Probability and randomness. Quantum versus classical (Q5890549)

The book expose the author's contribution on the contextual probability interpretation of quantum mechanics (QM). The author's allegiance to a ``strong anti-Copenhagen and realist'' attitude towards QM was baptized by him as ``Växjö Interpretation''. I should remind that Bohr's interpretation of QM predicts only probabilities that certain events take place and, by the act of measurement, the set of probabilities collapses to just one of these values (wavefunction collapse). Thus, in Bohr's view there exist complementary experimental arrangements designed for the same physical system which cannot be observed or measured simultaneously. By rejecting the Bohr's complementary principle, the author formulates a ``new fundamental principle'' called ``the principle of contextual relativity of probabilities '' which introduces the notion of ``complex physical conditions''. Thence, according to Växjö interpretation, all probabilities depend on the complex of physical conditions.NEWLINENEWLINEThe present book supports the contextual interpretation of QM and is structured as follows:NEWLINENEWLINEChapter 1 presents the foundations of the theory of probabilities within the axiomatic approach of Kolmogorov. Topics such as Bell's inequality, random variables, law of large numbers, random numbers, stochastic processes, von Mises frequency, Cournot's principle are shortly presented. The randomness in von Mises and then in the Kolmogorov-Chaitin approach is the subject of Chapter 2. In Chapter 3, the author describe the standard construction of the Lebesgue measure, the Jordan measureability, the notion of negative probability and the \(p\)-adic probability, etc., with the aim to show that the foundations of classical probability are more ambiguous than the foundations of quantum probability. The basic probabilistic apparatus of QM is briefly presented in Chapter 4. Here, one encounters themes such as : definition of pure and mixed states, projection measurements, Schrödinger and von Neumann equations, quantum bits, general theory of quantum instruments. The quantum vs. classical probability interplay is the matter of Chapter 5. In this context the ``classical probability'' concept is used for the Kolmogorov probability, while the ``quantum probability'' term is based on the complex Hilbert representation and Born's rule connecting states with probability. A large portion of this chapter illustrates the Kolmogorov probability model with the two-slit model, a Gedankenexperiment that proved to be instrumental in the early time developments of QM. On this occasion the author discusses the possibility of treating QM as a theory emerging from a subquantum theory employing classical variables and concludes that quantum ``interference of probabilities'' can be reduced to the classical interference of waves propagating in space. In the author's view ``complex wave of probability'' is seen as a special mathematical representation of general contextual probabilistic data and he advocates the applicability of this concept in cognition, psychology, sociology, economics and politics. The most important result of this chapter is that the quantum formula of total probability contains an interference term which violates the classical probability theory. In Chapter 6, various interpretations of QM are directly attacked by adopting a manicheistic approach, i.e. by dividing them in two categories: realistic interpretations (with adherents such as Einstein, de Broglie, Schrödinger, Bohm, the author, etc.) and non-realistic interpretations (Bohr, Heisenberg, Pauli, Dirac, Landau, etc.). In the author's conception, a realist interpretation makes possible the representation of quantum systems and processes by means of QM's mathematical apparatus or by a subquantum framework that still remains obscured. Chapter 7 shortly discusses the quantum randomness, whereas Chapters 8 and 9 are dedicated to the applications of quantum probability.