# Length contraction.

1. Dec 2, 2007

### azatkgz

Let's say that objects also contracts in y and z direction.

Let's cut some part of the wall.Firstly we look from the frame of the wall.In wall's frame the length of the piece contracts,so it can easily pass through the hole on the wall.Now let's look from the frame of the piece.Here the length of the hole contracts,it means that the piece cannot pass through the hole.Conclusion is the objects cannot contract in y and z direction.

Now my dilemma.

There's a garage,whose door opens with neglible time.The length of the garage is equal to the length of the car.Doors close when the car enters the garage. The car is approaching to the door with some velocity.In garage's frame the length of car is shorter ,so no problem here.But what if in car's frame the length of the car is longer than garage's length.In garage's frame he already entered inside and the doors are closed.Because the length of the car in car's frame is longer,what is happening here?

2. Dec 2, 2007

### JesseM

Yes, this seems like a good proof by contradiction, showing why length can only contract in the x direction.
This is solved by the relativity of simultaneity--two events at different locations which happen at the "same time" in one frame can happen at "different times" in another. If the doors close simultaneously in the garage's frame, then in the car's frame the back door actually closes some time before the front door, so there is time for the back of the car to pass through. Also, if the front of the car stops rather than breaking through the back door, either by hitting the brakes or by its front being stopped by the back door, it takes some time for the compression wave to travel through the car and begin to decelerate the back of the car. There must be some frame where the event of the front of the car reaching the back door and the event of the back of the car reaching the front door happen simultaneously, meaning there is a "spacelike separation" (see here or here if you're not familiar with this term) between these events, so in every frame it would be impossible for a signal traveling at the speed of light or slower (like a compression wave) from the event of the front of the car reaching the back door to reach the second event of the back of the car reaching the front door, which tells us that even if we are using a frame where the front of the car decelerates before the back of the car has reached the front door, the back of the car will continue to sail along inertially and will not be affected by what happened to the front until after it has already reached the front door.

The seeming paradox you discuss is actually a pretty common one used in teaching relativity, sometimes called the "pole and barn paradox"--you can find more information here: