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Help with deriving Lorentz Factor

  1. Feb 24, 2008 #1
    1. The problem statement, all variables and given/known data
    I am trying to show how the Lorentz factor is derived but i am unsure how to get past a certain stage..
    2. Relevant equations/ attempt
    Let:
    c = velocity of light.
    v = the velocity as observed from where time t is measured.
    D = distance AB.
    t = time light occupies to pass from A to B.
    t1 = time light occupies to return from B to A.
    Firstly we can see that
    t= D/(c+v)
    And
    t1= D/(c-v)
    So for the total distance,
    t+t1=D/(c+v)+D/(c+v)
    Make a common denominator and add the two fractions,
    t+t1=(D(c-V)+D(c+v))/((c+v)(c-v))
    Expand the brackets,
    (Dc+Dv+Dc-Dv)/(c^2+cv-cv-v^2)
    Simplify, cancel out where possible,
    (2Dc)/(c^2-v^2)
    And take out the factor of 2D
    t+t1=2D(c/(c^2-v^2)) or 2D(1/(c-(v^2/c))
    ( I am unsure whether or not taking it that far is right yet..)

    Above is where i have arrived and the next step i am supposed to arrive at..
    2D (c^2 / (c^2 - v^2)) = 2D (1 + (v^2 / c^2)]

    Any help asap please?

    thankyou
     
  2. jcsd
  3. Feb 24, 2008 #2
  4. Feb 25, 2008 #3

    Fredrik

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    Staff Emeritus
    Science Advisor
    Gold Member

    What's A and B? Are they events? Points in space? Wouldn't this make t=t1?

    I'm not sure what you're doing, but this looks wrong.
     
  5. Feb 25, 2008 #4
    It doesn't matter now, i decided to start over using a light clock idea, and it seemed to work perfectly. Thanks anyway
     
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