Quantum Probability: New Perspectives for the Laws of Chance

AbstractThe main philosophical successes of quantum probability is the discovery that all the so-called quantum paradoxes have the same conceptual root and that such root is of probabilistic nature. This discovery marks the birth of quantum probability not as a purely mathematical (noncommutative) generalization of a classical theory, but as a conceptual turning point on the laws of chance, made necessary by experimental results.On the other hand this was only the beginning of an historical process, lasted more than 30 years, that has lead to a renovation in probability which can only be compared with the renovation which took place in geometry between the 19th and the 20th century.The present paper shortly reviews the qualitative and conceptual milestones in the development of this new mathematical discipline from the early years, when the solution of the so-called paradoxes of quantum theory were the dominating motivation, to the contemporary researches on the existence of non-Kolmogorovian statistical data in experimental situations not necessarily related to quantum physics (mainly economy and medicine) will be shortly described.The present paper deals only with the conceptual and philosophical aspects of this development. The last section is a condensed guided bibliography for the reader who wants to have an idea of the width and depth of the connections naturally emerged (and not artificially constructed), in the past 30 years, between quantum probability and practically all fields of mathematics and most branches of theoretical physics.This material might also be useful for the reader who wants to meet the challenge proposed in section (1.2) and to experimentally check, through existing documents, if quantum probability fulfils the 4 criteria enunciated therein.