Objetivo The project deals with the historical roots of wave mechanics; with some of its foundational peculiarities,especially entanglement; and with consequences, some practical, of that entanglement. The peculiarities in question did not come out of nowhere; they were the outcome of a long and natural evolution. I derive wave mechanics and the Schrödinger equation from a historical programme¿whose (largely unattained) goal was to \'bring together matter and light\'¿rather than from logical requirements, as has oft en been attempted in the quantum logic programme. I point out that matter and light were seen as fundamental constituents (in one or more appropriate senses) of the world, suggest it was appropriate to bring them together, and show how it was that a natur al, perhaps even inevitable synthesis of staple classical theories led to the entangled wavefunctions of wave mechanics¿and hence to quantum teleportation and so many other surprising possibilities¿which seriously undermine the world view to which those cl assical theories belonged (an interesting historical paradox in itself). I propose the first set-theoretical characterization of Hamilton-Jacobi theory and the optico-mechanical analogy, which had such an important part in the genesis of wave mechanics. T his analogy is usually expressed by describing analytical mechanics and geometrical optics, then pointing out their similarities. I begin with a description of the bare mathematical theory the two theories have in common, and view mechanics and optics as d isjoint classes of models of the common axioms. To bring out the paradoxical character of entanglement, I propose an original approach to Bell\'s inequality: first a purely formal (\'structural\') scheme, in which the inequality is derived and a bare \'q uantum-mechanical\' formalism (an appropriate kind of multilinear algebra) is introduced, without semantics. Different kinds of semantics can be associated with the formal scheme. Ámbito científico natural sciencesphysical sciencesquantum physicsnatural sciencesmathematicspure mathematicsalgebranatural sciencesphysical sciencesopticsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesphysical sciencestheoretical physicsparticle physicsphotons Palabras clave Bell inequality EPR Hamilton-Jacobi theory Schrödinger equation entanglement optico-mechanical analogy quantum information tensor product Programa(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Tema(s) MOBILITY-4.1 - Marie Curie European Reintegration Grants (ERG) Convocatoria de propuestas FP6-2002-MOBILITY-11 Consulte otros proyectos de esta convocatoria Régimen de financiación ERG - Marie Curie actions-European Re-integration Grants Coordinador UNIVERSITA DEGLI STUDI DI URBINO "CARLO BO" Aportación de la UE Sin datos Dirección Via Saffi 2 URBINO Italia Ver en el mapa Coste total Sin datos
