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Exotic probability is a branch of probability theory that deals with probabilities which are outside the normal range of [0, 1].

According to the author of various papers on exotic probability, Saul Youssef, the valid possible alternatives for probability values are the real numbers, the complex numbers and the quaternions.^[1] 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."^[2]

References

^ Youssef, Saul (2001). "Physics with exotic probability theory". arXiv:hep-th/0110253.
^ Jefferys (2002) Newsgroup discussion on sci.physics.research accessed 1-Sept-2010

External links

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[1] Youssef, Saul (2001). "Physics with exotic probability theory". arXiv:hep-th/0110253.

[2] Jefferys (2002) Newsgroup discussion on sci.physics.research accessed 1-Sept-2010

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-'''Exotic probability''' is a branch [[measure theory|advanced measure theory]] dealing with probabilities outside the normal range of [0,1].
+'''Exotic probability''' is a branch of [[probability theory]] that deals with probabilities which are outside the normal range of [0, 1].
+According to the author of various papers on exotic probability, [[Saul Youssef]], the valid possible alternatives for probability values are the [[real number]]s, the [[complex number]]s and the [[quaternion]]s.<ref>{{cite arXiv |arxiv=hep-th/0110253 |first=Saul |last=Youssef |title=Physics with exotic probability theory |date=2001 }}</ref> Youssef also cites the work of [[Richard Feynman]], [[P. A. M. Dirac]], [[Stanley Gudder]] and [[S. K. Srinivasan]] as relevant to exotic probability theories.
-== History ==
-The original exotic probablity theories (EPTs) were studied in papers by such mathematicians as [[Henri Lebesgue]] and [[Paul Erdös]] in the early [[1920s]], but aroused little interest.
+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."<ref>Jefferys (2002)  [http://www.lns.cornell.edu/spr/2002-03/msg0040195.html Newsgroup discussion on sci.physics.research] accessed 1-Sept-2010</ref>
-In the [[1970s]], researchers in [[quantum electrodynamics]], especially [[Richard Feynman]] and [[Lawrence M. Krauss]], realised that by using a renormalized form of exotic probability theory, many problems involving [[quark]] interactions could be reformulated into simpler soluble mathematical problems. Krauss won the [[Nobel Prize]] for his work in this field.
+==See also==
-In [[1996]] [[William Timothy Gowers|Timothy Gowers]] of the [[University of Cambridge]] published a ground-breaking paper linking EPT to advanced [[combinatorics]], bringing Exotic Probability Theory to the forefront of modern mathematical research.
+* [[Negative probability]]
+* [[Signed measure]]
+* [[Complex measure]]
+==References==
-== Forms of exotic probability ==
+{{reflist}}
+==External links==
-=== Super-unitary probability ===
+* http://physics.bu.edu/~youssef/quantum/quantum_refs.html
-<table align="right"><tr><td>
+* https://web.archive.org/web/20040327004613/http://fnalpubs.fnal.gov/library/colloq/colloqyoussef.html
-[[Image:20-sided_dice_250.jpg]]
+* [http://flux.aps.org/meetings/YR97/BAPSAPR97/vpr/layn18-4.html Measuring Negative Probabilities, Demystifying Schroedinger's Cat and Exploring Other Quantum Peculiarities With Trapped Atoms]
-</td></tr></table>
+* [https://web.archive.org/web/20101126224737/http://mathpages.com/home/kmath309.htm MathPages - The Complex Domain of Probability]
-This is when the probability of an event (naturally we use the Lebesgue definition of probability), is strictly greater than 1. Lebesgue illustrated these examples with the famous hypothetical [[Lebesgue Dice]]. If the probability of rolling a five on the Lebesgue dice were 2, then the we expect on average after 10 rolls, five to appear 20 times. Super-Unitary Probability can be associated with the [[SU(3)]] group of matrices.
+[[Category:Probability theory]]
-=== Negative-probability ===
+[[Category:Exotic probabilities| ]]
-This is when the Lebesgue-Probability of an event is strictly less than 0. If the probability of rolling a five on the Lebesgue Dice were &minus;1, then the we expect on average after 10 rolls, five never to appear by a factor of 1. negative probability can be associated with the [[GL(4)]] group of matrices over the field of [[quaternions]].
-=== Complex-probability ===
+{{probability-stub}}
-This is when the real part of the Lebesgue-probability of an event is not equal to zero. If the probability of rolling a five on the Lebesgue Dice were 0.5+i, then the we expect on average after 10 rolls, five never to appear 5 times and the disappear through another dimension. No isomorphism has been found between complex probability and a standard group, and the [[Manning-McArdle conjecture]] states that complex-probability does not lead to consistent answers unless the imaginary part is equal to some integer times the square root of 7.
-==See also==
-* [[Spin (physics)]]
-* [[List of mathematical topics]]
-* [[Probability]]
-* [[Lorentz group]]
-* [[Churchill College, Cambridge]]
-==External links==
-* http://physics.bu.edu/~youssef/quantum/quantum_refs.html