洛伦兹变换 $S\to S^\prime$

正变换:

\[\begin{aligned} x^\prime &= \dfrac{x-vt}{\sqrt{1-\left(\dfrac{v}{c}\right)^2}} \\ y^\prime &= y \\ z^\prime &= z \\ t^\prime &= \dfrac{t-\dfrac{vx}{c^2}}{\sqrt{1-\left(\dfrac{v}{c}\right)^2}} \end{aligned}\]

逆变换:

\[\begin{aligned} x &= \dfrac{x^\prime + vt^\prime}{\sqrt{1-\left(\dfrac{v}{c}\right)^2}} \\ y &= y^\prime \\ z &= z^\prime \\ t &= \dfrac{t^\prime + \dfrac{vx^\prime}{c^2}}{\sqrt{1-\left(\dfrac{v}{c}\right)^2}} \end{aligned}\]