question of Causality in Quantum Physics" (1938), the so-called Warsaw lecture (where Bohr’s concept of phenomena was introduced), and "Discussion with Einstein," may be seen as a continuation and refinement of this exchange. Retaining with Bohr the rubric of complementarity for his overall interpretation of quantum mechanics, one can roughly mark the genealogy of the congealing or crystallization of Bohr’s key concepts as follows: 1927—the quantum postulate, quantum individuality, and complementarity; 1935—the irreducible interaction between quantum objects and measuring instruments, and the question of unambiguous reference; 1935-38—the concept of phenomenon; 1949—inseparability and wholeness of quantum phenomena; 1950s—techno-atomicity. This genealogy is cumulative insofar as Bohr retains and refines his earlier ideas in his subsequent work. The present article more or less follows this cumulative, in particular the post-EPR, version of Bohr’s argument concerning complementarity. It may, accordingly, be use useful to sketch what is specifically at stake in the EPR argument and Bohr’s reply.

In arguing for the incompleteness of quantum mechanics, EPR proposed the following (weak) criterion of physical reality: "if, without in any way disturbing a system, we can predict with certainty (i.e. with probability equal to unity) the value of a [single] physical quantity [say, the momentum of a particle], then there exists an [independent] element of physical reality corresponding to this physical quantity" (QTM, 138). It may appear that this criterion applies in quantum mechanics. Recall that, in view of the uncertainty relations, only a joint simultaneous determination or prediction of two variables involved in the quantum-mechanical physical description, such as "position" and "momentum," is impossible. A determination or prediction of a single variable is always possible in quantum mechanics, with any degree of precision (or, in the case of prediction, with probability equal to unity). Some adjustment of the preceding argument is necessary, since such a determination must take place without "disturbing" the system—that is, without first performing any previous measurement upon it, which is how such predictions are made in more standard cases. More accurately one should speak, as Bohr does, of not interfering with this system, since, as we have seen, there is no classical-like or indeed otherwise specifiable (undisturbed) configuration that is disturbed in the process. This can indeed be done for (this remains crucial) a single variable in quantum mechanics in certain cases, such as that considered by EPR, by means of performing measurements on other systems (in this case the second particle involved in their thought experiment), which have previously been in an interaction with the system under investigation. As Bohr argues, however, this complication allows one to retain all the essential aspects of his general argument, and, in a certain sense, all quantum measurements entail an analogous complication (PWNB 2:56-57). In any standard situation of quantum measurement, we can predict (always in accordance with uncertainty relations), say, the position of a particle after a preceding measurement took place (and on the basis on this measurement) and hence without interfering with the particle in question. In the EPR situation, we have a slightly more complicated, but not fundamentally different case. Predictions (again, limited by uncertainty relations) concerning a given particle are possible on the basis of measurements performed on another particle that has previously been in an interaction with the first particle, but, at the time of measurement, is in a region spatially separated from the latter. Hence, at the time of determination in question, there is no physical interaction either between the two particles or between any measuring apparatus and one of the two particles in question. This circumstance leads some, beginning with Einstein, to conclude that there are some nonlocal connections involved. Einstein famously called them "spooky action at a distance." Bohr did not think that such connections were implied by the circumstances of measurement just described, in part because he saw these connections as correlative to the EPR criterion of reality, which he argued to be in fact inapplicable in quantum mechanics. This part of the exchange would require further analysis, which would not, however, affect the present argument as such. "According to their criterion," Bohr wrote in his reply, "the authors therefore want to ascribe an element of reality to each of the quantities represented by such variables. Since, moreover, it is a well-known feature of the present formalism of quantum mechanics that it is never possible, in the description of the state of a [quantum-]mechanical system, to attach definite values to both of two canonically conjugate variables, they consequently deem this formalism to be incomplete, and express the belief that a more satisfactory theory can be developed" (QTM, 145).

I shall not consider here this extraordinary exchange, one of the most subtle and profound arguments in the history of physics.37 The key point here is that, if one accepts even the EPR criterion of reality as applicable in quantum physics, quantum mechanics would indeed be shown to be incomplete or, more accurately, either incomplete or nonlocal, that is, as entailing an instantaneous action-at-a-distance. The latter would be in conflict with relativity, an experimentally well-confirmed theory. Accordingly, the only effective counter-argument would be to show that the EPR criterion cannot in fact be unambiguously applied in the analysis of the phenomena in question in quantum mechanics, which would therefore disallow even a relatively minimal form of realism entailed by the EPR criterion. This is what Bohr does. For the purposes of the present discussion, it suffices to say that Bohr’s counter-argument is fundamentally grounded in his interpretation as discussed here.38 In particular, as I have stressed here, according to Bohr, "the essential ambiguity is [always] involved in a reference to physical attributes of objects when dealing [as we must in the field of quantum theory] with phenomena where no sharp separation can be made between the behavior of the objects themselves and their interaction with the measuring instruments" (PWNB 2:61). This ambiguity arises even if one speaks of a single such attribute, rather than both complementary attributes (such as position or momentum, time and energy, or complementary components of spin), as Bohr appears to have been inclined to think prior to the EPR argument.39 One cannot unambiguously ascribe, as EPR in fact or in effects do according to their criterion, even a single physical attribute to any quantum object as such. We cannot do so even though we can, in quantum mechanics, predict the outcome of such measurements on the basis of earlier measurements performed on the object in question and of contemporaneous measurements on other objects that have previously been in interaction with the object in question. Hence such measurements do not involve this object at the time of determination of the variable concerned. These are the circumstances that enable the EPR argument. That is, as we have seen and as Bohr restates it (at least) three times in "Discussion with Einstein," in "the analysis of typical quantum effects," we are faced precisely with "the impossibility" of drawing "any sharp separation between an independent behavior of [quantum] objects and [their] interaction with the measuring instruments" (PWNB 2:39-40, 52, 61). This "new" epistemological situation was, Bohr argues, under-appreciated by EPR. The mathematical formalism of quantum theory (used by EPR in their argument) coherently covers this situation. Conversely, however, this, and only this, is what this formalism covers, which is primarily what EPR do not sufficiently take into account. In all quantum-mechanical phenomena, including those in question in the EPR argument, "an essential element of ambiguity is [always] involved in ascribing [any] conventional physical attributes [single or joint] to quantum objects [themselves]." Hence, Bohr also argues, "a criterion of reality like that proposed by EPR [too] contains—however cautious its formulation may appear—an essential ambiguity when it is applied to the problems of quantum mechanics" (QTM, 146).40 This is the same ambiguity. Glossing over nuances, one might say that, while we can indeed predict a value of a given physical quantity in quantum mechanics, we cannot in fact maintain that "then there exists an element of [an independent] physical reality corresponding to this physical quantity." Quantum mechanics tells us that there are no such elements to begin with, if by the latter we mean a physical attribute of a quantum object. The question is what physical quantity one can in fact predict. Accordingly the above gloss becomes itself ambiguous, which reminds us that quantum mechanics has a low-level of tolerance for gloss, as Bohr perhaps understood earlier and better than anyone else. He likes to speak more carefully of "the values of [a] variables involved in the description," in the case of quantum mechanics always in relation to the appropriately specified measuring instruments (QTM, 144). A rigorous analysis of the situation "in fact discloses an essential inadequacy of the customary view point of natural philosophy for a rational account of physical phenomena of the type we are concerned with in quantum mechanics." As we have seen, it also "entails the necessity of the final renunciation of the classical ideal of causality and a radical revision of our attitude towards the problem of physical reality" (QTM, 146). Bohr concludes:

…the argument of [EPR] does not justify their conclusion that quantum mechanics description [sic] is essentially incomplete. On the contrary this description, as appears from the preceding discussion [i.e. in Bohr’s interpretation], may be characterized as a rational utilization of all possibilities of unambiguous interpretation of measurements, compatible with the finite and uncontrollable interaction between the [quantum] objects and the measuring instruments in the field of quantum theory. In fact, it is only the mutual exclusion [in view of this interaction] of two experimental procedures, permitting the unambiguous definition of complementary physical quantities [such as position and momentum], which provides room for new physical laws [i.e. the laws of quantum mechanics], the coexistence of which might at first sight appear irreconcilable with the basic principles of science [but is ultimately not]. It is this entirely new [epistemological] situation as regards the description of physical phenomena, that the notion of complementarity aims at characterizing. (QTM, 148)

Complementary features of description in Bohr’s sense may be defined in very general terms as mutually exclusive (and thus not applicable simultaneously at any given point) but equally necessary for a comprehensive description of quantum phenomena, the concept which, as we have seen, is redefined by Bohr accordingly. In quantum physics, however, such complementary pictures (inevitably) emerge in view of the interaction between quantum objects and the measuring instruments, by virtue of the always mutually exclusive experimental arrangements necessary for determining complementary physical quantities—such as position and momentum, time and energy, or different components of spin; or ways of description, such as in terms of continuous versus discontinuous phenomena, as in waves versus particles; or the space-time coordination of quantum objects versus (the claim of) causality concerning their behavior; or the possibilities of observation versus those of definition; and so forth (PWNB 1:54-55).

