## 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 rule

*see*bra–ket notation), then

- 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:

“The
extended Bloch representation of quantum mechanics and the hidden-measurement
solution to the measurement problem.”

http://dx.doi.org/10.1016/j.aop.2014.09.020 0003-4916/©2014

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.

_{0}is deposited at a particular point, which allows the resultant wavefunction as the membrane deteriorates. There is no suggestion as to the physical nature of the membrane and the action that causes the membrane to begin to deteriorate in any particular position.

_{ }ψ

_{1 }ψ

_{2 }ψ

_{3}, or why the membrane deteriorates where it does.

But applying Unified Absolute Relativity to Figure 3, as ψ

_{0}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 ψ

_{0 }between the three alternatives:

_{0}.

_{}

^{}

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