Geometric representation of the Galilean transformation

Abstract

Galilean transformation is a set of equations in Galilean relativity that relate the space and time coordinates of two reference frames moving at a constant velocity to each other. In this paper, all equations of Galilean transformation will be derived using the geometrical method, concretely using a space–time diagram. But this powerful method of derivation reveals a new Galilean transformation. The credibility of the geometrical method and the fact that the wave equation is invariant to the transformed Galilean transformation make this new Galilean transformation respectable. Moreover, the transformed Galilean transformation reinforces the principle of relativity, making this principle unique to all physics.