Seeing the ties between length contraction, time dialation, and the "skewing of Now", is almost as hard as seeing the ties between Republicans and morality.  Unlike quantum mechanics and Republicans however, you don't need spin.

The classic example is a relativistic cloud guy running through a barn with a pole.  The pole is longer than barn is, but, due to length contraction, is can fit entirely inside if cloud guy is moving fast enough.  The farmer (just to see if he can) slams the first door shut, so that the pole is contained inside the barn.  Then opens the second door to let the cloud guy out (a collision with his door at these speeds would make a bang).
The cloud guy, however, calls foul.





Because he's standing still and the barn is rushing at him, the barn undergoes length contraction.  After the front of his pole enters the barn the back door opens.  For a short time he sees both doors open, with both ends of his pole outside of the barn.  On the way out the back door closes.


The cloud guy and the farmer disagree on exactly when things are happening.  The cloud guy sees the back door as "running ahead" of the front door in time.  While the farmer sees the back of the pole as running fast.

The moral of the story is: one person's length contraction is another man's time dialation.  But more than that, they are two sides of the same coin.  While the farmer observes the front and back doors to be closed simultaneously, the cloud guy sees both doors open simultaneously.  Since the doors are seperated by some distance, no two events affecting them can be considered by everyone (in all frames) to be "simultaneous".