Nonexistence of a realistic model for the two dimensional Hilbert space

By using Bell’s strategy we analyse assumptions of previous “nogo”theorems and propose a new assumption on a prequantum classical model. This assumption – Kolmogorovness of statistical data– is natural from the point of view of classical statistical mechanics. The crucial point is Kolmogorovness of conditional probabilities. We prove an analogue of Bell’s inequality for conditional probabilities. This inequality can be applied not only to pairs of correlated particles, but also to a single particle. This inequality is violated for spin-projections of a single particle. Thus a realistic (in our sense) prequantum model does not exist even for the two dimensional Hilbert space.