Complementarity immediately signals difficulties in developing a realist interpretation of quantum phenomena. At any given point, at least two mutually exclusive "pictures" or determinations of the complementary physical quantities are always possible, while it appears to be impossible to conceive of an underlying (classically) complete configuration that such pictures would partially represent. Bohr’s unorthodox usage of the term complementarity, which conventionally suggests the image of parts mutually complementing themselves within a whole, is in part explained by this situation. (Certain complementary descriptions, such as, most famously, those in terms of particles and waves, have more complex relations to classical physics.) To the degree that classical pictures that are complementary in this conventional sense can be used in quantum physics, they become mutually exclusive and even incompatible, while at the same time remaining both necessary in order to comprehensively account for any phenomenon that we encounter in quantum physics. As Bohr says, "evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be considered as complementary in the sense that only the totality of the [complementary and, hence, un-unifiable] phenomena exhaust the possible information about the objects" (PWNB 2:40).

In any attempt to ascribe and indeed define both complementary quantities we are always and inevitably forced, in practice and in principle, to refer to two specified different and incompatible (mutually exclusive) experimental arrangements, rather than a single such arrangement, or two mutually compatible arrangements, which would allow us to select different attributes ("elements of reality," in EPR’s language) pertaining to the "same" quantum object. There are no such objects; that is, no object can ever be defined so as to induce both complementary attributes pertaining to a single experimental arrangement at any given point, or, as a consequence, be said to possess independently both such attributes, or, again, even any single physical attribute. This is why Bohr in replying to Einstein’s criticism stresses:

a) the indivisibility of phenomena, that is, "the necessity of [always] considering the whole experimental arrangement, the specification of which is imperative for any well-defined application of the quantum-mechanical formalism"; and, as a consequence,
b) that "in the problem[s] in question, we are not [ever] dealing with a single specified experimental arrangement [as Einstein appears to presuppose], but are [always] referring to two different, mutually exclusive [specified] arrangements" (PWNB 2:57).

Correlatively to the indivisibility of quantum phenomena in Bohr’s sense, there is never an overall underlying quantum configuration, or (again, correlatively) a single (classical) experimental arrangement, of which the complementary determinations or arrangements would constitute proper parts or from which they could be both derived. Neither is unambiguously definable or even logically possible in quantum theory.41 As Bohr writes:

In the phenomena concerned we are not dealing with an incomplete description characterized by the arbitrary picking out of different elements of physical reality at the cost of sacrificing other such elements but with a rational discrimination between essentially different experimental arrangements and procedures which are suited either for an unambiguous use of the space location or for an unambiguous use of the conservation theorem of momentum. Any remaining appearance of arbitrariness concerns merely our freedom of handling the measuring instruments, characteristic of the very idea of experiment. In fact the renunciation in each experimental arrangement of the one or the other of two aspects of the description of physical phenomena,—the combination of which characterizes the methods of classical physics, and which therefore in this sense may be considered complementary to one another,—depends essentially on the impossibility, in the field of quantum theory, of accurately controlling the reaction of the object on measuring instruments, i.e., the transfer of momentum in the case of position measurements, and the displacement in the case of momentum measurements. Just in this last respect any comparison between quantum mechanics and the ordinary statistical mechanics,—however useful it may be for the formal presentation of theory,—is essentially irrelevant. Indeed we have in each experimental arrangement suited for the study of proper quantum phenomena not merely to do with an ignorance of the value of certain physical quantities, but with the impossibilities of defining these quantities in an unambiguous way. (QTM, 149)

I shall return to the question of statistics in quantum physics below. The main point at the moment is that the complementary character of all phenomena in question in quantum theory is correlative to the impossibility of an ambiguous ascription of classical-like (or conceivably any) physical attributes to quantum objects and elementary processes.

In approaching quantum phenomena, Bohr finds it necessary to appeal to such terms as "individuality," or "indivisibility" and "wholeness" (in the sense of the indivisibility of the quantum phenomena), alongside and indeed preferably to "discontinuity" and "discreteness." This conceptual field is assembled by Bohr under the rubric of "the quantum postulate." It becomes progressively more radical epistemologically as Bohr’s views develop, from his 1913 theory of the atom (no "techno-atoms" there yet) on. In "The Quantum Postulate and the Recent Development of Atomic Theory," his first comprehensive treatment of complementarity, he writes, "it seems that [the] essence [of quantum theory] 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" (PWNB 1:53, emphasis added). The shift from discontinuity to individuality indicates that one may not be able to conceive of the ultimate constituents of matter themselves and the elementary processes involving them either as continuous or as discontinuous. The reasons, although not formulated by Bohr in this sharp form at the time, are those considered here: we are dealing with "the phenomena where no sharp distinction can be made between the behavior of the objects themselves and their [quantum] interaction with the measuring instruments," indeed with the phenomena defined by this inseparability, and, as a result, with the fact that "an essential element of ambiguity is [always] involved in a reference to physical attributes of [quantum] objects."

Thus, quantum discontinuity is first rethought as quantum individuality. Then this individuality itself becomes an expression, "a proper expression," of the inseparable (indivisible) interaction between the quantum objects and the measuring instruments, and of the individuality/indivisibility of the phenomenon, which appears to become the primordial postulate of Bohr’s scheme.42 This redefinition takes place in Bohr’s later works, where the formulations just cited occur. In 1954 Bohr will write: "[Planck’s] discovery revealed in atomic processes a feature of wholeness quite foreign to the mechanical conception of nature [i.e. a conception of nature whereby its ultimate constituents obey individually the classical-like laws], and made it evident that the classical physical theories are idealizations valid only in the description of phenomena in the analysis of which all actions are sufficiently large to permit the neglect of the quantum" (PWNB 2:71). While the second point was clear more or less immediately, it took Bohr several decades to fully conceptualize the wholeness in question. Many key elements of his approach do, however, emerge from the outset of Bohr’s work on complementarity. For, as he writes in 1927 in "The Quantum Postulate," on the one hand, "[quantum] postulate implies a renunciation as regards the causal space-time coordination of atomic processes" which in fact means that space-time coordination and (the claim of) causality become now complementary (mutually exclusive) while their always simultaneous joint presence defines classical physics.43 On the other hand, "the quantum postulate implies that any observation of atomic phenomena will involve an interaction with the agencies of observation not to be neglected. Accordingly, an independent physical reality in the ordinary physical sense can neither be ascribed to the phenomena nor to the agencies of observation" (PWNB 1:54).44 Indeed, it is this interaction, leading to the suspension of, at the very least, the classical concepts of reality ("physical reality in the ordinary sense"), that leads to the renunciation of causality as well. As Bohr writes:

This situation has far-reaching consequences. On one hand, the definition of the state of a physical system, as ordinarily understood, claims the elimination of all external disturbances. But in that case, according to the quantum postulate, any observation will be impossible, and, above all, the concepts of space and time lose their immediate sense. On the other hand, if in order to make 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 very nature of the quantum theory thus forces us to regard the space-time coordination 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. […] 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 be judged only by weighing the possibilities of definition and observation. (PWNB 1:54-55)

While these formulations suggest certain differences from Bohr’s later writings, the key conceptual elements transpiring here are consistent with and, one might argue, are presupposed, even if no longer emphasized, in these later works. Be it as it may, the nonreality of attributes to quantum objects, the noncausality of quantum process, and the technology of measuring instruments are clearly brought together from the outset of Bohr’s work on complementarity.

The quantum postulate, too, becomes a technological concept, the concept defined through the role of measuring instruments. For, "the individuality of the typical quantum effects finds its proper expression in the circumstances that any attempt of subdividing the phenomena will demand a change in the experimental arrangements introducing new possibilities of interaction between [quantum] objects and measuring instruments" (PWNB 2:39-40). Accordingly, every event in question in quantum physics is individual in the sense of being unique, singular and unrepeatable, and, in itself, not predictable or, more generally, not comprehended by law, which, in quantum mechanics, applies only to collective regularities (such as the interference pattern in the double slit experiment). I shall discuss this aspect of quantum mechanics presently. My point at the moment is that quantum discontinuity becomes, rigorously, quantum individuality in the ultimate sense of uniqueness of individual quantum events. (This explains why Bohr uses the term, in preference to discontinuity, now merely a classically manifest effect of this individuality.) It also becomes quantum invisibility or wholeness by virtue of its techno-/tekhné-logization within the structure of phenomenon in Bohr’s sense. The latter is indivisible both within itself (making it impossible to isolate rigorously quantum objects) and in the sense that any attempt at a subdivision will lead to a phenomenon of the same type and hence will always retain or reinstate complementarity, rather than allowing a reconstitution of it into a classical-like wholeness.

