Let's go back to Jackie and you freely floating in your respective spaceships. If Jackie is moving at 0.95c and is zipping past you, what would you measure for the length of her spaceship?
You can measure the length of her spaceship by measuring how much time it takes her to pass by you – by starting your stopwatch when the front of her spaceship reaches you and stopping your watch when the end of her spaceship passes you. Because we know Jackie’s velocity and how much time passes, we can easily calculate the length of the spaceship:
We have already established that your clock records less time than Jackie’s as she passes from one end of your spaceship to the next. So you measure the length of her spaceship to be shorter than she would measure! This is called Length Contraction .
Length becomes shorter in the direction of motion .
Notice that Jackie’s ship is not any shorter in height, only in the direction of motion which is the length.
The length contraction formula is similar to the time dilation one, except that it deals with lengths:
where lmoving is the length measured for the moving reference frame, lrest is length measured in the reference frame of the observer, v is the velocity of the moving object, and c is the speed of light.
Example problem:
If Jackie is moving at 0.95c and her spaceship is 300 meters long when measured at rest (you know this because you have identical spaceships), what would you measure for the length of her spaceship?
Reminder: before you calculate the length, make a prediction for what sort of number you expect, shorter or longer?
Wow, that is significantly shorter than 300 m!