## The Copenhagen Interpretation

Quantum physics has as it's root that every particle may be described by a wavefunction. The wavefunction – which describes the motion of the particle – has no real physical interpretation. In general the wavefunction may take non real or imaginary values with no physical meaning. Nevertheless it does contains all the information that can be known about the particle:

It's position.

It's momentum.

It's energy.

It's angular momentum.

Some particles also possess a quantity called spin. Whatever can be known about this is also contained in the wavefunction.

The wavefunction however often determine any of these things uniquely. It is a function of position, but does not tell us where the particle is. All that can be deduced from the wavefunction about the position of the particle is where it might be. The Copenhagen interpretation states that if the value of the wavefunction at a particular point and a particular time is given bythen the probability of finding the particle in a small volume centred at that point is given by

In general the particle will exist in many possible states simultaneously – the wavefunction representing the particle will be a superposition of possible states. If a certain quantity is measured, then we will find a value for that quantity that is one of the possible values that the particle may have, and the particle will 'collapse' into that component (or set of components) of the total wavefunction that has that particular value of that particular property.

Because the wavefunction representing a particle is composed of many components, each a particle may effectively interfere with itself. This explains many things. Maybe the most important are

The electron diffration experiments in which electrons are fired at two parallel slits one at a time. Classically the electron may pass through one or the other, but the interference pattern produced implies the electron is interfering with itself. This is quite easy to understand it the e;ectron is made up of many different components, which may interfere with each other.

In general although the position of a particle is not known, it is not completely unknown either. We may know a region within which the particle must be. The particle is then a selection of waves with differing wavelengths, interfering constructively in the region if the particle and destructively outside it.