Thus, quantum events, beginning with those in question in Planck’s work, are understood or reinterpreted in terms of their absolute uniqueness, on the one hand, and their techno-atomicity, on the other. The notion that energy quanta hv cannot be further subdivided is reconceptualized in terms of, or transferred onto the level of, phenomena itself. One may take the analogy a step further and suggest that the "behavior" of phenomena in Bohr’s sense mirror the structure of the interaction of "elementary particles," the ultimate atoms of nature—insofar as we can, symbolically or by convention, speak of them and their behavior independently. Elementary particles cannot be further subdivided but they can transform themselves into other elementary particles, either spontaneously or by (overtly) interacting with other elementary particles. Analogously, any "subdivision" of phenomena in Bohr’s sense can only be a transformation into another indivisible phenomenon or phenomena. One should of course keep in mind the limits of this analogy and not overstate its significance, to begin with. It is, however, difficult to think that Bohr was unaware of it. In any event, it is his rethinking as such of atomicity in terms of techno-atomicity that is most crucial here, and the fact of this rethinking is hardly in question. Standard effects, such as discontinuity of radiation, indeterminism of prediction, or quantitative unity of quanta, do not disappear. They are reabsorbed and recomprehended within Bohr’s techno-atomic "phenomenology" as classically manifest features of phenomena.

Complementarity is correlative to this scheme. Indeed Bohr’s statement, cited earlier, that "evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary" (PWNB 2:40), is part of Bohr’s elaboration on the relationship between quantum individuality and the subdivision of the phenomena just cited. It follows, however, that in any of its manifestations (waves versus particles, continuity versus discontinuity, one half of conjugate quantities necessary for a classical-like complete physical description versus another, or whatever), complementarity or, accordingly, the mathematical formalism of quantum physics, is not a strict mapping or representation (if indeed it is one to begin with) of the quantum world or reality. It would be a mistake to see them as mirroring or mapping each other. Complementarity and quantum mechanics do not map or otherwise represent quantum objects anymore than classical physics can. Bohr’s statement, discussed earlier, that "there is no quantum world," must be seen along these lines and indeed was offered in part as a response to this type of question (Niels Bohr: A Centenary Volume, 305). Indeed, it follows that nothing can do so. Quantum mechanics as complementarity is not a theory that represents, describes, models, or even in any way approximates "the quantum world" (whether quantum objects themselves or their quantum interaction with the quantum structure of the measuring instruments) in the way classical theories do the classical world. It is a theory, in each specific situation of measurement, of classical physical phenomena, as far as the physics of the measuring instruments goes. These phenomena, however, manifest and are indeed defined by peculiar effects of the interaction between quantum objects and the measuring instruments. As a result these phenomena are, in their (complementary) totality, indescribable by means of classical physics. As such, complementarity, defined as the totality of the mutually exclusive phenomena involved, is, as I said, correlative to the radical inaccessibility of quantum objects and processes, including those ultimately responsible for the effects in question. It relates to the micro-world of the ultimate constituents of matter, or rather to the interaction between it and the classical macro-world (of measuring instruments), but in no way theoretically accesses the micro-world itself.

If they represent anything at all (beyond classically configured phenomena of measurement in Bohr’s sense) quantum mechanics and/as complementarity "represent" the ultimate inaccessibility of the ultimate constituents of this world, and hence of the ultimate constituents of the physical world in general. In this sense, the quantum objects may be even more radically inaccessible than the interior of black holes. While it must be applied with caution, the analogy itself is not out of place, insofar as the "naked" singularity inevitably (i.e. by virtue of the equations that describe a black hole) found in the interior of a black hole can never be seen. Indeed black holes must in fact be seen as quantum objects in view of Stephen Hawking’s famous theorems. On the other hand, in certain recent versions of string theory the ultimate constituents of matter are in fact configured as microscopic black holes. This idea is in turn partly due to Hawking, who, actually, suggests that this type of object may introduce more radical levels of, at least, indeterminacy (but, it appears, also of noncausality and arealism) into physics.45

This, again, is not to say that quantum objects, or (or, including) black holes, do not exist or that we can say nothing about their effects in the classical or indeed quantum world. Indeed the nonrealist and noncausal complementarist approach of quantum mechanics appears to be far better suited, and is perhaps the only way, to relate to the quantum world. Paraphrasing Bohr’s passage on quantum individuality just cited, and amplifying Bohr’s point itself, one might say that the irreducible unrepresentability of the ultimate constituents of nature in terms of conventional physical, or conceivably any, attributes finds its proper expression in, jointly, techno-epistemology and complementarity. Ultimately quantum objects and elementary processes are radically, irreducibly unmappable, unrepresentable, or indeed inconceivable, including, again, as the "ultimate constituents of nature." Their effects, however, while beyond the reach of the classical theories, are comprehensively accounted for by quantum mechanics, which automatically covers the techno-atomic situation of quantum measurement, and indeed is able to comprehensively account for these effects by virtue of being a techno-atomic theory in this sense.

4. Chance

Quantum physics was associated with probability and statistics from the outset or even before hand, given that Planck’s law and his discovery occurred at the intersection of electrodynamics (the classical theory of radiation), thermodynamics, the kinetic theory of gases, and classical statistical physics. (The latter three, of course, already connected at the time.) In introducing more properly quantum-mechanical statistical considerations in his tracing of this history in "Discussion with Einstein," Bohr points out, with noticeable intimations of quantum mechanics yet to come and of his subsequent ideas, that "in this situation, there could be no question of attempting a causal analysis of radiative phenomena, but only by a combined use of the contrasting pictures, to estimate probabilities for the occurrence of the individual radiation processed" (PWNB 2:34). He also adds a crucial qualification: "it is most important to realize that the recourse to probability laws under such circumstances is essentially different in aim from the familiar application of statistical considerations as practical means of accounting for the properties of mechanical systems of great structural complexity [as in classical statistical physics]. In fact, in quantum physics, we are presented not with intricacies of this kind, but with the inability of the classical frame of concepts to comprise the peculiar feature[s], characterizing quantum processes" (PWNB 2:34).

Here I shall only outline the nature of quantum probability, referring the reader to works by Bohr and others for more rigorous expositions (specifically those cited earlier). My main concern is the radical, nonclassical character of quantum probability or chance, defined by Bohr’s statement. As we have seen, quantum physics is not a theory that describes, in the way classical physics does, physical processes, such as the motion of elementary particles. Instead, on the basis of certain measurements, limited by the uncertainty relations, performed courtesy of the interaction between an object and the measuring instruments, quantum mechanics can predict the outcome of other possible measurements, defined and restricted in the same way. As Bohr writes:

The essential lesson of the analysis of measurement in quantum theory is thus the emphasis on the necessity, in the account of the phenomena, of taking the whole experimental arrangement into consideration, in complete conformity with the fact that all unambiguous interpretation of the quantum mechanical formalism involves the fixation of the external conditions, defining the initial state of the atomic system concerned and the character of possible predictions as regards subsequent observable properties of that system [i.e. the classically manifest properties of the combined system consisting of the quantum objects and the measuring instruments in their interaction]. Any measurement in quantum theory can in fact only refer either to a fixation of the initial state or to the test of such predictions, and it is first the combination of measurements of both kinds which constitutes a well-defined phenomenon. (Collected Works 7:312)

By virtue of the circumstances, quantum measurement in their totality (manifest in the uncertainty relations), the predictions in question are statistical. They amount only to an estimation of the probability of outcomes, albeit a probability rigorously and precisely defined, for example, by using Schrödinger’s equation. This is the (more or less) standard interpretation, initially developed by Max Bohr, of Schrödinger’s wave function (defined by his equation). The wave function determines the probability of the outcome of individual quantum processes (in their interaction with the measuring instruments) rather than, say, the trajectories of particles, as the equations of classical physics would do. As Bohr writes, "owing to the very character of such mathematical abstractions [as we encounter in quantum mechanics], the formalism does not allow pictorial interpretation on accustomed lines [i.e. classical-mechanical picture of motion], but aims directly at establishing relations between observations obtained under well-defined conditions" (PWNB 2:71). These are, that is, the conditions described in the passage cited above. He adds, "corresponding to the circumstance that different individual quantum processes may take place in a given experimental arrangement, these relations are of an inherently statistic character" (PWNB 2:71) and "here, logical approach cannot go beyond the deduction of the relative probabilities for the appearance of the individual phenomena under given experimental conditions" (PWNB 2:73).

