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Proving that Maxwell's equations for the propagation of electromagnetic wave are Lorentz invariant

  1. Jul 20, 2015 #1
    I want to know how can i prove that Maxwell's equations for the propagation of electromagnetic wave are Lorentz invariant.
     
  2. jcsd
  3. Jul 20, 2015 #2

    Mentz114

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  4. Jul 20, 2015 #3
    Yes, this give me a clear understanding on both the lorentz and maxwell. Thank you
     
  5. Jul 20, 2015 #4

    vanhees71

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    Puh, that looks complicated ;-)). It's much easier to reformulate Maxwell's equations in manifestly covariant form with four-vectors and four-tensors. Then you immideately see, without to preform the pretty time-consuming Lorentz transformations, because then it's clear that the equations are covariant by construction!
     
  6. Jul 21, 2015 #5
    Can you elaborate on what you are talking about....
     
  7. Jul 21, 2015 #6

    Mentz114

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    Here is an introduction https://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism.

    When equations are written in tensor form then invariance under certain transformations is 'built-in'.

    Transformed tensor contractions eg ##v^a v_a \rightarrow \Lambda v^a {\Lambda}^{-1} v_a ## do not change because contravariant components transform with the inverse of the transformation of the covariant ones.

    For instance ##f_{\alpha} = F_{\alpha\beta}J^{\beta}## is manifestly covariant because ##F## and ##J## are tensors. The contraction ##f^\alpha f_\alpha## is unaffected by a Lorentz transformation.
     
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