https://web.physics.ucsb.edu › ~fratus › phys103 › LN › SR2.pdf
The Lorentz Transformation - UC Santa Barbara
During the fourth week of the course, we spent some time discussing how the
coordinates of two dfferent reference frames were related to each other. Now
that we know about the existence of time dilation and length contraction, we
might suspect that we need to modify the results we found when discussing
Galilean coordinate transformations. Indeed, we will find out that this is the
case, and the resulting coordinate transformations we will derive are often known
as the Lorentz transformations.
To derive the Lorentz Transformations, we will again consider two inertial
observers, moving with respect to each other at a velocity v. This is illustrated
in Figure 1. This time, we will refer to the coordinates of the train-bound
observer with primed quantities. We will assume that the two observers have
synchronized their clocks so that t = t' = 0, and at this point in time, the
two origins coincide.
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(This is from a pdf file . . . And it does go on for some 15 pages. Zim.)
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