Discussion
The events are represented by coordinates \((ct, x, y, z)\) in some frame of reference. Which of the following statements is/are correct?
[\(c\) is the speed of light]
Answer: D
The correct statement is that events \((9, -1, 1, -1)\) and \((-10, 1, 0, -1)\) are time-like separated.
The invariant interval is \(\Delta s^2 = (c\Delta t)^2 - \Delta x^2 - \Delta y^2 - \Delta z^2\): positive for time-like, zero for light-like and negative for space-like separation. The differences for each pair are:
\[ \begin{aligned} \text{A:}\ (-2, 1, 1, 0) &\Rightarrow 4 - 1 - 1 = 2 \\ \text{B:}\ (2, 1, -1, 0) &\Rightarrow 4 - 1 - 1 = 2 \\ \text{C:}\ (1, 1, -2, 0) &\Rightarrow 1 - 1 - 4 = -4 \\ \text{D:}\ (-19, 2, -1, 0) &\Rightarrow 361 - 4 - 1 = 356 \end{aligned} \]
Pair D has a positive interval, so it is time-like, as stated. Pairs A and B are also time-like, not space-like, and pair C is space-like, not light-like. So only D is correct.
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