Exotic probability
Encyclopedia
Exotic probability is a branch of probability theory
that deals with probabilities which are outside the normal range of [0, 1]. The most common author of papers on exotic probability theory is Saul Youssef. According to Youssef, the valid possible alternatives for probability values are the real number
s, the complex number
s and the quaternion
s.
Youssef also cites the work of Richard Feynman
, P. A. M. Dirac, Stanley Gudder and S. K. Srinivasan as relevant to exotic probability theories.
Of the application of such theories to quantum mechanics
, Bill Jefferys has said: "Such approaches are also not necessary and in my opinion they confuse more than they illuminate."
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
that deals with probabilities which are outside the normal range of [0, 1]. The most common author of papers on exotic probability theory is Saul Youssef. According to Youssef, the valid possible alternatives for probability values are the real number
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
s, the complex number
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
s and the quaternion
Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space...
s.
Youssef also cites the work of Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
, P. A. M. Dirac, Stanley Gudder and S. K. Srinivasan as relevant to exotic probability theories.
Of the application of such theories to quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, Bill Jefferys has said: "Such approaches are also not necessary and in my opinion they confuse more than they illuminate."
External links
- http://physics.bu.edu/~youssef/quantum/quantum_refs.html
- Physics with exotic probability theory - paper by Youssef on arXivArXivThe arXiv |Chi]], χ) is an archive for electronic preprints of scientific papers in the fields of mathematics, physics, astronomy, computer science, quantitative biology, statistics, and quantitative finance which can be accessed online. In many fields of mathematics and physics, almost all...
. - http://fnalpubs.fnal.gov/library/colloq/colloqyoussef.html
- Measuring Negative Probabilities, Demystifying Schroedinger's Cat and Exploring Other Quantum Peculiarities With Trapped Atoms
- MathPages - The Complex Domain of Probability