The genius that was Niels Bohr

Niels Bohr was either one of the great visionary figures of all time or merely the only person courageous enough to confront head on the most imponderable mystery we have yet unearthed. — David Mermin

By placing the subject matter of physical science squarely into the context of human experience, Immanuel Kant had dispelled many qualms that had been shared by thinkers at the end of the 18th century — qualms about the objective nature of geometry, about the purely mathematical nature of Newton’s theory, about the unintelligibility of action at a distance, and about Galileo’s principle of relativity.

Concerning the laws of geometry, which apply to objects constructed by us in the subjective space of our imagination, the question was why they should also apply to the physical world. Kant’s answer was that they apply to objects perceived as well as to objects imagined because visual perception and visual imagination share the same space.¹ As to the mathematical nature of Newtonian mechanics, it was justified, not by the Neo-Platonic belief that the book of nature was written in mathematical language, but by its being a precondition of the possibility of empirical science. What made it possible to conceive of appearances as aspects of an objective world was the mathematical regularities that obtain between them. Newton’s refusal to explain action at a distance — “I feign no hypothesis”² — was similarly justified, inasmuch as the only intelligible causality available to us consists in lawful mathematical relations between phenomena: for the Moon to be causally related to the Earth is for the Moon to stand in a regular mathematical relation to the Earth. As to the principle of relativity, ditto.³

By the time quantum mechanics came along, scientists and philosophers alike had realized that renouncing ontological ambitions and sticking to operationally definable notions was the safest way to arrive at reliable knowledge. If I jiggle the electrons in this antenna, then in due course the electrons in that antenna will jiggle as a result. Given the details of how I jiggle the electrons here, the fundamental equations of classical electrodynamics allow me to predict how the electrons will jiggle there. Classical electrodynamics thus serves as a predictive tool. It makes it possible to calculate the observable effects of observed causes.

But classical electrodynamics could also be seen as describing a physical process by which causes produce effects. It made it possible to transmogrify a calculational tool — the electromagnetic field — into something as real as the electrons and their motions. The resulting story is well known. On being jiggled, the electrons in this antenna locally act on the electromagnetic field. On being jiggled by the electrons, the field then acts locally on itself. (Imagine a bucket brigade with infinitely many infinitesimal buckets separated by infinitely many infinitesimal distances.) In this way the jiggles of the field propagate as an electromagnetic wave, and when this reaches the electrons in another antenna, it causes them to jiggle as well.

What made it possible to reconcile the conceptual economy of operationalism with a seemingly unabashed metaphysical realism was Kant’s theory of science. The latter was therefore widely considered to be tightly linked with classical physics. When classical physics failed to account for such things as the radiation spectrum of a glowing hot object or the stability of atoms, Kant’s philosophy seemed to have gone out the window as well. What happened when quantum physics came along has been engagingly recounted by David Mermin (as his alter ego Mozart):

All the verities of the preceding two centuries, held by physicists and ordinary people alike, simply fell apart — collapsed. We had to start all over again, and we came up with something that worked just beautifully but was so strange that nobody had any idea what it meant except Bohr, and practically nobody could understand him. So naturally we kept probing further, getting to smaller and smaller length scales, waiting for the next revolution to shed some light on the meaning of the old one.

That revolution never came. Quantum mechanics works as beautifully in the nucleus as it does in the atom; and it works as beautifully in the nucleon (proton or neutron) as it does in the nucleus, seven or eight orders of magnitude below the level for which it was designed. It also works beautifully many orders of magnitude above that level, as for example in a superconductor.

Niels Bohr

Two distinct rescue efforts ensued: one fundamentally philosophical, the other fundamentally mathematical; one spearheaded by Niels Bohr, the other set in motion by John von Neumann; one eventuating in QBism, a novel view of science which to Mermin represents “as big a break with 20th century ways of thinking about science as Cubism was with 19th century ways of thinking about art,” the other beset with a spurious problem which originates from the attempt to apply to quantum mechanics that time-honored sleight-of-hand — the reification of a calculational tool. (The gist of this problem, if you can believe it, is to understand how it is possible for measurements to have outcomes.)

