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Special Relativity Question

  1. Oct 29, 2011 #1

    bon

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    1. The problem statement, all variables and given/known data


    Two photons travel along the x-axis of S, with a constant distance L between them.
    Find the distance between them as observed in S' (standard config - i.e. moving with speed v in x direction wrt S)
    How is this result connected to the Doppler effect?


    2. Relevant equations



    3. The attempt at a solution

    So normally the distance would be lorentz contracted - right? So it would be L/gamma

    but i guess it is not here? and how is it related to doppler? any hints would be great ! thanks
     
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  3. Oct 31, 2011 #2

    Simon Bridge

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    What you see is a pair of photons pass S at speed c, S determines the distance to be L.

    S', at speed v wrt to S also sees the photons pass at speed c - what length will S' measure?

    Presumably S has timed them, S' gets the same time dilated, so the distance between the photons that S' measures is expanded.

    Reality check:
    imagine S and S' are both at x'=x=0 when the first photon arrives.
    in the time it takes for the second photon to arrive at S (still at the origin) S' has moved on and has yet to see the photon pass. He has to wait a bit longer for the second photon to pass... so he measures a longer time. Longer time, same speed, means longer distance.

    This also means that S' and S will disagree about the color of the photons - S' will decide the photons are a bit redder... in terms of the relativistic doppler shift, this is because the wavelength has expanded.
     
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