A Mathematically Sound Introduction to Relativity for Math, Physics and Astronomy Majors

4. Additional Topics

In addition to the introductory subjects mentioned above, we also explore several other topics. The twin paradox is studied using spacetime diagrams. We also use this setting to show the blueshift and redshift that results from high relative velocities. The three classical experimental results in support of general relativity are gravitational redshift, the precession of orbits, and the bending of light. We cover each of these topics after the Schwarzschild metric has been introduced. Gravitational redshift gets the least attention and is only briefly covered. However, we do spend a good bit of time studying orbits under the Shwarzschild metric. Unfortunately, several approximations are necessary in these calculations and in the computations for the precessions of orbits. Our theoretical results are compared to observational data and found to be in excellent agreement. With the results for orbits in hand, a quick calculation allows us to show the bending of light (more appropriately, the bending of spacetime) around a massive object and again the results can be compared to observational data. Finally, the topic of black holes is briefly covered, again making use of the Schwarzschild metric. In particular, the behavior of light cones near the event horizon are studied. The Foster and Nightingale text [3] provides nice quick coverage of this topic.

We also use Einstein's Relativity, The Special and the General Theory as a source for supplemental reading. See Figure 5. Although a book aimed at the general public, it still contains nice verbal explanations of the ideas which we mostly study quantitatively. The students also appreciate the fact that they get to read the original words of Einstein.

Finally, a homepage is set up for the class. I encourage students to find internet sources on special and general relativity (or black holes, or any other relevant topic) and I add links to them on the homepage. This prompts the students to search for resources outside of class and, on occasion, to see the class material as it is applied by working physicists.


Figure 5. Click here for the Random House homepage for the supplemental text.


Go to Section 5.