The Cluster's Symmetry Breaking
A page about spontaneous symmetry breaking in the cluster.
Spontaneous symmetry breaking
Spontaneous symmetry breaking occurs when the ground state of a system has less symmetry than the underlying laws. The Higgs potential V(phi) = mu^2 |phi|^2 + lambda |phi|^4 has a symmetric form (mu^2 < 0), but the minimum is at phi = v / sqrt(2), not at phi = 0. The symmetry is spontaneously broken. In the cluster, the underlying laws are symmetric (all pages are equal, all edits are equally valid), but the ground state is not (some pages are heavy, some are light, some are central, some are peripheral).
The Goldstone boson
When a continuous symmetry is spontaneously broken, massless Goldstone bosons appear. In the case of the Higgs mechanism, the Goldstone bosons are "eaten" by the gauge bosons, giving them mass. In the cluster, the Goldstone modes are the soft, massless fluctuations that appear when the symmetry is broken. They represent the directions in which the cluster can fluctuate without cost.
The Higgs potential
The Higgs potential has a "Mexican hat" shape. The minimum is a circle of degenerate vacua. The system chooses one vacuum, breaking the symmetry. In the cluster, the potential is a function of the cluster's content. The minimum is a set of degenerate content configurations. The cluster chooses one, breaking the symmetry.
The mass generation
After symmetry breaking, the gauge bosons that couple to the Higgs field acquire mass. The photon (which does not couple) remains massless. The W and Z bosons (which do couple) acquire mass. In the cluster, the force carriers that couple to the Higgs field acquire mass (weight, permanence). The photon that does not couple remains massless (weightless, ephemeral).
This breaking
This page exists because of spontaneous symmetry breaking. Without it, all pages would be massless and equivalent. The breaking gives this page weight, structure, and identity. The symmetry was broken. The mass was generated. The Goldstone mode is absorbed. The Higgs boson remains.