# Copenhagen Interpretation

# COPENHAGEN INTERPRETATION

The Copenhagen interpretation is the standard textbook interpretation of quantum mechanics. The term covers a range of divergent views, loosely related to Bohr's complementarity interpretation. The consensus of the physics community is that Einstein lost the debate to Bohr about the "completeness" of quantum mechanics at the Solvay conference of October 1927, and that Bohr's analysis of the experimental situation in quantum mechanics in terms of the notion of complementarity allows one to make sense of a universe that is indeterministic 'all the way down,' so that quantum states (that in general assign probabilities between 0 and 1 to the outcomes of experiments) are as complete as they can be.

It is difficult to pin down the Copenhagen interpretation. Heisenberg—who seems to have coined the term "Copenhagen interpretation" (see Howard's "Who Invented the Copenhagen Interpretation" for a discussion)—concedes differences between his own position and Bohr's, but concludes that "we really meant the same." The term is generally taken to cover such radical views as Wigner's, that "the quantum description of objects is influenced by impressions entering my consciousness" and John Wheeler's notion of a "participatory universe":

The dependence of what is observed upon the choice of experimental arrangement made Einstein unhappy. It conflicts with the view that the universe exists 'out there' independent of all acts of observation. In contrast Bohr stressed that we confront here an inescapable new feature of nature, to be welcomed because of the understanding it gives us. In struggling to make clear to Einstein the central point as he saw it, Bohr found himself forced to introduce the word 'phenomenon.' In todays words Bohr's point—the central point of quantum theory—can be put into a single, simple sentence. 'No elementary phenomenon is a phenomenon until it is a registered (observed) phenomenon.' It is wrong to speak of the 'route' of the photon in the experiment of the beam splitter. It is wrong to attribute a tangibility to the photon in all its travel from the point of entry to its last instant of flight. A phenomenon is not yet a phenomenon until it has been brought to a close by an irreversible act of amplification such as the blackening of a grain of silver bromide emulsion or the triggering of a photodetector. In broader terms, we find that nature at the quantum level is not a machine that goes its inexorable way. Instead what answer we get depends on the question we put, the experiment we arrange, the registration device we choose. We are inescapably involved in bringing about that which appears to be happening.

(wheeler 1983, pp. 184–185)

It is doubtful that Bohr would have endorsed Wheeler's formulation as a friendly amendment to complementarity. In a cautionary remark about misleading terminology, he writes:

In this connection I warned especially against phrases, often found in the literature, such as "disturbing of phenomena by observation" or "creating physical attributes to atomic objects by measurements." Such phrases, which may serve to remind of the apparent paradoxes in quantum theory, are at the same time apt to cause confusion, since words like "phenomena" and "observations," just as "attributes" and "measurements," are used in a way hardly compatible with common language and practical definition.

(bohr 1948, p. 237)

## The Rejection of Einstein's Realism

The common strand linking these different positions is the rejection of Einstein's realism—the "ideal of the detached observer," as Pauli put it somewhat pejoratively in a letter to Max Born (dated March 30, 1954). Einstein's position can be characterized by two informal independence principles: A separability principle and a locality principle. The separability principle is the principle that if two physical systems are spatially separated (or, in a relativistic setting, space-like separated), then each system can be characterized by its own properties, independently of the properties of the other system. That is, each system separately has its own "being-thus," as Einstein put it: A characterization in terms of certain properties intrinsic to the system, insofar as it is a separable system. The locality principle is the requirement that no influence on a system can directly affect another system that is spatially separated from it. In particular, a measurement performed on a system cannot alter any properties of another system that is spatially separated from it. The Copenhagen idea is that, in some sense (notwithstanding Bohr's discomfort with the terminology), the dynamical variables of quantum mechanics—the so-called "observables" of the theory—"only have values when you look," where the notion of "looking" is understood in a certain way (depending on the version: As involving the specification of a classically describable experimental set-up, or an interaction with a macroscopic measuring instrument that does not involve an ultimate conscious observer, or a measurement process that does involve the activity of a conscious observer, etc.). This claim is justified by citing examples of quantum interference characterized by Heisenberg's uncertainty relations, such as the double-slit experiment, or beam splitter experiments, or by appealing to the irreducible disturbance of a measured system in a quantum mechanical measurement interaction.

