ABSTRACT
In my first attempts to get back to work, I tried to find criteria for
the type of experiments that could always be described by functions
on one probability space and, therefore, could be modeled for sure
by Kolmogorov’s probability theory. My answer was: one can find
a common probability space for all types of experiments that can be
modeled by two functions, for example Aa and Ab. It does not matter whether or not these experiments involve quantum effects. This
fact provided a big hint that quantization (involvement of integer
numbers) by itself was not the culprit for Bell-type conundrums.
The problems started when the experiments were so constituted
that one was tempted to model them with three or four functions, such as Aa, Ab, Ac, Ad, that permitted to form a Vorob’ev cyclicity. As we know, it is then possible to form a Bell-type inequality that
contains the cyclicity and is based on it. In case of a statistical
violation of the inequality, one cannot find a probability space for
these three or four functions, and one needs to introduce many
more functions, such as Astia with i = 1, 2, 3, . . . to describe the
experiments without contradictions or influences at a distance. If
one has a different space-time coordinate for each different function,
the Vorob’ev cyclicity is automatically removed because all the terms
of the inequality are now in principle different.