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CATEGORIES:Statistics
SUMMARY:Quantum randomness and Kolmogorov probability - Pa
tricia Grambsch\, University of Minnesota\, visiti
ng Cambridge
DTSTART;TZID=Europe/London:20071102T140000
DTEND;TZID=Europe/London:20071102T150000
UID:TALK8590AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/8590
DESCRIPTION:``Quantum phenomena are more truly random than any
other phenomena one can imagine" (R. Gill\, 1997)
. Do they follow Kolmogorov probability? \n\nThis
talk has two parts. After a very brief review of K
olmogorov probability\, we summarize Feynman's 195
1 talk to the 2nd Berkeley symposium on mathematic
al statistics and probability in which he discusse
d applying Young's two-slit experiment to electron
s. While his main point was to develop a new calcu
lus of probabilities for the quantum world\, he cl
aimed that the two-slit experment gave empirical r
efutation to Kolmogorov's axiom of the additivity
of probability of disjoint events. We discuss some
of the more cogent and interesting critiques of t
his work. \n\nIn the second part\, we describe bas
ic aspects of the mathematical field of quantum pr
obability in which events are subspaces of a Hilbe
rt space rather than subsets of a sigma-field and
random variables are observables\, represented by
Hermitian operators rather than measurable functio
ns. Exploring these distinctions gives rise to a b
estiary of differences from Kolmogorov probability
. Conditional quantum probability allows us to vie
w the two-slit experiment from a different perspec
tive. \n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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