The eminent mathematical physicist Sir Hermann Bondi once said: “There is no more to science than its method, and there is no more to its method than Popper has said.” Indeed, many regard Sir Karl Raimund Popper the greatest philosopher of science in our generation. Much of what Popper “has said” refers to physics, but physicists, generally speaking, have little knowledge of what he has said. True, Popper's philosophy of science and, in particular, his realistic interpretation of quantum mechanics deviates (...) considerably from the generally accepted doctrine. But as Popper, rightly I think, points out, it is precisely the proliferation of divergent theories which promotes the growth of scientific knowledge; it would be a danger for physics if physicists were dogmatically tied to a single theory or would not test their theory against alternatives. It is for this purpose that, on the occasion of the nonagenarian celebration of Popper's birthday, the present essay has been written. (shrink)

The use of probability theory is widespread in our daily life as well as in scientific theories. In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics, which gives rise to a new probability theory: quantum probability theory. This dissertation deals with the question of how this formalism can be understood from a philosophical and physical perspective. The dissertation is divided into three parts. In the first (...) part, the formalism of quantum probability theory and its relation to quantum mechanics is presented. The second part considers the possibility of reformulating quantum probability theory to embed it within classical probability. Mathematically, this possibility overlaps with the possibility of the existence of hidden variables theories of quantum mechanics: theories that attempt to solve fundamental problems in quantum mechanics by introducing additional physical properties of systems. The conclusion of this part is that, although classical reformulations of quantum probability theory are formally possible, they offer little insight into the formalism of quantum probability theory itself. The third part regards a more direct investigation of quantum probability theory. A reformulation of quantum probability theory is obtained by constructing a quantum logic on the basis of empirical non-probabilistic predictions of quantum mechanics. In this reformulation quantum probability functions are conditional probability functions on an algebra of propositions about measurements and measurement outcomes. (shrink)

This thesis compares the concepts presented in the Seventeenth Discussion of al-Ghazali's Tahafut al-Falasifa with concepts currently being discussed in the field of quantum physics. Written as an attack on the neo-Platonic and Aristotelian thinking which challenged the orthodox theology of Medieval Islam, Tahafut al-Falasifa questions the understanding of physical reality forwarded by the philosophers of al-Ghazali's times. The Seventeenth Discussion in particular, with its aim of proving the possibility of miracles, questions the acceptance of notions such as necessary causality (...) and the validity of scientific observation in the natural world. (shrink)