SUMMARYThis article proposes some cosmological reflections at the qualitative and conjectural level, suggested by the Fantappié-Arcidiacono projective relativity theory. The difference will firstly be discussed between two types of singularity in this theory: geometric (de Sitter horizon) and physical (big bang, big crunch). The reasons for the existence of geometric singularities are deeply rooted in the principle of inertia and in the principle of relativity, while physical singularities are associated with the creation or destruction of matter. In this framework, quantum mechanics is introduced through a particular interpretation of Bohm's holomovement. Finally, a possible mechanism is discussed for the genesis of the cosmological term. No form of inflation appears in the scenario described.

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In this work, we examine in depth the physical aspects of the archaic universe described by Euclidean 5-sphere geometry, by using Projective Relativity techniques. We hypothesize that the expansion of the Universe was "ignited" by primordial R processes, and that the big bang consisted of a spatially extended nucleation process which took place at the end of a pre-cosmic phase, characterized by the evolution parameter x 0 . This parameter, which can be considered a quantum precursor of ordinary physical time, is a coordinate of Euclidean 5-sphere metrics. It is so possible to avoid many of the difficulties with standard model and to get rid of ad hoc assumptions. A complete solution to Projective General Relativity (PGR) equations is provided, so as to establish univocal relations between the scale factor R(τ ) and cosmic time τ . In this way, the physics and geometry of the cosmological model are specified completely.

Some ideas are explored concerning the structure of elementary particles (specifically, leptons and hadrons), formulated within the context of a theory of the objective collapse of the wavefunction recently proposed by the authors. In accordance with this hypothesis, to each interaction that induces a discontinuity (quantum jump) in the evolution of the state of an elementary particle, two de Sitter half-spaces are associated, respectively, connected with the outgoing state and its conjugate. It is in these spaces that the structural constituents of the particle lie (quarks in the case of a hadron). The mass of free particles (leptons and hadrons) is given by the energy associated with their time localization in the jump, while the interaction between quarks belonging to a same hadron leads to a chromodynamic coupling constant that ensures both confinement and asymptotic freedom. It is possible to write a toy Hamiltonian in which the organization of quarks in hadrons appears ab initio, and which includes terms both for the exchange of quarks and for the creation/annihilation of pairs, thus avoiding the problem of bottom-up hadronization. In this scenario, the genesis of Regge trajectories is briefly discussed and it is argued that their slope can be quantized; finally, a reinterpretation is suggested of the classical Veneziano and Virasoro amplitudes. Keywords Quantum jump • de Sitter spacetime • Elementary particles • Strong interactions • Regge trajectories • Veneziano and Virasoro amplitudes

This paper explores an event-based version of quantum mechanics which differs from the commonly accepted one, even though the usual elements of quantum formalism, e.g., the Hilbert space, are maintained. This version introduces as primary element the occurrence of micro-events induced by usual physical (mechanical, electromagnetic and so on) interactions. These micro-events correspond to state reductions and are identified with quantum jumps, already introduced by Bohr in his atomic model and experimentally well established today. Macroscopic bodies are defined as clusters of jumps; the emergence of classicality thus becomes understandable and time honoured paradoxes can be solved. In particular, we discuss the cat paradox in this context. Quantum jumps are described as temporal localizations of physical quantities; if the information associated with these localizations has to be finite, two time scales spontaneously appear: an upper cosmological scale and a lower scale of elementary “particles”. This allows the interpretation of the Bekenstein limit like a particular informational constraint on the manifestation of a micro-event in the cosmos it belongs. The topic appears relevant in relation to recent discussions on possible spatiotemporal constraints on quantum computing.