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Three random variable transformations giving Heisenberg-type uncertainty relations

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  • D'Angiò, Roberto

Abstract

Though intrinsically probabilistic, the 1927 quantum mechanics Heisenberg uncertainty relation is still non-existent as a native Kolmogorov probability construct. This paper fills the gap via three random variable transformations that generate Heisenberg-type uncertainty relations on Kolmogorov probability space ([Omega],[Sigma],[mu]) without resorting to any quantum mechanics notion or formalism. A sufficient condition is given under which a class of Heisenberg uncertainty relations on ([Omega],[Sigma],[mu]) is a bounded distributive lattice. Some applications in progress of the above results are anticipated.

Suggested Citation

  • D'Angiò, Roberto, 2006. "Three random variable transformations giving Heisenberg-type uncertainty relations," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 423-430, February.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:4:p:423-430
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