Facts : 1 Symmetry The principle of relativity (according to which the laws of nature must assume the same form in all inertial reference frames) requires that length contraction is symmetrical: If a rod rests in inertial frame S, it has its proper length in S and its length is contracted in S br Facts : 2 However, if a rod rests in S , it has its proper length in S and its length is contracted in Sbr Facts : 3 This can be vividly illustrated using symmetric Minkowski diagrams (or Loedel diagrams), because the Lorentz transformation geometrically corresponds to a rotation in four-dimensional spacetimebr Facts : 4 First image: If a rod at rest in S is given, then its endpoints are located upon the ct axis and the axis parallel to itbr Facts : 5 In this frame the simultaneous (parallel to the axis of x ) positions of the endpoints are O and B, thus the proper length is given by OBbr Facts : 6 But in S the simultaneous (parallel to the axis of x) positions are O and A, thus the contracted length is given by OAbr Facts : 7 On the other hand, if another rod is at rest in S, then its endpoints are located upon the ct axis and the axis parallel to itbr Facts : 8 In this frame the simultaneous (parallel to the axis of x) positions of the endpoints are O and D, thus the proper length is given by ODbr Facts : 9 But in S the simultaneous (parallel to the axis of x ) positions are O and C, thus the contracted length is given by OCbr Facts : 10 Second image: A train at rest in S and a station at rest in S with relative velocity of are givenbr Facts : 11 In S a rod with proper length is located, so its contracted length in S is given by: Then the rod will be thrown out of the train in S and will come to rest at the station in S br Facts : 12 Its length has to be measured again according to the methods given above, and now the proper length will be measured in S (the rod has become larger in that system), while in S the rod is in motion and therefore its length is contracted (the rod has become smaller in that system): ^ Albert Shadowitz (1988)