Suppose a meter stick is traveling at a high speed but not f

Suppose a meter stick is traveling at a high speed (but not faster than light). Draw a Minkowski diagram showing the world lines of the two ends of the meter stick.

Solution

Relativistic length contraction means that the proper length of an object moving relative to an observer is decreased and finally also the space itself is contracted in this system. The observer is assumed again to move along the ct-axis. The world lines of the endpoints of an object moving relative to him are assumed to move along the ct-axis and the parallel line passing through A and B. For this observer the endpoints of the object at t = 0 are O and A. For a second observer moving together with the object, so that for him the object is at rest, it has the proper length OB at t = 0. Due to OA < OB. the object is contracted for the first observer.

The second observer will argue that the first observer has evaluated the endpoints of the object at O and A respectively and therefore at different times, leading to a wrong result due to his motion in the meantime. If the second observer investigates the length of another object with endpoints moving along the ct-axis and a parallel line passing through C and D he concludes the same way this object to be contracted from OD to OC. Each observer estimates objects moving with the other observer to be contracted. This apparently paradoxical situation is again a consequence of the relativity of simultaneity as demonstrated by the analysis via Minkowski diagram.

For all these considerations it was assumed, that both observers take into account the speed of light and their distance to all events they see in order to determine the actual times at which these events happen from their point of view.