A coordinate transformation which ensures the principle of relativity holds. This principle requires that an experiment performed in a reference frame S (typically this reference frame is the rest frame of the observer) will lead to the same result if it is performed in another reference frame S' moving at a constant velocity V with respect to the first reference frame.
If the frame S' is moving at a constant speed V along the x-axis and the two frames coincide at t=0 then the transformation may be written as follows
Thus, the coordinates of an object
in S and S' can be simply related. Differentiating
the first equation
with respect to time
In other words a velocity measured in the frame S' will appear greater by V in the frame S.
Although the Galilean transformation agrees with our everyday experiences, at high speeds it is no longer valid. It has been shown by experiment that the veloctity of light is the same in the reference frame S and the moving frame S'. Furthermore, maxwell's equations are not invariant under the Galilean transformation. Thus, it is incompatible with Electromagnetism and Special Relativity. The Lorentz transformation includes these effects.