What is the Copenhagen interpretation?

The Copenhagen interpretation is an explanation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg in 1927, when scientists worked together in Copenhagen. Bohr and Heisenberg were able to improve the probabilistic interpretation of the function formulated by M. Born and tried to answer a number of questions, the origin of which is due to particle-wave dualism. This article will consider the main ideas of the Copenhagen interpretation of quantum mechanics, and their influence on modern physics.

Problems

Interpretations of quantum mechanics called philosophical views on the nature of quantum mechanics, as a theory that describes the material world. With their help it was possible to answer questions about the essence of physical reality, the way it is studied, the nature of causality and determinism, and also the essence of statistics and its place in quantum mechanics. Quantum mechanics is considered to be the most resonant theory in the history of science, but there is still no consensus in its deep understanding. There are a number of interpretations of quantum mechanics, and today we will get acquainted with the most popular of them.

Basic Ideas

As you know, the physical world consists of quantum objects and classical instruments for measurement. The change in the state of measuring devices describes an irreversible statistical process of changing the characteristics of microobjects. When a microobject interacts with the atoms of a measuring instrument, the superposition reduces to one state, that is, the reduction of the wave function of the measuring object occurs. The Schrödinger equation does not describe this result.

From the point of view of the Copenhagen interpretation, quantum mechanics describes not microobjects in themselves, but their properties, which manifest themselves in the macro conditions created by typical measuring instruments during observation. The behavior of atomic objects can not be separated from their interaction with instruments for measurements, which fix the conditions for the origin of phenomena.

A look at quantum mechanics

Quantum mechanics is a static theory. This is due to the fact that the measurement of a microobject leads to a change in its state. This gives rise to a probabilistic description of the initial position of the object, described by the wave function. The complex wave function is the central concept of quantum mechanics. The wave function changes to a new dimension. The result of this measurement depends on the wave function, in a probabilistic manner. The physical value is only the square of the modulus of the wave function, which confirms the probability that the microobject being studied is in a specific place in space.

In quantum mechanics, the causality law is performed with respect to a wave function that varies with time in relation to the initial conditions, and not relative to the particle velocity coordinates, as in the classical treatment of mechanics. Due to the fact that only the square of the modulus of the wave function is assigned to the physical value, its initial values can not be determined in principle, which leads to some impossibility of obtaining an accurate knowledge of the initial state of the quantum system.

Philosophical basis

From the philosophical point of view, the basis of the Copenhagen interpretation is epistemological principles:

1. Observability. Its essence consists in excluding from the physical theory those statements that can not be verified by direct observation.
2. Additionality. It assumes that the wave and corpuscular description of the objects of the microworld complement each other.
3. Uncertainty. It says that the coordinate of microobjects and their momentum can not be determined separately, and with absolute accuracy.
4. Static determinism. Supposes that the present state of a physical system is determined by its previous states not uniquely, but only with a share of the probability of implementing the trends of change laid down in the past.
5. Conformity. According to this principle, the laws of quantum mechanics are transformed into the laws of classical mechanics, when it is possible to neglect the magnitude of the quantum of action.

Benefits

In quantum physics, information about atomic objects, obtained through experimental installations, is in a peculiar relationship with each other. In the uncertainty relations of Werner Heisenberg, the inverse proportionality between the inaccuracies in fixing the kinetic and dynamic variables determining the state of the physical system in classical mechanics is seen.

A significant advantage of the Copenhagen interpretation of quantum mechanics is the fact that it does not operate with detailed statements directly about physically unobserved quantities. In addition, with a minimum of prerequisites, it constructs a conceptual system that exhaustively describes the experimental facts that are available at the moment.

The meaning of the wave function

According to the Copenhagen interpretation, the wave function can be subject to two processes:

1. Unitary evolution, which is described by the Schrödinger equation.
2. Measurement.

There was no doubt about the first process in scientific circles of anyone, and the second process aroused discussion and gave rise to a number of interpretations, even within the framework of the Copenhagen interpretation of consciousness. On the one hand, there is every reason to believe that the wave function is nothing more than a real physical object, and that it undergoes a collapse during the second process. On the other hand, the wave function can act not as a real entity, but as an auxiliary mathematical tool, the only purpose of which is to provide an opportunity to calculate the probability. Bohr emphasized that the only thing that can be predicted is the result of physical experiments, therefore all secondary issues should not be related to exact science, but to philosophy. He professed in his workings the philosophical concept of positivism, which requires that science discuss only realistic things.

Double-slit experience

In a two-gap experiment, light passing through two slits falls on a screen on which two interference fringes appear: dark and light. This process is explained by the fact that light waves can mutually amplify in some places, and in others they can be mutually extinguished. On the other hand, the experiment illustrates that light has stream properties of a part, and electrons can exhibit wave properties, thus giving an interference pattern.

