Invariant (physics)

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In mathematics and theoretical physics, an invariant is a property of a system which remains unchanged under some transformation.

The gravitational field of the Sun is invariant under a change of time (from, say, now to tomorrow). It is also invariant under change of angular position.

Examples of invariants include the speed of light under a Lorentz transformation and time under a Galilean transformation. Many such transformations represent shifts between the reference frames of different observers, and so by Noether's theorem invariance under a transformation represents a fundamental conservation law. For example, invariance under translation leads to conservation of momentum, and invariance in time leads to conservation of energy.

Invariants are very important in modern theoretical physics, and many theories are in fact expressed in terms of their symmetries and invariants.

Covariance and contravariance generalize the mathematical properties of invariance in tensor mathematics, and are frequently used in electromagnetism, special relativity, and general relativity.