The de Sitter-Castelnuovo universe and elementary particle physics

Particle model from quantum foundations

“…And since T = −l 0 , one has l = l 0 ; in other words, the distance x between the two quarks remains unchanged. By elevating from q 2 the perpendicular to its contemporaneousness space, it will meet the q 2 horizon in a point of the Cayley-Klein absolute [25,27,31]. The horizon tangent to the absolute in this point will not coincide with that passing through P and indicated with PB in Fig.…”

“…We geometrically interpret the creation/annihilation of a physical particle as a geodetic (or "gnomonic") projection of an "internal" de Sitter spacetime on the external spacetime, with local preservation of the light cone. This projection produces a Castelnuovo spacetime (Beltrami representation) in which the proper time is limited according to (1), while the contemporaneousness space of the fixed point extends to infinity [25]. However, in the original de Sitter spacetime this space is closed.…”

“…To understand how the state vector ψ is associated with a given de Sitter micro-universe, it is necessary to proceed by successive steps. Let us remember that de Sitter spacetime having radius cθ 0 /z is tangent, in the point-event O, to the external spacetime on which it is projected [25,26]. In any frame of reference in external time, the time coordinate of the point-event O ≡ O corresponds to the instant of the jump.…”

“…The spatial position of O can be (and normally is) subject to quantum delocalization (superposition of states); in other words, the spatial coordinates of point-event O in the ordinary spacetime generally remain indefinite, unless the jump is a spatial localization (with maximal precision) of the particle. Putting aside delocalization and assuming that O is exactly defined, the projection of de Sitter spacetime on external spacetime is a Castelnuovo spacetime [25,27], such as that shown in Fig. 1.…”