Example 4
Event A happens at the spacetime coordinates $(x, y, z, t)=(2 \mathrm{m}, 3 \mathrm{m}, 0,0.1 \mathrm{s})$ and event B happens at the spacetime coordinates $(x, y, z, t)=\left(0.4 \times 10^{8} \mathrm{m}\right.$ $3 \mathrm{m}, 0,0.2 \mathrm{s}) .$ (a) Is it possible that event A caused event B? (b) If event B occurred at $\left(0.2 \times 10^{8} \mathrm{m}, 3 \mathrm{m}, 0,0.2 \mathrm{s}\right)$ instead, would it then be possible that event A caused event B? [Hint: How fast would a signal need to travel to get from event $\mathrm{A}$ to the location of $\mathrm{B}$ before event $\mathrm{B}$ occurred?]