Geometro-stochastic locality in quantum spacetime and quantum diffusions

Eduard Prugovaki

Eduard Prugovečki

Eduard Prugovečki

By taking into account the quantum aspects intrinsic to any operational definition of spatio-temporal relationships, a stochastic concept of spacetime emerges. In relation to its classical counterpart is realized as a stochastic mean around which quantum fluctuations become negligible only in the limit of macroscopic spacetime intervals. The test-particle propagators used in the proposed quantum concept of spacetime are derived by solving in a consistent manner the localizability problem for relativistic particles. This is achieved in the framework of the stochastic phase space formulation of quantum mechanics, which in the nonrelativistic context is shown to result from systems of imprimitivity related to phase space conserved probability currents derivable from bona fide convariant probability densities in stochastic phase spaces of one particle systems, which can be interpreted as due to measurements performed with extended rather than pointlike test particles. The associated particle propagators can be therefore consistently related to coordinate probability densities measurable by the exchange of photons in between test particles from a chosen standard. Quantum spacetime is defined as the family of propagators corresponding to all conceivable coherent flows of test particles. This family of free-fall propagators has to satisfy certain self-consistency conditions as well as consistent laws ofmore » motion which inplicitly determine the stochastic geometro-dynamics of quantum space-time. Field theory on quantum spacetime retains many of the formal features of conventional quantum field theory. On a fundamental epistemological level stochastic geometries emerge as essential prerequisites in the construction of spacetime models that would be operationally based and yet consistent with the relativity principle as well as with the uncertinty principle.« less

Eduard Prugovečki

G. Gómez i Blanch, And M.J. Fullana i Alfonso

In a previous paper [G.Gomez Blanch and M.J.Fullana, 2017] we dened, in the frame of a geometro-dynamic approach, a metric corresponding to a lorentzian spacetime were the electron stationary trajectories in an hydrogenoid atom, derived from the de Broglie-Bohm model, are geodesics. In this paper we want to complete this purpose: we will determinate the remaining relevant geometrical elements of that approach and we will calculate the energetic density component of the energy-momentum tensor. We will discuss the meaning of the obtained results and their relationship with other geometro-dynamic approaches.Furthermore, we will derive a more general relationship between the lorentzian metric tensor and the wave function for general stationary states. The electron description by the wave function ψ in the Euclidean space and time is shown equivalent to the description by a metric tensor in an lorentzian manifold. In our approach, the particle acquires a determining role over thewave function, in a similar manner as the wave function determines the movement of the particle. This dialectic approach overcomes the de Broglie-Bohm model. And furthermore, a non local element (the quantum potential) is introduced in the model, that therefore goes beyond the relativistic locality.