[BikerNYC]

If recollection serves, for every symmetry (Charge, Parity, & Time) in QM, there is a corresponding Conservation Law.

Understood. But how did it come to be that a rule developed (or even that one could possibly develop) such that for every symmetry in QM there is a corresponding Conservation Law?

[longshadow]

Understood. But how did it come to be that a rule developed (or even that one could possibly develop) such that for every symmetry in QM there is a corresponding Conservation Law?

First, allow me to correct my earlier response. It turns out that it isn't limited to QM. For each continuous symmetry in nature (wherein the rules of physics are invariant under some transformation) there is a corresponding Conservation Law, and vice-versa.

Spatial translational invariance <=> Conservation of Momentum

Spatial rotational invariance <=> Conservation of Angular Momentum

Temporal invariance <=> Conservation of Energy (and, by extension via Relativity: E=mc²) Matter.

Given the "nature" of nature, logic requires that the symmetries be equivalent to the corresponding Conservation Law. It's based on Noether's Theorem.

A web search will take to sites that can tell you more details that I can.

There are also discrete symmetries in QM that give rise to conservation of various properties.

Hope that helps.