"For every continuous symmetry of the law of physics, there must exist a conservation law.
For every conservation law, there must exist a continuous symmetry"
Conservation laws and symmetryThe symmetry properties of a physical system are intimately related to the conservation laws characterizing that system. Noether's theorem gives a precise description of this relation. The theorem states that each continuous symmetry of a physical system implies that some physical property of that system is conserved. Conversely, each conserved quantity has a corresponding symmetry. For example, the isometry of space gives rise to conservation of (linear) momentum, and isometry of time gives rise to conservation of energy.
The following table summarizes some fundamental symmetries and the associated conserved quantity.
|Proper orthochronous |
|translation in time |
|translation in space |
|rotation in space |
|Discrete symmetry||P, coordinate inversion||spatial parity|
|C, charge conjugation||charge parity|
|T, time reversal||time parity|
|CPT||product of parities|
|Internal symmetry (independent of |
|U(1) gauge transformation||electric charge|
|U(1) gauge transformation||lepton generation number|
|U(1) gauge transformation||hypercharge|
|U(1)Y gauge transformation||weak hypercharge|
|U(2) [U(1)xSU(2)]||electroweak force|
|SU(2) gauge transformation||isospin|
|SU(2)L gauge transformation||weak isospin|
|SU(3) "winding number"||baryon number|
|SU(3) gauge transformation||quark color|
|SU(3) (approximate)||quark flavor|
From Wikipedia, the free encyclopediaIn 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 energy
- Conservation of linear momentum
- Conservation of angular momentum
- Conservation of electric charge
- Conservation of color charge
- Conservation of weak isospin
- Conservation of probability
- Conservation of mass (applies for non-relativistic speeds)
- 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
- CP symmetry
- Charge conservation
- Conserved quantity
- 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