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"We need to assume, at least provisionally, that Bohr's words make sense"
Don Howard

"(T)hose physicists who accuse this interpretation of operating with a mysterious collapse of the wave function during measurement do not understand a word of it"
Jan Faye

Understanding Niels Bohr

A guide through the literature

It seems to be notoriously hard to understand the writings of Niels Bohr in general and his interpretation of quantum physics in particular. However, given that it dominated the understanding of quantum mechanics for some time it seems worth some trouble. This page reflects my ongoing effort and is by no means finished!

Bohr's interpretation of quantum theory is often summarized by slogans and concepts like

  • The correspondence rule
  • The quantum postulate
  • Complementarity (of e.g. kinematic and dynamic properties)
  • The indispensability of classical concepts
Let us give a brief overview first. The last notion ("classical concepts") seems to be central and a prerequisite for a proper understanding of the others.

The correspondence rule

The correspondence rule appears in many textbooks on quantum mechanics and is usually taken to say something like "in the limit of high quantum numbers quantum mechanics approaches classical physics". In addition the choice of the "right" operators for certain "observables" is supposed to be guided by some sort of "classical correspondence". While Faye (2002) acknowledges that "correspondence" had also this technical meaning as a methodological and heuristic principle (at least in the beginning), its scope is much wider. Faye argues, that to compare the numerical predictions of quantum and classical theory would be useless if there is no common ground for the meaning of the corresponding terms. He states:

"The correspondence rule was based on the metaphysical idea that classical concepts were indispensable for our understanding of physical reality, and it is only when classical phenomena and quantum phenomena are described in terms of the same classical concepts that we can compare different physical experiences."
As indicated above, a proper understanding of "correspondence" needs reference to the doctrine of classical concepts (see further below).

Complementarity and the quantum postulate

Bohr's Como lecture (delivered on the 16th September 1927 and published 1928 under the title "The Quantum Postulate and the Recent Development of Atomic Theory") is generally regarded as the reliable source of Bohr's pre '35 (i.e. pre EPR) view on the interpretation (btw: whether the EPR paper made a big change (or a change at all) is disputed). As the title suggests the "Quantum Postulate" seems to be important. What is it? He writes

"...das sog. Quantenpostulat, wonach jeder atomare Prozeß einen Zug von Diskontinuität oder vielmehr Individualität enthält, der den klassischen Theorien vollkommen fremd ist und durch das PLANCKsche Wirkungsquantum gekennzeichnet ist." (Bohr 1928, p.245)
He continues to argue that the classical ideal of an disturbance-free measurement can not be hold up because Planck's quantum of action sets a limit which can not be undercut. Like Heisenberg's X-ray microscope argument (which Bohr cites) this seems to suggest that all (or most) quantum-novelties (ramdomness, uncertainty,..) can be traced to the inevitable disturbance. Bohr argues that the quantum theory does not allow to find a description which is both, causal and spatio-temporal. However, I can not find any textual evidence in Bohr (1928) for the often made claim that - on the basis of the unobservability - the very existence of the "quantum entities" is denied, i.e. that they miss "reality" if they are not measured and somehow created by this act. Indeed, Bohr writes:
"Nun bedeutet aber das Quantenpostulat, daß jede Beobachtung atomarer Phänomene eine nicht zu vernachlässigende Wechselwirkung mit dem Messgungsmittel fordert, und daß also weder den Phänomenen noch dem Beobachtungsmittel eine selbstständige physikalische Realität im gewöhnlichen Sinne zugeschrieben werden kann."
However, the emphasize seems to be on "selbstständige" reality, and not on reality per se. But there is still an important piece missing, namely "complementarity". This concept is also introduced on the first page of Bohr (1928), when he writes:
"Nach dem Wesen der Quantentheorie müssen wir uns also damit begnügen, die Raum-Zeit Darstellung und die Forderung der Kausalität [...] als komplementäre aber einander ausschließende Züge der Beschreibung des Inhalts der Erfahrung aufzufassen [...]"
With respect to the particle and wave aspect of matter he writes:
"In der Tat handelt es sich hier nicht um einander widersprechende, sondern um komplementäre Auffassungen der Erscheinungen, die erst zusammen eine naturgemäße Verallgemeinerung der klassischen Beschreibungsweise darbieten."
This quote is interesting for two reasons: (i) it states that complementary properties are not contradictory and that (ii) complementarity should be viewed as a "naturgemäße" generalization of the classical description. Elsewhere Bohr has called "complementarity" a generalization of "causality". To call the relation between the "causal" vs. the "spatio-temporal" description "complementary" sounds grandiose. Seemingly Bohr is dealing here with deep and far-reaching philosophical concepts. However, "spatio-temporal" is to be understood as the the specification of position and time-coordinates and "causal" is by Bohr usually used synonymously for "obeying energy-momentum conservation". Following this reading the claim is less spectacular, essentially it is contained in Heisenberg's uncertainty relation.

Classical concepts

At least to a large degree an understanding of Bohr's philosophy of quantum theory boils down to the understanding of his infamous doctrine of the "indispensability of classical concepts". To quote a typical Bohr statement:

"It must above all be recognized that, however far quantum effects transcend the scope of classical physical analysis, the account of the experimental arrangement and the record of the observation must always be expressed in common language supplemented with the terminology of classical physics." (Bohr 1948, p.313)
What is that supposed to mean? According to Howard (1994) most commentators have made the mistake not to question (i) what "classical concept" actually means and (ii) where exactly they need to be employed. Common Bohr-wisdom takes "classical" to be the classical physics of e.g. Newton and Maxwell and the system-apparatus division as being identical to the quantum-classical distinction.

Howard offers a different reading (interpretation or reconstruction). In a nutshell he claims that Bohr's classical-quantum distinction corresponds (in (not so) modern terminology) to the mixture vs. pure state distinction. Further more the application of a quantum or classical description cuts across the system-apparatus distinction, i.e. some part of the apparatus have to be described quantum mechanically and (even more surprising) some features of the system need to be described classically as well.

Bohr and Einstein

In "When champions meet: Rethinking the Bohr-Einstein debate", Landman tries to relate some of Bohr's and Einstein's doctrines. He argues, that both were realists of some sort, i.e. concerned with the notion of "objectification". To Einstein this was related to spatial separability, while Bohr insisted on his infamous doctrine of classical concepts. Landsman now makes the ingenious move to translate these conditions (or what he takes for them) into the language of algebraic quantum theory. Thanks to Raggio's theorem these two positions turn out to be mathematical equivalent. But, as Landsman remarks, "This is not to say that their - now joint - doctrine is necessarily consistent."

Common misconceptions which should be avoided

To be sure, there are many subtle issues which divide the Bohr scholars in various camps. However, some frequent claims are outdated and disqualify the author. These are:

  • The "indispensability of classical concepts" is often construed as the claim, that there is a separate realm of Nature (which contains e.g. measuring devices) and which is intrinsically classic and can not be described quantum mechanically. This can't be true, since many of Bohr's arguments consist in a change of perspective. Here a system initially treated as a measuring device is suddenly seen as a quantum system - subject to the uncertainty relations (see Bohr 1928, p.145 or Landman 2006).
  • It seems as if Bohr never used the concept of "wavefunction collapse" and that even the eigenstate-eigenvalue link was not endorsed by him (see Halvorson and Clifton 2001, p.5)