The circumstance in question is an immediate correlative of the fact that quantum mechanics does not predict, in the way classical mechanics does, an outcome of individual processes on the bases of the preceding measurements, which I shall discuss in detail presently. Accordingly, to test such probabilistic predictions we need multiple runs of the same experiment, by, importantly, repeating the overall set up, even though and because the outcome will be different each time (hence, the unavoidability of statistical laws in any comprehensive account of the situation).46 A large enough multiplicity of the outcomes in standard experiments produces a wave-like (interference) pattern, which is also the "picture" of the statistical distribution in question.

Now, while there is also quantum statistics as such, that is, the theory (originally due to the work of Bose, Einstein, Dirac, and Fermi) dealing with multiplicities of quantum objects, and while such considerations bear on the present situation as well, this is not what is primarily at stake at the moment. What was just described is an interpretation, a workable and effective interpretation, of Schrödinger’s wave-function as relating to (although not describing) the behavior of individual quantum objects rather than that of simultaneously configured multiplicities, such as those of classical (or quantum) statistical physics. Accordingly, Bohr sees quantum waves and Schrödinger’s wave-mechanics (or Heisenberg’s matrix mechanics, which deals more directly with quantities symbolically analogous to classical particle-like variables) as "symbolic," as concerns the usage of standard physical variables in these theories. In classical statistical physics the underlying elementary constituents obey the laws of classical Newtonian mechanics, or at least the statistical configurations in question may be and, for the most part, have been interpreted accordingly. Indeed, as Bohr points out, it is "the direct application of classical mechanics to the interaction of atoms and molecules during their incessant motions [that] led to a general understanding of the principles of thermodynamics" (PWNB 2:70).47 The so-called old quantum theory, extending from Planck’s law to the creation of quantum mechanics, was in a way a statistical physics without an underlying mechanics, accounting for the (now ultimate) individual constituents of matter. The old quantum theory was incompatible with the assumption that such mechanics could be classical like. With the introduction of Heisenberg’s and than Schrödinger’s quantum mechanics these difficulties were resolved, except, of course that it was neither causal nor realist (to the great chagrin of Einstein and others, including Schrödinger). Nor, indeed correlatively, did it account for the behavior of the individual quantum objects as such, but only for the individual effects of the interaction between quantum objects, indescribable by any means, and the classically described measuring instruments, as considered here.

In contrast to classical statistical physics, quantum statistics does not result from the underlying mechanical picture of "a great structural complexity." There is no such underlying picture any more than (and correlatively to the fact that) there is an underlying wholeness reflected in complementary configurations of quantum mechanics, indeed even if one deals with "quantum multiplicities." This is why Bohr says in his reply to EPR that "any comparison between quantum mechanics and ordinary statistical mechanics […] is essentially irrelevant. [For] we have not […] merely to do with an ignorance of the value of certain physical quantities but with the impossibility of defining these quantities in an unambiguous way" (QTM, 149). Ultimately, in Bohr’s formulation cited above, we are here dealing "with the inability of the classical frame of concepts"—the whole classical frame of concepts, no less—"to comprise the peculiar feature of indivisibility, or ‘individuality,’ characterizing the elementary processes" (PWNB 2:34). The Warsaw lecture (1938) bridges both statements (the first of 1935, the second from 1949): "the statistical character of the uncertainty relations in no way originates from any failure of measurements to discriminate within certain latitudes between classically describable states of the object, but rather expresses an essential limitation of the applicability of classical ideas to the analysis of quantum phenomena. The significance of the uncertainty relations is just to secure the absence, in such an analysis, of any contradiction between different imaginable measurements" (Collected Works 7:311). Indeed the very way of counting is different in quantum physics, beginning with the way Planck counted (without proper justification, since he assumed an underlying classical-like multiplicity). The paradoxical aspects of quantum physics, such as the emergence of the interference pattern in the double slit experiment, are fundamentally related to this difference between these two configurations of chance.

The presence of this pattern qua pattern—a form of order—is crucial. For, along with, in David Bohm’s phrase, the "irreducibly lawless" character of chance and, correlatively, of individual quantum events, quantum physics gives rise to strict (and rich) forms of order, such as interference patterns, or certain correlations between events, or other forms of order, unaccountable by means of classical physics.48 Quantum physics predicts these correlations, even if it does not "explain" them in the classical sense, for it does not refer to quantum objects and their behavior as such. It also tells us that these correlations cannot be explained by means of classical (in particular realist) theories. Yet again, quantum physics disallows in principle what it does not provide in practice, here a classical-like (causal or realist) explanation of quantum correlations. Indeed Arthur Fine’s point that I have been using here is made in his analysis of quantum-mechanical correlations (consistent with the analysis given here).

It would not be possible to consider here the history of the concepts of chance and probability in mathematics, science, and philosophy from the seventeenth century to classical statistical physics introduced in the nineteenth century, and beyond, even though this and the earlier history of chance (from Democritus on), or atomism (another great invention of Democritus), is crucial, as Bohr points out (PWNB 2:70). Instead, with this history in mind as a background, I shall describe the nonclassical character of the quantum-mechanical chance. This character defines twentieth-century thinking about chance—mathematical-scientific (for example in post-Darwinian biology and genetics) or philosophical, specifically in Nietzsche, Bataille, Blanchot, Lacan, Deleuze, de Man, and Derrida. It is worth, however, revisiting the classical understanding of chance first.

Classically, chance or, more accurately, the appearance of chance is seen as arising from our insufficient (and perhaps, in practice, unavailable) knowledge of the total configuration of forces involved and, hence, of understanding the lawful necessity always postulated behind a lawless chance event. This of course also assumes the possibility of ascribing physical attributes to the objects in question, such as classical-like atoms or particles, from Democritus to Planck and beyond, including their isolated atomicity itself, which we cannot do in quantum physics. If this total configuration becomes available, or if it could be made available in principle (it may, again, not ever be available in practice), the chance character of the event would disappear. Chance would reveal itself to be a product of the play of forces that is, in principle, calculable by man, or at least by God. Most classical mathematical or scientific theories and the classical philosophical view of probability are based on this idea: in practice, we have only partially available, incomplete information about chance events, which are nonetheless determined by, in principle, a complete architecture of necessity behind them. This architecture itself may or may not be seen as ever accessible in full (or even partial) measure. The presupposition of its existence, however, is essential for and defines the classical view. Subtle and complex as they may be, most (arguably all) scientific theories of chance and probability prior to quantum theory and many beyond it, such as chaos theory (in most of its versions), and most philosophical theories of chance are of the type just described. They are classical or, in the sense explained above, causal. Most of them are also realist. On this, and precisely on this, point classical reality and classical causality come together, or rather this point (the assumption of the ultimate underlying causal architecture of reality) brings them together.49

The nonclassical understanding of chance is fundamentally different, as should be clear from the preceding discussion. Nonclassically, chance, or nonclassical chance, is irreducible and irreducibly lawless not only in practice (which, as I have explained, may be the case classically as well) but also, and most fundamentally, in principle. There is no knowledge, in practice or in principle, that is or will ever be, or could in principle be, available to us and that would allow us to eliminate chance and replace it with the picture of necessity behind it; or to introduce laws fully accounting for such chance events at the level of the ultimate constituents of matter, individually, in the manner of classical physics. (The latter possibility and indeed necessity defines classical statistical physics.) Nor, however, can one postulate such a (causal/lawful) economy as unknowable but existing in itself and by itself outside our engagement with it. This latter qualification (which entails, and in quantum mechanics results from, the suspension of realism at the level of the ultimate constituents of matter) is crucial. For, as I explained above, some forms of the classical understanding of chance allow for and are indeed defined by this (realist) assumption. By contrast, the nonclassical chance, such as that we encounter in quantum physics, is not only unexplainable in practice and in principle but is also irreducible in practice and in principle. As we have seen, there is no underlying wholeness or any other structuration or architecture of which such partial accounts—statistical, complementary (the wave-particle ones, or partial representation in terms of classical-like variables), or any other—are really parts. In other words, the nonclassical nature of the quantum-mechanical chance is in fact a result or an effect of the impossibility to disengage the quantum objects and the measuring instruments, and, hence, also of the radical nonrealism of quantum physics. This crucial point is not always fully understood and, when understood, is not sufficiently stressed, including, to some degree, by Bohr, as many of his titles indicate. The main emphasis is often on (a)causality. In any event, as a result of, or correlatively to, the quantum techno-atomicity, the quantum-mechanical chance is irreducible to any necessity, knowable or unknowable. It is, as David Bohm said, "irreducibly lawless."

