Simultaneous emergence of curved spacetime and quantum mechanics

TL;DR

This paper proposes a model where quantum mechanics and gravity emerge simultaneously from a flat spacetime, leading to a Finslerian structure and discrete spacetime, with implications for quantum field equations at Planck scale.

Contribution

It introduces a framework where curved spacetime and quantum mechanics arise together from flat spacetime via quantum Weyl spinors, linking gravity and quantum phenomena.

Findings

Emergence of curved spacetime from flat spacetime on quantum spinor appearance

Derivation of a generalized uncertainty principle leading to discrete spacetime

Quantum field equations for Planck-scale spinors in Finslerian background

Abstract

It is shown in this paper that the geometrically structureless 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 sympleic 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 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.