It can be assumed that the experiment is carried out with a flux of photons (or electrons) of such low intensity that only one particle passes through the slots each time. Nevertheless, when the points of photons hit the screen, from overlapping waves, the same interference pattern is obtained , in spite of the fact that the experience concerns supposedly separate particles. This is explained by the fact that we live in a "probabilistic" universe in which each future event has a redistributed degree of opportunity, and the probability that something unexpected will happen at the next moment of time is rather small.

Issues

Slit experience raises such questions:

1. What are the rules for the behavior of individual particles? The laws of quantum mechanics point to the place of the screen in which the particles will appear statistically. They make it possible to calculate the location of light bands, in which, most likely, there will be many particles, and dark bands, where fewer particles are likely to fall. However, the laws to which quantum mechanics obeys can not predict where the individual particle actually turns out to be.
2. What happens to the particle at the time between emission and registration? According to the results of observations, it may appear that the particle is in interaction with both gaps. It seems that this contradicts the laws governing the behavior of a pointlike particle. Moreover, when a particle is registered, it becomes pointlike.
3. Under the action of which the particle changes its behavior from static to non-static, and vice versa? When a particle passes through the slits, its behavior is caused by a non-localized wave function that simultaneously passes through both slits. At the moment of registering a particle, it is always fixed as a point, and a blurred wave packet is never obtained.

Answers

The Copenhagen theory of quantum interpretation answers the questions posed as follows:

1. It is fundamentally impossible to eliminate the probabilistic nature of the predictions of quantum mechanics. That is, it can not accurately testify to the limitation of human knowledge about any hidden variables. Classical physics refers to the probability in those cases when it is necessary to describe a process of throwing a dice type . That is, probability replaces incomplete knowledge. The Copenhagen interpretation of the quantum mechanics of Heisenberg and Bohr, in contrast, asserts that the result of measurements in quantum mechanics is fundamentally nondeterministic.
2. Physics is a science that studies the results of measurement processes. It is wrong to think about what happens in their investigation. According to the Copenhagen interpretation, questions about where the particle was before its registration, and other such fabrications are meaningless, and therefore should be excluded from consideration.
3. The measurement act leads to an instantaneous collapse of the wave function. Consequently, the measurement process randomly selects only one of the possibilities that the wave function of a given state allows. And to reflect this choice, the wave function must instantly change.

Formulations

The formulation of the Copenhagen interpretation in its original form gave birth to several variations. The most common of them is based on the approach of non-contradictory events and such a concept as quantum decoherence. Decoherence makes it possible to calculate the fuzzy boundary between macro and micro worlds. The remaining variations differ in the degree of "realism of the wave world".

Criticism

The full value of quantum mechanics (Heisenberg and Bohr's answer to the first question) was questioned in the thought experiment conducted by Einstein, Podolsky and Rosen (EPR paradox). Thus, scientists wanted to prove that the existence of hidden parameters is necessary in order that the theory does not lead to an instantaneous and non-local "long-range" action. However, during the verification of the EPR paradox, which became possible due to Bell's inequalities, it was proved that quantum mechanics is correct, and various theories of hidden parameters have no experimental confirmation.

But the most problematic was the answer of Heisenberg and Bohr to the third question, which placed the measuring processes in a special position, but did not determine the presence of distinctive features in them.

Many scientists, both physicists and philosophers, flatly refused to accept the Copenhagen interpretation of quantum physics. The first reason was that the interpretation of Heisenberg and Bohr was not deterministic. And the second - in that it introduced an indefinite concept of measurement, which turned probabilistic functions into reliable results.

Einstein was convinced that the description of physical reality, given by quantum mechanics in the interpretation of Heisenberg and Bohr, is inadequate. According to Einstein, he found a share of logic in the Copenhagen interpretation, but his scientific instincts refused to accept it. Therefore, Einstein could not refuse to search for a more complete concept.

In his letter to Borne Einstein said: "I am sure that God does not throw dice!". Niels Bohr, commenting on this phrase, told Einstein that he did not tell God what to do. And in his conversation with Abraham Pice, Einstein exclaimed: "Do you really think that the Moon exists only when you look at it?"

Erwin Schroedinger invented a thought experiment with a cat, through which he wanted to demonstrate the inferiority of quantum mechanics during the transition from subatomic systems to microscopic ones. At the same time, the necessary collapse of the wave function in space was considered problematic. According to Einstein's theory of relativity, instantness and simultaneity are meaningful only for an observer located in one frame of reference. Thus, there is no time that could become one for all, and hence an instantaneous collapse can not be determined.

Spread

An informal poll conducted in scientific circles in 1997 showed that the prevailing earlier Copenhagen interpretation, briefly discussed above, is supported by less than half of the respondents. Nevertheless, she has more adherents than other interpretations individually.

Alternative

Many physicists are closer to another interpretation of quantum mechanics, which is called "no". The essence of this interpretation is exhaustively expressed in the saying of David Mermin: "Shut up and calculate!", Which is often attributed to Richard Feynman or Paul Dirac.