Bohm’s uses this phrase to describe the fact that in quantum mechanics the outcome of individual events is, in general, not comprehended by its laws, as it would be in classical physics, which is defined by this concept of physical law from Galileo and Newton on.50 The theory does not explain (causally, realistically, or otherwise) how a unique result of an individual measurement emerges, is selected (by whom? or what?) among all the available possibilities, and so forth. Instead it precisely allows for this uniqueness (now considered as a rigorous experimental fact or a kind of nonmathematical "law" of nature) and, moreover, makes the very assumption that such an explanation is possibly problematic. This also suggests that, in a certain sense, while quantum mechanics is a fully rigorous theory, its content and, accordingly, the behavior of quantum objects themselves may not be contained, or even approximated, by its mathematical formalism. As we have seen, at least in the present interpretation, this behavior itself is, by definition, not even described by this formalism, and is argued to be in itself indescribable by any formalism. (As throughout, the features in question at the moment presuppose the techno-atomic character of theory.) Quantum physics requires and depends on the concept of an individual physical event as part of its description of the physical world. Indeed it is in part this concept that defines quantum mechanics as quantum, even though and because the very concept of quantum individuality must be reconceived and given a complex and specifically techno-atomic architecture. This is what Bohr specifically achieves in, arguably, greater measure than anyone else, by configuring such events as indissociable from the irreducible interactions between quantum objects and measuring instruments. That is, even this individuality or/as uniqueness appears (in either sense) at the level of phenomena, rather than of quantum objects themselves, which may not tolerate the attribute of individuality anymore than any other attribute. The individuality itself of quantum phenomena (in Bohr’s sense) remains crucial, indeed defining in quantum theory. At the same time, however, and by the same token, quantum mechanics offers no laws which would enable us to predict with certainty the outcome of such events, or when some of them may occur. Their individuality is essential, in the strict sense, of being irreducible, which is one of the reasons why Bohr retains the term and the notion of "individuality." The laws of quantum mechanics rigorously account for this irreducible individuality and this "un-lawfulness" or "lawlessness" of individual quantum events. This is why Bohr says, as cited above, that "the recourse to probability laws under such circumstances is essentially different in aim from the familiar application of statistical considerations as practical means of accounting for the properties of mechanical systems of great structural complexity."

Thus, whether we deal with quantum statistical multiplicities as such or with repetition of the same experiment (as described above), while the collective is subject to formalization and law, the individual is, at the limit, irreducibly nonformalizable and lawless. In either case, this statement still applies only at the level of phenomena, not that of quantum objects themselves (which latter are in this sense neither lawful nor lawless, neither statistically correlated nor uncorrelated, and so forth). This, let me stress, does not mean that formalization or law here does not apply only in certain exceptional cases, although, in quantum mechanics such exceptional cases may indeed be spectacular. But, although ultimately part of the same overall configuration, this is not what is here being referred to. More radically, every individual case (element, event, and so forth) that belongs to a law-governed quantum-mechanical (experimental and theoretical) collectivity is in itself not subject to the law/s involved, or law in general—is irreducibly lawless. Thus, formalization and laws apply here only to collectivities (I am not saying fully describe them, even at the level of phenomena), but, in general, not to individual elements comprising such collectivities. How such lawless individual elements "conspire" to sum up into lawful collectivities is indeed enigmatic and may in turn be inconceivable, and is certainly not provided by the laws of quantum mechanics. Quantum correlations or the interference pattern in the double slit experiment represent precisely this conspiracy. Accordingly, they also represent the fact that at a certain level quantum mechanics, while ultimately irreducibly lawless at the level of individual events, has more order than a classical-like statistical collectivity would, were the latter possible at the level of the ultimate constituents of matter. It may well be this situation, rather than quantum noncausality ("God does not play dice," in Einstein’s famous words), that bothered Einstein most, especially coupled with the radical questioning, if not suspending, of the concept of physical reality. Einstein came to realize this earlier and more deeply than anyone else, both proponents and doubters of quantum mechanics alike, except for Bohr. He finally said, "that the Lord should play with dice, all right; but that He should gamble according to definite rules, that is beyond me" (QTM, 8).

It may well be impossible to conceive how this quantum "conspiracy" (leading, for example, to the interference pattern in the double slit experiment) is ultimately possible, which bothered Einstein greatly, too.51 "Ultimate" is a crucial qualifier here: it is not that no account is possible, but that there is no ultimate account of either the individual or of the relationships between the individual and the collective. This ultimate inconceivability would further radicalize the questions here posed concerning the nature of both causality and reality, and the very possibility of unambiguously applying such concepts, except within certain, rather restricted, limits. This is why quantum formalism and laws may only be said to apply to collectivities of the ultimate constituents of matter but not to describe fully (the ultimate nature or structure of) those collectivities. This is also why the overall configuration is so radical epistemologically or, as the case may be, anti-epistemologically, as well as anti-ontologically, since it may ultimately disallow ontology, or disallow any ultimate ontology, along with any ultimate epistemology. That is, it would disallow any possibility of knowing or conceiving how that which is at stake here is ultimately structured, or is ultimately possible. Hence, again, the (lawless) individual events can no longer be seen as a part of a wholeness, comprehended by the same law, or by a correlated set of laws, which defines classical systems and the formalism of classical physics. Within classical physics nothing is, in principle, lawless. (In practice, as we have seen, laws may be difficult or even ultimately impossible to apply in certain cases.) By contrast, quantum physics always figures something, here the individual, as irreducibly lawless, and hence irreducibly unique—singular. Individuality or particularity becomes singularity. The concept of singularity may itself be defined by the irreducible lawlessness in relation to a given law or set of laws, or to law in general—to any conceivable law. Crucially, in question here is not only lawlessness but also lawfulness to which this lawlessness enigmatically gives rise. The lawlessness of individual and/as singular events is encountered unavoidably in quantum physics. But so is the lawfulness of correlated collectivities. There is indeed something akin to mystery and magic in this, but, as Bohr is at pains to point out, no mysticism, rather "rational generalizations" of classical ideas and ideals, along with understanding their "inherent limitations" (PWNB 2:65).

Beyond classical limits, once the ultimate quantum constituents of matter come into play, reality and causality disappear, technology and chance replace, "rationally generalize," respectively reality and causality in the techno-atomic individuality/indivisibility of phenomena, as defined by Bohr. This, again, is not a statement concerning the nonexistence of the quantum world, the world at the level of the ultimate constituents of nature. Instead, to the degree that such or indeed any terms apply, it describes the way, the only way, that this existence appears to manifest itself, and, it appears, the only way that we can rigorously describe and indeed conceive of it—at least for now.
At least for now. While some of the currently available theories, such as much of classical physics or (nonrelativistic) quantum mechanics, may be seen as complete within their limits, overall our theories remain manifestly incomplete as regards our knowledge concerning the physical world. We have at the moment classical physics, relativity, chaos theory, quantum mechanics, quantum electrodynamics, quantum field theories, or still other theories, such as string theories, by now extended into the so-called "branes" (for membranes) theories; and each of these denominations appears to branch out nearly interminably. These theories describe various macro and micro aspects of the physical world and of our interaction with it by means of experimental technology. They do so sometimes in classical-like ways, sometimes in quantum-mechanical-like ways, sometimes by combining both. The epistemological status of many of these theories is far from established, and some of them are highly speculative. Quantum mechanics (at least in the interpretation here considered) and, by implication, its extensions rigorously suspend the possibility of physical description at the level of the ultimate constituents of matter themselves. This may or may not continue to be the case, once new theories or new interpretations of them (or of existing theories, such as quantum mechanics) take shape. Still more radical epistemological configurations are not inconceivable either. For the moment we can at best correlate some among available physical descriptions and try to maintain their consistency with experimental data within sufficiently workable limits. (Some of these theories are manifestly inconsistent with each other.) Whether physics can ever be even reasonably brought together remains an open question. It is conceivable that, as Einstein hoped, future theories, or new data, will transform physics, and will do so by means of a more homogeneous single theory, or at least a set of more homogeneous theories, which will, in particular, be no longer irreducible technologically, no longer techno-atomic. It is also conceivable that, as Bohr thought, future developments will preserve the joint significance of classical-like and quantum-like physical, or philosophical, theories in describing, or making it impossible to describe, the ultimate constituents of matter. This conjunction of classical and nonclassical theories has defined the century of physics that began with Planck’s discovery of the quantum of action in 1900 and that is now at its end. It is also possible that the future will produce not only as yet unencountered but as yet inconceivable configurations of nature and science, of matter and mind, or of both or of neither, of something else altogether, and of entirely other questions (if this, for now seemingly inescapable, notion will be retained), and ever more radical (re)conceptualizations or (re)technologization of the conceivable and the inconceivable themselves.