Here is how Mermin remembers his initiation into quantum physics and his realization that what is true of quantum physics has always been true of classical physics as well; it just took quantum physics to bring it to light:

When I was an undergraduate learning classical electromagnetism, I was enchanted by the revelation that electromagnetic fields were real. Far from being a clever calculational device for how some charged particles push around other charged particles, they were just as real as the particles themselves, most dramatically in the form of electromagnetic waves, which have energy and momentum of their own and can propagate long after the source that gave rise to them has vanished.

That lovely vision of the reality of the classical electromagnetic field ended when I learned as a graduate student that what Maxwell’s equations actually describe are fields of operators on Hilbert space. Those operators are quantum fields, which most people agree are not real but merely spectacularly successful calculational devices. So real classical electromagnetic fields are nothing more (or less) than a simplification in a particular asymptotic regime (the classical limit) of a clever calculational device. In other words, classical electromagnetic fields are another clever calculational device.

The crucial premise of Kant’s inquiry was that (i) “space and time are only forms of sensible intuition,⁴ and therefore only conditions of the existence of the things as appearances,” that (ii) “we have no concepts of the understanding and hence no elements for the cognition of things except insofar as an intuition can be given corresponding to these concepts,” and that therefore (iii) “we can have cognition of no object as a thing in itself, but only insofar as it is an object of sensible intuition, i.e. as an appearance.” Niels Bohr could not have agreed more, insisting as Kant did that meaningful physical concepts have not only mathematical (quantifiable) but also visual (spatiotemporal) content. But Bohr also realized that “the facts which are revealed to us by the quantum theory ... lie outside the domain of our ordinary forms of perception’’ [BCW6:217].⁵ By “our ordinary forms of perception” Bohr meant

the conceptual structure upon which our customary ordering of our sense-impressions depends and our customary use of language is based. The basis of this ordering is, certainly, the possibility for recognition and comparison and accordingly the usual description of nature is characterized by the attempt to express all experience by stating the locations of material bodies and changes of location with time relative to a coordinate system defined in the traditional manner by means of measuring rods and clocks. [BCW10:xxxv-xxxvi]

In other words, he meant the system of concepts that allows us to unambiguously identify (recognize and compare) objects in space and time. But this is the very system of concepts whose applicability Kant has shown to be a precondition of the possibility of empirical knowledge. What Kant did not anticipate was the possibility of an empirical knowledge that, while being obtained by means of sense impressions organized into objects, was not a knowledge of sense impressions organized into objects. Bohr realized that quantum mechanics was that kind of knowledge.

What Bohr added to Kant’s theory of science was his insight that empirical knowledge was not necessarily limited to what is directly accessible to our senses, and that, therefore, it did not have to be solely a knowledge of sense impressions organized into objects. It can also be a knowledge of properties that (i) are defined by experimental arrangements (which are directly accessible to our senses), and that (ii) actually exist only if their presence is indicated by the results of actual experiments. The click of a counter does not simply indicate the presence of something inside the region monitored by the counter. The counter defines a region, and the click constitutes the presence of something within it. Without the click, nothing is there, and without the counter, there is no there.

As long as (human) thought and sensory experience was the only relevant context of empirical science (as it was for Kant), the elision of the subject — Schrödinger called it objectivation (see this post) — could be achieved: one could think and behave as if the objective world existed independently of perceiving and thinking subjects. But now there was more than one relevant context.

In classical physics, a single picture could accommodate all of the properties a system could have at any moment of time. When quantum mechanics came along, that all-encompassing picture fell apart. Unless certain experimental conditions obtained, it was impossible to picture the electron as following a trajectory (which was nevertheless a routine presupposition in setting up Stern-Gerlach experiments and in interpreting cloud-chamber photographs), and there was no way in which to apply the concept of position. And unless certain other, incompatible, experimental conditions obtained, it was impossible to picture the electron as a traveling wave (which was nevertheless a routine presupposition in interpreting the scattering of electrons by crystals), and there was no way in which to apply the concept of momentum.

