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Lorentz transformation and its inverse : Define an event to have spacetime coordinates  ( t , x , y , z )  in system  S  and  ( t ′, x ′, y ′, z ′)  in a reference frame moving at a velocity v with respect to that frame,  S ′. Then the Lorentz transformation specifies that these coordinates are related in the following way: {\displaystyle {\begin{aligned}t'&=\gamma \ (t-vx/c^{2})\\x'&=\gamma \ (x-vt)\\y'&=y\\z'&=z,\end{aligned}}} where {\displaystyle \gamma ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}} is the Lorentz factor and  c  is the speed of light in vacuum, and the velocity  v  of  S ′, relative to  S , is parallel to the  x -axis. For simplicity, the  y  and  z  coordinates are unaffected; only the  x  and  t  coordinates are transformed. These Lorentz transformations form a one-param...