Simultaneous emergence of curved space–time and quantum mechanics

Abstract

It is shown in this paper that the geometrically structure-less spacetime manifold is converted instantaneously to a curved one, the Riemannian or may be a Finslerian spacetime with an associated Riemannian spacetime, on the appearance of quantum Weyl spinors dependent only on time in that background flat manifold and having the symplectic property in the abstract space of spinors. The scenario depicts simultaneous emergence of the gravity in accord with general relativity and quantum mechanics.The emergent gravity leads to the generalized uncertainty principle, which in turn, ushers in discrete space time. The emerged space time is specified here as to be Finslerian and the field equation in that space time has been obtained from the classical one due to the arising quantized space and time. From this field equation we find the quantum field equation for highly massive (of the Planck order) spinors in the associated Riemannian space of the Finsler space, which is in fact, the background homogeneous and isotropic FRW space time of the universe.These highly massive spinors provide the mass distribution complying Einstein equivalence principle. All these occurred in the indivisible minimum time considered as zero time or spontaneity. 98.80.Jk Pacs