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Student understanding of time in special relativity: Simultaneity and reference frames Rachel E. Scherr, Peter S. Shaffer, and Stamatis Vokos Department of Physics, University of Washington, Seattle, Washington 98195-1560 ͑Received 26 July 2000; accepted 2 January 2001͒ This article reports on an investigation of student understanding of the concept of time in special relativity. A series of research tasks are discussed that illustrate, step-by-step, how student reasoning of fundamental concepts of relativity was probed. The results indicate that after standard instruction students at all academic levels have serious difficulties with the relativity of simultaneity and with the role of observers in inertial reference frames. Evidence is presented that suggests many students construct a conceptual framework in which the ideas of absolute simultaneity and the relativity of simultaneity harmoniously co-exist. © 2001 American Association of Physics Teachers. ͓DOI: 10.1119/1.1371254͔ I. INTRODUCTION particular, relative motion͒. In many cases, the research tasks used ͑e.g., multiple-choice questions or single questions There is growing national interest in increasing the expo- ͒ sure of students in introductory courses to modern physics given to a small number of students do not provide the kinds topics, such as relativity. Proponents of enlarging the scope of insights that are necessary to understand the prevalent of the curriculum argue that in the beginning of the 21st modes of student reasoning and to develop effective instruc- century the content of introductory classes should reflect tional strategies. We review salient results from relevant in- some of the major intellectual breakthroughs of the 20th cen- vestigations. tury. Others hold that the list of topics that must be covered Galilean relativity: Investigations of physics undergradu- is already too daunting. Physics education research can play ates in India have identified the belief that reference frames a pivotal role in this debate. Whether students first encounter have limited physical extent. Studies by Panse et al. and Ra- modern physics concepts at the introductory level or in ad- madas et al. suggest that, for many students, frames of ref- vanced courses, it is important to identify what students can erence have limited physical extent. Students claim that a and cannot do after instruction and what steps can be taken body can ‘‘emerge’’ from the reference frame of an object by leaving the vicinity of the object ͑e.g., ‘‘a ball can be thrown to help deepen their understanding of the material. In addi- ͒ 4 tion, analyzing the ways in which students undergo the tran- to ‘go outside’ a reference frame’’ . sition between understanding phenomena to which they have An investigation by Saltiel and Malgrange has identified difficulties with relative motion among 11-year-old children immediate access and understanding phenomena that lie out- 5 side their everyday experience can help us identify reasoning and first- and fourth-year university students in France. The skills that are needed for the study of advanced topics. three groups showed little difference in error rates to written Over the last five years, the Physics Education Group at questions. Many students tended to identify an object’s mo- the University of Washington has been investigating student tion as intrinsic, not a quantity that is measured relative to a understanding of key ideas in Galilean, special, and general reference frame. Students tended to make a distinction be- relativistic kinematics. Extensive research has already been tween ‘‘real’’ motion, which has a dynamical cause, and conducted on student understanding of nonrelativistic kine- ‘‘apparent’’ motion, which is ‘‘an optical illusion, devoid of matics in the laboratory frame.1 We wanted to expand this any physical reality.’’ research base to relativity in order to provide a guide for the Special relativity: Villani and Pacca have demonstrated development of instructional materials by ourselves and that university students’ reasoning in relativistic contexts is 2,3 similar to that observed by Saltiel and Malgrange in Galilean others. 6 This article reports on an investigation of student under- contexts. A case study by Hewson with a physics graduate student illustrated the importance of ‘‘metaphysical beliefs’’ standing of time in special relativity. A major purpose is to ͑ ͒ identify and characterize the conceptual and reasoning diffi- e.g., time is absolute to his understanding of special relativity.7 The student in the study classified certain relativ- culties that students at all levels encounter in their study of ͑ ͒ special relativity. The emphasis is on the relativity of simul- istic effects including length contraction as distortions of perception. Posner et al. report similar results in interviews taneity and the role of reference frames. We found that, after 8 instruction, many students are unable to determine the time with introductory students and their instructors. at which an event occurs, recognize the equivalence of ob- O’Brien Pride has conducted interviews and administered servers at rest relative to one another, or apply the definition early versions of some of the research tasks described here in which university students appear to believe that the order of of simultaneity. We illustrate the process through which we 9 gradually obtained a detailed picture of student thinking by events depends on observer location. Her results provided the design and successive refinement of a set of research impetus for the investigation detailed in this paper. tasks. II. PRIOR RESEARCH III. FOCUS OF THE RESEARCH There is currently only a small body of research on student A major goal of the investigation was to determine the understanding of relativity, mostly in Galilean contexts ͑in extent to which students, after instruction, are able to apply S24 Phys. Educ. Res., Am. J. Phys. Suppl. 69 ͑7͒, July 2001 http://ojps.aip.org/ajp/ © 2001 American Association of Physics Teachers S24 basic ideas of special relativity to simple physical situations. universities. Fourteen instructors at our university and one The context is one spatial dimension. The concepts probed faculty member at each of the other universities have coop- are summarized below. erated with the Physics Education Group in this study. The construct of a reference frame is at the heart of rela- tive motion. Most courses in special relativity begin with a A. Student populations discussion of a reference frame as a system of observers ͑or devices͒ by which the positions and times of events are de- Most of the research was conducted at the University of termined. Understanding the concept of a reference frame Washington in courses that include special relativity. The forms the foundation for understanding any topic in special study has involved about 800 students from about 30 sec- relativity. It provides the basis for the determination of all tions of various courses. The populations include: non- kinematical ͑and other physical͒ quantities and serves as the physics students ͑in the descriptive course for non-majors͒; framework for relating measurements made by different ob- introductory students ͑in the introductory calculus-based servers. The concept of a reference frame presupposes an honors course and in the sophomore-level course on modern understanding of more basic measurement procedures. For physics͒; students in the junior-level courses on electricity clarity in the discussion that follows, we review some of the and magnetism and relativity and gravitation; and students in operational definitions associated with reference frames, i.e., our upper-division course for prospective high school phys- the determination of the position and time of an event and ics teachers.16 We also present results from physics graduate the conditions under which two events are simultaneous.10 students at the University of Washington who participated in An event in special relativity is associated with a single interviews and others who were given a written question on location in space and a single instant in time. The position of a graduate qualifying examination. In addition, the investiga- an event is defined to be the coordinate label on a rigid ruler tion includes students in the honors section of the calculus- at the location of the event. The ruler is envisioned to extend based course at one of the other research universities and indefinitely from some chosen origin.11 The time of an event advanced undergraduate students from the other collaborat- is most naturally defined as the reading on a clock located at ing university. We found that student performance from all the event’s position at the instant at which the event occurs. three universities was similar. The results, therefore, have The rulers and clocks used by any observer are at rest rela- been combined for corresponding classes.17 tive to the observer. All observers in special relativity are assumed to be ‘‘in- telligent observers’’ who use synchronized clocks. To deter- B. Research methods mine the time of a distant event, an observer corrects for the The research was conducted through the analysis of stu- 12,13 travel time of a signal originating at the event. Inertial dent responses to written questions and the analysis of inter- observers at rest relative to one another determine the same views with individual students. The written questions were positions and times for events ͑and hence the same relative posed on course examinations and on ungraded problems ordering of events͒. Such observers are said to be in the same given during class.18 In some classes the questions were ad- 14 reference frame. ministered before instruction on the relevant concepts; in Events are defined to be simultaneous in a given frame if other classes, the questions were administered after instruc- their corresponding time readings are identical, according to tion. Except where otherwise noted, no class was given the the definition of the time of an event discussed above. A same question twice.

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