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Presenting Author:          Neil Ashby

Institution:                    Dept. of Physics
UCB 390, University of Colorado
                                Boulder, CO 80309-0390 

Abstract Title:               Relativity in the Global Positioning System

Body                     The Global Positioning System (GPS) provides a superb opportunity to discuss special and general relativity in an elementary way, as there are many relativistic effects that can be related to a few fundamental principles with simple    arguments.  The principles needed include the first and second postulates of special relativity, particularly the constancy of the speed of light c, and the weak principle of equivalence.  Thought experiments using the constancy of c lead directly to the relativity of simultaneity, the first-order Doppler effect, time dilation, and the Sagnac effect.  Then the principle of equivalence leads to the gravitational effect on clock frequencies.  In the GPS all these effects are large.  Also, GPS data from many receivers is widely available on the world-wide-web, and can be downloaded and analyzed by anyone with sufficient patience to develop his or her own software.  This provides opportunities for nontrivial projects, as well as for new applications to be developed and tested. 


Presenting Author:          John Belcher

Institution:                    Kavli Center for Astrophysics and Space Research
37-695 MIT
Cambridge, MA 02139 

Abstract Title:       Visualizing Gravitational Radiation:  Can Dynamic Line Integral Convolution Help?


Body                       Line integral convolution (LIC) is a technique introduced by Cabral and Leedom (1993) for visualizing the spatial structure of two dimensional vector fields at a resolution close to the resolution of the display.  Sundquist (2003) has developed a way to extend LIC visualization to time dependent vector fields (DLIC).  In particular, he has used the DLIC technique to make movies of electromagnetic electric dipole radiation that show the details of the time dependent structure of that radiation in the near, intermediate, and far zone, at a resolution close to the resolution of the display.  Examples of these DLICs can be found on the web through links at  The purpose of this poster is to acquaint the GR community with the existence of this technique, to show examples of it, and to solicit input as to whether this technique can be used to visualize gravitational radiation. 


Presenting Author:        Steven Carlip

Institution:                    UC Davis
Physics Dept. One Shields Ave.
                                           Davis, CA 95616 

Abstract Title:               General Relativity in a "Physics for Nonscientists" Course

Body     UC Davis offers a "Topics in Physics for Nonscientists" course with an emphasis that changes from year to year.  I describe an attempt to teach general relativity, using Thorne's Black Holes and Time Warps as a text and assigning a final essay   rather than an exam.  The goal was for students to learn both some qualitative features of general relativity -- what does it mean that spacetime is "four dimensional" and "curved," what is the principle of equivalence, what is an event horizon, how might we detect gravitational waves, etc. -- and something about how theoretical physics works -- how physicists approach new questions, what kinds of patterns we look for, how we view the "aesthetics" of physics, what roles experiment and theory play, etc.


Presenting Author:          Soumya Chakravarti

Institution:                   California State Polytech. University Pomona
3801 W. Temple Ave
Pomona CA 91768 

Abstract Title:               Ten Weeks with Uncle Albert

Body     I present an outline of a course on GR being designed for seniors and juniors of my department, keeping in mind their varied backgrounds and abilities. The course will have a multi-layered and multi-level structure, incorporating in-class lectures and discussions, reading assignments, online research, and individual computational projects. I shall seek ideas and input from participants at the AAPT workshop.  


Presenting Author:          Wolfgang Christian

Institution:                            Department of Physics
                                                Davidson College
                                                Davidson NC 28035-6926

Additional           Mario Belloni, Davidson College
Authors           Anne Cox, Eckerd College

Abstract Title:               Open Source Physics Curriculum Material for Teaching Relativity

Body     There are many reasons to create computer-based material for relativity.  Special and general relativity are full of (apparent) paradoxes, and, like quantum mechanics, captivate students’ interest in physics.  Because relativity focuses on abstract concepts, visualization is especially valuable.  This poster will report on the development of new Open Source Physics (OSP) simulations and curricular material created for the exploration of relativity. Examples, including the gravitational red shift and the trajectories of particles and light rays in the vicinity of non-spinning and spinning black holes, will be available on CD. OSP is an NSF-funded curriculum development project that is developing and distributing a code library, programs, and examples of computer-based interactive curricular material.  The OSP code library, documentation, and sample curricular material can be downloaded from

Partial funding for this work was obtained through NSF grant DUE-0442581.


Presenting Author:          Tevian Dray

Institution:                    Oregon State University
Dept of Mathematics, Oregon State University
Corvallis OR 97331 

Abstract Title:               The Geometry of Special Relativity

Body     The Lorentz transformations at the heart of special relativity are just hyperbolic rotations.  We outline here how to use "hyperbolic triangle trig" to solve problems in special relativity.

