to the signal that travels from Bob to Alice Equating the two expressions for and rearranging, This establishes that the quantity is an invariant: it takes the same value in any inertial coordinate system and is known as the invariant interval. The Lorentz transformation The two equations for in the previous section can be solved as simultaneous equations to obtain: These equations are the Lorentz transformation expressed in terms of the Bondi k-factor instead of in terms of velocity. By substituting the more traditional form is obtained. Rapidity Rapidity can be defined from the k-factor by and so The k-factor version of the Lorentz transform becomes It follows from the composition rule for , , that the composition rule for rapidities is addition: References External links Review of Bondi k-Calculus Special relativity