We address the problem of observables in generally invariant spacetime theories such as Einstein’s general relativity. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we propose a generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, that is naturally identified with the physical spacetime.

The hydrodynamical formalism for the quantum theory of a nonrelativistic particle is considered, together with a reformulation of it which makes use of the methods of kinetic theory and is based on the existence of the Wigner phase-space distribution. It is argued that this reformulation provides strong evidence in favor of the statistical interpretation of quantum mechanics, and it is suggested that this latter could be better understood as an almost classical statistical theory. Moreover, it is shown how, within this (...) context, the Wigner and the Margenau-Hill functions are not equivalent, and that the latter is essentially unsatisfactory, as well as the associated symmetrization rule. Arguments in favor of a stochastic picture of the phenomena at the microscopic level are also presented. (shrink)

Between the microscopic domain ruled by quantum gravity, and the macroscopic scales described by general relativity, there might be an intermediate, “mesoscopic” regime, where spacetime can still be approximately treated as a differentiable pseudo-Riemannian manifold, with small corrections of quantum gravitational origin. We argue that, unless one accepts to give up the relativity principle, either such a regime does not exist at all—hence, the quantum-to-classical transition is sharp—, or the only mesoscopic, tiny corrections conceivable are on the behaviour of physical (...) fields, rather than on the geometric structures. (shrink)