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Joint distributions, the uncertainty principle and positive distributions†

Published online by Cambridge University Press:  28 March 2014

LEON COHEN
LEON COHEN*
Affiliation:
City University of New York, 695 Park Avenue, New York, NY 10065, U.S.A. Email: Leon.Cohen@hunter.cuny.edu
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Abstract

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We examine the construction of joint probabilities for non-commuting observables. We show that there are indications in standard quantum mechanics that imply the existence of conditional expectation values, which in turn implies the existence of a joint distribution. We also argue that the uncertainty principle has no bearing on the existence of joint distributions but only constrains the marginal distributions. In addition, we show that within classical probability theory there are mathematical quantities that are similar to quantum mechanical wave functions. This is shown by generalising a theorem of Khinchin on the necessary and sufficient conditions for a function to be a characteristic function.

Footnotes

†

This work was supported by the Office of Naval Research

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