Lorentz Boost in One Direction

Analogously, for any time f2 0 the second light signal to the right defines an event E2 whose coordinates in IS and IS are given by 

We therefore find A q = — (d/c) A q and may write down the desired Lorentz transformation as 

So far we have only exploited the principle of constant speed of light in all inertial frames, but not the (first part of the) relativity principle itself, cf. section 3.1.2. Due to the relativity principle the Lorentz back transformation from IS to IS must have the same form as given by Eq. (3.60) with v replaced by —v, 

Considering the Lorentz back and forth transformations for the x-coordinate, for example, we find 

This determines the last free parameter A q, for which it is convenient to introduce the new symbol 7, 

---