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Unclear approximation in relativistic calculation of particle's distance travelled

  1. Sep 20, 2014 #1
    From "Martin & Shaw", regarding problem 3.5 (sometimes it uses natural units "c=1"):

    "The particle has [itex]\gamma = E/m \approx 10[/itex], hence [itex]\tau \approx c[/itex] (?) and the average distance is [itex]d \approx c \gamma \tau \approx 3 \times 10^{-14}m[/itex] if we assume a lifetime for the particle at rest of [itex]10^{-23}[/itex]."

    I don't understand why [itex]\tau \approx c[/itex].
    Since [itex]v = c \sqrt{1 - \frac{1}{\gamma^2}}, v = 0.994 c[/itex] and I would agree that [itex]v \approx c[/itex], not [itex]\tau[/itex].
  2. jcsd
  3. Sep 20, 2014 #2


    Staff: Mentor

    Hmm, I am with you on that. In natural units where c=1 you get energy and mass in the same units, but not speed and time.
  4. Sep 20, 2014 #3


    User Avatar

    Staff: Mentor

    It's probably a typographical error, and it was supposed to say ##v \approx c##. That gives his result for the average distance: ##d = vt = v \gamma \tau \approx c \gamma \tau##.
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