Energy of an electromagnetic wave

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Discussion Overview

The discussion revolves around the relationship between the energy of electromagnetic (EM) waves as described by classical wave theory and quantum mechanics. Participants explore how energy is represented in both models and the apparent contradictions that arise from their different perspectives.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant notes that according to the wave model, the energy in an EM wave is proportional to the energy in the electric (E) and magnetic (B) fields, which can vary.
  • Another participant asserts that in quantum mechanics, the energy of a photon is proportional to the frequency of light, suggesting that the energy of an EM wave is the sum of the energies of many photons.
  • A later reply questions the perceived contradiction, indicating that the wave and photon descriptions refer to different aspects of EM energy.
  • One participant explains that for a large number of photons, the average number per unit volume can be related to the classical electric and magnetic field strengths through energy per unit volume.
  • Another participant initially suggests that a plane wave could transport energy without energy per unit volume, but later corrects themselves, stating that energy per unit volume is indeed necessary and is proportional to E² + B².

Areas of Agreement / Disagreement

Participants express differing views on the relationship between the classical and quantum descriptions of EM wave energy, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about energy per unit volume and the conditions under which the wave and photon models apply. The relationship between the classical and quantum descriptions is not fully reconciled.

rmberwin
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I'm trying to teach myself some basic physics, and so maybe this question is stupid! But according to the wave model, the energy in an EM wave is proportional to the energy in the E and B fields, which can assume a range of values, no? But according to the quantum model, the energy of a photon is simply proportional to the frequency of the light. There seems to be a contradiction here. What am I missing?
 
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The basic answer is that Quantum Mechanics is ultimately correct. An EM wave is made up of many photons, each of which has a discrete, quantized energy value, so the energy of an EM wave is the sum of the energy of every photon.
 
But according to the wave model, the energy in an EM wave is proportional to the energy in the E and B fields, which can assume a range of values, no? But according to the quantum model, the energy of a photon is simply proportional to the frequency of the light. There seems to be a contradiction here. What am I missing?

Could you please state more carefully where do you see the contradiction? The two sentences talk about different things; the wave and the photon.
 
For a system with a very large number of photons (any macroscopically measurable electromagnetic field), you can relate the average number of photons per unit volume to the strength of the classical electric and magnetic fields via the energy per unit volume.
 
although, there doesn't need to be any energy per unit volume. There could just be a plane wave which is transporting energy, which has zero energy per volume.

But yeah, I think that is the rough idea. The energy of a classical EM wave is given by both the frequency of the wave and the amplitude of the electric and magnetic fields. So, we can relate the frequency of the wave to the frequency of each of the photons, and the amplitude of the fields to the number of photons per volume.

edit: wait, no sorry, that's totally incorrect. there does need to be energy per unit volume, which is proportional to E2+B2
 

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