Previously, we discussed the flaws of Galilean relativity, which led to the need for a new theory of relativity—special relativity.
In Galilean relativity, we had the following transformation between two inertial frames of reference, and :
where is the relative velocity between the two frames of reference.
In special relativity, this transformation must be replaced with a new one, known as the Lorentz transformation.
Strictly speaking, there are six Lorentz transformations, corresponding to the six generators of the Lorentz group.
They comprise of three rotations and three boosts.
However, for the sake of simplicity, we will first discuss the boost in a single direction, which is the most important one.