Take an event A with coordinates (ct_A, x_A) = (4, 3). Is the displacement vecto

Question

Take an event A with coordinates (ct_A, x_A) = (4, 3). Is the displacement vector from the origin to A spacelike, lightlike, or timelike? What time difference is measured by a clock moving uniformly from the origin to A? Compute the displacement vector from the origin to A seen by an observer moving with half the speed of light along the x-axis. Is this vector spacelike, lightlike, or timelike? Repeat part (ii) by graphical methods: Draw event A in a space-time diagram with two frames (ct, x) and (ct', x') and read off the coordinates (ct'_A, x'_A) by measuring distances in your diagram. How fast should an observer move along the x-axis to experience the origin and A at the same point in space? What time difference separates the two events in this frame?

Explanation / Answer

(i) if the interval is time like the separation in time is larger then theseparation in space.

here ct is greater then x . ct is time and x is space.

so the event is time like.

ii) x=x0 sqrt(1-v2 /c2 )

here x0 =3 and v=c/2

so x= 3sqrt{1-(1/4)}

x={3*1.732/2}=[5.169 /2}=2.58

this vector is time like.

iv) if two events are separated by a time like interval, there does not exist a frame in which both are simalteneously.

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