My professorIn my lecture notes, there are two frames S and S'. Now the isThe prime frame moves with uniform velocity with respect to the unprimed frame. In this frame now, she drivesderives the time dilation equation in the following way he:
She assigns $t$ as time on thein S as t,and distance xas $x$. Now from inverse transformations $t_1= \gamma (t_1' + \frac{vx_1'}{c^2})$ ;;$ t_2 = \gamma (t_2' + \frac{vx_1'}{c^2})$ then:
$$t_1= \gamma (t_1' + \frac{vx_1'}{c^2})$$
$$t_2 = \gamma (t_2' + \frac{vx_1'}{c^2})$$
Now, if betweenthe both the positions are the same, how S' is S' moving?