Teaching general relativity to undergraduates

eneral relativity lies at the heart of a wide variety of exciting astrophysical and cosmological discoveries made during the past decade or so. Whereas in 1919 Arthur Eddington was allegedly at a loss to name a third person who understood general relativity, presently its knowledge and use are widespread. We have come a long way in a century. Perhaps the most compelling of the new results is the 1998 discovery that not only is the universe expanding, but the expansion is accelerating. The 2011 Nobel Prize in Physics was awarded for observations of high-redshift supernovae whose distance and brightness revealed the accelerated expansion and therefore showed that the cosmos is filled with “dark energy” (see PHYSICS TODAY, December 2011, page 14). Observations of the cosmic microwave background have also provided evidence for dark energy—and for nonluminous dark matter. Because the revolution in the scientific community’s understanding of the universe has been widely reported, undergraduate students are interested in learning more about cosmology. New astrophysical observations are also piquing students’ curiosity. Astronomers observe supermassive black holes in the centers of galaxies, including our own Milky Way. We now recognize that neutron stars are abundant in our galaxy and that they provide the basis for extreme and intriguing astrophysical phenomena. The Laser Interferometer Gravitational-Wave Observatory and the Virgo interferometer are expected to see gravitational waves within a few years. That discovery will be an important confirmation of general relativity in its own right; moreover, the gravitational waves will provide a new means to view the universe and will reveal relativistic events in regions shielded from electromagnetic observation. General relativity is also important close to home. Gravity Probe B, which had been orbiting Earth, recently observed frame-dragging and geodetic effects predicted by general relativity. The global positioning system, which students regularly use, requires general relativity to ensure its meter-scale accuracy (see the article by Neil Ashby in PHYSICS TODAY, May 2002, page 41). In a way that was not true even two decades ago, general relativity has become an issue of practical concern to mainstream physicists and even engineers.1