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SUMMARY:Quantum randomness and Kolmogorov probability - Patricia Grambsch\
 , University of Minnesota\, visiting Cambridge
DTSTART:20071102T140000Z
DTEND:20071102T150000Z
UID:TALK8590@talks.cam.ac.uk
CONTACT:6845
DESCRIPTION:``Quantum phenomena are more truly random than any other pheno
 mena one can imagine" (R. Gill\, 1997). Do they follow Kolmogorov probabil
 ity? \n\nThis talk has two parts. After a very brief review of Kolmogorov 
 probability\, we summarize Feynman's 1951 talk to the 2nd Berkeley symposi
 um on mathematical statistics and probability in which he discussed applyi
 ng Young's two-slit experiment to electrons. While his main point was to d
 evelop a new calculus of probabilities for the quantum world\, he claimed 
 that the two-slit experment gave empirical refutation to Kolmogorov's axio
 m of the additivity of probability of disjoint events. We discuss some of 
 the more cogent and interesting critiques of this work. \n\nIn the second 
 part\, we describe basic aspects of the mathematical field of quantum prob
 ability in which events are subspaces of a Hilbert space rather than subse
 ts of a sigma-field and random variables are observables\, represented by 
 Hermitian operators rather than measurable functions. Exploring these dist
 inctions gives rise to a bestiary of differences from Kolmogorov probabili
 ty. Conditional quantum probability allows us to view the two-slit experim
 ent from a different perspective. \n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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