Final answer:
Lengths of objects traveling at relativistic speeds appear contracted to a stationary observer, not increased. The more an object's length is contracted, the faster it is moving. Therefore, differences in contracted lengths can be used to compare the speeds of objects traveling near the speed of light.
Step-by-step explanation:
The student asked whether the lengths of four identical objects traveling at nearly the speed of light as viewed by a stationary observer can be used to rank their speeds. Contrary to the statement 'When the speed of an object approaches the speed of light, its length appears to increase when viewed by a stationary observer', the actual relativistic effect is known as Lorentz contraction, where objects appear shorter in the direction of motion to a stationary observer. The faster the object moves, the more its length contracts.
As such, if a stationary observer notices differences in the lengths of objects moving at relativistic speeds, these differences in length can indeed be used to compare their speeds, with shorter lengths indicating higher velocities. It's important to note, however, that when moving at speeds very close to that of light, practical observation of this effect would be incredibly challenging due to the extreme speeds involved.
A crucial concept is the proper length, which is the length of an object measured by an observer at rest relative to the object and is always the maximum length observed. So, any measured length less than the proper length suggests motion relative to the observer. Different observers may agree on the relative speed, but not necessarily on the length or the simultaneity of events due to the noticeable effects of relativity at high velocities.