- #1
sergiokapone
- 302
- 17
The Maxwell's equations in vacuum leads to the wave equations for the fields of the form
[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?
[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?