Conditional Probability, Three-Slit Experiments, and the Jordan Algebra Structure of Quantum Mechanics
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-13
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
Most quantum logics do not allow for a reasonable calculus of conditional probability.
However, those ones which do so provide a very general and rich mathematical structure, including classical probabilities, quantum mechanics, and Jordan algebras.
This structure exhibits some similarities with Alfsen and Shultz's noncommutative spectral theory, but these two mathematical approaches are not identical.
Barnum, Emerson, and Ududec adapted the concept of higher-order interference, introduced by Sorkin in 1994, into a general probabilistic framework.
Their adaption is used here to reveal a close link between the existence of the Jordan product and the nonexistence of interference of third or higher order in those quantum logics which entail a reasonable calculus of conditional probability.
The complete characterization of the Jordan algebraic structure requires the following three further postulates: a Hahn-Jordan decomposition property for the states, a polynomial functional calculus for the observables, and the positivity of the square of an observable.
While classical probabilities are characterized by the absence of any kind of interference, the absence of interference of third (and higher) order thus characterizes a probability calculus which comes close to quantum mechanics but still includes the exceptional Jordan algebras.
American Psychological Association (APA)
Niestegge, Gerd. 2012. Conditional Probability, Three-Slit Experiments, and the Jordan Algebra Structure of Quantum Mechanics. Advances in Mathematical Physics،Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-450288
Modern Language Association (MLA)
Niestegge, Gerd. Conditional Probability, Three-Slit Experiments, and the Jordan Algebra Structure of Quantum Mechanics. Advances in Mathematical Physics No. 2012 (2012), pp.1-20.
https://search.emarefa.net/detail/BIM-450288
American Medical Association (AMA)
Niestegge, Gerd. Conditional Probability, Three-Slit Experiments, and the Jordan Algebra Structure of Quantum Mechanics. Advances in Mathematical Physics. 2012. Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-450288
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-450288