# Copenhagen Interpretation

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The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. Bohr and Heisenberg extended the probabilistic interpretation of the wave function, proposed by Max Born. Their interpretation attempts to answer some perplexing questions which arise as a result of the quantum mechanics, such as wave-particle duality and the measurement problem.

## The meaning of the wave function

There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.

-- Aage Petersen paraphrasing Niels Bohr, Quantum Reality by Nick Herbert

There is no definitive statement of the Copenhagen Interpretation [1]since it consists of the views developed by a number of scientists and philosophers at the turn of the 20th Century. The following have been associated with the Copenhagen interpretation

1. A system is completely described by a wave function $\psi$, which represents an observer's knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic. The probability of an event is related to the square of the amplitude of the wave function. (Max Born)
3. Heisenberg's uncertainty principle ensures that it is not possible to know the values of all of the properties of the system at the same time; those properties that are not known with precision must be described by probabilities.
4. (Complementary Principle) Matter exhibits a wave-particle duality. An experiment can show the particle like properties of matter, or wave-like properties, but not both at the same time.(Niels Bohr)
5. Measuring devices are essentially classical devices, and measure classical properties such as position and momentum.
6. The Correspondence Principle of Bohr and Heisenberg. The quantum mechanical description of large systems should closely approximate to the classical description.

The Copenhagen Interpretation denies that the wave function is real, it is a mathematical tool for calculating probabilities of specific experiments. The concept of collapse of a "real" wave function was introduced by John Von Neumann and was not part of the original formulation of the Copenhagen Interpretation[How to reference and link to summary or text]. There are some who say that there are variants of the Copenhagen Interpretation that allow for a "real" wave function [2];, but it is questionable whether that view is really consistent with Positivism and some of Bohr's statements.

Niels Bohr emphasized that Science is concerned with the predictions of experiments, additional questions are not scientific but rather meta-physical. Bohr was heavily influenced by Positivism.

## Acceptance among physicists

According to a poll at a Quantum Mechanics workshop in 1997, the Copenhagen interpretation is the most widely-accepted specific interpretation of quantum mechanics, followed by the Many-worlds interpretation.[1] Although current trends show substantial competition from alternative interpretations, throughout much of the twentieth century the Copenhagen interpretation had strong acceptance among physicists.

## Consequences

The nature of the Copenhagen Interpretation is exposed by considering a number of experiments and paradoxes.

1. Schrödinger's Cat - A cat is put in a box with a radioactive source and a radiation detector. There is a 50-50 chance that a particle will be emitted and detected by the detector. If a particle is detected, a poisonous gas will be released and the cat killed. The wave function is in a 50-50 mixture of alive cat and dead cat. How can the cat be both alive and dead?

The Copenhagen Interpretation: The wave function reflects our knowledge of the system. The wave function $(|dead\rangle + |alive\rangle)/\sqrt 2$ simply means that there is a 50-50 chance that the cat is alive or dead.

2. Wigner's Friend - Wigner puts his friend in with the cat. The external observer believes the system is in the state $(|dead\rangle + |alive\rangle)/\sqrt 2$. His friend however is convinced that cat is alive. I.e. for him, the cat is in the state $|alive>$. How can Wigner and his friend see different wave functions?

The Copenhagen Interpretation: Wigner's friend highlights the subject nature of probability. Each observer (Wigner and his friend) have different information and therefore different wave functions. The distinction between the "objective" nature of reality and the subjective nature of probability has lead to a great deal of controversy. C.f. Bayesian versus Frequentist interpretations of probability.

3. Double Slit Diffraction - Light passes through double slits and onto a screen resulting in a diffraction pattern. Is light a particle or a wave?

The Copenhagen Interpretation: Light is neither. A particular experiment can demonstrate particle (photon) or wave properties, but not both at the same time (Bohr's Complementary Principle).

The same experiment can in theory be performed with electrons, protons, atoms, molecules, viruses, bacteria, cats, humans, elephants and planets. In practice it has been performed for light, electrons, buckminsterfullerene, and some atoms. Matter in general exhibits both particle and wave behaviors.

