The challenge of changing deeply held student beliefs about the relativity of simultaneity

R. E.

Scherr

,

P. S.

Shaffer

, and

S.

Vokos

, “,” , – (July).

R. E. Scherr, “An investigation of student understanding of basic concepts in special relativity,” Ph.D. dissertation, Department of Physics, University of Washington, 2001 (unpublished).

For research by other investigators on student understanding of special relativity, see, for example,

A.

Villani

and

J. L. A.

Pacca

, “,” , – () and

A.

Villani

and

J. L. A.

Pacca

, “,” , – ().

For research by other investigators on student understanding of Galilean relativity, see, for example,

S.

Panse

,

J.

Ramadas

, and

A.

Kumar

, “,” , – ();

J.

Ramadas

,

S.

Barve

, and

A.

Kumar

, “,” , – ();

E.

Saltiel

and

J. L.

Malgrange

, “,” , – ().

Einstein considered and rejected a definition of simultaneity that is position dependent. See, A. Einstein, “On the electrodynamics of moving bodies,” in The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity (Dover, New York, 1952).

G.

Posner

,

K.

Strike

,

P.

Hewson

, and

W.

Gertzog

, “,” , – ();

P. W.

Hewson

, “,” , – ().

L. C. McDermott, P. S. Shaffer, and the Physics Education Group at the University of Washington, Tutorials in Introductory Physics (Prentice–Hall, Upper Saddle River, NJ, 2002).

For a description of the tutorial system at the University of Washington, see, for example,

P. R. L.

Heron

and

L. C.

McDermott

, “,” (), – ();

P. S.

Shaffer

and

L. C.

McDermott

, “,” , – ();

L. C.

McDermott

,

P. S.

Shaffer

, and

M. D.

Somers

, “,” , – ().

For an example of a presentation of the train paradox, see E. F. Taylor and J. A. Wheeler, Spacetime Physics (Freeman, New York, 1996), p. 62.

For an interesting historical analysis of the intellectual climate in Europe in which Einstein decided on a way to synchronize clocks, see

P.

Galison

, “,” , – ().

To appreciate the extent to which simultaneity is a concept that requires definition, it is important to separate, as Einstein did in his 1905 paper, local from distant simultaneity. (See the article in Ref. 5.) Two distant events are defined to be simultaneous if their time coordinates in a specific reference frame are identical. This definition presupposes a definition for the time coordinate of a single event in a reference frame—a coordinate most naturally defined as the reading on a clock located at the event’s position “at the instant at which the event occurs.” The concept of local simultaneity (the identification of the time of the event in question with the time that a local clock reads “at that instant”) is assumed, therefore, to be a notion that does not require definition. Furthermore, to establish a particular clock reading for an event as the time coordinate of the event throughout a whole reference frame, a measurement procedure for how time may be “spread over space” needs to be specified. Our approach is consistent with those described in other texts. See, for example, P. W. Bridgman, A Sophisticate’s Primer of Relativity (Wesleyan U.P., Middletown, CT, 1962) and A. B. Arons, A Guide to Introductory Physics Teaching (Wiley, New York, 1990).

For a discussion of various instructional strategies by the Physics Education Group, including elicit, confront, and resolve, see

L. C.

McDermott

, Oersted Medal Lecture: “,” , – () and

L. C.

McDermott

, Millikan Award Lecture: “,” , – ().

We are indebted to E. F. Taylor for numerous discussions that led us to incorporate the char marks into our instructional approach.

We did not use an approach based on the invariant interval $ds2,$ because in most courses on special relativity, time-like, space-like, and light-like intervals are discussed after the relativity of simultaneity.

The fact that the music will be Doppler shifted is something that is not germane to the logical structure of the tutorial. Few students raise the issue.

For a theoretical discussion of the circumstances under which encounters with new ideas produce dissatisfaction with an existing conception, see the last article in Ref. 3 and K. A. Strike and G. J. Posner, “A revisionist theory of conceptual change,” in Philosophy of Science, Cognitive Psychology and Educational Theory and Practice, edited by R. A. Duschl and R. J. Hamilton (SUNY Press, Albany, NY, 1992).

Cognitive disequilibrium and the approach toward equilibration is a major issue in developmental psychology. For examples of how children return to equilibrium through assimilation, accommodation, and adaptation, see J. Piaget, The Moral Judgement of the Child (Free Press, New York, 1965); B. Rogoff, Apprenticeship in Thinking: Cognitive Development in Social Context (Oxford U.P., New York, 1990); P. H. Miller, Theories of Developmental Psychology (Freeman, New York, 1993); A. N. Perret-Clermont, Social Interaction and Cognitive Development in Children (Academic, New York, 1980).

The conversation took place in a course for prospective high school science teachers. S1 and S3 are advanced undergraduate physics students; S2 is a first-year graduate student in physics. The course used an adaptation of the tutorial sequence that is being developed for Physics by Inquiry, a laboratory-based curriculum for the preparation of K–12 teachers, L. C. McDermott and the Physics Education Group at the University of Washington, Physics by Inquiry (Wiley, New York, 1996), Vols. I and II.

This conversation was recorded in a modern physics course in a California high school that served as a pilot site for the Events and reference frames and Simultaneity tutorials.

The interviews are discussed in Ref. 1. In addition to serving as a setting for probing student ideas about simultaneity, the interviews often helped us in identifying contexts and lines of questioning that might be effective as instructional strategies. These were eventually incorporated in the Events and reference frames and Simultaneity tutorials.

We have found each question to be useful in eliciting specific student difficulties. For a detailed discussion about the development of the questions, see Ref. 1.

An analysis based on the Lorentz transformations is given in Ref. 1.

The graduate student data are for the explicit version of the Spacecraft question, which is similar but not identical to the tutorial post-test (the location-specific version). See Ref. 1 for a detailed discussion of each version of the Spacecraft question.

For other examples in which undergraduate students perform, after tutorial instruction, as well as or better than graduate students without tutorial instruction, see the last article in Ref. 8. See also,

S.

Vokos

,

P. S.

Shaffer

,

B. S.

Ambrose

, and

L. C.

McDermott

, “,” , – (July);

B. S.

Ambrose

,

P. S.

Shaffer

,

R. N.

Steinberg

, and

L. C.

McDermott

, “,” , – ();

K.

Wosilait

,

P. R. L.

Heron

,

P. S.

Shaffer

, and

L. C.

McDermott

, “,” , – ().

For an example in another areas, see,

K.

Wosilait

,

P. R. L.

Heron

,

P. S.

Shaffer

, and

L. C.

McDermott

, “,” , – (July), and the last article in Ref. 8.

For other research by our group consistent with this statement, see, for example, the third article in Ref. 24.