Invariant (physics) - Definition

In physics, invariants are usually quantities conserved (unchanged) by the symmetries of the physical system. (See Noether's theorem.)

The correspondence between symmetries and conserved quantities is apparent through conservation laws. Much work has been done, especially in quantum physics, to relate every conserved quantity to some symmetry. One such quantity that still defies all such attempts is mass. Some other examples include:

• Acceleration is invariant under the Galilean transformations.
• The speed of light invariant under the Lorentz transformations of special relativity.
• time invariance makes energy a conserved quantity, hence an invariant.
• translational invariance implies that momentum is conserved.
• rotational invariance implies that angular momentum is conserved.

See also:

• covariant, contravariant
• principle of relativity