5. Two events occur at positions on the x-axis separated by a distance of Ax and by a time interval of At, according to one observer (Ann). Ann notes that when the first event occurs (a flash of light, at a position closer to her origin than the second event), the light wave from that event goes past the position of the second event before the second event occurs, i.e. Ar < cAt. Other observers moving in the +x direction relative to Ann measure different time intervals between these two events. Use the fact that the proper time interval between two events is measured in the frame where the two events occur at the same position, to find the speed (relative to Ann) of the observer that witnesses the shortest time interval between the two events she witnessed. b. The values measured by Ann are already measured and are therefore not variable. The time interval measured by the other observer is therefore exclusively a function of the velocity of that observer as measured by Ann. Show that of all the possible other frames (defined by the choice of v), the frame in which the minimum time interval is observed is the one you found in part (a). c. Suppose the events that Ann witnesses are two flashes of light, one on Earth, and one on the moon (these are separated by a distance of 360,000 km), which she measures to be 2 seconds apart. An alien happens to be flying by in a very fast spaceship parallel to the line joining the Earth and moon, and it witnesses the same two flashes. Find the shortest time interval that the alien can possibly measure between these flashes.