Galilean invariance

Galilean invariance is the principle that physical laws retain the same form in inertial frames related by Galilean transformations, including constant-velocity changes of frame.

Galilean transformation: A coordinate transformation between inertial frames using spatial translations, rotations, and constant relative velocity while leaving time unchanged. It specifies the frame changes under which invariant laws must keep their form.
Classical mechanics: The framework describing motion and forces at speeds far below the speed of light and at ordinary scales. Galilean invariance is a symmetry of its standard laws.
Special relativity: The theory that physical laws are invariant in inertial frames related by Lorentz transformations, with light speed the same in each. It replaces Galilean invariance when relativistic speeds or electromagnetic phenomena matter.
Galilean group: The group of spatial rotations, translations, time translations, and constant-velocity boosts in Newtonian spacetime. It organizes the transformations that leave Galilean-invariant laws unchanged.
Galilean relativity: The principle that mechanical experiments cannot distinguish rest from uniform straight-line motion. It states the physical content behind invariance under changes of inertial frame.
Newtonian mechanics: A formulation of classical mechanics based on Newton's laws of motion and universal gravitation. Its equations provide the principal setting for Galilean invariance.
Lorentz transformation: A coordinate transformation relating measurements in inertial frames while preserving the spacetime interval and light speed. Unlike a Galilean transformation, it mixes space and time.
Noether's theorem: A theorem connecting continuous symmetries of an action to conserved quantities. It links continuous spacetime symmetries, including boosts, to conservation laws.
Inertial frame: A reference frame in which a force-free body moves at constant velocity. Galilean invariance compares laws only between inertial frames.
Reference frame: A coordinate system and clock convention used to describe physical events and measurements. Invariance compares descriptions made in different reference frames.

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