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Student Understanding of Time in Special Relativity: Simultaneity and Reference Frames

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Student Understanding of Time in Special Relativity: Simultaneity and Reference Frames 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, WA 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. relativistic kinematics in the laboratory I. INTRODUCTION frame.1 We wanted to expand this research There is growing national interest in base to relativity in order to provide a guide increasing the exposure of students in for the development of instructional 2,3 introductory courses to modern physics materials by ourselves and others. topics, such as relativity. Proponents of This article reports on an investigation enlarging the scope of the curriculum argue of student understanding of time in special that in the beginning of the 21st century the relativity. A major purpose is to identify content of introductory classes should reflect and characterize the conceptual and some of the major intellectual breakthroughs reasoning difficulties that students at all of the 20th century. Others hold that the list levels encounter in their study of special of topics that must be covered is already too relativity. The emphasis is on the relativity daunting. Physics education research can of simultaneity and the role of reference play a pivotal role in this debate. Whether frames. We found that, after instruction, students first encounter modern physics many students are unable to determine the concepts at the introductory level or in time at which an event occurs, recognize the advanced courses, it is important to identify equivalence of observers at rest relative to what students can and cannot do after one another, and apply the definition of instruction and what steps can be taken to simultaneity. We illustrate the process help deepen their understanding of the through which we gradually obtained a material. In addition, analyzing the ways in detailed picture of student thinking by the which students undergo the transition design and successive refinement of a set of between understanding phenomena to which research tasks. they have immedia te access and understanding phenomena that lie outside II. PRIOR RESEARCH their everyday experience can help us There is currently only a small body of identify reasoning skills that are needed for research on student understanding of the study of advanced topics. relativity, mostly in Galilean contexts (in Over the last five years, the Physics particular, relative motion). In many cases, Education Group at the University of the research tasks used (e.g., multiple -choice Washington has been investigating student questions or single questions given to a understanding of key ideas in Galilean, small number of students) do not provide the special, and general relativistic kinematics. kinds of insights that are necessary to Extensive research has already been understand the prevalent modes of student conducted on student understanding of non- reasoning and to develop effective Student understanding of time in special relativity Scherr, et al. 1 instructional strategies. We review salient III. FOCUS OF THE RESEARCH results from relevant investigations. A major goal of the investigation was to Galilean relativity determine the extent to which students, after Investigations of physics undergraduates instruction, are able to apply basic ideas of in India have identified the belief that special relativity to simple physical reference frames have limited physical situations. The context is one spatial extent. Studies by Panse et al. and Ramadas dimension. The concepts probed are et al. suggest that, for many students, frames summarized below. of reference have limited physical extent. The construct of a reference frame is at Students claim that a body can “emerge” the heart of relative motion. Most courses in from the reference frame of an object by special relativity begin with a discussion of leaving the vicinity of the obje ct (e.g., “a a reference frame as a system of observers ball can be thrown to ‘go outside’ a (or devices) by which the positions and 4 reference frame”). times of events are determined. An investigation by Saltiel and Understanding the concept of a reference Malgrange has identified difficulties with frame forms the foundation for relative motion among eleven-year-old- understanding any topic in special relativity. children and first- and fourth-year university It provides the basis for the determination of 5 students in France. The three groups all kinematical (and other physical) showed little difference in error rates to quantities and serves as the framework for written questions. Many students tended to relating measurements made by different identify an object’s motion as intrinsic, not a observers. The concept of a reference frame quantity that is measured relative to a presupposes an understanding of more basic reference frame. Students tended to make a measurement procedures. For clarity in the distinction between “real” motion, which discussion that follows, we review the basic has a dynamical cause, and “apparent” operational definitions associated with motion, which is “an optical illusion, devoid reference frames, i.e., the determination of of any physical reality.” the position and time of an event and the Special relativity conditions under which two events are Villani and Pacca have demonstrated treated as simultaneous.10 that university students’ reasoning in An event in special relativity is relativistic contexts is similar to that associated with a single location in space observed by Saltiel and Malgrange in and a single instant in time. The position of 6 Galilean contexts. A case study by Hewson an event is defined to be the coordinate label with a physics graduate student illustrated on a rigid ruler at the location of the event. the importance of “metaphysical beliefs” The ruler is envisioned to extend indefinitely (e.g., time is absolute) to his understanding from some chosen origin.11 The time of an 7 of special relativity. The student ni the event is most naturally defined as the study classified certain relativistic effects reading on a clock located at the event’s (including length contraction) as distortions position at the instant at which the event of perception. Posner et al. report similar occurs. The rulers and clocks used by any results in interviews with introductory observer are at rest relative to the observer. 8 students and their instructors. All observers in special relativity are O’Brien-Pride has conducted interviews assumed to be “intelligent observers” who and administered early versions of some of use synchronized clocks. To determine the the research tasks described here in which time of a distant event, an observer corrects university students appear to believe that the for the travel time of a signal originating at order of events depends on observer the event.12,13 Inertial observers at rest 9 location. Her preliminary results provided relative to one another determine the same impetus for the investigation detailed in this positions and times for events (and hence paper. the same relative ordering of events). Such Student understanding of time in special relativity Scherr, et al. 2 observers are said to be in the same A. Student populations 14 reference frame. Most of the research was conducted at Events are defined to be simultaneous in the University of Washington in courses that a given frame if their corresponding time include special relativity. The study has readings are identical, according to the involved about 800 students from about 30 definition of the time of an event discussed sections of various courses. The populations above. A judgment of the simultaneity of include: non-physics students (in the widely separated events necessarily includes descriptive course for non-majors students); an appropriate definition of the time of a introductory students (in the introductory 15 distant event. The invariance of the speed calculus-based honors course and in the of light has an inevitable and unsettling sophomore-level course on modern physics); implication. Two events at different students in the junior-level courses on locations that occur at the same time in a electricity and magnetism and relativity and given frame are not simultaneous in any gravitation; and students in our upper- other frame. division course for prospective high school The relativity of simultaneity is among physics teachers.16 We also present results the key results of special relativity and one from physics graduate students at the that is particularly difficult to grasp, as University of Washington who participated evidenced by the numerous “paradoxes” that in interviews and others who were given a arise from it. It is not reasonable to expect written question on a graduate qualifying that students (even those facile with examination. In addition, the investigation mathematical formalism) will master all the includes students in the honors section of the intricacies of the counterintuitive results that calculus-based course at one of the other follow from the operational definition of research universities and advanced simultaneity. In this study, we considered a undergraduate students from the other meaningful understanding of relativistic collaborating university. We found that simultaneity to include the ability to identify student performance from all three relevant events, to determine the time at universities was similar. The results, which an event occurs (by correcting for therefore, have been combined.17 signal travel time), and to recognize that the time interval between two events is not B.
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