The Born Rule
The Born rule (also called the Born law, Born's rule, or Born's law) is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. 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.
- the measured result will be one of the eigenvalues of , and
- the probability of measuring a given eigenvalue will equal , where is the projection onto the eigenspace of corresponding to .
- (In the case where the eigenspace of corresponding to is one-dimensional and spanned by the normalized eigenvector , is equal to , so the probability is equal to . Since the complex number is known as the probability amplitude that the state vector assigns to the eigenvector , it is common to describe the Born rule as telling us that probability is equal to the amplitude-squared (really the amplitude times its own complex conjugate). Equivalently, the probability can be written as .)
- the probability that the result of the measurement lies in a measurable set will be given by .
Representation of The Born Rule, by Diederik Aerts, Massimiliano Sassoli de Bianchi:
extended Bloch representation of quantum mechanics and the hidden-measurement
solution to the measurement problem.”
A simplified overview of the above paper can be viewed at:
Using an extended Bloch representation of quantum mechanics, Diederik Aerts and Massimiliano Sassoli de Bianchi have developed a model that allows a visualisation of Born’s rule using an elastic connection between the alternatives:
either in the form of a band when n = 2, or a membrane when n>2.
But applying Unified Absolute Relativity to Figure 3, as ψ0 is never a particle, but the wave effect from an originating atom , it can be shown that the illustrated system works when the sphere is so positioned to share the wavefunction ψ0 between the three alternatives: