Homework Chapter 13 and Chapter 19 (Ranking Task: Time Dilation)
Each figure below shows a spaceship moving past your spaceship ("YOU") at the indicated speed. Imagine that you watch the other spaceship as its clock ticks off one second. Rank the figures according to how much time you would say passes (on your own ship) while the other ship's clock ticks off one second, from the shortest to the longest amount of time.
Shortest: speed = 0.7c speed = 0.75c speed = 0.8c Longest: speed = 0.85c The faster an object is moving relative to you, the slower its time will run relative to yours. Slower time means its clock takes longer to tick off each second, which is why the rankings go in order of increasing speed (relative to YOU).
The four figures below are the same as those in Part A. This time, imagine that the passengers on the other spaceship are watching your clock as its ticks off one second. Rank the figures according to how much time the passengers (on the other ship) would say passes (on their ship) while they watch your clock tick off one second, from the shortest to the longest amount of time.
Shortest: speed = 0.7c speed = 0.75c speed = 0.8c Longest: speed = 0.85c The passengers on the other ship must observe the same effects on you as you observe on them, because both of you are in free-float reference frames and there is no way to say who is "really" moving. In other words, just as you say time is running slow on their ship, they say time is running slow on your ship. That is why the answer here is the same as the answer in Part A.
Consider again the spaceships from Parts A and B. Suppose that, at rest, both you and a passenger on the other spaceship have the same heart rate of 60 beats per minute. How will you and the passenger on the other spaceship observe each other's heart rates as you pass by in your spaceships?
You would observe that the passenger in the other spaceship has a slower heart rate than you do, and she would observe that you have a slower heart rate than hers. Strange as it may sound, you will claim that time is running slow on her spaceship while she will claim that time is running slow on your spaceship. This is an example of what Einstein told us when he discovered that measurements of time and space are relative.
