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 wavefunction, proposed by Max Born. Their interpretation attempts to answer some perplexing questions which arise as a result of the wave-particle duality in quantum mechanics, such as the measurement problem.

According to a poll at a Quantum Mechanics workshop in 1997, the Copenhagen interpretation is the most widely-believed 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 has had obvious majority acceptance among physicists.

## The meaning of the wavefunction

The Copenhagen interpretation assumes that there are two processes influencing the wavefunction:

While there is no ambiguity about the former, the latter admits several interpretations, even within the Copenhagen interpretation itself. One can either view the wavefunction as a real object that undergoes the wavefunction collapse in the second stage, or one can imagine that the wavefunction is an auxiliary mathematical tool (not a real physical entity) whose only physical meaning is our ability to calculate the probabilities. Niels Bohr emphasized that it is only the results of the experiments that should be predicted, and therefore the additional questions are not scientific but rather philosophical. Bohr followed the principles of positivism from philosophy that imply that only measurable questions should be discussed by the scientists.

In the classic double-slit experiment, when light passes through double slits onto a screen, alternate bands of bright and dark regions are produced. These can be explained as areas in which the light waves reinforce or cancel. However it became experimentally apparent that light has some particle-like properties and items such as electrons have wave like properties and can also produce interference patterns.

This poses some interesting questions. Suppose one were to do the double slit experiment and reduce the light so that only one photon (or electron) passes through the slits at a time. In performing the experiment, one will see the electron or photon hit the screen one at a time. However, when one totals up where the photons have hit, one will see interference patterns that appear to be the result of interfering waves even though the experiment dealt with one particle at a time.

## Consequences

The questions this experiment poses are

- The rules of quantum mechanics tell you
*statistically* where the particles will hit the screen, and will identify the bright bands where many particles are *likely* to hit and the dark bands where few particles are *likely* to hit. However, for a single particle, the rules of quantum mechanics cannot predict where the particle will *actually* be observed. What are the rules to determine where an individual particle is observed?
- What happens to the particle in between the time it is emitted and the time that it is observed? The particle seems to be interacting with both slits and this appears inconsistent with the behavior of a point particle, yet when the particle is observed, one sees a point particle.
- What causes the particle to appear to switch between statistical and non-statistical behaviors? When the particle is moving through the slits, its behavior appears to be described by a non-localized wave function which is travelling through both slits at the same time. Yet when the particle is observed it is never a diffuse non-localized wave packet, but appears to be a single point particle.

The Copenhagen interpretation answers these questions as follows:

- The probability statements made by quantum mechanics are irreducible in the sense that they don't exclusively reflect our limited knowledge of some hidden variables. In classical physics, probabilities were used to describe the outcome of rolling a die, even though the process was thought to be deterministic. Probabilities were used to substitute for complete knowledge. By contrast, the Copenhagen interpretation holds that in quantum mechanics, measurement outcomes are fundamentally indeterministic.
- Physics is the science of outcomes of measurement processes. Speculation beyond that cannot be justified. The Copenhagen interpretation rejects questions like "where was the particle before I measured its position" as meaningless.
- The act of measurement causes an instantaneous "collapse of the wave function". This means that the measurement process randomly picks out exactly one of the many possibilities allowed for by the state's wave function, and the wave function instantaneously changes to reflect that pick.

The original formulation of the Copenhagen Interpretation has led to several variants; the most respected one is based on Consistent Histories ("Copenhagen done right?") and the concept of quantum decoherence that allows us to calculate the fuzzy boundary between the "microscopic" and the "macroscopic" world. Other variants differ according to the degree of "reality" assigned to the waveform.

## Criticisms

The completeness of quantum mechanics (thesis 1) was attacked by the Einstein-Podolsky-Rosen thought experiment which was intended to show that there have to be hidden variables in order to avoid non-local, instantaneous "effects at a distance". However, experimental tests of the EPR paradox using Bell's inequality have supported the predictions of quantum mechanics, while showing that local hidden variable theories do not match the experimental evidence.

Of the three theses above, the third is maybe the most problematic from a physicist's standpoint, because it gives a special status to measurement processes without cleanly defining them nor explaining their peculiar effects.

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 quotes "God does not play dice" 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 that attempts to illustrate the incompleteness of the theory of quantum mechanics when going from subatomic to macroscopic systems.

## Alternatives

Many physicists have subscribed to the null interpretation of quantum mechanics summarized by Feynman's famous dictum: "Shut up and calculate!"

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

## See also

## Further reading

- G. Weihs et al., Phys. Rev. Lett. 81 (1998) 5039
- M. Rowe et al., Nature 409 (2001) 791.

## External links

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Last updated: 05-13-2005 07:56:04