Conservation law

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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.

Exact laws[edit]

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 LawRespective Noether symmetry invarianceNumber of dimensions
Conservation of mass-energyTime invarianceLorentz invariance symmetry1translation about time axis
Conservation of linear momentumGalilean invariance3translation about x,y,z position
Conservation of angular momentumRotation invariance3rotation about x,y,z axes
CPT symmetry (combining charge, parity and time conjugation)Lorentz invariance1+1+1(charge inversion q→-q) + (position inversion r→-r) + (time inversion t→-t)
Conservation of electric chargeGauge invariance1⊗4scalar field (1D) in 4D spacetime (x,y,z + time evolution)
Conservation of color chargeSU(3) Gauge invariance3r,g,b
Conservation of weak isospinSU(2)L Gauge invariance1weak charge
Conservation of probabilityProbability invariance1⊗4total probability always=1 in whole x,y,z space, during time evolution

Approximate laws[edit]

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

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