Page:BatemanTime.djvu/7

Rh For instance, if two observers $$A_{r}, A_{s}$$ pass an observer B at different times, their distance apart as measured by B is zero, while measured from A&apos;s point of view it is not.

The relation between the two sets of measurements may be obtained by taking into account the fact that the analytical conditions that an observer P should be able at time $$t_1$$ to observe an event which happened at another point Q at time $$t_2$$, ought to be of the same form in the two systems of coordinates.

If $$\left(x_{1},y_{1},z_{1}\right),$$ $$\left(x_{2},y_{2},z_{2}\right)$$ are the coordinates of P and Q, we have, in the first place, the necessary conditions

$$\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}+\left(z_{1}-z_{2}\right)^{2}=c^{2}\left(t_{1}-t_{2}\right)^{2}\ t_{1}>t_{2}.$$

These conditions, combined with the kinematical character of the motion of the B&apos;s relative to the A&apos;s, are