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Photonbundle in two different inertial frames

  1. Dec 5, 2014 #1

    VVS

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    1. The problem statement, all variables and given/known data
    A point P is emitting a bundle of photons. In inertial system I the opening angle of the bundle is [itex]d\Omega[/itex] which hits a plane at a distance R. The same process is being observed by an inertial frame I' moving wrt. I.
    Show that: [itex]R^2d\Omega=R'^2d\Omega'[/itex]

    2. Relevant equations / The attempt at a solution
    I know the general Lorentz boost is given by the boost matrix:
    [itex]L_v=\begin{bmatrix} \gamma & -\gamma v^T \\ -\gamma v & \mathbb{1}+\frac{\gamma^2}{1+\gamma}vv^T \end{bmatrix} [/itex]
    In two dimensions I can choose [itex]v=v\begin{bmatrix}cos(\theta) \\ sin(\theta)\end{bmatrix}[/itex]
    Then I can apply the Lorentz boost onto the origin [itex]\vec{0}[/itex], at the center of the plane [itex]\vec{R}[/itex] and the edge of the light bundle at the plane [itex]\vec{P}[/itex].
    To find the new angle [itex]d\Omega'[/itex] I can use the following equation [itex]d\Omega'=\frac{\left|\vec{P'R'}\right|}{\left|\vec{R'0'}\right|}[/itex]
    However there is a problem because of the relativity of simultaneity. I don't know how to go about it from here.
     
  2. jcsd
  3. Dec 10, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. Dec 10, 2014 #3

    rude man

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    I think this post belongs in the advanced physics forum.
     
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