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Please check my Lorentz Transforms

  1. Oct 14, 2008 #1
    1. The problem statement, all variables and given/known data

    At x = x' = 0 and t = t' = 0, a clock ticks on a fast spaceship (gamma = 100). The captain of the ship heads it tick again 1.0 s later. Where and when do we (the stationary observers) measure the second tick to occur?

    2. Relevant equations

    [tex]t = \frac{t'}{\gamma}[/tex]
    [tex]x' = \gamma(x - vt)[/tex]
    [tex]\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]

    3. The attempt at a solution

    First, I solve for velocity.
    [tex]v = c\sqrt{1 - \frac{1}{100}^2} = 0.9995c[/tex]

    Next, solve for t when t' = 1.
    [tex]t = \frac{t'}{\gamma} = \frac{1}{100} sec[/tex]

    Finally, solve for x'.
    [tex]x' = \gamma(x - vt) = 100(0 - (0.9995c)(\frac{1}{100})) = 0.9995c [/tex]

    Have I answered this correctly? Thanks.
  2. jcsd
  3. Oct 15, 2008 #2
    The spaceship is defined as the moving object, so proper time is measured on the Earth. Time appears to be going slower for the spaceship. So we could write that:

    [tex]t_{earth} = \gamma t_{spaceship}[/tex]

    Sam :smile:
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