Solving the Paradox of the Frame of Reference

[shaner-baner]

Here is a question one of my physics teachers mentiones a long time ago.
Say you have a 10 ft. car and a 10 ft. barn, so the car will just barely fit. Now say the car saw traveling at an appreciable fraction of the speed of light, and you are traveling next to the car, on the line perendicular between the car and the barn. It appears to you that the barn is smaller than 10 ft., and the car won't fit in the barn. Now imagine the same situation, but you are standing next to the barn. The car now looks less than 10ft. long, so it should fit in the barn with room to spare.
I can understand things like simultaniety being an illusion. But how can the car both fit and not fit in the barn? Thanks ahead of time, and I hope this isn't to stupid of a question.

 

[Dale]

It is not that simultaneity is an illusion, it is just that different frames will disagree. Same with time, time is well-defined in every frame but different frames disagree. So the key to this "paradox" is just that in the barn's frame the rear of the car enters the barn before the front of the car leaves, while in the car's frame the front of the car leaves first.

Here is a more detailed explanation: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/polebarn.html#c1

-Dale