The Maxwell's equations in vacuum leads to the wave equations for the fields of the form(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\nabla^2 \vec E = \frac{1}{c^2} \frac{\partial ^2 \vec E}{\partial t^2}[/itex]

(the same for the magnetic field)

Such equations are Lorentz-invariant.

Let's consider now the electromagnetic field in a homogeneous medium.

Field in a medium subject to a rate lower than in vacuum [itex]v=c/n[/itex], where [itex]n=\sqrt{\epsilon\mu}[/itex] and the equations have the form:

[itex]\nabla^2 \vec E = \frac{\epsilon\mu}{c^2} \frac{\partial ^2 \vec E}{\partial t^2}[/itex]

But such equations are obviously not Lorentz-invariant. Why is this a paradox?

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# Lorent-invariance of the Maxwell's equations in the medium

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