The Distance Between Two Inertial Observers in Relative Motion in Special Relativity

When two inertial observers A and B in relative motion measure the distance between them, will they obtain the same value? Although there is a lack of detailed expositions on this issue, many relativity articles and books seem to suggest that the observers on the earth measure a longer distance than that measured by the observers moving relative to the earth. The present study has examined this issue in detail, using two fundamental conditions of special relativity: 1) the space time interval between two events in the Minkowski space is independent of the inertial reference frame chosen; and 2) there is no privileged reference frame and all inertial reference frames are equal. The results of the present study shows that the value of the distance between A and B measured by observer B in a frame where B is stationary is the same as that obtained by observer A in a frame where A is stationary. The idea that distance measured by observer A is longer than that measured by observer B contradicts special relativity, because it designates de facto more privileged reference frames, which cannot be correct within the framework of special relativity.