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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 41, Issue 1
  • June 1945, pp. 71-73

Negative probability

  • M. S. Bartlett (a1)
  • DOI:
  • Published online: 24 October 2008

It has been shown that orthodox probability theory may consistently be extended to include probability numbers outside the conventional range, and in particular negative probabilities. Random variables are correspondingly generalized to include extraordiary random variables; these have been defined in general, however, only through their characteristic functions.

This generalized theory implies redundancy, and its use is a matter of convenience. Eddington(3) has employed it in this sense to introduce a correction to the fluctuation in number of particles within a given volume.

Negative probabilities must always be combined with positive ones to give an ordinary probability before a physical interpretation is admissible. This suggests that where negative probabilities have appeared spontaneously in quantum theory it is due to the mathematical segregation of systems or states which physically only exist in combination.

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1M. S. Bartlett J. Roy. Statist. Soc. 103 (1940), 129.

2P. A. M. Dirac Proc. Roy. Soc. A, 180 (1942), 140.

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Mathematical Proceedings of the Cambridge Philosophical Society
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  • EISSN: 1469-8064
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