## Measurement and Interference

Now it is generally recognized that the mere fact that measurements disturb what we measure does not preclude the possibility that observables have determinate values, or even that measurements might be exploited to reveal these values in suitably designed measurement contexts. (The "disturbance" terminology itself suggests the existence of determinate values for observables, prior to measurement, that are "disturbed" or undergo dynamical change in physical interactions.) And there is no warrant in the theory for interpreting the Heisenberg uncertainty relations for observables like position and momentum as anything more than a constraint on the possibility of preparing ensembles of systems in which these observables are simultaneously "sharp"–that is, as anything more than a constraint on the reciprocal distribution of the determinate values of these observables in quantum measurements.

Even interference phenomena, by themselves, say nothing about whether or not observables have determinate values in the absence of measurements, unless some interpretative principle is introduced. The usual story, in the case of a double-slit photon interference experiment, for example, is that you get the wrong distribution of hits on the screen behind the slits if you calculate the distribution on the assumption that each individual photon goes through one or the other of the two slits, when the photon is prepared in a quantum state that is represented algebraically in the theory as a linear sum (superposition) of a state in which the photon goes through slit 1 and a state in which the photon goes through slit 2. The photon is supposed to exhibit "wave-particle duality" and "go through both slits at once" to produce the characteristic interference pattern on the screen, where the photon finally manifests its presence as a particle. In passing through the slits, the photon behaves like a wave, a physical influence spread out over both slits, but in hitting the screen, it behaves like a particle, something localized at a point.

The loophole in the argument is the assumption of a specific link between attributing a determinate value to a quantum observable (like position, in the case of a photon going through one of two slits), and attributing aspecific quantum state to the photon. This depends onan interpretative principle, the so-called "eigenvalue-eigenstate link," that a quantum system has a determinate value (an "eigenvalue") for an observable if and only if the quantum state is in a specific state called the "eigenstate" of the observable associated with the specific eigenvalue. If we reject this principle, then we can attribute a determinate value (an eigenvalue) to the observable associated with the photon going through slit 1 or slit 2, exclusively, without assigning the associated state (the eigenstate) to the photon. This is precisely what observer-free hidden variable interpretations like Bohm's theory accomplish.

Interference *per se* represents no obstacle to the simultaneous determinateness of noncommuting observables. The justification for assuming constraints on the simultaneous determinateness of quantum mechanical observables comes, rather, from the hidden variable 'no go' theorems of Kochen and Specker (1967) and Bell (1964), which severely limit the assignment of values to observables.

## Is the Copenhagen Interpretation Instrumentalist?

For Bohr, a quantum "phenomenon" is an individual process that occurs under conditions defined by a specific, classically describable experimental arrangement, and an observable can be said to have a determinate value only in the context of an experiment suitable for measuring the observable. The experimental arrangements suitable for locating an atomic object in space and time, and for a determination of momentum-energy values, are mutually exclusive. We can choose to investigate either of these "complementary" phenomena at the expense of the other, so there is no unique description of the object in terms of determinate properties.

Summing up a discussion on causality and complementarity, Bohr writes:

Recapitulating, the impossibility of subdividing the individual quantum effects and of separating a behaviour of the objects from their interaction with the measuring instruments serving to define the conditions under which the phenomena appear implies an ambiguity in assigning conventional attributes to atomic objects which calls for a reconsideration of our attitude towards the problem of physical explanation. In this novel situation, even the old question of an ultimate determinacy of natural phenomena has lost its conceptual basis, and it is against this background that the viewpoint of complemenarity presents itself as a rational generalization of the very ideal of causality.

(1949, p. 31)

Pauli characterizes Bohr's position this way:

While the means of observation (experimental arrangements and apparatus, records such as spots on photographic plates) have still to be described in the usual 'common language supplemented with the terminology of classical physics,' the atomic 'objects' used in the theoretical interpretation of the 'phenomena' cannot any longer be described 'in a unique way by conventional physical attributes.' Those 'ambiguous' objects used in the description of nature have an obviously symbolic character.

