In a recent paper published in Physical Review D, is a groundbreaking theoretical framework that bridges quantum mechanics and general relativity through statistical mechanics and information theory. At its core, the theory treats the spacetime metric as a quantum operator, essentially functioning as a “renormalizable density matrix” at each point in spacetime.
The key innovation is the introduction of an entropic action for gravity, defined as the quantum relative entropy between two metrics: the actual spacetime metric and a metric induced by matter fields. These matter fields are described topologically using a Dirac-Kähler formalism as a direct sum of differential forms (0-form, 1-form, and 2-form).
A crucial component of this theory is the introduction of an auxiliary field called the “G-field,” which functions as a set of Lagrangian multipliers enforcing constraints on the matter-induced metric. This approach leads to modified Einstein equations that retain second-order characteristics in both the metric and G-field. In the low coupling regime, these equations reduce to the classical Einstein equations, providing consistency with established physics.
Notably, the theory predicts an emergent positive cosmological constant that depends solely on the G-field, potentially explaining the observed acceleration of cosmic expansion. This addresses a significant challenge in contemporary physics more effectively than previous theories.
The paper builds upon the author’s (Ginestra Bianconi) previous work but makes significant advances by developing a continuous, Lorentz-invariant theory and establishing clear connections to the Einstein-Hilbert action. The local nature of the theory—defining entropy at each spacetime point rather than globally—creates opportunities for connections with quantum entanglement theory.
This framework opens promising avenues for understanding dark matter through the G-field and may provide insights into quantum gravity through canonical quantization. While currently focused primarily on scalar bosonic fields with brief extensions to Abelian gauge fields, the theory lays groundwork for future investigations into Dirac and non-Abelian gauge fields.
Reference: “Gravity from entropy” by Ginestra Bianconi, 3 March 2025, Physical Review D. DOI: 10.1103/PhysRevD.111.066001
