Lesson 4: Time Dilation and the Twin Paradox
Despite thoughts to the contrary, all time is relative to an observer. That is, there is no such thing as absolute time. The observation that the time on a clock that is moving with respect to an observer seems to run slower than the time on a clock that is stationary with respect to said observer is called time dilation. Time dilation takes place whether the “clock” that we are observing is a watch, a bouncing spring, a pendulum or a solar eclipse since all time is relative to the observer and not absolute.
The central focus of this chapter is to understand that time is also a relative concept, like simultaneity, and to be able to use the time dilation formula correctly.
- Coming to understand that proper time is the time interval separating two events as seen by an observer for whom the events occur at the same time.
- Realizing that time dilation is simply a slowing down of time in a system as seen by an observer who is in motion with respect to said system.
- Knowing how to use the time dilation formula correctly and grasping that time is not an absolute concept.
One way to introduce time dilation is through the use of the twin paradox:
- Tell the Twin Paradox but in a way that makes it sound like a story and emphasize the possibility that physical time can flow differently for two people. See if students believe the story and their arguments.
For this class, it is important to foster a conceptual understanding of the formulas in special relativity by going through the derivation of the time dilation formula with students and assigning problems for groups of students to work through which will be taken up next class.
Also consider leading a debate around the Twin Paradox with the following question:
Click on the link below for a helpful simulation of time dilation.
Below is a video that clearly explains time dilation as the slowing down of clocks.
The following video establishes a conceptual understanding of time dilation.
The video below uses cartoons and does an excellent job of explaining the Twin Paradox.
The following video has acclaimed astrophysicist Neil DeGrasse Tyson explain the Twin Paradox and its relationship with time dilation.
Ask the following questions as a way of debriefing the lesson and to gauge their thought process and understanding of prior concepts:
- Suppose people were moving in a spaceship at nearly the speed of light. What would the passengers life expectancy be relative to the inertial frame of Earth versus their frame of reference on the ship? (Ans: They’re living life at slower rate, their normal life cycle takes an enormous amount of our time.)
- How was it possible to build a theory of time dilation if this phenomenon escapes our intuition?
- Hirsch, A., Stewart, C., Martindale, D, & Barry, M. (2011). Nelson Physics 12. Toronto: Nelson Thomson Learning