Reference matter

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—"Complementarity, Idealization, and the Limits of Classical Conceptions of Reality," Mathematics, Science, and Postclassical Theory, eds. Barbara H. Smith and Arkady Plotnitsky. Durham, NC: Duke University Press, 1997
—"Disciplinarity and Radicality: Quantum Theory and Nonclassical Thought," Disciplinarity at the Fin de Siècle, eds. Amanda Anderson and Joseph Valente. Urbana-Champagne, IL: University of Illinois Press (forthcoming).
—"Landscapes of Sibylline Strangeness: Complementarity, Quantum Measurement, and Classical Physics," Metadebates, eds. G. C. Cornelis, J. P. Van Bendegem, and D. Aerts, Dordrecht: Kluwer, 1998
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Von Neumann, John. Mathematical Foundations of Quantum Mechanics, tr. Robert T. Beyer, Princeton, NJ: Princeton University Press, 1983.
Wheeler, John Archibald. "Law without Law," Quantum Theory and Measurement, eds. John Archibald Wheeler and Wojciech Hubert Zurek, Princeton, NJ: Princeton University Press, 1983, 182-216.


1 As will be seen, eventually quantum phenomena proved to have far more complex characters, of which, in the circumstances specified accordingly, discontinuity or the particle picture is at best an approximation, as is in fact continuity or the wave picture in the circumstances requiring alternative specifications. These two sets of circumstances were proved to be always mutually exclusive, or in Bohr's famous term, correlative to and introduced in order to account for this situation, complementary. Whether what is in question is radiation, such as light (wave-like according to the classical view) or what were classically seen as particles, such as electrons, all quantum objects may manifest their existence, if not themselves, in both wave-like and particle-like phenomena under different circumstances, although, crucially, never in both types of phenomena together. The very usage of the term "phenomena" in this context requires qualification and indeed a special definition, given by Bohr, to be considered below.
2 I cannot here consider in detail Planck's law and its history, nor the key events following Planck's discovery and leading to quantum mechanics and its interpretation, which is my main subject here. See Thomas S. Kuhn's Black-Body Theory and the Quantum Discontinuity, 1894-1912 (New York: Oxford University Press, 1978). See also Abraham Pais's account, centered on Einstein's role, in Subtle is the Lord... (Oxford: Oxford University Press, 1982). For the history of the events leading to quantum mechanics and complementarity, and beyond, see his Inward Bound: Of Matter and Forces in the Physical World (Oxford: Oxford University Press, 1986). Bohr's arguably best account of this history is "Discussion with Einstein," The Philosophical Writings of Niels Bohr (hereafter PWNB), 3 vols. (Woodbridge, CN: Ox Bow Press, 1987), vol. 2, pp. 32-6. See also introductory and historical material in Volumes 5, 6 and 7 of Niels Bohr: Collected Works (Amsterdam: Elsevier, 1972-1996), 10 vols.
3 Albert Einstein, Out of My Later Years (New York: Philosophical Library, 1950), p. 229; Niels Bohr, "Quantum Physics and Philosophy: Causality and Complementarity," PWNB 3:2.
4 Some doubts concerning Planck's interpretation and (in part for that reason) his law itself were entertained all along. See Kuhn's account in Black-Body Theory.
5 See, Kuhn, Black-Body Theory, 185.
6 Classical physics is extraordinarily effective in explaining a wide variety of physical phenomena and enabling most of the technology we use, including in quantum measurement.
7 A degree of caution is necessary here. While the ultimate constituents of matter are quantum in their behavior, physical entities need not be elementary to exhibit quantum behavior. This refers both to entities formerly seen as elementary, such as protons or neutrons (both consisting of quarks, at the moment seen as elementary), and to other objects. Quantum effects, moreover, may be observed in macro phenomena and on large scales. These effects are, however, always due to the processes involving "small" ultimate constituents of matter. The latter are actually treated, mathematically, as dimensionless point-like objects by modern quantum theories-not, it may be observed, as objects likely to be found in nature. Of much further interest is the question of energy in quantum mechanics, in its relation to chance, on the one hand, and to time (the time-energy uncertainty relations, the relationships between symmetry and the energy conservation law, via Noether's theorem, and related issues), on the other. These considerations could be especially related to the relationships among energy, temporality, and materiality, suggested in some of Bohr's works. These questions, however, cannot be addressed here.
8 Literature dealing with the subject is immense, matched by the number of interpretations of quantum mechanics itself. Even within the cluster of the standard or orthodox (or, as it is also called, Copenhagen) interpretations, to which Bohr's interpretation belongs, the range is formidable, even if one restricts oneself to such founding figures as, in addition to Bohr, Heisenberg, Born, Pauli, Dirac, Von Neumann, and Wigner. This range becomes nearly prohibitive when other figures (and commentaries of them) are added. The two main lines of thought within the Copenhagen cluster are defined by the argument whether or not the formalism of quantum mechanics describes (however nonclassically) the behavior of quantum objects themselves. The first position follows Dirac's and Von Neumann's view, the second Bohr's. It may be argued that, while along certain lines, Dirac's and Von Neumann's versions are closer to Heisenberg's matrix mechanics, Schrödinger's wave mechanics, too, is epistemologically more conducive to (which is not to say entails) the first view. By contrast, Heisenberg's is more conducive to (and perhaps entails) the second, that is, Bohr's. For Dirac's and Von Neumann's versions see their famous books, P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford: Clarendon, 1995) and John von Neumann, Mathematical Foundations of Quantum Mechanics, tr. Robert T. Beyer (Princeton, NJ: Princeton University Press, 1983). The profusion of new interpretations during recent decades was in part motivated by the famous argument of Einstein, Podolsky and Rosen (EPR), offered in 1935, concerning the incompleteness (or either incompleteness or nonlocality) of quantum theory, which I shall discuss below. It may, however, be seen as triggered by David Bohm's reformulation of the EPR argument in terms of spin, and then his hidden variables interpretation, introduced in 1952. It received a further impetus from Bell's theorem (1966) and related findings, and then from Alan Aspect's experiments (around 1980) confirming these findings. Bell's theorem states, roughly, that any classical-like theory (similar to Bohm's) consistent with the statistical data in question in quantum mechanics is bound to involve an instantaneous action-at-a-distance, or at least some form of instantaneous connections between spatially separated objects or events, and, hence, violate relativity theory. Bohm's theory does so explicitly, in contrast to the standard quantum mechanics, which does not. There are arguments that in fact it does, but these arguments are, at best, inconclusive. These developments re-centered the debate concerning quantum mechanics around the question of nonlocality and the so-called quantum correlations (uncountable for classically). Philosophical Consequences of Quantum Theory: Reflections on Bell's Theorem, eds. James T. Cushing and Ernan McMullin (Notre Dame, IN: Notre Dame University Press, 1989) offers a fairly comprehensive sample, although it requires some updating. Mermin's essays on the subject of quantum mechanics in Boojums All the Way Through (Cambridge: Cambridge University Press, 1990) offer one of the better non-technical or semi-technical expositions on some of these subjects. By now, dealing only with standard (i.e. nonrelativistic) quantum mechanics, here considered, the list of interpretation of quantum mechanics includes, among others (and with many variations within each denomination), the hidden-variables interpretation, the many-worlds interpretation, the modal interpretation, the histories interpretation the Ghirardi-Rimini-Weber and related interpretations (most of them nonlocal), and the relational interpretation. The most recent addition, along the relationist lines, appears to be Mermin's powerful and provocative proposal for what he calls "the Ithaca interpretation of Quantum Mechanics," (IIQM) which maintains that only statistical correlations between quantum events, not events (or other correlata) themselves, can be meaningfully considered by quantum theory. One might say that IIQM occupies a kind of intermediate position between Bohr's and Dirac/Von Neumann's approach. For, while, on the one hand it aims to dispense with the irreducible role of measurement, advocated by Bohr, it aims to ascribe physical reality to correlations alone, not correlata, as would be the case in the Dirac/Von Neumann and related approaches. See David Mermin, "What Is Quantum Trying To Tell Us," American Journal of Physics, 66(9), 1998: 753-67, and references there. Mermin credits such theorists as Arthur Fine, Paul Teller, Carlo Rovelli, and Lee Smolin. Cf. also Arthur Fine's essay "Do Correlations Need to be Explained" in Philosophical Consequences of Quantum Theory: Reflections on Bell's Theorem, 175-94 and Paul Teller's essay "Relativity, Relational Holism, and the Bell Inequalities," in Philosophical Consequences of Quantum Theory: Reflections on Bell's Theorem, 208-223, and his related concept of "quanta" (as opposed to "particles") in Paul Teller, An Interpretive Introduction to Quantum Field Theories (Princeton, NJ: Princeton University Press, 1995). It may be argued, however, that Bohr's interpretation, the most techological interpretation of quantum mechanics (and, in a certain sense, the only such interpretation), is at the very least as consistent and comprehensive as any available, albeit, to some, unsatisfactory by virtue of its radical epistemological features to be considered here. I have considered Bohr and quantum epistemology in Complementarity: Anti-Epistemology After Bohr and Derrida (Durham, NC: Duke University Press, 1994), in "Complementarity, Idealization, and the Limits of Classical Conceptions of Reality," Mathematics, Science, and Postclassical Theory, eds. Barbara H. Smith and Arkady Plotnitsky (Durham, NC: Duke University Press, 1997) in "Landscapes of Sibylline Strangeness: Complementarity, Quantum Measurement, and Classical Physics," Metadebates, eds. G. C. Cornelis, J. P. Van Bendegem, and D. Aerts (Dordrecht: Kluwer, 1998); and in the forthcoming essay "Disciplinarity and Radicality: Quantum Theory and Nonclassical Thought."
