What was Niels Bohr’s interpretation of quantum mechanics?

In asking this seemingly innocent question, we have sinned twice. First, we have neglected that Bohr’s thought was a moving target: Finely sifting his words, one can make a good case that his thinking changed, not so much in the big ideas he advocated but in how he advocated for them. Second, more fundamentally, the idea of an “interpretation of quantum mechanics” is a modern one. It presumes that the mathematics of quantum theory is established, agreed upon and empirically validated beyond all reasonable doubt, and that what we lack is only a narrative about how these equations tie back to nature. But Bohr was a pioneer, and his heyday was the age of ferment, when those equations and their interconnections were being hashed out, co-evolving with the individually unstable and mutually contradictory worldviews of all the pioneers. To ask for Bohr’s “interpretation” is to demand an anachronism.

So, then, let us contemplate Bohrian thinking at its most refined and battle-tested. If we focus upon Bohr’s later writings, after the hurly-burly of the Einstein—Podolsky—Rosen affair, we can articulate a mature Bohr-ism that provides the most fruitful position for analysis. Bohr has a reputation for opacity, typically blamed on his writing style but also due on a more subtle level to the fact that he is often concerned with issues other than what a modern reader expects to find in a “quantum foundations” essay. If one jumps in and opens one’s eyes beneath the surface, there will be more to see than the rumors foretold. His 1938 Warsaw lecture is a good place to start.

A colleague has elsewhere paraphrased Bohr as saying that quantum physics gives predictions for the outcomes of quantum measurements, which are instances of “irreversible amplification in devices whose design is communicable in common language suitably refined by the terminology of classical physics.” This bare-bones account can be elaborated. First, for the mature Bohrian, any measurement is a comparison between a physical property of one system and a physical property of another. He says so himself, quite plainly: “In the first place, we must recognize that a measurement can mean nothing else than the unambiguous comparison of some property of the object under investigation with a corresponding property of another system, serving as a measuring instrument.” Second, following upon this, any talk of measurements “creating” the values they measure is off-base, a confusion and a distraction. In Bohr’s words, “Speaking, as is often done, of disturbing a phenomenon by observation, or even of creating physical attributes to objects by measuring processes, is, in fact, liable to be confusing, since all such sentences imply a departure from basic conventions of language which, even though it sometimes may be practical for the sake of brevity, can never be unambiguous.” Third, any concept of classical physics, like energy or momentum, can in principle be extrapolated down to the subatomic level and retain its validity. However, not all sets of such concepts can be simultaneously extrapolated down together. Whether or not a particular concept of classical physics can be applied within the atom depends upon the circumstances, upon the choice of laboratory apparatus being employed to measure that atom. Using one apparatus will make classical concept $A$ applicable, but another classical concept $B$ cannot even be defined in the context established by that apparatus. In special relativity, so ordinary a concept as the simultaneity of two events cannot be defined without fixing a reference frame. For the mature Bohrian, quantum mechanics is likewise: The definability of a classical-physics concept depends upon fixing the physical context by specifying the experimental conditions.

It is a genre convention to accuse Bohr of allowing a “shifty split” between quantum and classical levels of reality. This critique is really applicable to Heisenberg rather than Bohr. It is Heisenberg who would have said, “We cannot precisely locate the boundary between the classical measuring device and the quantum system.” The mature Bohrian replies, “Sounds like a skill issue.” A complete accounting of the experimental situation, in ordinary language augmented by classical-physics concepts, fixes the boundary in place by definition. If the boundary is shiftable, the description of the experiment was incomplete. Similar experiments, involving boundaries that are not quite identical, can give statistically similar predictions, but there is no surprise in that, any more than there would be in clocks of nearly identical pendulum lengths keeping almost exactly the same time.

It is also common to accuse Bohr’s view of suffering from “the measurement problem.” Quantum states evolve smoothly with time, so the campfire story goes, except when interrupted by “measurements” that change them stochastically at ill-defined moments. “It’s like having a body obey $F = ma$ at almost all times, except at random instants where suddenly $F = ma/2$ for no reason that you can explain.” Bohr himself seldom discussed quantum states; it seems that he did not believe that staring at a $\psi$ could reveal the mysteries of the quantum. Again, his 1938 Warsaw lecture clears up the matter:

[A]ll 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 the possible predictions as regards subsequent observable properties of that system. 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.

In more modern language, a wavefunction is calculated in the first place from classical information, and symmetrically, it is “collapsed” by conditioning on classical information. There is no more mystery in “collapsing” a wavefunction than there is in writing one in the first place. The very mindset that allows the “measurement problem” to be a problem is simply foreign to Bohr.

Bohr’s thinking is more robust than it is given credit for in Internet forums, philosophy conferences and other disreputable venues. To a QBist, however, it still fails to satisfy. A QBist treats a measurement as an action, not a mere comparison of pre-existing properties. Bohr has none of the personalism that QBists have found, after long struggles toward self-consistency, to be necessary. And, perhaps most vexingly, Bohr invokes “the quantum postulate”, a premise that ostensibly captures the essence of what quantum mechanics is about, without saying what that postulate is. It is “completely foreign” to classical physics; fine. It is “symbolized by Planck’s constant of action”; OK, unless one works in natural units, we suppose. Bohr draws an analogy with special relativity, as we have noted above. But what “quantum postulate” is the counterpart of Every agent who feels herself motionless will measure the same speed of light?