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Copenhagen interpretation

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The Copenhagen interpretation of quantum mechanics was worked out by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. The interpretation attempts to answer some preplexing questions which arise as a result of particle-wave duality in quantum mechanics.

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, in the late 19th century, it became experimently 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 at a time passes through the slits. Alternatively, one can perform the experiment by passing electrons through one 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. The results of this experiment are particularly preplexing when one considers that this is not a thought experiment, but an actual real experiment that can be quite easily performed with photons, electrons, atoms, molecules, and even small viruses.

The questions this experiment poses are

  1. 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 were few particles are likely to hit. However, for a single particle, the rules of quantum mechanics tells you nothing about where the particles will be observed. What are the rules to determine where an individual particle is observed.
  2. What happens to the particle in between the time it is emitted and the time that it is observed? The particle seems 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.
  3. What causes the particle to appear to switch between statistical and non-statistical behaviors? When the particle is moving through the slits, it's behavior appears to be described by a non-localize wave function which is travelling through both slits at the same time. Yet when the particle is observed it is never diffuse non-localized wave packet, but appears to be a single point particle.

The Copenhagen interpretation answers these questions as follows:

  1. The probability statements made by quantum mechanics are irreducible in the sense that they don't just 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.
  2. 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.
  3. 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 completeness of quantum mechanics (thesis 1) has been 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". Bell's inequality about the measurement outcomes of such an experiment was derived on the assumption that these hidden variables exist and no non-local effects are present. In 1982, Aspect finally carried out the experiment and found Bell's inequality to be violated. This experiment has since been criticized and improved experiments have been described by Weihs and Rowe, confirming Aspect's results. These results show that interpretations which postulate locally acting hidden variables, in a sense precisely defined by Bell, are untenable.

Among laypeople, the Copenhagen interpretation is often considered the mainstream interpretation of quantum mechanics. However, it has always been controversial among physicists. Historically, many physicists have subscribed to the null interpretation summarized by Feynman's famous dictum: "Shut up and calculate!"

Since the 1980s, theoretical developments such as quantum entanglement and quantum superposition have displaced the concepts which the Copenhagen interpretation relies on, leading to an erosion of support. The preferred interpretation by most theoreticians working in fundamental physics and cosmology (fields in which the null interpretation is intolerable) is the Everett many-worlds interpretation, which many theoreticians find much more theoretically elegant than the Copenhagen interpretation. Nevertheless, in the absence of observational evidence which can distinguish between Copenhagen and many-worlds, the choice between them is viewed as one of personal taste. Most physicists find this situation unsatisfactory, and the creation of experiments which can distinguish between the intepretations of quantum mechanics is an active area of research. One dramatic but highly impractical experiment that has been proposed that would distinguish the two is the quantum suicide experiment proposed by Michael Tegmark.

Of the three theses above, the third is maybe the most problematic from a physcist's standpoint, because it gives a special status to measurement processes without cleanly defining them nor explaining their peculiar effects. However, in contrast to some incorrect popularizations of quantum mechanics, it is not believed that the measurement process involves consciousness. It can be demonstrated that the collapse of the wave function occurs when the wave function encounters a non-conscious measurement instrument. In fact, this characteristic of quantum mechanics has practical uses in quantum cryptography.

Many notable 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. Schrödinger's cat was originally intended as an example to show how absurd the model was. Other physicists are even blunter; David Deutsch accuses the Copenhagen interpretation of being meaningless gibberish.

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