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Two examples in noncommutative probability

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Abstract

A simple noncommutative probability theory is presented, and two examples for the difference between that theory and the classical theory are shown. The first example is the well-known formulation of the Heisenberg uncertainty principle in terms of a variance inequality and the second example is an interpretatio of the Bell paradox in terms of noncommuntative probability.

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References

  1. S. P. Gudder,Stochastic Methods in Quantum Mechanics (North-Holland, Amsterdam, 1979).

    Google Scholar 

  2. R. Jajte,Strong Limit Theorems in Non-Commutative Probability (Lecture Notes in Mathematics 1110) (Springer, Berlin, 1984).

    Google Scholar 

  3. G. W. Mackey,The Mathematical Foundations of Quantum Mechanics (Benjamin, New York, 1963), p. 78.

    Google Scholar 

  4. A. Einstein, B. Podolsky, and N. Rosen,Phys. Rev. 47, 777 (1935).

    Google Scholar 

  5. J. S. Bell,Physics 1, 195 (1964).

    Google Scholar 

  6. J. S. Bell,Rev. Mod. Phys. 38, 447 (1966).

    Google Scholar 

  7. N. D. Mermin,Phys. Today 39(4), 38 (1985).

    Google Scholar 

  8. A. Aspect, J. Dalibard, and G. Roger,Phys. Rev. Lett. 46, 460 (1981).

    Google Scholar 

  9. A. Aspect, J. Dalibard, and G. Roger,Phys. Rev. Lett. 49, 91 (1982).

    Google Scholar 

  10. A. Aspect, J. Dalibard, and G. Roger,Phys. Rev. Lett. 49, 1804 (1982).

    Google Scholar 

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Bar-Natan, D. Two examples in noncommutative probability. Found Phys 19, 97–104 (1989). https://doi.org/10.1007/BF00737769

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  • DOI: https://doi.org/10.1007/BF00737769

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