4. EPR paradox. Entangled "particles" are emitted by a common source. Conservation laws ensure that the measured spin of one particle is the opposite of the measured spin of the other. The spin of one particle is measured. The spin of the other particle is now instantaneously known. (If the waveform is real, then one observer has caused the waveform to collapse instanteously).

The Copenhagen Interpretation: Assuming wave functions are not real, wave function collapse is interpreted subjectively. The moment one observer measures the spin of one particle, he knows the spin of the other. However another observer cannot benefit until the results of that measurement have been relayed to him, at less than or equal to the speed of light.

Copenhagenists claim that interpretations of quantum mechanics where the wave funtion is regarded as real have problems with EPR-type effects, since they imply that the laws of physics allow for influences to propagate at speeds greater than the speed of light. However, proponents of Many worlds [3] and the Transactional interpretation [4] [5] dispute that their theories are fatally non-local.

## Criticisms

The completeness of quantum mechanics (thesis 1) was attacked by the Einstein-Podolsky-Rosen thought experiment which was intended to show that quantum physics could not be a complete theory.

Experimental tests of Bell's inequality using entangled particles have supported the predictions of quantum mechanics.

The Copenhagen Interpretation gives special status to measurement processes without cleanly defining them or explaining their peculiar effects. In his article entitled "Criticism and Counterproposals to the Copenhagen Interpretation of Quantum Theory," countering the view of Alexandrov that (in Heisenberg's paraphrase) "the wave function in configuration space characterizes the objective state of the electron." Heisenberg says,

Of course the introduction of the observer must not be misunderstood to imply that some kind of subjective features are to be brought into the description of nature. The observer has, rather, only the function of registering decisions, i.e., processes in space and time, and it does not matter whether the observer is an apparatus or a human being; but the registration, i.e., the transition from the "possible" to the "actual," is absolutely necessary here and cannot be omitted from the interpretation of quantum theory.

-- Heisenberg, Physics and Philosophy, p. 137

Many physicists and philosophers have objected to the Copenhagen interpretation, both on the grounds that it is non-deterministic and that it includes an undefined measurement process that converts probability functions into non-probabilistic measurements. Einstein's comments "I, at any rate, am convinced that He (God) does not throw dice."[6] and "Do you really think the moon isn't there if you aren't looking at it?" exemplify this. Bohr, in response, said "Einstein, don't tell God what to do". Erwin Schrödinger devised the Schrödinger's cat experiment.

Steven Weinberg in "Einstein's Mistakes", Physics Today, November 2005, page 31, said:

All this familiar story is true, but it leaves out an irony. Bohr's version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wave function (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?
Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wave function, the Schrödinger equation, to observers and their apparatus.

## Alternatives

The Ensemble Interpretation is similar; it offers an interpretation of the wave function, but not for single particles. The consistent histories interpretation advertises itself as "copenhagen done right". Consciousness causes collapse is often confused with the Copenhagen interpretation.

If the wave function is regarded as ontologically real, and collapse is entirely rejected, a many worlds theory results. If wave function collapse is regarded as ontologically real as well, an objective collapse theory is obtained. Dropping the principle that the wave function is a complete description results in a hidden variable theory.

Many physicists have subscribed to the null interpretation of quantum mechanics summarized by Paul Dirac's famous dictum "Shut up and calculate!" (often attributed to Richard Feynman).[7]

A list of alternatives can be found at Interpretation of quantum mechanics.

## Notes

1. 'In fact Bohr and Heisenberg never totally agreed on how to understand the mathematical formalism of quantum mechanics, and none of them ever used the term “the Copenhagen interpretation” as a joint name for their ideas. In fact, Bohr once distanced himself from what he considered to be Heisenberg's more subjective interpretation Stanford Encyclopedia of Philosophy
2. 'While participating in a colloquium at Cambridge, von Weizsäcker (1971) denied that the CI asserted: "What cannot be observed does not exist". He suggested instead that the CI follows the principle: "What is observed certainly exists; about what is not observed we are still free to make suitable assumptions. We use that freedom to avoid paradoxes."'John Cramer on the Copenhagen Interpretation
3. Michael price on nonlocality in Many Worlds
4. Relativity and Causality in the Transactional Interpretation
5. Collapse and Nonlocality in the Transactional Interpretation
6. "God does not throw dice" quote
7. "Shut up and calculate" quote.