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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.