Presenting Author:          David M Harrison

Institution:                    Dept. of Physics, Univ. of Toronto
60 St. George St.
Toronto, ON M5S 1A7 Canada 

Abstract Title:               A Voluntary Straitjacket: Teaching General Relativity without Mathematics

Body     In 1975 Bohm remarked that “Our mathematical procedures seem to obscure our intuitive and imaginative understanding.” For the past few decades I have been exploring ways to discuss General Relativity with undergraduate students without using any mathematics whatsoever. Instead, I have used pictures, words, analogies, and anything else I could think of. These discussions have been with both Physics majors and non-science liberal arts students. As is common, although I believe many of my students have learned a great deal, I have certainly learned much more by forcing myself to re-think this topic in a non-mathematical way.


Presenting Author:          Mark Haugan

Institution:                    Department of Physics
Purdue University,
                                           West Lafayette, IN 

Abstract Title:       Improving Undergraduates’ Readiness to Learn General Relativity

Body     In thinking about the resources that undergraduate students’ could bring to a course on general relativity (GR), I will   focus on a sound understanding of the special relativistic physics and mathematics of dynamics and of spacetime structure. 
     Students encounter this material in courses on mechanics and on electromagnetism and in units, or entire courses, devoted to special relativity (SR).  Unfortunately, there is ample evidence that most students do not develop a coherent understanding of SR and relativistic dynamics from traditional instruction.  For example, Scherr, Shaffer and Vokos (2002) and references therein document profound student difficulties that survive traditional SR instruction.  More informally, John Bell (1987) recounts an amusing and disturbing anecdote about the difficulties that his CERN colleagues of the late 1970’s had with a problem involving two rockets connected by a thread.  Matsuda and Kinoshita (2004) report similar difficulties among their colleagues. 
     What accounts for such difficulties?  Bell suggests, I think rightly, that they stem from the failure of traditional instruction to relate dynamical explanations of the structure and behavior of physical systems, including rulers and clocks, to the structure and behavior of physical systems implied by axiomatic presentations of SR.  This failure deprives students of a valuable resource for learning, namely, their sense of mechanism, and it leaves individuals who do master axiomatic SR, like Bell’s colleagues, struggling to reconcile their dynamical and kinematical understandings of relativistic physics. 
     Bell argues that to link these understandings one ought to analyze the structure and behavior of physical systems moving through a given inertial coordinate system to obtain dynamical accounts of kinematical effects like Lorentz contraction.  Since such analyses can be technically demanding, my poster explores other ways of realizing Bell’s vision of a linked dynamical/kinematical approach to learning SR.  In particular, I discuss the how linking students’ dynamical and kinematical understanding of Galilean relativity can be a major step toward a correspondingly linked dynamical and kinematical understanding of SR.  Note that innovative introductory physics curricula like Matter and Interactions, Chabay and Sherwood (2006), provide the somewhat unusual conceptual and technical resources that students need in order to learn SR in this new way.  Bohm remarked that “Our mathematical procedures seem to obscure our intuitive and imaginative understanding.” For the past few decades I have been exploring ways to discuss General Relativity with undergraduate students without using any mathematics whatsoever. Instead, I have used pictures, words, analogies, and anything else I could think of. These discussions have been with both Physics majors and non-science liberal arts students. As is common, although I believe many of my students have learned a great deal, I have certainly learned much more by forcing myself to re-think this topic in a non-mathematical way.

Bell, J.; 1987, ‘How to teach special relativity’ in Speakable and unspeakable in quantum mechanics, Cambridge. 
Chabay, R. and Sherwood, B.; 2006, Matter & Interactions, Wiley. 
Matsuda, T. and Kinoshita, A.; 2004, AAPPS Bull. 14, 3. 
Scherr, R.; Shafer, P. and Vokos, S.; 2002, Am. J. Phys. 70, 1238. 

Presenting Author:          Russell L. Herman

Institution:                    UNC Wilmington
601 S College Road
Wilmington, NC 28403

Abstract Title:       Lessons on Teaching Undergraduate General Relativity and Differential Geometry Courses

Body     We describe the course content and lessons learned teaching simultaneously offered courses to undergraduate physics and mathematics majors. A subset of students took both courses. The general relativity course was offered in the physics curriculum and focused more on the physics with standard mathematics prerequisites. The differential geometry course aimed at the geometry of curves and surfaces ending with a study of Cartan's equations and applications to computing curvatures in general relativity.  


