Proving Maxwell's Equations are Lorentz Invariant

Bakali Thendo
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I want to know how can i prove that Maxwell's equations for the propagation of electromagnetic wave are Lorentz invariant.
 
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Yes, this give me a clear understanding on both the lorentz and maxwell. Thank you
 
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!
 
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Can you elaborate on what you are talking about...
 
Bakali Thendo said:
Can you elaborate on what you are talking about...
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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