The Born rule (also called the Born law, Born's rule, or Born's law) formulated by German physicist Max Born in 1926, is a law of quantum mechanics giving the probability that a measurement on a quantum system will yield a given result. In its simplest form it states that the square of the magnitude of the wavefunction of a particle gives the probability of finding the particle at each point. The Born rule is one of the key principles of quantum mechanics. There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results.
Contents
The rule
The Born rule states that if an observable corresponding to a Hermitian operator
In the case where the spectrum of
If we are given a wave function
History
The Born rule was formulated by Born in a 1926 paper. In this paper, Born solves the Schrödinger equation for a scattering problem and, inspired by Einstein's work on the photoelectric effect, concluded, in a footnote, that the Born rule gives the only possible interpretation of the solution. In 1954, together with Walther Bothe, Born was awarded the Nobel Prize in Physics for this and other work. John von Neumann discussed the application of spectral theory to Born's rule in his 1932 book.
Interpretations
Within the Quantum Bayesianism interpretation of quantum theory, the Born rule is seen as an extension of the standard Law of Total Probability, which takes into account the Hilbert space dimension of the physical system involved. In the ambit of the so-called Hidden-Measurements Interpretation of quantum mechanics the Born rule can be derived by averaging over all possible measurement-interactions that can take place between the quantum entity and the measuring system. Pilot Wave Theory can also statistically derive Born's law. While it has been claimed that Born's law can be derived from the Many Worlds Interpretation, the existing proofs have been criticized as circular.