# 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.