Video Problem #2, Lecture #12: Two observers A and B at either ends of a high speed train (v = 0.6c) decide to check whether their watches are synchronized. The length of the train is 2 lt-s from end to end according to observers A and B moving with the train. At some time a light pulse is sent from the middle of the train towards both observers A and B.

Observers A and B discover that the pulses arrive simultaneously and conclude that their watches are synchronized. A spacetime diagram for this situation is shown in the diagram below right.

(a) On the space-time diagram, place dots indicating the events corresponding to the reception of each of the light pulses by observer A and B.

(b) On the spacetime diagram, indicate on the t-axis the time interval Δt between the arrival of these two pulses as measured by an observer at rest on the train tracks.

(c) The distance between reception of the two pulses as measured by someone next to the tracks is 2.5 lt-s. Using the invariant interval, calculate a numerical value for the time interval Δt between the arrival of these two pulses as measured by the observers in the track reference frame.