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Galilean Transformation

The numerical values of various physical quantities generally change under a co-ordinate transformation. Trivial example is the value of position co-ordinates (x, y, z) of particle P, which change to (x’, y’, z’) under the transformation. It means that the value of position co-ordinates itself has no objective reality, or in other words, it is not an objective property of the particle. It is simply the geometrical position of the particle relative to a particular co-ordinate system.

The physical quantities whose values do not change under a transformation are called the invariants of the transformation. Such physical quantities reflect the objective properties of the object (or phenomenon) under consideration in the sense that these properties remain independent of the choice of the co-ordinate system. In the following discussion, we look into the invariants of Galilean transformation.