Question

3. In an inertial frame S two events A and B take place at different locations and at different times such that A (XA, ta) and B (Xa, to). Consider a second inertial frame S' moving at a constant speed u along the x axis with respect to S. Can the observer in S' observe these two events to be simultaneous and occurring at the same location i.e. (x'A=x'® and t's=t')? Make necessary calculations to justify your answer.

Answer 1

This problem can be solved by applying the lorentz transformation equations between the two frames and seeing if any velocity of frame S' can possibly make both events A and B simultaneous and occurring at the same position in frame S'. The answer turns out to be no. Detailed solution given below. Ask me if you have any doubts. Feedback will be helpful.


Solution 1 S is a it an event occuro in inertial frame s at position (e,t), same event occuro in s at position inst) given by the Lorent transtorme - atim w = 8(2-ut) ť = 0 (t- ure) where a is velocity of light and 8=. So, fore eunt A, 2 / for event B, NA = 8(4A-UtA I r6=8(~6-utg) ta = 8(tA - URA) I to=8 (to-u2g) i '-'B = x (x2-wa) - arta-te)] . it nA=na, na-nb=0 ..y [cmp -16) – uſta-to)]-o -in (XA-UB) .. ar a= tarto) this speed of frame s' is neccessary for these - two events to happen at same position in s Now, tá - tos = 8( (ta-tB) - UPRA-UB)] if these two events were to happen at - same time in s', táto=o.

so, o S(ta-to) - u (Mara)] =0 ar uz (ta-tB) e² IMA-MB) as we see, this neccessary spud is not the same as the me we obtained earlier. Hence me speed a of frame s' cannot satisfy both equation ris andsis. Hence the the the observer in I cannot two evente simultaneously same location. possibly obserne and occuring at