Going Further 9.2: Finding the Location of
the x'-Axis

To find the position of the x'-axis in the spacetime diagram, conduct the following thought experiment. Imagine that a flash of light is emitted from the point x' = 0 at some time t' = T < 0, or in other words, a flash of light is emitted from the origin of the primed system before it reaches the origin of the unprimed system. The flash is reflected and arrives back at x' = 0 at some time t' = T > 0. Because the return trip for the light is just the reverse of the outward trip, the time interval for the return trip ends T seconds after t' = 0. The geometry is shown in Figure B.9.1.

Figure B.9.1. A flash of light is emitted at event A, T seconds before t' = 0. It returns to its starting point at event C, T seconds after t' = 0. Event B, marking the reflection of the light, must lie on the x'-axis. Credit: NASA/SSU/Aurore Simonnet

Under these conditions, the reflection of the light must occur at t' = 0, and so that event, labeled event B, must lie on the x'-axis. Drawing a line from the origin through the reflection point locates the x'-axis.