Conservation law (physics)

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

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

Approximate laws

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

See also


  • 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.

External links

  • Conservation Laws — an online textbook