Conservation law

For the legal aspects of environmental conservation, see 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 conservation laws is Noether's Theorem, which states that there is a one-to-one correspondence between conservation laws 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 conservation laws that are said to be exact laws, or more precisely have never been shown to be violated:

• Conservation of mass-energy
• Conservation of linear momentum
• Conservation of angular momentum
• Conservation of electric charge
• Conservation of color charge
• Conservation of weak isospin
• Conservation of probability density
• CPT symmetry (combining charge, parity and time conjugation)
• Lorentz symmetry

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)

See also

• 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

References

• 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