Presenting Author:        Charles H. Holbrow

Institution:                   AAPT,
                                         College Park, MD

Abstract Title:              AAPT Topical Workshops

Body      This poster describes how the American Association of Physics Teachers is adopting some Gordon Research Conference practices for workshops that AAPT is organizing to be of particular interest to physics faculty in universities and colleges. The poster also points out features of the AAPT workshops that are quite different from those of a GRC. The inaugural AAPT topical workshop is an intensive two-day consideration of "Teaching General Relativity to Undergraduates" at Syracuse University on July 20 and 21, 2006. Supported by LIGO, AAPT, The Center for Gravitational Wave Physics at Penn State, and by the Syracuse Department of Physics, this workshop is bringing together fifty faculty who either have been teaching or aspire to teach GR to undergraduates. The participants will share their wide range of views of how this can best be done, and they will develop three model syllabi - one to teach GR with its full mathematical apparatus; one in which the solutions to Einstein's equations are taken as given and their physical significance is explored in depth; and one to convey important concepts of GR to students who want only a general acquaintance with the subject.


Presenting Author:        Savitri V. Iyer

Institution:                   SUNY Geneseo
                               Geneseo, NY

Abstract Title:              General Relativity at SUNY Geneseo

Body     As in many undergraduate programs, the typical physics major at SUNY Geneseo graduates without much exposure to gravitational physics beyond Newton's law of gravitation and Kepler's laws.  Students read about topics like black holes and cosmology mainly through popular expositions.  In the last few years, however, we have seen a growing interest in and enthusiasm for learning more about gravity.  This was clearly evident in an experimental course offering titled "GRAVITY: An Introduction to Einstein's General Relativity" in spring 2006.  We will present some ideas for course organization and teaching techniques, and student responses to an end-of-semester feedback survey.  We will also present our experience with involving undergraduates in research in general relativity at SUNY Geneseo.


Presenting Author:        Loretta Johnson

Institution:                   Kalamazoo College
                               Kalamazoo, MI

Abstract Title:              Experimental Tests of General Relativity:  What Students Need to Know

Body     Experimental results and experimental apparatus are fantastic ways to connect an abstract theory like general relativity with the tangible and physical with which many students are interested and familiar.  However, undergraduate students are likely not prepared to appreciate either results or apparatus without considerable assistance.  Some textbooks may provide adequate explication.  If the text does not, then either the professor will need to select some experiments to discuss in considerable detail, or the professor may assign learning about an experiment to each student and then allow the students to teach one another.  Professors who choose to teach undergraduates about experiments must bear in mind that these students are likely to have surprisingly weak understandings of apparatus and surprisingly little experience and ability to interpret graphs.  General relativity courses offer opportunities for faculty to introduce students to diverse apparatus and to enhance students’ abilities to read and interpret graphs.


Presenting Author:         Jean P. Krisch

Institution:                    The University of Michigan
Dept. of Physics; 450 Church Street
Ann Arbor, MI 48109 

Abstract Title:               GRavity in the Curriculum

Body     The poster to be presented at the GR Conference preceding the 2006 Summer Meeting in Syracuse presents details of
                gravity in the physics curriculum at the University of Michigan.

Presenting Author:          Shane L. Larson

Institution:                    Penn State University
104 Davey Lab, Box 033, Dept of Physics/Gravity
University Park, PA 16802
Additional           Deirdre M. Shoemaker
Authors            Dept. of Physics, Penn State University
William A. Hiscock,
Dept. of Physics, Montana State University

Abstract Title: Empowering Undergraduates with General Relativity: Stepping stones to build research skills

Body     While many calculations in general relativity require intimate knowledge of the theory, there are a large number of problems which can be reduced to calculations which exploit physics and skills that undergraduates possess or are in the process of developing.  These types of problems provide excellent opportunities to reinforce early lessons in fundamental physics by giving students an opportunity to apply their knowledge and practice their skills against the exciting backdrop of a modern and evolving branch of physics.  They also provide well defined problems for exercising and developing skills useful in later research endeavors (e.g., numerical programming).  This poster describes the elements of undergraduate training which we have found can be tapped and applied to good effect in undergraduate GR research projects.  Several real life examples which have led to publications in peer reviewed research journals are described to illustrate the basic philosophy we advocate.

