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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. |
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Answer» Solution :(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`. 
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