The philosophical relationship between mathematics and the natural sciences is the subject of Converging Realities, the latest work by one of the leading thinkers on the subject.

The possibility of consistency between the basic quantum principles of quantum mechanics and wave function collapse is reexamined. A specific interpretation of environment is proposed for this aim and is applied to decoherence. When the organization of a measuring apparatus is taken into account, this approach leads also to an interpretation of wave function collapse, which would result in principle from the same interactions with environment as decoherence. This proposal is shown consistent with the non-separable character of quantum mechanics.

A rather recent interpretation of quantum mechanics, known under the various names of consistent histories, decohering histories, or logical interpretation, has brought interpretation into a standard deductive theory and is now investigated in many places. A key difference with the Copenhagen interpretation is the status of classical physics, now derived completely from quantum principles in both its dynamical and logical aspects. After describing briefly this new interpretation in its essentials, leaving aside technical details, it is shown how its consequences in (...) epistemology differ drastically from the familiar outcomes of the Copenhagen interpretation, leading in particular to a well-defined theory of knowledge. Some more speculative philosophical consequences associated with the unsolved problem of actuality are also mentioned. (shrink)

When a quantum system is macroscopic and becomes entangled with a microscopic one, entanglement is not immediately total, but gradual and local. A study of this locality is the starting point of the present work and shows unexpected and detailed properties in the generation and propagation of entanglement between a measuring apparatus and a microscopic measured system. Of special importance is the propagation of entanglement in nonlinear waves with a finite velocity. When applied to the entanglement between a macroscopic system (...) and its environment, this study yields also new results about the resulting disordered state. Finally, a mechanism of wave function collapse is proposed as an effect of perturbation in the growth of local entanglement between a measuring system and the measured one by waves of entanglement with the environment. (shrink)

Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics. This `foundational debate' in computer science, mathematics and physics was already fully developed in 1930 in the (...) Vienna Circle. A special section is devoted to its real founder Hans Hahn, referring to his contribution to the history and philosophy of science. The documentation section presents articles on the early Philipp Frank and on the Vienna Circle in exile. Reviews cover important recent literature on logical empiricism and related topics. (shrink)

A famous essay by Wigner is reexamined in view of more recent developments around its topic, together with some remarks on the metaphysical character of its main question about mathematics and natural sciences.