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Determining components of 4-velocity

  1. Oct 9, 2012 #1
    1. The problem statement, all variables and given/known data

    A particle of mass m follows the spacetime trajectory x(τ) = (Aτ, Bτ , C cosτω, C sinτω ).

    What is the 4-velocity u(τ)? Why must A =sqrt[1+B^2+(ωC)^2]
    

    2. Relevant equations

    u(τ)=dx(τ)/dτ , u^2 = -c^2

    3. The attempt at a solution

    so I took the derivative of each comp of x with respect to tau and got:

    u(τ)=(A, B , -ωCsinτω, ωCcosτω)

    and 4-velocities always square to -c^2

    so -A^2 +B^2 +(ωC)^2 = -c^2, which gives A =sqrt[c^2+B^2+(ωC)^2]

    Why is my answer wrong?
     
  2. jcsd
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