- Conservation law
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)
- 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
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