1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lorentz-Invariance of Photons travelling parallel to each other

  1. Dec 5, 2014 #1

    VVS

    User Avatar

    1. The problem statement, all variables and given/known data
    Show the Lorentz-Invariance of the following spatial statement: Two photons are travelling parallel to each other. The relative position vector of the two photons is orthogonal to the velocity and has length d.

    2. Relevant equations / The attempt at a solution
    The first thing that comes to my mind is to represent the two photons with 4-Momentum Vectors.
    So this is done the following way:
    [itex]p_1=\hbar k=\hbar \left(\omega,k,0,0\right)[/itex]
    [itex]p_2=\hbar k=\hbar \left(\omega,\alpha k,0,0\right)[/itex]
    Now I need a 4-vector that connects the two photons. It is easy to see that the spatial component of that vector is just
    [itex]\vec{d}=\left(0,0,d\right)[/itex]
    But I am not sure what the first (time) component of that corresponding 4-vector would be?
    From here on I guess it is simple. All I need to do is show that under a Lorentz-Transformation for arbitrary [itex]\vec{v}[/itex] the four-momentum of the photons is always orthogonal to the relative position vector. I might be wrong here.
     
    Last edited: Dec 5, 2014
  2. jcsd
  3. Dec 5, 2014 #2

    MathematicalPhysicist

    User Avatar
    Gold Member

    What you wrote is antiparallel, i.e the direction reversed.

    Parallel would be multiplying by a positive factor the expression k.
     
  4. Dec 5, 2014 #3

    VVS

    User Avatar

    Thanks you're right. I edited it.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted