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Electromagnetic wave equation not invariant under galilean trans.

  1. Feb 11, 2013 #1
    1. The problem statement, all variables and given/known data
    Prove that the electromagnetic wave equation: 
    (d^2ψ)/(dx^2) + (d^2ψ)/dy^2) + (d^2ψ)/(dz^2) − (1/c^2) * [(d^2ψ)/(dt^2)]= 0 is NOT invariant under Galilean transformation. (i.e., the equation does NOT have the same form for a moving observer moving at speed of, say, v in the x direction).

    *note: all the "d"s in this equation are the partial derivatives.


    2. Relevant equations
    galilean transformation:
    t'=t, x'=x-vt, y'=y, z'=z

    3. The attempt at a solution
    -from what i understand to solve this involves the chain rule for partial derivatives.
    -looking at the equation i cant help but jump to something with the gradient of ∇ψ, but i dont know where to go from there.
     
  2. jcsd
  3. Feb 11, 2013 #2

    mfb

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    Staff: Mentor

    The y,z,t components in the equation just stay the same, you can ignore them. You just have to change the x-component.
    Hint: It will get an additional t-component afterwards.
     
  4. Feb 11, 2013 #3
    d/dx(dψ/dx' * dx'/dt + dψ/dt' * dt'/d(something)) ?
     
  5. Feb 11, 2013 #4
    wait is it d/dx(dψ/dx' * dx'/dx + dψ/dt' * dt'/dx), which equals d/dx(dψ/dx' * 1 + dψ/dt' * 0)?
     
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