The space-time diagram, shows three events A, B, and C which occurred on the x axis of some inertial reference frame. Find:
(a) the time interval between the events A and B in the reference frame where the two events occurred at the same point,
(b) the distance between the points at which the events A and C occured in the reference frame where these two events are simultaneous.

Explanation

(a) The four-dimensional interval between A and B (assuming `Deltay=Deltaz=0`) is:
`5^2-3^2=16units`
Therefore the time interval between these two events in the reference frame in which the events occurred at the same place is
`c(t_B^'-t_A^')=sqrt(16)=4m`
or `t_B^'-t_A^'=4/c=4/3xx10^-8s`
(b) The four dimensional interval between A and C is (assuming `Deltay=Deltaz=0`)
`3^2-5^2=-16`
So the distance between the two events in the frame in which they are simultaneous is `4 units =4m`.