# Copenhagen interpretation

The **Copenhagen** interpretation, also called the **Copenhagen interpretation**, is an interpretation of quantum mechanics. It was formulated around 1927 by Niels Bohr and Werner Heisenberg during their collaboration in Copenhagen and is based on the Bornian probability interpretation of the wave function proposed by Max Born. Strictly speaking, it is a collective term of similar interpretations that have been differentiated over the years. Especially on John von Neumann and Paul Dirac is based the version, which is also called *standard interpretation*.^{[1]}

According to the Copenhagen interpretation, the probabilistic character of quantum theoretical predictions is not an expression of the imperfection of the theory, but of the principally indeterministic character of quantum physical natural processes. However, it is not unproblematic to connect non-predictability with indeterminism. It is possible that we cannot predict certain events without having to assume that these events occur indeterministically. Furthermore, this interpretation refrains from ascribing a reality in an immediate sense to the objects of the quantum-theoretic formalism, that is, especially the wave function. Instead, the objects of the formalism are interpreted merely as means for *predicting* the relative frequency of measurement results, which are regarded as the only elements of reality.

Quantum theory and these interpretations are thus of considerable relevance to the scientific view of the world and its concept of nature.

## The Copenhagen Interpretation

The Copenhagen interpretation was the first completed and self-consistent interpretation of the mathematical edifice of quantum mechanics. It led to stronger philosophical discussions. The basic concept is built on the following three principles:

**Indispensability of classical terms**

Classical terms are also used in their usual meaning in the quantum world. Here, however, they receive regulations about their applicability. These rules include the definition limits of place and momentum, below which the terms place and momentum no longer make sense, i.e. are undefined. Classical physics is distinguished by the fact that an exact spatiotemporal representation and full compliance with the physical principle of causality are simultaneously taken as given. The exact spatiotemporal representation allows the precise location of an object at precisely determined times. The physical causality principle, given knowledge of the initial state of a physical system and knowledge of the laws of evolution at work, makes it possible to determine the time course of future system states. Classical terms are now indispensable, since quantum-physical measurements also require a measuring instrument which must be described in classical terms of time and space and which satisfies the causal principle. According to Carl Friedrich von Weizsäcker, the first condition states that we must be able to perceive the instrument at all, and the second that we must be able to draw reliable conclusions about the properties of the measured object from the perceived properties.^{[2]}

**Complementarity**

In areas where the so-called effect is of the order of Planck’s quantum of action

$$quantum effects occur. Quantum effects occur due to uncontrollable interactions between object and measuring device. Complementarity now means that spacetime representation and causality requirement cannot be fulfilled at the same time.

**Holism of quantum phenomena**

Niels Bohr and Werner Heisenberg, the two main founders of the Copenhagen interpretation, held relatively similar views, but differed on one point of interpretation:

- Niels Bohr was of the opinion that it is in
*the nature of a particle*to be unable to assign place and momentum to it below certain limits (which are given by the uncertainty principle), because these terms no longer make sense there. In this sense, place and momentum are no longer*objective*properties of a quantum object. - Werner Heisenberg, on the other hand, held the rather
*subjective*view that we as humans (as observers) are not able (e.g., due to interference with the measuring device, due to our inability, or due to an inadequate theory) to simultaneously measure the properties of location and momentum on a quantum object with any degree of accuracy.

## Interpretation of chance in quantum physics

Quantum theory does not allow exact prediction of individual events, e.g. in radioactive decay or in the diffraction of particle beams; they can only be predicted statistically. For example, when a radioactive atom emits particles is random in the mathematical sense.^{[3]} Whether this randomness is irreducible or traceable to underlying causes has been disputed since the formulation of this theory. The Copenhagen interpretation advocates objective indeterminism.^{[4]} However, there are also interpretations that explain quantum physical processes in a consistently deterministic way.

Albert Einstein was convinced that fundamental processes must be deterministic rather than indeterministic in nature, and considered the Copenhagen interpretation of quantum theory to be incomplete – as expressed in his saying “God does not play dice”.

Only a small fraction of physicists publish on differences between the various interpretations. One motive here may be that the essential interpretations do not differ with respect to the predictions, which is why falsifiability is excluded.

