The tree of paradox

The specific nature of the randomness arising when quantum subsystems interact (collide) is analyzed. It is shown that the Birkhoff–Khinchin ergodic theorem – the key theorem for classical statistics – or its analog is absent, in principle, in the quantum theory. Thus quantum probabilities cannot be defined within the ergodic concept. A metric definition of probability, based on von Neumann's theory of measurement, is proposed as a measure of comparison of a posteriori physical situation with the a priori situation. The workability of the adopted approach is demonstrated for random walk problems and the theory of thermal equilibrium.