Electromagnetic wave energy density

[Plane Wave]

An electromagnetic plane wave has an electric field and a magnetic field. Each component contributes equally to the energy density. Mathematically it is very straight forward to show this is true.

The question is, "Fundamentally, why is this true?" Again, I'm not looking for a derivation. There are no issues with the math, just interpreting the physics from the math. With such a beautiful symmetry there must be a fundamental reason why.

 

[mfb]

Without eletric charges, there is an exact symmetry between electric and magnetic fields (check Maxwell's equations in gaussian units with ρ=0 and j=0). There is no way to make the contributions different.

 

[Plane Wave]

As I said, I can do the math.

The question is why is there an exact symmetry.

Is your answer that there is simply no reason for there not to be an exact symmetry?

 

[mfb]

Physics is not about "why". We observe a symmetry, physics can describe this symmetry. But physics cannot explain why our laws of physics are that way.

I am sure you could develop some alternative theory without that symmetry. It would have to look different, and it disagrees with observations, but it would be a possible theory for other/alternative universes (if they exist) or whatever.

 

[Enthalpy]

Take a standing wave, small enough: at some times it contains only electrical energy and at other times only magnetic energy, so both are equal.

A propagating wave is a sum of two standing waves.