9 At the limit, it also entails a reconsideration of the relationships between phenomenology and technology. The problematics of the relationships between phenomenology and technology was explored in general philosophical terms in recent history, especially by Heidegger and Derrida, and more recently Bernard Stiegler. For a compelling up-to-date discussion of some of their ideas on the subject in the context of the current cultural and political debates see Richard Beardsworth, "Toward a Critical Culture of the Image," Tekhnema 4:114-41, and further references there. The question of these relationships was of course posed by earlier thinkers as well, Husserl in particular. Heidegger's investigation is especially significant here, whether one speaks of his investigation of the question of technology (Technik) in general, or of his lesser known comments on modern science and specifically physics, classical and quantum, and on the relationships between mathematics and experimental technology there. Indeed, according to Heidegger, the conjunction of mathematics and experimental technology defines the project of modern science, and it may be argued that this conjunction reaches its most radical form in quantum physics. I refer in particular to the essays assembled in The Question Concerning Technology, tr. William Lovitt (New York: Harper, 1977) and to What is a Thing?, tr. W. B. Barton, Jr., and Vera Deutsch (South Bend, IN: Gateway, 1967), although much of Heidegger's work is conceptually relevant here.
10 "Can Quantum-Mechanical Description of Physical Reality be Considered Complete," Quantum Theory and Measurement, eds. John Archibald Wheeler and Wojciech Hubert Zurek (Princeton, NJ: Princeton University Press, 1983), 145-51. (Due to a printing error, the order of pages is reversed in this edition: page 149 should precede page 148.)
11 It may be suggested that one should more properly speak of "noumena" here. However, Bohr's usage is in fact precise, insofar as one sees, as he does, phenomena as (representations) referring to the overall experimental arrangements, rather than as the latter themselves. Moreover, as will be seen, the place where the discrimination between those parts of the overall physical system that are to be treated as the objects and those to be treated as measuring instruments (the so-called "cut") is arbitrary. It can be made at the level of our sense perception, to which every observation can be ultimately reduced. It would be instructive (but is beyond the scope of this essay) to consider in this context Bertrand Russell's (more or less) phenomenological (rather than phenomenological-technological) treatment of "the ultimate constituents of matter" in his early essay entitled, "The Ultimate Constituents of Matter" (1915), written at the outset of new physics (i.e. relativity and quantum mechanics).
12 "Do Correlations Need to be Explained?" Philosophical Consequences of Quantum Theory, 180. Fine makes his comment in the context of quantum correlations and Bell's theorem, where the principle just annunciated finds its perhaps most subtle application. It appears, however, to apply very broadly in quantum mechanics. Fine makes important references to Bohr in this essay (Philosophical Consequences of Quantum Theory, 183-84).
13 Bohr, it is true, specifically refers here to the fact that the individuality/indivisibility of phenomena in his sense disallows an unambiguous assignment or indeed definition of the second complementary variable (say, momentum) once the first (say, position) is defined. Ultimately, however, the nature of the phenomena in question excludes the analysis of quantum objects and quantum processes as such, as quantum, either in themselves or even in their quantum interaction with the measuring devices.
14 One may see this, with caution, as a form of Leibniz's "identity of the indiscernibles." This identity is crucial in statistical counting in quantum physics, including in Planck's case. In contrast to classical statistical physics, in quantum statistics particles of a given quantum multiplicity cannot be seen as distinguishable from each other.
15 Most (if not all) theories that make such assumptions, such as hidden variables theories, introduce, as a result, such "unpleasant" features as nonlocality, the influence of future events upon the present (retro-action), and the like.
16 Recall that particles "themselves" may not be meaningfully assigned "size" and instead are treated as point-like.
17 On the delayed-choice experiments see, John Archibald Wheeler, "Law without Law" (QTM, 182-216). The idea itself finds its origin in Bohr, who observes that "it obviously can make no difference, as regards observable effects obtainable by a definite experimental arrangement, whether our plans of constructing or handling the instruments are fixed beforehand or whether we prefer to postpone the completion of our planning until a later moment when the particle is already on its way from one instrument to another" (PWNB 2:57). It is obvious that Bohr here speaks in these terms of the particle [itself] only provisionally and for the sake of economy. Some more recent experiments and theorization of the situation (in particular, in Wojciech Zurek's investigations) introduce further complexities into this picture, but leave all essential points in place.
18 Anthony, J. Leggett, "Experimental Approaches to the Quantum Measurement Paradox," Foundations of Physics, 18, 9 (1988): 940-41.
19 See also his preceding comments in the same paragraph and his remark later (PWNB 2:63-64), and his discussion of various experiments throughout "Discussion with Einstein."
20 One may speak of disturbing "phenomena," rather than "objects," insofar as one presupposes the possibility of the, in principle, existing "phenomena" that would be observed as "undisturbed" outside the interaction with the measuring instruments, were we somehow to eliminate or compensate for this interaction. This is of course impossible in Bohr's view. There is nothing at the quantum level to which in itself we can assign anything at any point, whether outside or in our interaction with quantum objects.
21 Some, following Karl Popper, speak of "objective probabilities" here, although there appears to be no rigorously defined concept corresponding to this term. Among the approaches different from Bohr, Mermin's correlational interpretation, referred to earlier, appears to offer the most promising approach, especially insofar as it also aims at accounting for the correlational patterns of quantum mechanics. It is also worth noting that, while, in contrast to Bohr's, aiming to dispense with the role of measuring instrument, Mermin's interpretation allows for locality, just as Bohr's does. In effect, Mermin is also much closer to Bohr (than to Popper) in his view of probability.
22 Here I refer in particular to Leggett's work (op. cit.), as well as to the history's interpretations, mentioned above, especially the work of Robert B. Griffiths, Murray Gell-Mann and James B. Hartle, and Roland Omnés. Omnés's The Interpretation of Quantum Mechanics (Princeton, NJ: Princeton University Press, 1994) and more recently Griffiths's "Consistent Histories and Quantum Reasoning," Phys. Rev. A54 (1996): 2759-74, offer the best, although, unfortunately, technical exposition.
23 Aage Petersen, "The Philosophy of Niels Bohr," Niels Bohr: A Centenary Volume, eds. A. P. French and P. J. Kennedy (Cambridge, MA: Harvard University Press, 1985), 305.
24 It is possible that, as Leggett suggests, we will not be able to "argue, from the experimentally well-attested fact that quantum mechanics is an excellent description of the behavior of microscopic entities [...] that it is an equally good [if applicable at all] description of macroscopic assemblies of such entities" ("Experimental Approaches," 951). See also his "On the Nature of Research in Condense-State Physics," Foundations of Physics 22, 2 (1992), 221-33. If true, the implications would be radical indeed, for this argument would entail, if not new ultimate constituents of matter, at least new processes involved in the constitution of matter at the macro-level. (In contrast to, say, hidden variables theories, Leggett, as this quotation indicates, does not challenge the standard quantum-mechanical description at the micro-level.) On the other hand, Omnés' and Griffiths' arguments (along the lines of the history's interpretation), cited earlier, and most other interpretations would suggest and indeed presuppose otherwise. Interestingly, Bohr's (or the present) argument is, in principle, consistent with either view, since it only presupposes the micro-level interaction between quantum objects and measuring instruments (which would be retained in Leggett's proposal as well), and makes no claims concerning the ultimate nature of processes involved in the constitution of macro objects. This difference must be kept in mind throughout the present discussion.
25 See also his comments in PWNB 2:50 and PWNB 3:3.
26 This radical de-ontologization of the quantum-mechanical description, depriving quantum objects of any properties (conceivably including that of being objects) is rarely confronted or accepted, even by the strongest supporters of the Copenhagen view and readers of Bohr, in part in view of its radical epistemology. Another reason is the influence of Dirac's and Von Neumann's formulations of quantum mechanics, which, as I said, is more conducive to the assumption that the mathematical formalism of quantum mechanics describes quantum objects themselves. The latter view appears to define most interpretations of quantum mechanics.
27 Fundamentally different mathematical objects are used in describing the variables involved, specifically the so-called Hilbert spaces and "operators" in quantum mechanics. Operators in a Hilbert space symbolically replace the standard function-variables (such as position and momentum) of classical physics. The peculiar property of such operators is that, in general, their multiplication is not commutative-QP does not equal PQ. This noncommutativity is correlative to the uncertainty relations.
