Invariant (physics)

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In classical and quantum mechanics, invariance of space under translation results in momentum being an invariant and the

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Another examples of physical invariants are the speed of light, and charge and mass of a particle observed from two reference frames moving with respect to one another (invariance under a spacetime Lorentz transformation^[1]), and invariance of time and acceleration under a Galilean transformation between two such frames moving at low velocities.

Quantities can be invariant under some common transformations but not under others. For example, the velocity of a particle is invariant when switching coordinate representations from rectangular to curvilinear coordinates, but is not invariant when transforming between frames of reference that are moving with respect to each other. Other quantities, like the speed of light, are always invariant.

Physical laws are said to be invariant under transformations when their predictions remain unchanged. This generally means that the form of the law (e.g. the type of differential equations used to describe the law) is unchanged in transformations so that no additional or different solutions are obtained.

For example the rule describing Newton's force of gravity between two chunks of matter is the same whether they are in this galaxy or another (

David Mermin

: It's About Time - Understanding Einstein's Relativity, Chapter 1