On July 20 and 21, 2006 the AAPT held a Topical Conference at Syracuse
University on Teaching General Relativity to Undergraduates. Why? Because
the time has arrived to incorporate special and general relativity fully into
the general physics curriculum. If you need to be convinced, consider that
the equivalence principle works so well it is almost obscene, GPS fails when
GR is ignored, gravitational red-shift is a fact, the Hulse-Taylor Binary
Pulsar is producing gravitational waves, gravitational lensing exists, the
expansion of the universe is essential for cosmological nucleosynthesis
(which produced the lighter elements H, He, Li, etc), supermassive black holes
in galactic centers appear to be the norm rather than the exception, and the
Laser Interferometer Gravitational-Wave Observatory is near its design
operation. Let us not forget that Dirac's great prediction of antimatter
came about after he merged the physics that is spacetime with quantum
mechanics. Although not a reason for inclusion in physics courses, it is
remarkable that Einstein's 
is an icon of popular culture, and no
doubt recognized by more people than Newton's 
. As always, knowing
why relativity should be incorporated is one thing, knowing how is
an entirely different matter.
This conference was my first introduction to the increasingly hot pursuit of pedagogically sound models and curricula for teaching relativity at the popular, high school, and undergraduate levels. I learned that one does not have to be a relativity expert to participate fully. In fact, one of the goals is to develop a curriculum that does not require such expertise (for the simple reason that we cannot expect schools to have a relativist on staff). Another goal is to streamline delivery of the mathematics of relativity so as to deliver the ``goods'' that the students want to study and that educators want to teach: black holes, gravitational waves, cosmology, and so on.
Pearson Addison-Wesley and Cambridge University Press provided participants with desk copies of five of their important GR textbooks. The authors of four of these texts, Jim Hartle, Bernard Schutz, and Edwin Taylor, were in attendance, and we were able to ``pick their brains'' and get first-hand accounts of their texts. Broadly speaking, most of the books reflect two different approaches: math first or physics first. The notable exception is a new text by Schutz which is designed for a general audience; namely, students who are taking their first (and perhaps only) physics course. The math first approach develops the mathematical foundations (tensors and differential geometry), introduces the Einstein equations, and then provides applications. In the physics first approach, applications occur first and only after key physics concepts are encountered do the mathematical underpinnings and Einstein equations appear. Understanding of gravity as a curved spacetime phenomenon is acquired via analysis of specific solutions to the Einstein equations (such as those for black holes, gravitational waves, and cosmology). Loosely speaking, we can think of math first as going from the general to the specific, and physics first as the other way around.
The speakers were well chosen, their presentations were fascinating, and the discussions afterward and in breakout sessions were captivating. My desire for teaching relativity was invigorated, and I came away truely optimistic about the possibilities. Jorge Pullin gave a very good review of the central ideas of relativity (without inundating us with complicated mathematics) for participants who were new to teaching a GR course. Jim Hartle presented his rationale for the physics first approach. He has found that students can understand many GR physical effects quickly if they have some knowledge of mechanics. He emphasized that the structure of a course on GR very much depends on the context of where it is delivered: Who will teach it? How much time is available? What is the target audience? Tom Moore, who has a remarkable wealth of experience in teaching relativity to undergraduates, discussed ways in which the mathematics of GR can be more easily grasped by the students. For example, he has found that basic concepts can be effectively presented via analysis of two-dimensional metrics, such as using non-Cartesian coordinates for the flat-space metric and exploring the metric properties of the sphere. His experience also shows that students need lots of drilling on index manipulation.
While Neil Ashby and Rai Weiss talked seriously about GPS and observation and experiment in GR, respectively, they also gave us some really juicy tabloid tidbits. We learned from Neil Ashby that while GR corrections were available to GPS, the necessary circuitry was not turned on initially (maybe because a highly placed, powerful individual was not convinced the corrections were needed). After the satellites were in orbit, it was, more or less, immediately determined that the system was not working. Only after the GR circuits were switched on, did GPS live up to its promise. As they say in football: ``Score!'' Rai Weiss regaled us with his personal experiences of learning and teaching relativity and performing experiments that test GR. While preparing to teach relativity for the first time (in the Sixties), he spent some time studying the existing data. In his own inimitable style, he expressed his, shall we say, disappointment--OK, it was disgust--with what he found for, say, measurements of light deflection by the Sun.
A major point that was emphasized several times is that there should be significantly expanded discussion of acceleration in special relativity. Even among professional physicists there is a common misconception (first created, apparently, by Einstein himself) that GR is needed to really understand acceleration. It was pointed out, however, that we have no conceptual difficulties with accelerations in elementary particle scattering, so why should we have a problem when applying it to, say, the twin paradox? Even better, Don Marolf showed how one can use acceleration in special relativity to understand salient features of horizons in GR.
While Marolf's talk indirectly addressed the misconception about acceleration, Peter Saulson's talk was a direct rebuttal of another, which is the misconception that laser interferometry cannot be used to detect gravitational waves. The incorrect reasoning says there will be no interference because a passing gravitational wave will stretch and squeeze the legs of the interferometer and the light in the same way. Of course, analysis based on GR and the Maxwell theory is uneqivocal; there is interference.
Finally, the talk of Stamatis Vokos had, perhaps, the most to say about roots of misconceptions of relativity. He and his colleagues have done rigorous studies on how students go about absorbing, processing, and applying what they learn in a relativity course. At the most basic level they have found that a student's understanding of simultaneity is crucial for learning relativity.
The main message of the conference is clear: there is much work to be done, but Relativity will soon rise out of the abyss of undergraduate syllabus topics that are labeled ``Time Permitting.'' The call is out and a concerted effort is in place. If you want to help, now is the time to act. As a matter of fact, I have a personal request: I am the editor of a new section on relativity that is to be put together for the ComPADRE project. It is a web-based network of educational resources supporting teachers and students in physics and astronomy (see http://www.compadre.org/portal/index.cfm). Bruce Mason, a P.I. of the project, visited the conference and spoke briefly about ComPADRE's basic philosophy, current status, and future goals. For those who would like to have their materials on relativity made available, please send an e-mail to comergl@slu.edu with (1) a link to the site, (2) the target students, or level of the course, and (3) a two or three sentence description.
The AAPT was assisted by LIGO/Caltech, the NSF Physics Frontier Center for Gravitational Wave Physics at Penn State, and the Syracuse University Department of Physics. Finally, many thanks go out to the Organizing Committee for producing such an excellent meeting: Michelle Larson (Chair), James Hartle, Charles Holbrow, Dale Ingram, Richard Price, Peter Saulson, John Thacker, and Stamatis Vokos. To learn more about results from the workshop go to http://www.aapt-doorway.org/TGRU.htm. Workshop posters, slides from presenters' talks, and workshop proceedings can all be found there.