Question

A car is moving at a rapid pace. It is approaching a garage with doors at either end. The proper length of the car is longer than the length of the garage. As the car travels through the garage, describe what the driver would observe. Describe what would be seen by a stationary observer inside the garage.

The answer in the book is: As the car is moving through the garage, the driver sees the car as unchanged. The garage will appear to have decreased in length. As the car goes through the garage the driver would see that the car would stick out from both ends of the garage. The stationary observer would see the car as having a decreased length. As the car went through the garage, it would appear that the car would actually fit inside the garage.

Can you please give a more detailed answer.

Answer 1

All the apparant contractions are happening here falls under the relativistic theory called Lorentz contraction. Things at relativistic speed sees other things contracted along the line of their motion.

On the other hand the observer from outside observes the same length contraction for the vehicle, it seems to that person that the car has shinked in size.

The person from one reference frame sees lengths from the other leference frame along the line of their relative motion contracted by a factor of . This is called the Lorentz factor. If the velocity is v and the velocity of the light is c, then,

,

is always > 1 because the speed of the object cannot surpass lightspeed.

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Say the car is moving through the barn in 90% of the speed of light. then = 2.29. So the car's rider will see the barn contracted by a factor of 2.29. And the observer from barn will see the car is contracted by the same amount.

This phenomenon is named as ladder paradox. You can look it up further if you want.