When something is said to be “invariant”, it is critical to understand what group of transformations it is invariant under.

$\vec{v}^2$ is an invariant under the group of rotations in three-dimensional Euclidean space, but is not an invariant under the group of Galilean boosts, which are the rotationless transformations to other inertial reference frames in uniform motion relative to the first.

When something is said to be “invariant”, it is critical to understand what group of transformations it is invariant under.

$\vec{v}^2$ is an invariant under the group of translations and rotations in three-dimensional Euclidean space, but is not an invariant under the group of Galilean boosts, which are the rotationless transformations to other inertial reference frames in uniform motion relative to the first.

When something is said to be “invariant”, it is important to understand what group of transformations it is invariant under.

$\vec{v}^2$ is an invariant under the group of rotations in three-dimensional Euclidean space, but not an invariant under the group of Galilean boosts, which are the rotationless transformations to other inertial reference frames in uniform motion relative to the first.

When something is said to be “invariant”, it is critical to understand what group of transformations it is invariant under.

$\vec{v}^2$ is an invariant under the group of rotations in three-dimensional Euclidean space, but is not an invariant under the group of Galilean boosts, which are the rotationless transformations to other inertial reference frames in uniform motion relative to the first.