Recent work by Scherr, and her collaborators determined student-held beliefs about the relativity of simultaneity and created paper-and-pencil exercises to help aid student understanding of relativity.  Their research, which goes hand-in-hand with commentary by others reveals that the teaching of introductory special relativity should focus less on the Lorentz transformations and more on the relativity of simultaneity, length contraction, and time dilation.  Several textbook authors have already taken this approach.   A focus on Lorentz transformations can obscure the fact that special relativity is about spatial and temporal intervals and not about single position measurements and clock readings.  In addition, an approach based on spatial and temporal intervals leads to the metric in special and general relativity while Lorentz transformations do not.

In our experience, pencil-and-paper exercises alone are often insufficient to aid student understanding of abstract ideas, such as those in special relativity.  We believe that the level of visualization and interactivity of carefully constructed Physlet-based exercises offers students a distinct learning advantage over such traditional exercises.  While there are other computer programs that simulate phenomena in special relativity, most notably Spacetime and RelLab, Physlets are free for noncommercial use and Physlet-based curricular material can be written to specifically target concepts that students find difficult.  Because our material is Web-based, it is flexible enough to be adapted to a variety of pedagogical strategies and local environments.  Finally, since Physlet-based material exists for all topics in introductory physics, students can use Physlet-based material throughout the course, rather than being forced to become familiar with numerous software packages.

For special relativity, we have incorporated the results from Scherr’s physics education research into our development of several interactive Physlet-based exercises that focus on visualizing the relativity of simultaneity, length contraction, time dilation, and spacetime diagrams.  These exercises can be used as interactive reading assignments, in-class demonstrations, interactive tutorials, and as part of an introductory physics laboratory in special relativity. The material described in this paper and the laboratory version of these exercises can be found at A brief description of each exercise follows.


[1] M. H. Dancy, W. Christian, and M. Belloni, “Teaching with Physlets®: Examples From Optics,” Phys Teach. 40, 40 (Nov. 2002).
[2] W. Christian and M. Belloni, Physlets: Teaching Physics with Interactive Curricular Material (Prentice Hall, Upper Saddle River, NJ, 2001). See also:
[3] W. Christian and M. Belloni, Physlet® Physics: Interactive Illustrations, Explorations, and Problems for Introductory Physics (Prentice Hall, Upper Saddle River, NJ, 2004).
[4] A. J. Cox, M. Belloni, W. Christian, and M. H. Dancy, “Teaching Thermodynamics with Physlets® in Introductory Physics,” Phys. Ed. 38, 433 (September 2003).
[5] R. E. Scherr, P. S. Shaffer, and S. Vokos, “The Challenge of Changing Deeply Held Student Beliefs about the Relativity of Simultaneity,” Am. J. Phys. 70, 1238 (2002).
[6] R. E. Scherr, P. S. Shaffer, and S. Vokos, “Student Understanding of Time in Special Relativity: Simultaneity and Reference Frames,” Phys. Educ. Res., Am. J. Phys. Suppl. 69, S24 (2001).
[7] A. J. Malincrott, “Relativity Theory Versus the Lorentz Transformations,” Am. J. Phys. 61, 760 (1993).
[8] N. D. Mermin, “Lapses in Relativistic Pedagogy,” Am. J. Phys., 62 11 (1994).
[9] E. F. Taylor and J. A. Wheeler, Spacetime Physics: An Introduction to Special Relativity, 2nd ed. (W. H. Freeman and Company, New York, 1992).
[10] K. Krane, Modern Physics, 2nd ed. (John Wiley and Sons, New York, 1997).
[11] T. A. Moore, Six Ideas That Shaped Physics, Unit R: The Laws of Physics are Frame-Independent, 2nd ed. (McGraw-Hill, New York, 2003).
[12] T. A. Moore, A Traveler’s Guide to Spacetime: An Introduction to the Special Theory of Relativity, 2nd ed. (McGraw-Hill, New York, 1995).
[13] See M. Belloni and W. Christian, “Physlets for Quantum Mechanics,” Comp. Sci. Eng. 5, 90 (2003) for our Force Concept Inventory (FCI) and Quantum Mechanics Visualization Instrument (QMVI) data that support this conclusion.
[14] P. Horwitz, E. F. Taylor, and P. Hickman, “‘Relativity Readiness’ Using the RelLab Program,” Phys. Teach. 32, 81 (Feb. 1994).
[15] Another way to do this is to synchronize all of the clocks at the location of the master clock and then slowly move all of the clocks into place, so that we do not incur any time-dilation errors due to their transport. An animated version of this method can be found on our website.
[16] E. F. Taylor and J. A. Wheeler, Exploring Black Holes: An Introduction to General Relativity (Addison Wesley Longman, New York, 2000).
[17] For all of the algebra, either visit the full exercise on our website or see pages 26-29 of Ref. [10].
[18] In “An Introduction to Space-Time Diagrams,” Am. J. Phys. 65, 476 (1997), Mermin suggests that the axes in spacetime diagrams are not necessary and are actually a source of confusion for students.
[19] The Open Source Physics code library, documentation, and curricular material can be downloaded from the website: