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 Born probability interpretation of the wave function proposed by Max Born . Strictly speaking, it is a collective term for similar interpretations that have been differentiated over the years. The version, which is also known as the standard interpretation , is based in particular on John von Neumann and Paul Dirac .

Copenhagen interpretation in the thought experiment of Schrödinger's cat : During radioactive decay, the state branches out. According to a random principle, however, one of the two branches collapses again immediately after the coherence between the states has decayed far enough, for example due to a measurement.

According to the Copenhagen interpretation, the probability 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 without its problems to combine unpredictability with indeterminism. It is possible that we cannot predict certain events without assuming that those events will occur indeterministically. Furthermore, this interpretation refrains from assigning a reality in the immediate sense to the objects of the quantum theoretical formalism, i.e. above all to the wave function . Instead, the objects of the formalism are interpreted merely as a means of predicting the relative frequency of measurement results, which are regarded as the only elements of reality.

The quantum theory and these interpretations are therefore of considerable relevance for the scientific worldview and its concept of nature.

The Copenhagen Interpretation

The Copenhagen Interpretation was the first complete and self-consistent interpretation of the mathematical structure of quantum mechanics . It led to more philosophical discussions. The basic concept is based on the following three principles:

Classic terms are indispensable

Classical terms are also used in their usual meaning in the quantum world. You will, however, receive regulations about their applicability here. These regulations encompass the definition limits of place and momentum , below which the terms place and momentum no longer make sense, i.e. are undefined. The classical physics is distinguished in that same exact spatiotemporal representation and full compliance with the physical causality principle are meant to be given. The exact spatiotemporal representation enables the exact location of an object at precisely defined times. The physical causal principle enables the determination of the temporal course of future system states with knowledge of the initial state of a physical system and knowledge of the laws of development. Classical terms are now indispensable, since quantum physical measurements also require a measuring instrument that has to be described in classical terms of time and space and that complies with the causal principle. According to Carl Friedrich von Weizsäcker , the first condition says that we can perceive the instrument at all, and the second that we can draw reliable conclusions about the properties of the measurement object from the perceived properties.

Complementarity

In areas where the so-called effect is in the order of magnitude of Planck's quantum of action , quantum effects occur . Quantum effects occur due to uncontrollable interactions between the object and the measuring device. Complementarity now means that spacetime representation and causality requirement cannot be fulfilled at the same time. ${\ displaystyle h}$

Wholeness 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 in the interpretation:

Niels Bohr was of the opinion that it is in the nature of a particle to no longer be able to assign position and momentum to it below certain limits (given by the uncertainty principle) because these terms no longer make sense there. In this sense, place and impulse are no longer objective properties of a quantum object.
Werner Heisenberg, on the other hand, took 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), the properties of place and momentum on a quantum object can be measured at the same time as precisely as required.

Interpretation of chance in quantum physics

Quantum theory does not allow an exact prediction of individual events, e.g. B. in radioactive decay or in the diffraction of particle beams, they can only be predicted statistically. When, for example, a radioactive atom emits particles, it is random in a mathematical sense. Whether this coincidence is irreducible or can be traced back to underlying causes has been disputed since the formulation of this theory. The Copenhagen interpretation advocates an objective indeterminism . But there are also interpretations that explain quantum physical processes consistently deterministically . Albert Einstein was convinced that the fundamental processes had to be deterministic and not indeterministic in nature, and considered the Copenhagen interpretation of quantum theory to be incomplete - which is expressed in his saying " God does not roll the dice ".

Only a small part of the physicists publishes on differences between the different interpretations. One motive here may be that the essential interpretations do not differ with regard 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. Objects of the real world and sensory experiences can now be assigned to these symbols within the framework of an interpretation. This gives the theory a scheme of meaning, its semantics .

Classical physics is characterized by the fact that its symbols can easily be assigned to entities of reality. However, quantum theory 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 position coordinates as a function of time, but by a wave function , etc. a. with the possibility of sharp maxima in more than one place. 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 cannot be measured as a whole for a single particle, since it is completely changed during the first measurement, a process that is also interpreted and referred to as the collapse of the wave function .

The Copenhagen interpretation in its original version by Niels Bohr now denies the existence of any relationship between the objects of the quantum theoretical formalism on the one hand and the "real world" on the other, which goes beyond its ability to predict the probabilities of measurement results. Only the measured values predicted by the theory, and thus classical terms, 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 non-local . This is the case because the state vector of a quantum mechanical system ( Dirac notation ) simultaneously defines the probability amplitudes everywhere (e.g. where eigenfunctions of the position operator and thus states are in a position measurement and the probability amplitude that is often referred to as the probability amplitude). ${\ displaystyle | \ psi \ rangle}$ ${\ displaystyle | \ psi \ rangle \ to | x \ rangle \ langle x | \ psi \ rangle}$ ${\ displaystyle | x \ rangle}$ ${\ displaystyle \ langle x | \ psi \ rangle}$ ${\ displaystyle \ psi ({\ vec {x}})}$

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

“The Copenhagen Interpretation is often misinterpreted, both by some of its supporters and some of its opponents, to mean that what cannot be observed does not exist. This representation is logically imprecise. The Copenhagen view only uses the weaker statement: 'What has been observed certainly exists; however, as to what has not been observed, we are free to make assumptions about its existence or non-existence. ' She then makes use of this freedom that is necessary to avoid paradoxes. "

- Carl Friedrich von Weizsäcker : The unity of nature. Hanser 1971, ISBN 3-446-11479-3 , p. 226.

This is made possible because the formalism of quantum mechanics does not include states in which a particle has a precisely defined momentum and a precisely defined location at the same time. The Copenhagen interpretation is thus apparently close to positivism , since it takes into account Mach's demand not to invent “things” behind the phenomena. This conception has profound consequences for the understanding of particles “in themselves”. Particles are phenomena that appear in portions and about the location of which only probability statements based on the assigned wave functions are possible during measurements. This fact is also known as wave-particle dualism . On the other hand, for Bohr phenomena were always phenomena in "things", since otherwise no scientific experience is possible. This is an insight that is close to Kant's transcendental philosophy, according to which the concept of the object is a condition of the possibility of experience.

The idea associated with the term “particle” according to the standards of our everyday experience that this portion must be in a certain place at any moment and thus permanently be part of reality as a particle, is not experimentally covered 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 evidence

↑ Jochen Pade: Quantum Mechanics on Foot 2: Applications and Extensions . Springer-Verlag, 2012, p. 225 ff .
^ ^A ^b Carl Friedrich von Weizsäcker: The unity of nature. Hanser, 1971, ISBN 3-446-11479-3 , p. 228
↑ Gregor Schiemann: Why God does not roll the dice, Einstein and quantum mechanics in the light of recent research . In: R. Breuniger (ed.), Building blocks for philosophy. 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.

[1] Jochen Pade: Quantum Mechanics on Foot 2: Applications and Extensions . Springer-Verlag, 2012, p. 225 ff .

[CFvW228-2] A ^b Carl Friedrich von Weizsäcker: The unity of nature. Hanser, 1971, ISBN 3-446-11479-3 , p. 228

[Schiemann-3] Gregor Schiemann: Why God does not roll the dice, Einstein and quantum mechanics in the light of recent research . In: R. Breuniger (ed.), Building blocks for philosophy. Vol. 27: Einstein . 2010, p. 111 ( online [PDF]).

[Schurz-4] Gerhard Schurz: Probability . De Gruyter, 2015, p. 56 ( limited preview in Google Book search).

[5] Carl Friedrich von Weizsäcker: The unity of nature. Hanser, 1971, ISBN 3-446-11479-3 , p. 226.