2 Responses

  1. Frank Munley

    Dear Ms. Wortel,

    I’m writing to you concerning your 2007 article in the American Journal of Physics (with Malin and Semon) titled “Two examples of circular motion for introductory courses in relativity.” I am particularly interested in Section VI on Thomas precession. In that section, you state: “It is important to remember that Thomas rotation and Thomas precession are observed by the traveling twin and not by the Earth twin…” Most other authors say just the opposite! I would like to submit that both views are right, depending on the perspective. To explain, consider the simplest explanation of Thomas precession ascribed to the late E.M. Purcell, in which an observer (the “traveler”) travels around a regular polygon of N sides, i.e., an N-gon. Purcell’s approach is described in the appendix to Richard Muller’s “Thomas precession: Where is the torque?” in AJP, vol. 60 (4), 1992, pp. 313-317. In this approach, Lorentz contraction of the “straight-ahead” component of the next leg of the N-gon requires the traveler to turn not through an angle of (2pi)/N, but through (2pi)*gamma/N, where gamma is 1/(1 – v^2/c^2)^1/2 and is always greater than 1. The scenario involves an “inertial bar” which points along the direction of travel along the starting leg of the N-gon. The properties of this inertial bar are such that when the traveler turns through an angle, the bar’s orientation changes with respect to the traveler by this angle. True, when the traveler turns through an angle of 2pi, its direction of travel is again aligned with the direction of the bar, and only in this sense is Thomas precession not observed by the traveler. But it takes an angle of 2pi*gamma for the traveler to get back to the starting point, because N turns, each of 2pi*gamma/N, must be made. When this point in the trip is reached, the traveler is back at the starting point, and in this sense the rod is not aligned with the direction of travel. Indeed, the rod is angled at precisely the value given by Thomas precession, i.e., the traveler does observe it, as does the laboratory (or stay-at-home) observer.

    I found Muller’s article most fascinating, especially his explanation of how a real physical torque causes the precession for a gyroscope. But he says nothing about torque on the inertial bar, and I will query him on it.

    I would be interested in your response. I will e-mail the above remarks to Drs. Malin and Semon also.

    Sincerely yours,

    Frank Munley
    Associate Prof. emeritus, Roanoke College

  2. Frank Munley

    Ms. Wortel,

    My apologies–I overlooked the fact that your paper uses Purcell’s argument. But I still believe your conclusion is wrong about the absence of Thomas precession in the lab frame. I should add that I am writing to you on your blog because I don’t have an e-mail address for you. And I have written to Drs. Malin and Semon concerning my question. One final note: I enjoyed reading your blog above on “Curiosity.”

    –Frank Munley

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