In the quiet of the quantum world, there is no emptiness. Particles are intertwined by invisible threads — entanglement. The authors of the work proposed that the very fabric of spacetime is woven from these threads. This is not just a metaphor: they built a mathematical framework where the distance between points is determined by how much shared information they hold.
This gives rise to fractal geometry. On large scales, the world looks three-dimensional, but when you peer deep down to Planck lengths, its dimensionality flows down to two.
Particle trajectories here are not smooth but jagged, like a coastline. Their random walks lead to the Schrödinger equation — the main law of quantum mechanics. It is not postulated but grows out of the geometry itself.
Gravity in this picture is a response to how the metric, set by entanglement, changes over time. In the familiar limit, Einstein's general relativity emerges, but with additions: new fields appear that slightly alter the law of gravity at extremely small distances. Thus, quanta and gravity for the first time coexist in a single framework, not conflicting but complementing each other. And the web's threads, where it all began, gain weight — literally.
as written by the authors arXiv:2607.26035
In this paper we propose that spacetime is an emergent fractal geometry generated by the entanglement structure of an underlying quantum information network. Indeed, it is developed a framework in which spacetime, quantum mechanics, and gravity emerge from the entanglement structure of a universal quantum state. Geometry is defined by an information-theoretic distance $$d_{ij}=-\ell_0\log(I_{ij}/I_0)$$ on an entanglement graph, producing a scale-dependent, fractal spacetime whose effective dimension flows toward $$D\to 2$$ near the Planck scale. In this fractal geometry, nondifferentiable trajectories lead to stochastic geodesics and a complex covariant derivative, from which the Schr\"odinger equation follows as an emergent dynamical law. Gravity arises from the time dependence of the entanglement-induced metric, yielding Einstein gravity in the macroscopic limit and fractal corrections encoded in a generalized field equation $$G_{\mu u}=8\pi G(T_{\mu u}+\alpha E_{\mu u}+\beta F_{\mu u})$$. The resulting \emph{Fractal Entanglement Quantum Gravity} (FEQG) framework predicts dimensional reduction, modified gravitational potentials, and possible deviations from standard quantum mechanics at ultrashort scales, offering a unified informational origin for quantum theory and gravitation.
If we could peer down to the Planck scale, the familiar three dimensions of space would seem to dissolve into a two-dimensional hologram — much like the shadow of a three-dimensional object on a wall.
The idea of fractal spacetime echoes the 'quantum foam' from Greg Egan's novels, where reality at the micro level becomes a seething, shifting structure.