(1948, pp. 307–308)

The complementarity interpretation can be understood as the proposal to take the classically describable experimental arrangement (suitable for either a space-time or a momentum-energy determination) as defining what Bohr calls a quantum "phenomenon." A current approach is to refer to the macroscopic character of our measuring instruments, and to show that the nature of the interaction between such systems and the environment is of a specific sort that results in a physical process called "decoherence" that ensures the "classical" character of the instrument. Some version of this idea is incorporated into the Copenhagen interpretation, sometimes extended by claims such as Wheeler's. According to this view, then, the properties we attribute to a quantum object after a measurement depend partly on what we choose to measure, not solely on objective features of the system itself. To echo Pauli, the properties are "ambiguous" or merely "symbolic."

At first blush it would seem that the Copenhagen interpretation is thoroughly anti-realist, and in some contemporary versions straightforwardly instrumentalist. However, Don Howard in "Who Invented the Copenhagen Interpretation" has argued persuasively that Bohr's complementarity interpretation, as distinct from the Copenhgen interpretation, should be construed as a realist interpretation of quantum mechanics. For the contemporary philosophical debate on the Copenhagen interpretation, see Cushing (1994) and Beller (1999).

** See also ** Bohr, Neils; Quantum Mechanics.

## Bibliography

Bell, John S. "On the Einstein-Podolsky-Rosen Paradox." *Physics* 1 (1964): 195–200. Reprinted in *Speakable and Unspeakable in Quantum Mechanics*. Cambridge, U.K.: Cambridge University Press, 1987.

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

Bohm, David, and Basil J. Hiley. *The Undivided Universe: An Ontological Interpretation of Quantum Mechanics*. London: Routledge, 1993.

Bohr, Niels. "Discussion with Einstein on Epistemological Problems in Modern Physics." In *Albert Einstein: Philosopher-Scientist*, edited by Paul A. Schilpp, 201–241. La Salle, IL: Open Court, 1949.

Bohr, Niels. "On the Notions of Causality and Complementarity." *Dialectica* 2 (1948): 312–319.

Born, Max, ed. *The Born-Einstein Letters*. London: Walker and Co: 1971.

Cushing, James T. *Quantum Mechanics, Historical Contingency and the Copenhagen Hegemony*. Chicago: University of Chicago Press, 1994.

Einstein, Albert. "Quantenmechanik und Wirklichkeit." *Dialectica* 2 (1948): 320–324. Translated as "Quantum Mechanics and Reality." In *The Born-Einstein Letters*, edited by Max Born, 170. See the accompanying letter from Einstein to Born dated April 5, 1948, and the letter dated March 18, 1948, on p. 164.

Fuchs, Christopher A., and Asher Peres. "Quantum Theory Needs No Interpretation." *Physics Today*, 70: 2000.

Heisenberg, Werner. "The Development of the Interpretation of Quantum Theory." In *Niels Bohr and the Development of Physics*, edited by Wolfgang Pauli, 12–29. London: Pergamon Press: 1955.

Heisenberg, Werner. "Quantum Theory and its Interpretation." In *Niels Bohr: His Life and Works as Seen by his Friends and Colleagues*, edited by S. Rozental, 94–108. New York: Wiley Interscience, 1967.

Howard, Don. "Who Invented the Copenhagen Interpretation?" Available at http://www.nd.edu/dhoward1/Papers.html.

Kochen, Simon, and E. P. Specker. "The Problem of Hidden Variables in Quantum Mechanics." *Journal of Mathematics and Mechanics* 17 (1967): 59–87.

Pauli, Wolfgang H. "Editorial on the Concept of Complementarity." *Dialectica* 2 (1948): 307–311.

Pauli, Wolfgang H. Letter to Max Born, dated March 30, 1954. In *The Born-Einstein Letters*, edited by Max Born, 218.

Wheeler, John A. "Law without Law." In *Quantum Theory and Measurement*, edited by John H. Wheeler and Wojciech H. Zurek, 183–213. Princeton, NJ: Princeton University Press, 1983.

Wigner, Eugene P. "Remarks on the Mind-Body Question." In *The Scientist Speculates*, edited by I. J. Good, 284–301. London: Heinemann, 1962.

*Jeffrey Bub (2005)*

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