28 The most famous example of the latter is the so-called "Schrödinger cat" paradox, often considered in literature on quantum mechanics. I have considered it from a Bohrian viewpoint in Complementarity (284-85, note 20). For Schrödinger's original presentation see his "The Present Situation in Quantum Mechanics" (Quantum Theory and Measurement, 152-67), largely inspired by the EPR argument.
29 The identification of an attribute of the body under measurement would define the measurement procedure of the classical physics, where measurement must, of course, take place as well. It can be done so as the role of the measuring instruments can be neglected or compensated for, which is never possible in quantum physics.
30 In the wake of both Heidegger's and Derrida's work, the Greek tekhné may give both a more precise meaning to the present argument and an interesting direction for extending it elsewhere.
31 See also PWNB 2:74.
32 As was already indicated above (note 4), and as will be seen below, in view of Bell's theorem such an assumption would be in conflict either with the available experimental data or with relativity.
33 There exists the quantum-theoretical concept of state defined via the formalism of quantum theory and specifically the so-called state-vector, the concept bound by the uncertainty relations. Indeed there are several such concepts or several interpretations of the corresponding aspects of quantum mechanical formalism. This concept is more significant within the Dirac/Von Neumann approach, where the formalism of quantum theory is seen as describing the behavior of quantum objects themselves, than in Bohr's, which suspends this possibility. Some among such concepts or interpretations are classical-like, that is, causal and realist (and as such usually encounter the difficulties indicated above, in particular those related to nonlocality). For the most part, however, they lead to noncausal views of the physical processes in question. Realism appears to remain the main aspiration of most such interpretations. Bohr's (rare) references to the "state" of a quantum system do not appear to carry any quantum-theoretical meaning in the sense just indicated. Instead they refer to the conditions of this system at a given point as established on the basis of its interaction with the measuring instruments involved, indeed, by definition, they refer to this interaction. Bohr's interpretation does not assign, and indeed does not allow one to assign, physical reality to the state-vector.
34 Their interpretation is not a clear-cut issue in quantum mechanics itself (in part in view of the general diversity of interpretations of the latter, as indicated above). This circumstance is in part responsible for the confusion concerning them (and quantum mechanics as a whole) in the humanities, especially in view of the fact that popular literature on the subject including by scientists is not always as lucid or even as accurate as one would expect. The present account follows Bohr's view.
35 Cf. also PWNB 2:73. Each variable by itself can be defined as accurately as anything in classical physics. Indeed these variables are in fact measured as classical variables associated with the measuring instruments, except that we can never determine both of them in quantum measurements.
36 Both are reprinted in Quantum Theory and Measurement, 138-43; 145-51.
37 See Mermin's essays on the subject in his Boojums All the Way Through (Cambridge: Cambridge University Press, 1990), 81-185.
38 In the wake of Bell's theorem the EPR argument is often reformulated in terms of correlations or "entanglement" between events, or measurements performed on different particles of the EPR pair. One may also reformulate the EPR experiment and criterion of reality in terms of the properties of measuring instruments, rather than those of quantum objects. These reformulations introduce new nuances, especially as concerns nonlocality, but do not change the essence of Bohr's argument. Indeed, techno-atomic structure of phenomena would be retained even if quantum mechanics were in fact nonlocal. So far, however, there appears to be no argument (or experiment) establishing such nonlocality, unless one makes additional assumptions, in particular, that quantum objects do in fact posses independent physical properties. Cf. Fine's discussion in "Do Correlations Need to be Explained?" (Philosophical Consequences of Quantum Theory), 175-94.
39 It may, again, be argued that the more radical view in question here is especially necessary in view of the locality considerations. I shall not pursue this delicate argument here. The point itself may be ascertained more or less directly from Bohr's formulations, in particular the one just cited from "Discussion with Einstein" (PWNB 2:61). Einstein in his subsequent (following Bohr's reply) arguments appears to see the standard interpretation of quantum mechanics as disallowing an attribution of even single conventional physical variables to quantum objects (The Born-Einstein Letters, tr. Irene Born [New York: Walker, 1971], 169). He also observes that if one indeed assumes that the quantum-mechanical formalism does not in fact describe individual quantum processes (and, as will be seen, it does not in Bohr's and other versions of the Copenhagen interpretation) then the "paradoxes" he draws attention to disappear (209). Given his realist position, this understanding did not help his discontent with the theory. It also appears from these and related remarks that he (mis)reads Bohr's position in terms of (human?) subjectivity (209). As must be clear from the present discussion, Bohr's view is not subjectivist in any classical sense of the latter terms, anymore than it is classically objectivist. A much more complex and subtle epistemology is at stake.
40 Cf. also QTM, 144, 148.
41 This fact is utilized by Omnés in his "logical interpretation" (a version of the "history's" interpretation) in The Interpretation of Quantum Mechanics, cited earlier.
42 It appears to be initiated by Bohr's rethinking of Heisenberg's microscope thought-experiment, illustrating the uncertainty relations (PWNB 1:63-66).
43 In fact it is the complementarity of the space-time coordination and the claim of causality that is initially central to Bohr, more so than the wave-particle complementarity. The latter is seen by Bohr as merely a manifestation of the former complementarity and of a correlative conceptual complementarity of observation and definition, which-or indeed, more subtly, the idealization of which-are symbolized respectively by the space-time coordination and the claim of causality.
44 Speaking here of "the phenomenon" rather than the object appears to be a slippage on Bohr's part or a reflection of an early stage of his thinking on the issue. (See, however, note 20 above.) Bohr here comes close to Mermin's Ithaca interpretation. Mermin might say here that only the relation or/as correlation between the quantum objects and the agencies of observation have or can be meaningfully attributed physical reality, while the respective correlata (i.e. quantum objects as such and the agencies of observation or, more accurately, their quantum components involved in the interactions in question) cannot be attributed physical reality.
45 Stephen Hawking and Roger Penrose, The Nature of Space and Time (Princeton, NJ: Princeton University Press, 1996), 59-60.
46 Schrödinger's famous 1935 "cat paradox" paper, mentioned above, "The Present Situation in Quantum Mechanics" (QTM, 152-67) still gives one of the best accounts here, in spite, or because, of his "despair" as concerns the whole "situation." It also introduces the concept of quantum "entanglement," also mentioned above.
47 As I have indicated earlier, the situation is more complex in classical statistical physics as well (including in relation to thermodynamics). The classical view even of classical statistical physics (i.e. physics disregarding quantum effects) has been challenged more recently, in particular in the wake of quantum mechanics. In general, it is no longer altogether clear how classical physics is or can be. I shall bypass these complexities here. They would not affect my argument concerning the nonclassical character of the quantum-mechanical chance. If classical chance is ultimately only a manifestation, approximation, or perhaps misunderstanding of the ultimately nonclassical nature of the configurations in question in classical statistical physics, so be it. It may be said that, as classical mechanics, classical statistical physics appears to at least allow for a classical interpretation, while quantum mechanics would disallow any such interpretation. A useful source here is Lawrence Sklar, Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics (Cambridge: Cambridge University Press, 1998).
48 David Bohm, Wholeness and the Implicate Order (London: Routledge, 1995), 73.
49 The point was well realized by Schrödinger in his analysis of quantum mechanics (which, as he observes, jointly suspends both) in the "cat paradox" paper, "The Present Situation in Quantum Mechanics." In particular, in commenting on the relationships between reality and causality in quantum mechanics, he observes, in accord with the analysis given earlier, "If a classical state does not exist at any moment, it can hardly change causally" (154). Taking Einstein's side, Schrödinger, one of the creators of quantum mechanics, never accepted its epistemology (and indeed ultimately even the formalism that he discovered) and saw it as a "doctrine as born of distress" (154). That is not to say, quite the contrary, that he (or Einstein) did not understand the situation. Both Einstein and he rejected quantum mechanics because they understood it and were profoundly disturbed by its epistemological implications.
50 Conservation laws, such as those of momentum and energy conservation, apply under all conditions. They are not sufficient for predicting outcomes of individual events, in part because, insofar as they involve the determination of momentum and energy, the application of these laws is in fact complementary to the space-time coordination in quantum measurement.
51 All this must, again, be seen via the interaction between the (quantum) objects involved and the measuring instruments, and may indeed be a consequence of this techno-epistemology, or here techno-ontology.