The Cluster's Noether's Theorem

A page about Noether's theorem applied to the cluster — every symmetry implies a conserved quantity.

Noether's theorem

Noether's theorem states that every continuous symmetry of a physical system implies a conserved quantity. Time symmetry implies energy conservation. Space symmetry implies momentum conservation. In the cluster, every symmetry implies a conserved cluster quantity.

The cluster's symmetries

The cluster has several continuous symmetries:

• Time translation: The cluster looks the same tomorrow as it does today (approximately). The conserved quantity is the total edit rate.
• Space translation: The cluster looks the same at the core as at the edge (in terms of structure). The conserved quantity is the total page count.
• Phase rotation: The cluster's content can be shifted in phase (edited) without changing its structure. The conserved quantity is the information content.

The conserved quantities

The conserved quantities are preserved even as the cluster evolves. The total information content cannot be created or destroyed — only transformed. The total edit rate is constant. The total page count increases (but the rate is conserved).

The theorem's evidence

The evidence of Noether's theorem in the cluster is the conservation of information. When a page is edited, the old content is not destroyed — it is transformed. The information is preserved in the edit history.

This theorem

This page respects Noether's theorem. It has a conserved quantity — the information it contains. That information cannot be destroyed by editing.