Three random variable transformations giving Heisenberg-type uncertainty relations

Roberto D'Angiò

Statistics & Probability Letters, 2006, vol. 76, issue 4, 423-430

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.

Keywords: Heisenberg; uncertainty; relation; Kolmogorov; probability; Distributive; lattice; Boolean; algebra; Cramer-Rao; inequality (search for similar items in EconPapers)
Date: 2006
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