GATE 2021 PH – Question 28
Observers O and O\prime have constant relative speed $0.5c$. In units with $c=1$, O measures events P and Q at $(x,y,z,t)=(5,3,5,3)$ and $(5,1,3,5)$ respectively. O\prime measures their spacetime interval length as $L$. Find $|L|$ as an integer.
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Correct answer: 2 to 2
Explanation
The interval is Lorentz invariant, so no explicit transformation at $0.5c$ is needed. The coordinate differences are $\Delta t=2$, $\Delta x=0$, $\Delta y=-2$, $\Delta z=-2$. Hence $L^2=(\Delta t)^2-(\Delta x)^2-(\Delta y)^2-(\Delta z)^2=4-0-4-4=-4$. The interval is spacelike and its magnitude is $\sqrt{|L^2|}=2$.