Rather, they are a generalization of classical probability theory that modiﬁes the ef-fects of physical forces. If you have ﬁrmly accepted classical probability, it is tempting to suppose that Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism. Yes. The simple question that has been bothering me is that of why one can’t just take as answer the same place as in the classical theory: in one’s lack of precise knowledge about the initial state. Quantum probability is a subtle blend of quantum mechanics and classical probability theory. 1. In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. To precisely this end, von Neumann initiated the study of what are now called von Neumann algebras and, with Murray, made a first classification of such algebras into three types. In fact there is quantum probability theory which is well suited to quantum mechanics. Quantum probability theory is a generalisation of standard (classical) probability theory that admits non-commuting random variables. QUANTUM PROBABILITY The precepts of quantum mechanics are neither a set of physical forces nor a geometric model for physical objects. Quantum probability was developed in the 1980s as a noncommutative analog of the Kolmogorovian theory of stochastic processes. Quantum theory as nonclassical probability theory was incorporated into the beginnings of noncommutative measure theory by von Neumann in the early 1930s, as well. There are extensions to this idealized "projection valued" probability measures to more realistic descriptions of weaker measurement descriptions, based on the approach defining probabilities by positive operator valued measures, but that's not necessary to start understanding quantum theory. “Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory… A central question of the interpretation of quantum mechanics is that of “where exactly does probability enter the theory?”. This means that it matters in which order we look at various observable quantities of a quantum system.

quantum probability theory 2020