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.