The implication was what is now known as contextuality: the properties of quantum systems owe their existence to the experimental conditions under which they are observed. The positions indicated by the droplets forming track in a cloud chamber are the positions of a particle because they are indicated by the droplets. The momenta indicated by two successive droplets (or by the tangent on an imaginary interpolating track) are the momenta of a particle because they are similarly indicated. As Werner Heisenberg put it: “die ‘Bahn’ entsteht erst dadurch, daß wir sie beobachten” (a particle's path only comes into being because we observe it).

If atoms and subatomic particles owe their properties to the experimental conditions under which they are observed, the experimental apparatus cannot owe its properties to the quantum-mechanical systems of which it is commonly said to be composed. This means that we can no longer conceive either of microscopic objects (like atoms and subatomic particles) or of macroscopic objects (like the experimental apparatus) as independently existing substances. And this comes to saying that the elision of the subject can no longer be achieved.

Surely you can see why the rescue effort initiated by von Neumann has become a growth industry dedicated to interpreting the mathematical apparatus of quantum mechanics realistically, while Bohr’s views, as Clifford Hooker writes, have come to be “almost universally either overlooked completely or distorted beyond recognition — this by philosophers of science and scientists alike.”

Catherine Chevalley has identified three reasons why today Bohr seems obscure to most physicists. The first is that Bohr’s mature views, which remained more or less stable from about 1932 onwards, have come to be equated with one variant or another of the Copenhagen interpretation. The latter only emerged in the mid-1950’s, in response to David Bohm’s hidden-variables theory and the Marxist critique of Bohr’s alleged idealism, which had inspired Bohm. The second reason is that Bohr’s readers will usually not find what they expect to find, while they will find a number of things that they did not expect. What they expect is a take on problems arising in the context of “Ψ-ontology” (realism about quantum states).⁶ What they find instead is discussions of the meaning of “objectivity,”  “truth,” or “reality” and the epistemological roles played by language and communication. The third reason is that the task of making sense of quantum mechanics is seen today as one of grafting a metaphysical narrative onto a mathematical formalism, in a language that is sufficiently vague philosophically to be understood by all and sundry. For Bohr, as also for Werner Heisenberg and Wolfgang Pauli, the real issues lay deeper. They judged that the conceptual difficulties posed by quantum mechanics called in question the general framework of contemporary thought, its concepts, its criteria of consistency.

The fact that the elision of the subject is no longer attainable explains Bohr’s intense concern about the objectivity of the quantum-mechanical description of atomic phenomena.  To Kant, the ability to attribute properties to substances, and to connect them by causality, were preconditions of the possibility of objective knowledge, and so they were to Bohr, inasmuch as “the objective character of the description in atomic physics depends on the detailed specification of the experimental conditions under which evidence is gained” [BCW10:215], and this has to be given in terms of property-carrying substances and causal laws. Instead of discarding the classical universe of discourse staked out by Kant, Bohr to his great merit expanded it, annexing to it an intrinsically unspeakable domain of quantum phenomena, which becomes speakable only in terms of statistical correlations between events that happen or can happen in the classical domain.

Nothing could be farther from Bohr’s thinking than the instrumentalist construal of these events as readings of mind-independently existing instruments. To Bohr, who held that “the emphasis on the subjective character of the idea of observation is essential” [BCW10:496], these events were first of all subjective experiences. If the description of atomic phenomena nevertheless has “a perfectly objective character,” it is because “no explicit reference is made to any individual observer” [BCW10:128]. (The emphases are mine.) The perfectly objective character of quantum phenomena therefore boils down to intersubjective agreement among a community of observers⁷:

From our present standpoint physics is to be regarded not so much as the study of something a priori given, but rather as the development of methods for ordering and surveying human experience. In this respect our task must be to account for such experience in a manner independent of individual subjective judgement and therefore objective in that sense, that it can be unambiguously communicated in the common human language. [BCW10:157-158]