## Interpretation of the formalism of quantum physics

Physical theories consist of a formalism and an associated interpretation. The formalism is realized by a mathematical symbolism, the syntax, which allows the prediction of measured quantities. These symbols can now be assigned objects of the real world and sensory experiences within the framework of an interpretation. This gives the theory a scheme of meaning, its semantics.

Classical physics is characterized by the fact that entities of reality can be assigned to its symbols without any problems. Quantum theory, however, contains formal objects whose direct mapping to reality leads to difficulties. For example, in quantum theory the location of a particle is not described by its spatial coordinates as a function of time, but by a wave function, including the possibility of sharp maxima at more than one location. According to the Copenhagen interpretation, however, this wave function does not represent the quantum object itself, but only the probability of finding the particle there when searching via a measurement. This wave function is not measurable as a whole for a single particle, because it is completely changed at the first measurement, a process which is also interpreted and called collapse of the wave function.

The Copenhagen interpretation in its original version by Niels Bohr now denies the existence of any relation between the objects of the quantum-theoretical formalism on the one hand and the “real world” on the other hand, which goes beyond its ability to predict probabilities of measurement results. Only the measured values predicted by the theory, and thus classical concepts, are assigned an immediate reality. In this sense, quantum mechanics is a *non-real* theory.

On the other hand, if one considers the wave function as a physical object, the Copenhagen interpretation is *nonlocal*. This is the case because the state vector of a quantum mechanical system is

(Dirac notation) simultaneously specifies the probability amplitudes everywhere (e.g

$$where

$$Are eigenfunctions of the spatial operator and thus states in a spatial measurement, and

$$which are often called

$$denoted probability amplitude).

According to the Copenhagen interpretation, quantum mechanics makes no statement about the form or location of a particle between two measurements.

“The Copenhagen interpretation is often misinterpreted, both by some of its adherents and by some of its opponents, as asserting that what cannot be observed does not exist. This account is logically inaccurate. The Copenhagen view uses only the weaker statement: ‘What has been observed certainly exists; but with respect to what has not been observed we have freedom to introduce assumptions about its existence or non-existence.’ Of this freedom it then makes such use as is necessary to avoid paradoxes.”

*Unity of Nature*. Hanser 1971, ISBN 3-446-11479-3, p. 226.

^{[5]}

This is made possible because the formalism of quantum mechanics does not include states in which a particle simultaneously has, say, a precisely determined momentum and a precisely determined location. The Copenhagen interpretation is thus ostensibly close to positivism, since it takes into account Mach’s requirement not to invent “things” behind phenomena. This conception has profound consequences for the understanding of particles “in themselves”. Particles are phenomena that appear in portions, and about whose location in measurements only probability statements are possible on the basis of the associated wave functions. This circumstance is also known as wave-particle-dualism. On the other hand, for Bohr phenomena were always phenomena on “things”, since otherwise no scientific experience was possible. This is an insight close to Kant’s transcendental philosophy, according to which the concept of object is a condition of the possibility of experience.^{[2]}

On the other hand, the idea associated with the term “particle” according to the standards of our everyday experience, that this portion must be at a certain place at every moment and thus be a permanent part of reality as a particle, is not covered experimentally and, on the contrary, leads to contradictions with the empirical measurement results. This idea is abandoned in the Copenhagen interpretation.

## Web links

- Entry in Edward N. Zalta (ed.):
*Stanford Encyclopedia of Philosophy*.

## Individual references

- ↑ Jochen Pade: Quantum mechanics on foot 2: Applications and extensions. Springer-Verlag, 2012, p. 225ff.
- ↑
^{a}^{b}Carl Friedrich von Weizsäcker:*The Unity of Nature.*Hanser, 1971, ISBN 3-446-11479-3, p. 228 - ↑ Gregor Schiemann: Warum Gott nicht würfelt, Einstein und die Quantenmechanik im Licht neuerer Forschungen. In: R. Breuniger (ed.), Bausteine zur Philosophie. Vol. 27: Einstein. 2010, p. 111 (Online [ PDF]).
- ↑ Gerhard Schurz: Probability. De Gruyter, 2015, p. 56 (limited preview in Google Book Search).
- ↑ Carl Friedrich von Weizsäcker:
*The Unity of Nature*. Hanser, 1971, ISBN 3-446-11479-3, p. 226.

- Quantum Mechanics
- Philosophy of Physics