Is the Quantum-Entangled Universe a Small World?

This paper asks a provocative question: if entangled particles can be separated by very large distances, could entanglement make the universe into a small-world network? The author treats particles on a space-like hypersurface as nodes in a network, and defines a long-range link when two particles are connected by a chain of exchanged particles involving no more than a chosen maximum number of interactions.

The motivation comes from network theory. In a small-world network, most connections are local, but a few long-range links dramatically shorten path lengths between nodes. The paper explores whether partial entanglement could supply those long-range links in the real universe.

The paper builds a simple probabilistic model for how likely two particles are to remain sufficiently entangled after traveling a distance. The key idea is that each interaction along a particle’s path dilutes entanglement, so the number of intervening interactions is used as a proxy for entanglement strength. Using mean free path as the relevant scale, the author derives a distance-dependent probability that two particles are linked by partial entanglement.

That probability is then compared with standard small-world criteria from network theory. Because the derived distribution falls off exponentially rather than as a power law, the paper does not claim a universal small-world proof. Instead, it argues that on finite, physically relevant ranges of distance, the entanglement link pattern can still behave like a small-world or random network depending on the region of space and the particle type considered.

The central result is that large, low-density regions of the universe are the best candidates for entanglement-based small-world structure. In intergalactic space, and often within galaxies or the solar system, the mean free paths of relevant particles are so large that partial entanglement can create long-range links over enormous distances. In those regimes, the network can have short path lengths characteristic of a small world, and in some distance ranges it behaves more like a random network because clustering is lost.

By contrast, on very small scales such as inside stars and planets, the entanglement-only picture is not enough. There the paper argues that other kinds of connections would have to be added to preserve a small-world interpretation.