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 occurrence of which is due to wave-particle duality. This article will discuss the main ideas of the Copenhagen interpretation of quantum mechanics, and their impact on modern physics.

Issue

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 method of its study, the nature of causality and determinism, as well as 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 consensus in its deeper understanding still does not exist. There are a number of interpretations of quantum mechanics, and today we will get to know the most popular of them.

Main ideas

As you know, the physical world consists of quantum objects and classical instruments for measuring. A change in the state of measuring instruments describes an irreversible statistical process of changing the characteristics of micro-objects. When a micro-object interacts with the atoms of the measuring device, the superposition is reduced to one state, that is, the wave function of the measuring object is reduced. The Schrödinger equation does not describe this result.

From the point of view of the Copenhagen interpretation, quantum mechanics does not describe microobjects per se, but their properties, which are manifested in macro conditions created by typical measuring instruments during observation. The behavior of atomic objects cannot be distinguished from their interaction with measurement instruments that record 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 micro-object leads to a change in its state. So there is 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 until a new measurement. The result of this measurement depends on the wave function, in a probabilistic manner. Only the square of the modulus of the wave function has physical significance, which confirms the probability that the micro object under study is located in a certain place in space.

In quantum mechanics, the law of causality is satisfied with respect to the wave function, which varies in time depending on the initial conditions, and not relative to the coordinates of the particle velocity, as in the classical interpretation of mechanics. Due to the fact that only the square of the modulus of the wave function is endowed with physical value, its initial values ​​cannot be determined in principle, which leads to some impossibility to obtain accurate knowledge about the initial state of the quantum system.

Philosophical Foundation

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

1. Observability. Its essence is the exclusion from the physical theory of those statements that cannot be verified by direct observation.
2. Complementarity. It suggests that the wave and particle description of the objects of the microworld complement each other.
3. Uncertainties. It says that the coordinate of microobjects and their momentum cannot be determined separately, and with absolute accuracy.
4. Static determinism. It suggests that the current state of the physical system is not determined unambiguously by its previous states, but only with a fraction of the likelihood of the implementation of trends in the past.
5. Compliance. 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 facilities is in a peculiar relationship with each other. In the Werner Heisenberg uncertainty relations, there is an inverse proportionality between the inaccuracies in fixing kinetic and dynamic variables that determine the state of a physical system in classical mechanics.

A significant advantage of the Copenhagen interpretation of quantum mechanics is the fact that it does not operate with detailed statements directly about physically unobservable quantities. In addition, with a minimum of prerequisites, she builds 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.

No one had any doubts about the first process in the scientific community, and the second process provoked discussions and generated a number of interpretations, even within the framework of the Copenhagen interpretation of consciousness itself. 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 collapse during the second process. On the other hand, the wave function may not be a real entity, but an auxiliary mathematical tool, the sole 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, so all secondary issues should not relate to exact science, but to philosophy. He confessed in his work the philosophical concept of positivism, requiring that science discuss only really measurable things.

Dual Slit Experience

In a two-slit 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 mutually cancel out in others. On the other hand, the experiment illustrates that light has the properties of a part flux, while electrons can exhibit wave properties, giving an interference pattern.

It can be assumed that the experiment is conducted with a stream of photons (or electrons) of such low intensity that only one particle passes through the slits each time. Nevertheless, when adding the points of the photons entering the screen, the overlapping waves produce the same interference pattern, despite the fact that the experiment concerns supposedly individual particles. This is explained by the fact that we live in a “probabilistic” universe, in which every future event has a redistributed degree of possibility, and the probability that something absolutely unforeseen happens at the next moment of time is rather small.

Questions

Slit experience poses such questions:

1. What will be the rules of behavior of individual particles? The laws of quantum mechanics indicate the place of the screen in which the particles appear, statistically. They allow you to calculate the location of light bands in which there are likely to be many particles, and dark bands where less particles are likely to fall. However, the laws that quantum mechanics obey cannot predict where a single particle will actually be.
2. What happens to a particle in the moment between emission and registration? According to the results of observations, it may seem that the particle is in interaction with both cracks. It seems that this contradicts the laws of behavior of a point particle. Moreover, when a particle is registered, it becomes pointlike.
3. Under the influence of what does a particle change its behavior from static to non-static, and vice versa? When a particle passes through slits, its behavior is determined by an unlocalized wave function that simultaneously passes through both slits. At the moment of registration of a particle, it is always fixed as a point one, and a blurred wave packet is never obtained.

The 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 cannot accurately indicate the limitation of human knowledge of any hidden variables. Classical physics refers to probability in cases where it is necessary to describe a process such as tossing dice. That is, probability replaces incomplete knowledge. The Copenhagen interpretation of the quantum mechanics of Heisenberg and Bohr, on the contrary, argues that the result of measurements in quantum mechanics is fundamentally non-deterministic.
2. Physics is a science that studies the results of measurement processes. It is unlawful to reflect on what is happening in their consequence. 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 reflection.
3. The act of measurement leads to an instant collapse of the wave function. Therefore, 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 change instantly.

Wording

The wording of the Copenhagen interpretation in its original form gave rise to several variations. The most common of them is based on the approach of consistent events and such a concept as quantum decoherence. Decoherence allows you to calculate the fuzzy boundary between the macro and micro worlds. Other variations vary in the degree of "realism of the wave world."

Criticism

The usefulness of quantum mechanics (Heisenberg and Bohr's answer to the first question) was questioned in a thought experiment conducted by Einstein, Podolsky and Rosen (EPR paradox). Thus, the scientists wanted to prove that the existence of hidden parameters is necessary so that the theory does not lead to instantaneous and nonlocal "long-range". 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 put measurement 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 is 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 was inferior. 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 abandon the search for a more complete concept.

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

Erwin Schrödinger devised 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, instantaneous and simultaneous only make sense to an observer in the same reference frame. Thus, there is no time that could become one for all, which means that instant collapse cannot be determined.

Spread

An unofficial survey conducted in academia in 1997 showed that the previously dominant Copenhagen interpretation, briefly discussed above, is supported by less than half of the respondents. However, she has more followers than other interpretations individually.

Alternative

Many physicists are closer to another interpretation of quantum mechanics, which was called "no." The essence of this interpretation is fully expressed in David Mermin's dictum: “Shut up and figure it out!”, Which is often attributed to Richard Feynman or Paul Dirac.