One day during tea at his institute, Bohr was sitting next to Edward Teller and Carl Friedrich von Weizsäcker. Von Weizsäcker recalls that when Teller suggested that “after a longer period of getting accustomed to quantum theory we might be able after all to replace the classical concepts by quantum theoretical ones,” Bohr listened, apparently absent-mindedly,  and said at last: “Oh, I understand. We also might as well say that we are not sitting here and drinking tea but that all this is merely a dream.” If we are dreaming, the possibility of unambiguous communication does not exist. Therefore “it would be a misconception to believe that the difficulties of the atomic theory may be evaded by eventually replacing the concepts of classical physics by new conceptual forms” [BCW6:294]. Which is why

the physical content of quantum mechanics is exhausted by its power to formulate statistical laws governing observations obtained under conditions specified in plain language [BCW10:159],

or why

the quantum-mechanical formalism … represents a purely symbolic scheme permitting only predictions … as to results obtainable under conditions specified by means of classical concepts [BCW7:350-351].

By “classical concepts” Bohr did not mean concepts proprietary to classical physics but concepts which owe their meanings to our forms of perception. (Among these concepts are position, orientation and the ones that are defined in terms of invariances under spacetime transformations, such as energy and linear and angular momentum.)

Bohr did not venture to explore the possible ontological implications of this purely symbolic scheme. To him, our purpose in describing nature was not “to disclose the real essence of the phenomena but only to track down, so far as it is possible, relations between the manifold aspects of our experience” [BCW6:296]. It is, however, eminently worthwhile to explore the ontological implications of the quantum-mechanical formalism (without succumbing to Ψ-ontology). This is what I did in a number of papers published since the year 2000, and what I intend to do in a couple of future mailings.

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Niels Bohr: Collected Works, Vol. 6 (North-Holland, 1985).

Niels Bohr: Collected Works, Vol. 7 (Elsevier, 1996).

Niels Bohr: Collected Works, Vol. 10 (Elsevier, 1999).

“…the most imponderable mystery we have yet unearthed”: N.D. Mermin, Boojums All the Way Through: Communicating Science in a Prosaic Age (Cambridge University Press, 1990).

“…shed some light on the meaning of the old one”: N.D. Mermin, What's wrong with those epochs, Physics Today 43 (11), 1990.

“…another clever calculational device”: N.D. Mermin, What’s bad about this habit, Physics Today 62 (5), 2009.

M. Friedman, Einstein, Kant, and the relativized a priori. In Constituting Objectivity, edited by M. Bitbol, P. Kerszberg, and J. Petitot (Springer, 2009).

C.A. Hooker, The nature of quantum mechanical reality: Einstein versus Bohr. In Paradigms & Paradoxes: The Philosophical Challenge of the Quantum Domain, edited by R.G. Colodny (University of Pittsburgh Press, 1972).

C. Chevalley, Why do we find Bohr obscure? In Epistemological and Experimental Perspectives on Quantum Physics, edited by D. Greenberger, W.L. Reiter,  and A. Zeilinger (Springer, 1999).

1. It is noteworthy that Kant’s argument applies, not to Euclidean geometry specifically, even though this was the only geometry known in Kant’s time, but to geometry in general, and thus to whichever geometry is best suited to formulating the laws of physics. It has even been said that Kant’s theory of science set in motion a series of re-conceptualizations of the relationship between geometry and physics that eventuated in Einstein’s theories of relativity (Friedman).

2. While the Latin fingo is usually translated as “I frame,” the verb “feign” retains the original implication of falsehood.

3. Here, too, it would be an anachronism to argue that Kant singled out Galilean relativity, which was the only relativity known in his time. His argument holds for every possible principle of relativity, including Einstein’s.

4. “Intuition” is the standard translation of Anschauung, which covers both visual perception and visual imagination. Perception is sensible (that is, filled with actual sensations), imagination is not.

5. These references are to the Collected Works of Niels Bohr [Volume:page number(s)].

6. The near homonymy with “scientology” is not altogether unintentional.

7. For the complete argument see my paper “Niels Bohr, objectivity, and the irreversibility of measurements” (Quantum Studies: Mathematics and Foundation, DOI: 10.1007/s40509-019-00213-6), a pre-copyedit version of which is available here.