Length Contraction
Not only would you observe time moving more slowly on a train moving relative to you at
half the speed of light, you would also observe the train itself becoming shorter. The
length of an object, , contracts in the direction of motion to a length when observed
from a reference frame moving relative to that object at a speed v.
EXAMPLE
You measure a train at rest to have a length of 100 m and width of 5 m. When you observe
this train traveling at 0.6c (it’s a very fast train), what is its length? What is its width?WHAT IS ITS LENGTH?
We can determine the length of the train using the equation above:
WHAT IS ITS WIDTH?
The width of the train remains at 5 m, since length contraction only works in the
direction of motion.
Addition of Velocities
If you observe a person traveling in a car at 20 m/s, and throwing a baseball out the
window in the direction of the car’s motion at a speed of 10 m/s, you will observe the
baseball to be moving at 30 m/s. However, things don’t quite work this way at relativistic
speeds. If a spaceship moving toward you at speed u ejects something in the direction of
its motion at speed relative to the spaceship, you will observe that object to be moving
at a speed v: