This paper proposes that space and time are not fixed, smooth things. Instead they emerge as a scale-dependent fractal geometry made by the entanglement structure of a single, universal quantum state. In that view, the pattern of quantum connections between microscopic degrees of freedom sets which parts of the system are “close’’ or “far’’ in the emergent geometry.

The author builds a concrete mapping from entanglement to distance. Nodes in a quantum-information network represent microscopic degrees of freedom and edges carry entanglement. Distance is defined from mutual information I by a simple information-theoretic formula d_{ij} = −ℓ0 log(I_{ij}/I0). Mutual information is an information measure of how strongly two parts are correlated. The logarithm formula is motivated by the common quantum-field result that correlations fall off exponentially with geometric distance, I ∼ e^{−d}, so inverting that relation gives d ∼ −log I. When the entanglement network shows recursive, scale-invariant clustering, the induced geometry becomes fractal and its effective dimension depends on scale. The paper reports that this effective dimension flows toward D → 2 near the Planck scale (the very small length scale where quantum gravity is expected to appear).

Quantum behavior is argued to arise from the fractal, nondifferentiable nature of paths in this geometry. At very small scales trajectories behave like stochastic processes. The usual derivative does not exist, so the author replaces it with a scale-covariant operator that has both deterministic and random parts. This requires treating forward and backward velocities separately. Combining them produces a complex velocity and a complex covariant derivative. In this framework the Schrödinger equation appears as an emergent law rather than being postulated.

Gravity is tied to the time dependence of the same entanglement-induced metric. Slow, large-scale changes of the entanglement pattern produce smooth curvature and recover Einstein’s gravity in the macroscopic limit. The author writes a generalized field equation G_{μν} = 8πG(T_{μν} + αE_{μν} + βF_{μν}) where the extra terms encode fractal corrections coming from the microstructure. From this picture the framework predicts dimensional reduction at ultrashort scales, possible modifications of gravitational potentials, and potential deviations from standard quantum mechanics at the smallest scales.