Simultaneous emergence of curved space–time and quantum mechanics

Abstract

It is shown in this paper that the geometrically structureless space–time manifold is converted instantaneously to a curved, a Riemannian, or may be a Finslerian space–time with an associated Riemannian space–time, on the appearance of quantum Weyl spinors dependent only on time in a background flat manifold and having the symplectic property in the abstract space of spinors. The scenario depicts simultaneous emergence of 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 Friedmann–Robertson–Walker space–time of the universe. These highly massive spinors provide the mass distribution complying with the Einstein equivalence principle. All these occurred in the indivisible minimum time considered as zero time or spontaneity.