Imagine that we have two metal rods, and both measure 1 meter, a measurement done from the same inertial system when they are at speed = 0. These two rods are equal, the extreme points of the first one are called a and b and its inertial system is called F, the extreme points of the other rod are called c and d and its inertial frame is called F'. Now imagine there is a third reference system F'' , this system is in the middle of these two rods at point O, the rods are traveling towards O in the same direction but obviously with opposite velocities. According to F'' the rods at F and F' are coming at speed v and -v. Everything is disposed so the extremes a and c will coincide at the same space point at some given instant. (Lets imagine they don't collide, it is just they will run very close in a parallel maner, or that they are not metallic simply imaginary). At some instant in F'' the extremes a and c coincide in the same point O, that means both b and d coincide since the lenghts are the same. Let's imagine the speeds are close to the speed of light, that means maybe F'' will measure length of rod in F= 0.3 meters, lenght of F'= 0.3 meters.(Nothing strange here) Now, according to the system F, he is quiet obviously, and the rod at F' is coming with speed= 2v. According to this system the rod in F does not change its size, it measures 1 meter. Also the rod at F' measures 1 meter as observed from F', but this meter compared with the metter of F is much shorter according to F. The conclusion is that points a and c will coincide at the same point, but now seen from F the point b is at a larger distance than the point d, which is closer to c, and from the F rulers is shorter than 1 meter. Is this correct? (In that case points c and d don't coincide and the lenghts are different, How could be this consistent with F'' measurements?) Now the bizarre stuff is this, What does F' see? For F' it is F who is traveling, it is the rod at F who will contract the lenghts, and when a and c coincide the point d will be 1 meter away from c, no contraction here, but the distance a - b in these rulers will be shorter than 1 meter. Just the opposite that F measured. Both cannot be right at the same time. Do you see the point? Let me know. UNderstanding that from 1 system another changes its lenght when moving as measured from the "quiet" system looks consistent to me. But if I change to the other moving system I can't see how his measurements could be consistent with the first ones.