A comprehensive formal system is developed that amalgamates the operational and the realistic approaches to quantum mechanics. In this formalism, for example, a sharp distinction is made between events, operational propositions, and the properties of physical systems.

The abstract description of a physical system is developed, along lines originally suggested by Birkhoff and von Neumann, in terms of the complete lattice of propositions associated with that system, and the distinction between classical and quantum systems is made precise. With the help of the notion of state, a propositional system is defined: it is remarked that every irreducible propositional system (of more than three dimensions) is isomorphic to the lattice of all closed subspaces of a Hilbert space constructed (...) on some division ring with involution. The propositional system consisting of a family of separable complex Hilbert spaces is treated as a particular case which is sufficiently general to include both classical and quantum mechanics. The theory of the Galilean particle without spin is given as an illustration. Finally, the basis for the statistical interpretation of wave mechanics is developed with the help of Gleason's theorem. In an appendix, a proof of essentially the first part of Gleason's theorem is given which is a little different (perhaps more geometric) from that originally given by Gleason. (shrink)

In this dialogue we explain why nonrelativistic and relativistic quantum mechanics are basically the same and how the Lorentz group operates canonically only on the dynamics.

Taking into account the experimental accuracy of the body motions in the solar system, we propose a General Relativity Theory which is new but nevertheless completely metric.

En nous laissant guider par la notion de champ qui en faitdomine toute la physique nous définissons la nature physique d'un système, ses propriétés et ses états possibles. Nous proposons alors un cadre très générale permettant la description de telssystèmes et la construction de modèles consistants.Nous en donnons des exemples et pour illustrer les concepts de notrethéorie nous décrivons différents types d'évolutions. Pour terminer nous discutons en détails unprocessus physique, les échos de spins.