In the reference frame K two very evenly matched sprinters are lined up a distance d apart on the y axis for a race parallel to the x axis. Two starters, one beside each man, will fire their starting pistols at slightly different times, giving a handicap to the better of the two runners. The time difference in K is T.
(a) For what range of time differences will there be a reference frame K′ in which there is no handicap, and for what range of time differences is there a frame K′ in which there is a true (not apparent) handicap?
(b) Determine explicitly the Lorentz transformation to the frame K′ appropriate for each of the two possibilities in part a, finding the velocity of K′ relative to K and the space-time positions of each sprinter in K′.