Presenting Author:         Dwight E. Neuenschwander

Institution:                    Southern Nazarene University
6729 N.W. 39th Expressway
Bethany, OK 73008

Abstract Title:               General Relativity Education at Southern Nazarene University, 1989-present

Body     On alternate years since 1989, I have taught GR for physics majors at SNU.  Prerequisites include Special Relativity, the inertia tensor, Poisson’s equation, partial derivatives.  From the Principle of Equivalence and Einstein’s interpretation of gravity as curvature, with the introduction of tensors and covariant derivatives we develop the Principle of General Covariance, applied at once to the freely-falling particle.  We next develop Einstein’s Field Equations, derive the Schwarzschild metric, and calculate the deflection of starlight and precession of perihelia.  We also explore the Friedmann-Robertson-Walker metric of cosmology.  Today our GR program includes a three-course sequence: Special Relativity, Black Holes Seminar, and PHYS 4311-2, General Relativity.  Local research experience includes student-authored papers in AJP and JURP.  One SNU student holds an internship at Stanford University this summer with Gravity Probe B.  Another GR teaching resource may be mentioned: articles published in the SPS Observer by the Society of Physics Students.

Presenting Author:          Louis J. Rubbo

Institution:                    Penn State University/Center for Gravitational Wave Physics
Department of Physics, 104 Davey Lab, PMB 56
University Park, PA 16802
Additional           Shane L. Larson
Authors          Penn State University/Center for Gravitational Wave Physics
Michelle B. Larson
Penn State University/Center for Gravitational Wave Physics

Abstract Title: Hands-On Gravitational Wave Astronomy: Extracting astrophysical information from simulated signals

Body     Observational astronomy stands at the threshold of an era where gravitational wave detectors are a tool that regularly contributes important information to the growing body of astrophysical knowledge.  Detectors such as LIGO and LISA will probe different regimes of the gravitational wave spectrum and observe sources that radiate at different gravitational wavelengths. Unlike their cousins, traditional electromagnetic telescopes, gravitational wave detectors are not imaging instruments.  How then does a gravitational wave astronomer take the output from a detector and extract astrophysical information about the emitting sources?  In this poster we introduce an activity in which students extract astrophysical information from a simulated gravitational wave signal. The process described mimics the way true gravitational wave analysis will be handled by using plots of a pure gravitational wave signal. The students directly measure the properties of the simulated signal, and use the measurements to evaluate standard formulae for astrophysical source parameters.

Presenting Author:         Roberto B Salgado

Institution:                    Syracuse University
Dept. of Physics
Syracuse, NY 

Abstract Title:               New Ideas for Teaching Relativity: Space-Time Trigonometry

Body     We present the foundations for a unified treatment of three planar geometries used in physics: Euclidean space, Galilean spacetime, and Minkowskian spacetime. Following I.M. Yaglom, using techniques familiar from the analytic geometry and trigonometry of Euclidean space, we develop the corresponding analogues for Galilean and Minkowskian spacetimes and suggest extensions to the constant-curvature de-Sitter space-times. We comment on how this unified treatment suggests a faithful visualization of tensors and their algebra [consistent with the pictorial representations in Schouten, Misner-Thorne-Wheeler, and Burke]. We feel that this provides a new geometric framework for teaching relativity.

Presenting Author:         Donald T. Schnitzler

Institution:                    Linfield College
900 SE Baker Street
McMinnville, OR 97128
          James Lindberg

Abstract Title:       Time Dilation Merry-Go-Round

Body     Understanding the twin paradox and resolving it thoroughly is an important first step for students beginning the study of general relativity.  The complete presentation of this topic given here is designed around a thought experiment that involves an easily visualized acceleration and deceleration of one of the twins relative to an inertial frame such that the twins are at rest together in the same inertial frame at start and finish.  It shows the calculations of the time that has passed for each twin according to the one remaining in the inertial frame and according to the one who travels.  Both twins agree that the one who traveled is younger at finish.  Motional and gravitational time dilation effects interplay to bring about this agreement.  A merry-go-round whose motion is governed by an explicit formula is used so that values of velocity, acceleration, gravitational potential, and proper time can be compared graphically at all places throughout the trip.

Presenting Author:         Slavomir Tuleja

Institution:                   Gymnazium arm. gen. L. Svobodu
Komenskeho 4
Humenne 066 51 Slovakia 

Abstract Title:               Orbits of particles and light around non-spinning and spinning black holes.

Body     An interactive JAVA program plots orbits of test particles and light flashes in the equatorial plane of a non-spinning (Schwarzschild) and a variable-spin (Kerr) black hole. The software displays either the time-development of an orbit or the entire orbit over extended time. In the latter case the orbit changes instantly and continuously as the operator varies initial conditions. For the spinning Kerr black hole, the display shows the ergosphere (in which no particle can remain at rest) as well as the outer horizon and inner (Cauchy) horizon. The operator can use alternative global coordinate systems appropriate to the given black hole: Schwarzschild, Boyer-Lindquist, Gullstrand-Panlevé, and Doran. The interactive time-dependent display complements the static, analytic presentation of textbooks.


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