## Bohr, Niels (1885–1962)

## Bohr, Niels (1885–1962)

# BOHR, NIELS

*(1885–1962)*

Quantum physics is often credited with far-reaching metaphysical and epistemological implications, including the denial of causality and determinism and the existence of strict limits on what can be known about natural systems. One of the main figures whose work has been used—and often misused—in support of such conclusions is the Danish physicist Niels Bohr. Bohr is rightfully viewed as one of the major figures in the history of quantum physics and is widely known both for his extraordinary contributions to the development of quantum theory and for his philosophically oriented work, which focused on the task of interpreting the quantum mechanics. Bohr's interpretation centers on his notion of complementarity, which he developed in 1927, two years after the development of quantum mechanics by Heisenberg, Born, Jordan, and Schrödinger and shortly after the publication of Heisenberg's famous uncertainty paper.

Bohr's interpretive approach attracted many followers but also many critics. Most notable among the latter was Einstein, whose public critique of quantum mechanics and Bohr's interpretation began in 1927 and culminated with his 1935 "EPR" paper, written with Podolsky and Rosen. Bohr's response to Einstein's criticisms, and part of his general interpretive approach, was that quantum mechanics is a complete theory the statistical indeterminacies of which neither need be nor could be overcome with a more foundational theory.

While Bohr is most philosophical after the introduction of complementarity, the overarching theme of much of his earlier work was also associated with certain clear philosophical ideas about the nature of physical theories and the appropriate method for developing a theory in a new realm, and complementarity can be seen as an application of these ideas to the new quantum mechanical formalism.

## Quantum Theory

Bohr's famous 1913 model of the hydrogen atom, with which he explained the hydrogen spectrum, marks the beginning of the quantum theory of the atom. Because classical electrodynamics had dictated that the oscillation of electrons is accompanied by the emission of electromagnetic radiation, the theory could account neither for the stability of the atom nor for the discreteness of the spectrum of frequencies emitted by excited hydrogen gas. Bohr's model solved this puzzle by suggesting that the electron orbits the nucleus in stable stationary states and that the emission of radiation occurs not during that orbit but rather in sudden transitions between the states; the radiation carries the difference in energy between the states according to a quantum frequency rule (based on work by Planck and Einstein) that correlates energy with frequency. Bohr eventually presented the rationale for his model in terms of the quantization of angular momentum, and that is how it is often presented in texts. However, Bohr's original rationale, and arguably the one closest to his actual approach to physics in the years afterwards, is that he read the existence of independent stationary states off the Balmer formula of the hydrogen spectrum by interpreting the spectrum with the quantum-frequency rule. That is, the discrete stationary states were not hypothesized but rather were inferred from an empirical generalization.

## The Correspondence Principle

Bohr eventually expanded this general approach of inferring atomic properties from empirical generalizations or phenomena with the development of his correspondence principle. The principle, first implicitly used in a general form in 1918 and named as a specific principle by Bohr in 1920, is a claim about the relationship between classical and quantum theory, and in particular about classical descriptions of empirical evidence and quantum models of the atom. As Bohr sometimes stated it—the way in which it is most often quoted—the new quantum theory ought to recapture classical electrodynamics in some limit—that is, the old theory ought to be shown to be an approximation that in retrospect is roughly accurate in the realms where quantum effects are negligible. In the hydrogen atom, according to Bohr's principle, that will occur when the quantum number is high, where the difference in energy between stationary states becomes small in comparison with the energies of the states themselves.

While it is tempting to understand the correspondence principle as a requirement for the rationality of the progression of theories, that is at best only one aspect of Bohr's approach with the principle. For Bohr, the correspondence principle was an intratheory claim, not an intertheory one, and it was important because the developing quantum theory had no account of the relation between the motions of the electrons within their orbits and the empirical phenomena of the atomic spectra, whereas classical theory had had such an account. Bohr consistently insisted that we need a stable description of observations from which we can infer atomic properties, and he emphasized that generalizations about atomic spectra—about the frequencies of radiation emitted or absorbed by atoms—are essentially claims about wave phenomena, because measurements of radiation frequencies with spectroscopy equipment unavoidably assume wave theory. Thus, even though the quantum theory might seem to call into question the wave nature of electromagnetic radiation (at least according to the light-quantum concept implied by the photoelectric effect, and later by the Compton effect), scientists still must use wave electrodynamics to provide evidence about atomic properties, so a link or coordination between the theories is needed.

The agreement in the limit between the theories was therefore not the goal of the correspondence principle but only a means of allowing the linkage of claims within the new theory. In particular, it let Bohr relate periodic motion within the atom to periodic aspects of the radiation in the spectrum. This principle both gave empirical content to parts of the model that previously had had none and allowed the inference of properties of certain atomic processes—for example, selection rules for quantum transitions—for which there was no other method of determination. For Bohr the principle was a way to relate observable, empirical phenomena with the quantum mechanisms (such as they were) "behind" the empirical phenomena.

