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On of the reasons I have come to UArk is to sit at the feet of some great professors and maybe learn quantum mechanics.
One of my new mentors is also a good friend, Bill Harter, who has a very original way of looking at both relativity and quantum mechanics. He believes that the mysteries and secrets of relativity are complementary to the mysteries and secrets of quantum mechanics. The secrets of one solve the mysteries of the other.
After a graduate course in relativity taken close to forty years ago and having thought about it and taught it at the undergraduate level for over thirty years, I'm only beginning to understand this myself. To explain it to you and my students, I must bring you along the path that I have traveled.
My close friend and former officemate at City College, Lew Epstein, wrote a book that has helped me a great deal. Relativity Visualized is still in print and available in some bookstore. The following development is thus influenced by both of my friends.
In the Modern Family development, I have chosen to view the same event from three frames of reference. Of course, only two frames of reference are essential, but in my own thinking I have found that having only two perspectives leads to a prejudice that one way of looking at it is really better than the other. This may seem silly to one who has mastered relativity, but it is a prejudice that was shared by most physicists a hundred years ago. So I choose to look at things from several points of view.
Further, one of the central points of relativity is that, no matter how you speed up, you can never exceed the speed of light. So, with three frames of reference, we can consider the addition of velocities.
I start with a discussion of simultaneity and the traditional light clock, deriving the time dilation in the usual way. I then use Lew Epstein's flashlight to relate the light clock to length contraction.