Electromagnetic wave energy density

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Discussion Overview

The discussion centers on the energy density of electromagnetic waves, specifically exploring the symmetry between electric and magnetic fields and the fundamental reasons behind this symmetry. Participants are not seeking mathematical derivations but rather a conceptual understanding of the underlying physics.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that both electric and magnetic fields contribute equally to the energy density of an electromagnetic wave, prompting a question about the fundamental reason for this symmetry.
  • Another participant points out that in the absence of electric charges, Maxwell's equations exhibit an exact symmetry between electric and magnetic fields, suggesting that the contributions cannot differ.
  • A participant questions whether the symmetry exists simply because there is no reason for it not to be present.
  • One participant argues that physics describes observed symmetries but does not provide explanations for why the laws of physics are structured in that way, suggesting the possibility of alternative theories that lack this symmetry.
  • Another participant introduces the concept of standing waves, indicating that at certain times, a standing wave can contain only electrical energy or only magnetic energy, thus supporting the idea of equal contributions over time.

Areas of Agreement / Disagreement

The discussion remains unresolved with multiple competing views on the fundamental reasons for the symmetry between electric and magnetic fields in electromagnetic waves.

Contextual Notes

Participants express varying perspectives on the nature of symmetry in physics, with some suggesting that alternative theories could exist, while others emphasize the limitations of current understanding regarding the "why" behind observed symmetries.

Plane Wave
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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.
 
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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.
 
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?
 
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.
 
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.
 

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