Invariant (physics)

Lore & Background

Invariance is an important concept in modern theoretical physics, and many theories are expressed in terms of their symmetries and invariants. In classical and quantum mechanics, invariance of space under translation results in momentum being an invariant and the conservation of momentum, whereas invariance of the origin of time results in energy being an invariant and the conservation of energy. By Noether's theorem, any invariance of a physical system under a continuous symmetry leads to a fundamental conservation law.

Reader's Guide

Invariance is a foundational concept in theoretical physics, linking symmetries of a system to conserved quantities. Examples include the invariance of the speed of light under Lorentz transformations, and the invariance of time and acceleration under Galilean transformations. Physical laws are said to be invariant when their predictions remain unchanged under transformations, meaning the form of the law (e.g., differential equations) is unchanged. The adjective 'covariant' is often used informally as a synonym for 'invariant', though more accurately, equations like the Klein–Gordon and Dirac equations are invariant under coordinate transformations of special relativity, while the Schrödinger equation is not. Covariance and contravariance generalize the mathematical properties of invariance in tensor mathematics, used in electromagnetism, special relativity, and general relativity.

Did You Know?

• Invariance of space under translation results in momentum being an invariant and the conservation of momentum.
• Invariance of the origin of time results in energy being an invariant and the conservation of energy.
• The speed of light is always invariant under Lorentz transformations.
• The Schrödinger equation does not keep its written form under the coordinate transformations of special relativity, so it is not invariant.