Critique of 'Elements of Quantum Probability'

We analyse the thesis of Kummerer and Maassen that classical probability is unable to model the the stochastic nature of the Aspect experiment in which violation of Bells inequality was experimentally demonstrated According to these authors the experiment shows the need to introduce the extension of classical probability known as Quantum Probability We show that their argument depends on hidden assumptions and a highly restrictive view of the scope of classical probability A careful probabilistic analysis shows on the contrary that it is classical deterministic physical thinking which cannot cope with the Aspect experiment and therefore needs revision The ulterior aim of the paper is to help mathematical statisticians and probabilists to nd their way into the fascinating world of quantum probability thus the same aim as that of Kummerer and Maassen by dismantling the bamboo curtain between ordinary and quantum probability which over the years has been built up as physicists and pure mathematicians have repeated to one another Feynmans famous dictum quantum probability is a dierent kind of probability