Gravity and the Quantum: Are they Reconcilable?

TL;DR

This paper explores the fundamental incompatibilities between general relativity and quantum mechanics, examines teleparallel gravity as an alternative framework, and suggests it could reconcile gravitation with quantum principles.

Contribution

It proposes that teleparallel gravity, which does not rely on the equivalence principle, may serve as a conceptual bridge between gravity and quantum mechanics.

Findings

Quantum objects in gravitational fields violate the weak equivalence principle.

Teleparallel gravity describes gravity via torsion, not curvature, and does not require equivalence principles.

Replacing general relativity with teleparallel gravity could reconcile gravity with quantum mechanics.

Abstract

General relativity and quantum mechanics are conflicting theories. The seeds of discord are the fundamental principles on which these theories are grounded. General relativity, on one hand, is based on the equivalence principle, whose strong version establishes the local equivalence between gravitation and inertia. Quantum mechanics, on the other hand, is fundamentally based on the uncertainty principle, which is essentially nonlocal in the sense that a particle does not follow one trajectory, but infinitely many trajectories, each one with a different probability. This difference precludes the existence of a quantum version of the strong equivalence principle, and consequently of a quantum version of general relativity. Furthermore, there are compelling experimental evidences that a quantum object in the presence of a gravitational field violates the weak equivalence principle. Now it so happens that, in addition to general relativity, gravitation has an alternative, though equivalent description, given by teleparallel gravity, a gauge theory for the translation group. In this theory torsion, instead of curvature, is assumed to represent the gravitational field. These two descriptions lead to the same classical results, but are conceptually different. In general relativity, curvature geometrizes the interaction, while torsion in teleparallel gravity acts as a force, similar to the Lorentz force of electrodynamics. Because of this peculiar property, teleparallel gravity describes the gravitational interaction without requiring any of the equivalence principles. The replacement of general relativity by teleparallel gravity may, in consequence, lead to a conceptual reconciliation of gravitation with quantum mechanics.