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For the legal aspects of environmental conservation, see environmental law and conservation movement.

In physics, a **conservation law** states that a particular measurable property of an isolated physical system does not change as the system evolves.

One particularly important physical result concerning laws of conservation is Noether's theorem, which states that there is a one-to-one correspondence between laws of conservation and differentiable symmetries of physical systems. For example, the conservation of energy follows from the time-invariance of physical systems, and the fact that physical systems behave the same regardless of how they are oriented in space gives rise to the conservation of angular momentum.

A partial listing of physical laws of conservation due to symmetry that are said to be **exact laws**, or more precisely *have never been [proven to be] violated:*

Conservation Law | Respective Noether symmetry invariance | Number of dimensions | ||
---|---|---|---|---|

Conservation of mass-energy | Time invariance | Lorentz invariance symmetry | 1 | translation about time axis |

Conservation of linear momentum | Galilean invariance | 3 | translation about x,y,z position | |

Conservation of angular momentum | Rotation invariance | 3 | rotation about x,y,z axes | |

CPT symmetry (combining charge, parity and time conjugation) | Lorentz invariance | 1+1+1 | (charge inversion q→-q) + (position inversion r→-r) + (time inversion t→-t) | |

Conservation of electric charge | Gauge invariance | 1⊗4 | scalar field (1D) in 4D spacetime (x,y,z + time evolution) | |

Conservation of color charge | SU(3) Gauge invariance | 3 | r,g,b | |

Conservation of weak isospin | SU(2)_{L} Gauge invariance | 1 | weak charge | |

Conservation of probability | Probability invariance | 1⊗4 | total probability always=1 in whole x,y,z space, during time evolution |

There are also **approximate** conservation laws. These are approximately true in particular situations, such as low speeds, short time scales, or certain interactions.

- Conservation of mass (applies for non-relativistic speeds and when there are no nuclear reactions)
- Conservation of baryon number (See chiral anomaly)
- Conservation of lepton number (In the Standard Model)
- Conservation of flavor (violated by the weak interaction)
- Conservation of parity
- Invariance under Charge conjugation
- Invariance under time reversal
- CP symmetry, the combination of charge and parity conjugation (equivalent to time reversal if CPT holds)

- Charge conservation
- Conserved quantity
- Some kinds of helicity are conserved in dissipationless limit: hydrodynamical helicity, magnetic helicity, cross-helicity.

- Continuity equation
- Noether's theorem
- Philosophy of physics
- Symmetry in physics
- Totalitarian principle

- Victor J. Stenger, 2000.
*Timeless Reality: Symmetry, Simplicity, and Multiple Universes*. Buffalo NY: Prometheus Books. Chpt. 12 is a gentle introduction to symmetry, invariance, and conservation laws.

- Conservation Laws — an online textbook