# Copenhagen interpretation

The Copenhagen interpretation is an interpretation of quantum mechanics. It was formulated in 1927 by Niels Bohr and Werner Heisenberg during their collaboration in Copenhagen and is based on the proposed by the Nobel laureate Max Born Born's probability interpretation of the wave function.

According to the Copenhagen interpretation of quantum probability character of theoretical predictions is not an expression of imperfection of the theory, but the principle indeterministic ( unpredictable ) nature of quantum physical processes of nature. Furthermore, it is omitted in this interpretation it to attribute to the objects of the quantum theoretical formalism, ie mainly the wave function, a reality in direct sense. Instead, the objects of the formalism to be interpreted only as a means to predict the relative frequency measurement results, which are regarded as the only elements of the reality.

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

## The Copenhagen interpretation

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

- Indispensability of classical concepts

Traditional terms are used in their ordinary sense in the quantum world. You get here, however, rules regarding their applicability. These rules include the definition of boundaries of position and momentum, below which the terms position and momentum not make sense anymore, so are undefined. Classical physics is characterized in that at the same time an exact spatio-temporal representation and full compliance with the physical principle of causality are meant to be given. The precise spatiotemporal representation allows the precise location of an object at specific times. The physical principle of causality allows the determination of the time course of future system states with knowledge of the initial state of a physical system and knowledge of the acting laws of development. Classical concepts are now indispensable, as well as quantum physics measurements require a measuring instrument that needs to be described in classical terms of time and space and which satisfies the principle of causality. According to Carl Friedrich von Weizsäcker says the first condition, that we can perceive the instrument at all, and second, that we can draw reliable conclusions about the characteristics of the DUT from the perceived properties.

- Complementarity

In areas where the so-called effect in order of Planck's constant, is, it comes to quantum effects. Quantum effects come into existence due to uncontrollable interactions between the object and the instrument. Complementarity now means that space-time representation and causality requirement can not both be satisfied simultaneously.

- Holism of quantum phenomena

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

- Niels Bohr took the view that it is in the nature of a particle, it is below certain limits (which are given by the uncertainty relation ) position and momentum of not being able to assign, because these terms would result in no more meaning there. Position and momentum so do not be more objective properties of a quantum object in this sense.
- Werner Heisenberg remained of the more subjective notion that we are as people unable ( as an observer ) (for example due to disturbances on the meter, by our inability or by an inadequate theory ), the properties of position and momentum of a quantum object simultaneously measure with arbitrary precision.

## Interpretation of chance in quantum physics

Unlike classical physics, quantum theory, in many cases not allowed for all measured quantities at a precise prediction. Instead, only probability statements are often possible. This fact has been controversial for the formulation of this theory and the discovery of the underlying phenomena. Who assumes that the fundamental laws of deterministic and not probabilistic in nature, sees in the non ability to make on the basis of quantum physics always deterministic predictions, usually an indication that this theory is imperfect - as " The old man rolls in Albert Einstein's phrase not " is expressed.

However, so far it has not succeeded despite great efforts to find a generally accepted and experimentally verified theory for the description of processes in the microcosm, which would always be deterministic with respect to all measured variables. So whilst there are proposals to modify the quantum physics or interpreted in such a way that so-called hidden variables are assumed to ensure a deterministic version of events. However, these proposals have little support among physicists. One motive is that some of these suggestions with regard to the predictions of the theory remain identical to quantum physics, which is why it is impossible to disprove such a theory directly or indirectly.

## Interpretation of the formalism of quantum physics

Physical theories consist of a formalism and an associated interpretation. The formalism is implemented through a mathematical symbolism, syntax, which allows the prediction of measured variables. These symbols can now be assigned as part of an interpretation of real world objects and sensory experiences. Thus, the theory gives a meaning scheme, their semantics.

Classical physics is characterized by the fact that their symbols can assign entities of reality easily. However, the quantum theory contains formal objects whose direct imaging leads to the reality to difficulties. As the location of a particle will not be described due to its spatial coordinates as a function of time, but. By a wave function, including the possibility of sharp maxima at more than one location, for example, in the quantum theory This wave function is used to logically only for each location to specify a probability to find in a search via a measurement of the particle there. This wave function is, however, for a single particle vermessbar not as a whole, since it is completely transformed in the first measurement, a process that is also interpreted as the collapse of the wave function, and referred to.

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 hand, goes beyond its ability to predict probabilities of measurement results. Only the predicted by the theory of measured values , and thus classical terms, an immediate reality is assigned. In this sense, quantum mechanics is not a real theory.

Quantum mechanics is not only not real after the Copenhagen interpretation, but also non-local. This is the case because the state vector of a quantum mechanical system simultaneously everywhere the probability amplitudes sets (eg, where eigenfunctions of the position operator, and thus states after the measurement of the location and are often referred to as a probability amplitude).

In what form or where a particle between two measurements exist, makes quantum mechanics according to the Copenhagen interpretation no statement.

" The Copenhagen interpretation is often, both by some of their followers as some of their opponents, to the effect misinterpreted, as they say, which can not be observed, which did not exist. This representation is logically inaccurate. The Copenhagen view uses only the weaker statement: What has been observed, there is certainly; with respect to what has been observed, however, we have the freedom to introduce assumptions about the existence or non-existence. 'Of this freedom makes them then use those, which is needed to avoid paradoxes. "

This is made possible because the formalism of quantum mechanics does not include states in which a particle simultaneously has about a well-defined pulse and a well-defined place. The Copenhagen interpretation is so seemingly close to positivism in that it incorporates Mach's demand to invent "things" behind the phenomena. This concept has profound implications for the understanding of particle " in itself". Particles are phenomena that occur in portions in appearance, and on their location in measurements only probability statements on the basis of the associated wave functions are possible. This condition is also known as wave -particle duality. On the other hand, were for drilling phenomena always phenomena of "things", otherwise no scientific experience is possible. This is one of Kant's transcendental philosophy related insight, after which the object term is a condition of the possibility of experience.

The by the standards of our everyday experience associated with the term " particle" idea, this portion should be in every moment in a particular place and thus be permanent as particles part of the reality is, however, experimentally not covered and leads on the contrary to contradictions with the empirical measurement results. This idea is given up in the Copenhagen interpretation.

## Other interpretations of quantum physics

Other important interpretations of quantum theory are the following:

- The everettsche many- worlds interpretation postulates the universal validity of the Schrödinger equation. It follows that each time the development is deterministic, so the time development of a measurement. So it is an interpretation which works without a collapse of the wave function. The different measurement results are realized in different worlds with different observers. The many-worlds interpretation, despite its apparent exoticism according to the Copenhagen interpretation, the second largest following.

- The Bohmian mechanics is a theory with hidden variables. Thereafter, the particles move classic, that is, with a certain position and momentum in a potential which is linked to the wave function itself. Thus, the Bohmian mechanics in the sense of Einstein's is a realistic but non-local interpretation. Apart from the general problems associated with hidden variables is as yet no convincing extension to relativistic situations succeeded.