Two events occur simultaneously at points A and B as observed in the lab frame. These events will also appear simultaneous in a frame moving with respect to the lab in a direction

Step-by-step solution

Let the lab frame be S and the moving frame be S' . The time interval between two events in S' is given by the Lorentz transformation: t' = ( t - v r c^2 ) Given that the events are simultaneous in the lab frame S , we have t = 0 . For the events to be simultaneous in the moving frame S' , we must have t' = 0 . Substituting t = 0 and t' = 0 into the equation, we get: 0 = ( 0 - v r c^2 ) v r = 0 Here, r is the position vector AB between the two events. The dot product is zero only if the velocity vector v is perpend