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4 vectors

  1. May 3, 2009 #1
    1. The problem statement, all variables and given/known data
    I am aving a bit of trouble understanding how to show something is a 4 vector. For example K = (v/c, 1/lamdba, 0, 0 ) Show it is a 4-vector. I am not quite sure how to start this.
    Similarly I have the amplitude of a wave in frame S described as A=cos[2PI(vt-x/lambda)] and need to show that the amplitude of te wave in S' can be written as cos[2PI(v't'-x'/lambda')


    2. Relevant equations



    3. The attempt at a solution
    I am not sure how to do the first part

    My attempt at the second part
    vt-x/lambda
    = vct/c - x/lambda
    =v/c(gamma(ct'+beta x')) -1/lambda *gamma(x'+beta ct')
    =ct' gamma(v/c-beta/lambda)-x'gamma (1/lambda-beta v/c)
    using a similar question in my notes but I don't think this is right and I don't know how it helps???
     
    Last edited: May 3, 2009
  2. jcsd
  3. May 3, 2009 #2
    I think we do this question by showing that K transforms by a Lorentz transformation (since the definition of a 4 vector is a 4 component vector that transforms under Lorentz transformations).

    When you do this, you'll see K'=(v'/c, 1/lambda',0,0), once you substitute in what you got for v' and 1/lambda' in the previous part. You got the same values for these as I did, by the way so I think they are correct. I'm pretty sure this is all you have to do to show it transforms by LT. Someone please correct me if I'm wrong.
     
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