Two related aspects of the correspondence principle were very important for Bohr's work after the development of quantum mechanics. First, although Bohr had been able to apply it only imprecisely and often only qualitatively, it inspired Heisenberg's approach in developing what was to become quantum mechanics, and Bohr claimed that quantum mechanics embodied the correspondence principle. Second, the general approach of incorporating independent, classically based descriptions of empirical phenomena within quantum theory became the foundation for his own interpretation of that quantum mechanics.

## Complementarity and the Interpretation of Quantum Mechanics

Bohr's interpretation is notoriously difficult to pin down, but the core ideas are that our descriptions of the properties of quantum systems must be based on classical concepts, that these concepts are restricted in scope to a particular experimental context, that different concepts are appropriate for different contexts, that the different contexts make the use of certain pairs of mutually exclusive concepts, and that those concepts do not fully capture the nature of quantum systems. Bohr used the word "complementarity" to describe this complex of ideas that together were meant to address interpretive problems posed by quantum mechanics.

Quantum mechanics, especially in Heisenberg's formulation, had retained some aspects of the old quantum theory but had abandoned the definite electron orbits of that theory and had substituted abstract, formal methods for calculating "observable" properties. Heisenberg's uncertainty paper had given a further argument for thinking in these terms by deriving equations that described a reciprocal relationship between the precisions with which certain pairs of properties (for example, position and momentum) could be measured. Although there is some indication in Heisenberg's paper that he might have thought of the tradeoffs in precision in terms of disturbance (every measurement of one property disturbs a specific other one in a way that prevents us from knowing simultaneously both properties to arbitrary precision), Bohr associated the uncertainty relations with his notion of complementarity and claimed that the uncertainty or indeterminacy described by the relations reflect not merely a lack of knowledge of the values of metaphysically definite properties of a system, but rather a degree to which our concepts just do not and cannot be made to apply to the system. Complementarity claims that, although we cannot simultaneously give both normal space-time and causal descriptions of the same quantum phenomenon and although neither description fully captures the nature of the phenomenon, we nevertheless have no other way to describe phenomena besides through these causal and spatiotemporal pictures.

Although Bohr's philosophy is sometimes called the Copenhagen interpretation, there are important distinctions between Bohr's actual views and what is often meant by that name. The name is sometimes used to describe what might better be called the standard interpretation, which is perhaps inspired by Bohr but is really based on von Neumann's work and includes the collapse of the wave packet, which had no part in Bohr's philosophy. Otherwise, it is used to describe a set of views held by Bohr and a number of his former students and associates from Copenhagen, especially Heisenberg and Pauli, but there are disputes regarding how much their views really had in common.

Central to Bohr's interpretation is a sort of holism that we can now understand in terms of entanglement. This holism is clear in Bohr's work starting in 1929 and certainly by 1935. Bohr then explicitly states that it is misleading to think that observation disturbs properties because that would imply the existence of preexisting complete sets of properties. Bohr emphasized that the novel and interpretively challenging aspect of quantum effects is not the discreteness of, say, the exchange of energy but rather the apparent mathematical and theoretical fact that quantum mechanical processes generally cannot be broken down in a way that allows us accurately to describe them in terms of an interaction between component systems such as a measuring instrument and a measured system. In order to describe or analyze an experiment, scientists nevertheless must treat measurement in this way, and the consequence is that descriptions of measured properties of subsystems of a larger whole system at best misconstrue the true quantum mechanical state or phenomenon. And it is precisely in this misconstrual that the statistical nature of quantum mechanical predictions arise.

Though not all interpreters of Bohr agree, this explicit emphasis in his later work did not represent a drastic change in his interpretation. Indeed, it is plausible to argue that complementarity is and was always for Bohr a conclusion based on his correspondence approach and the discovery of noncommutativity and the holism of entanglement. Bohr thought that although one can give an abstract mathematical representation of a quantum mechanical system independent of classical conceptualizations of the phenomena, the symbols used to represent quantum properties have empirical meaning only when they can be associated or put into correspondence with observable phenomena. Doing this requires first establishing independent theoretical descriptions of the observations, and for this it is necessary to use classical concepts to describe the measurement context. Complementarity is, then, an expression of the limitations that noncommutativity places on the degree to which different quantum symbols can be given empirical meaning.

Although Bohr was a realist about the entities described by quantum mechanics and he seems to have believed that quantum mechanics does describe the true nature of quantum-mechanical systems, the foregoing features of his work suggest certain antirealist aspects to his interpretation, especially with respect to the way the meaning and applicability of our concepts about quantum properties depend somehow on the context in which those properties are measured.

This tension is evident in Bohr's response to the EPR paper. That paper questioned the completeness of quantum mechanics precisely on the grounds of the quantum relations of entangled systems; EPR claimed that the ability to predict the properties of one of an entangled pair of particles after the measurement of the other, over distances and within times that preclude a causal interaction on relativistic grounds, indicates that quantum mechanics must assume that the prediction concerns a real, preexisting property that is independent of the other measurement. Bohr's response does not explicitly deny realism but says that any descriptive account of quantum reality is good only within the conditions of applicability of the concepts used in measurement and prediction and that the effect on the distant particle is not a causal, physical one but rather an effect on those conditions; this suggests, perhaps, that disentanglement is only conceptual.

Although in later years Bohr began to discuss complementarity in increasingly broad terms and as applied to other fields, especially biology, it is his philosophical work closest to physics that has had the greatest impact in both philosophy and physics. In the early twenty-first century theorems about the impossibility of certain kinds of hidden variable theories can be seen as a vindication of many of the intuitions in that work, intuitions that remain evident in the pragmatic approach to quantum mechanics assumed by many working physicists.

** See also ** Bell, John, and Bell's Theorem; Bohm, David; Copenhagen Interpretation; Einstein, Albert; Heisenberg, Werner; Quantum Mechanics.

## Bibliography

### general

Einstein, Albert, Boris Podolsky, and Nathan Rosen. "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" *Physical Review* 47 (1935): 777–780. Reprinted in Wheeler and Zurek.

Heisenberg, Werner. "Über den ansclauchichen Inhalt der quantentheoretischen Kinematik und Mechanik." *Zeitschrift für Physik* 43 (1927): 172–198. Translated as "The Physical Content of Quantum Kinematics and Mechanics" in Wheeler and Zurek.

Wheeler, John Archibald, and Wojciech Hubert Zurek. *Quantum Theory and Measurement*. Princeton, NJ: Princeton University Press, 1983.

### works by niels bohr

"On the Constitution of Atoms and Molecules." *Philosophical Magazine* 26 (1913): 1–25, 476–502, 857–875.

"The Quantum Postulate and the Recent Development of Atomic Theory." *Nature* 121 (supplement) (1928): 580–590.

"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" *Physical Review* 48 (1935): 696–702.

"Discussion with Einstein on Epistemological Problems in Atomic Physics." In *Albert Einstein: Philosopher-Scientist*, edited by P. A. Schilpp. Cambridge: Cambridge University Press, 1949. Reprinted in Wheeler and Zurek.

*Atomic Theory and the Description of Nature*, reprinted as *The Philosophical Writings of Niels Bohr*. Vol. 1. Woodbridge, CT: Ox Bow Press, 1934/1987.

*Essays 1932–1957 on Atomic Physics and Human Knowledge*. Reprinted as *The Philosophical Writings of Niels Bohr*. Vol. 2. Woodbridge, CT: Ox Bow Press, 1958/1987.

*Essays 1958–1962 on Atomic Physics and Human Knowledge*. Reprinted as *The Philosophical Writings of Niels Bohr*. Vol. 3. Woodbridge, CT: Ox Bow Press, 1963/1987.

*Causality and Complementarity*, edited by Jan Faye and Henry Folse as *The Philosophical Writings of Niels Bohr*. Vol. 4. Woodbridge, CT: Ox Bow Press, 1998.

### works about niels bohr

Beller, Mara. *Quantum Dialogue: The Making of a Revolution*. Chicago: University of Chicago Press, 1999.

Faye, Jan. *Niels Bohr: His Heritage and Legacy: An Anti-Realist View of Quantum Mechanics*. Dordrecht: Kluwer Academic Publishers, 1991.

Faye, Jan, and Henry J. Folse, eds. *Niels Bohr and Contemporary Philosophy*. Boston Studies in the Philosophy of Science 153. Dordrecht: Kluwer Academic Publishers, 1994.

Folse, Henry J. *The Philosophy of Niels Bohr: The Framework of Complementarity*. Amsterdam: North-Holland, 1985.

Jammer, Max. *The Conceptual Development of Quantum Mechanics*. New York: McGraw-Hill, 1966.

Pais, Abraham. *Niels Bohr's Times: in Physics, Philosophy, and Polity*. Oxford: Clarendon Press, 1991.

Tanona, Scott. "Uncertainty in Bohr's Response to the Heisenberg Microscope." *Studies in History and Philosophy of Modern Physics* 35 (2004): 483–507.

*Scott Tanona (2005)*

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**Bohr, Niels (1885–1962)**