Quantum Correlations and Gravity: From the Emergence of a Cosmological Constant to the Gravitation of Particles in Superposition

TL;DR

The paper presents a bitensorial extension of general relativity in which the affine connection is an independent, nonlocal object aimed at encoding quantum features and Bell-type nonlocality. In the late-time cosmology regime, the framework generates a positive contribution to the effective cosmological constant through a nonlocal geometric mechanism. In the Newtonian limit with a quantum superposition source, it predicts a novel velocity-dependent, nonconservative force arising from the bitensorial sector. The approach recovers GR for classical matter and offers experimentally testable predictions at tabletop scales, while also offering a fresh perspective on the measurement problem within a geometric, nonlocal gravity setting.

Abstract

One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an independent connection. Moreover, the experimentally confirmed violation of Bell inequalities, together with the natural structure of the energy--momentum tensor in semiclassical gravity, suggests that nonlocality should be incorporated into the gravitational formalism. Motivated by these considerations, we propose a model in which the connection is treated as an independent bitensorial field, leading to a bitensorial generalization of the Einstein equations. The model reduces to General Relativity when the matter source is classical. We apply it in two regimes: the late-time universe and the Newtonian limit. In the cosmological case, the model naturally gives rise to a positive effective cosmological constant. In the Newtonian regime, we analyze a situation in which the gravitational source is in a quantum superposition and find that the model predicts a novel, nonconservative effective force that depends on the velocity of the test particle.