Electromagnetic field in a medium

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Discussion Overview

The discussion revolves around the behavior of electromagnetic fields, specifically plane waves, in a medium and how these fields transform when observed from a moving reference frame. Participants explore the implications of refraction indices and the relativistic Doppler effect on frequency and wave characteristics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents the electromagnetic field in a medium as E = E0cos(ωt-kx) and questions the transformation of this field in a moving reference frame with v = c/n.
  • Another participant suggests that the combination (ωt-kx) is Lorentz invariant and will transform to (ω't'-k'x').
  • A later reply corrects the previous statement regarding the frequency, asserting that the new frequency ω' is not zero and is determined by the relativistic Doppler effect, which depends on the velocity v relative to c.
  • There is a suggestion that if ω and k are connected via c and n>1, there should exist a reference frame where the frequency ω' becomes zero, indicating a potential misunderstanding or disagreement on the implications of the transformations.

Areas of Agreement / Disagreement

Participants express differing views on the transformation of frequency in a moving reference frame, with some asserting that ω' should be zero while others argue it is determined by the relativistic Doppler effect. The discussion remains unresolved regarding the implications of these transformations.

Contextual Notes

Participants do not fully agree on the conditions under which the frequency ω' becomes zero, and there are unresolved assumptions regarding the relationship between ω, k, and the refractive index n.

Bob_for_short
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An electromagnetic field, as a plane wave, has a known space-time dependence:

E = E0cos(ωt-kx).

In a transparent medium it is the same except for involving the refraction indices n.

Now, let us look at the field in a moving reference frame - that with v = c/n. What solution is for the wave in such a frame? Isn't it

E' = E'0cos(ω't') ?
 
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Isn't it a challenging exercise?
 
The combination (ωt-kx) is a Lorentz invariant and so will transform to (ω't'-k'x').
 
Meir Achuz said:
The combination (ωt-kx) is a Lorentz invariant and so will transform to (ω't'-k'x').

Sorry, I meant cos(k'x'). In this moving reference frame the new frequency ω'=0, isn't it?
 
Last edited:
Bob_for_short said:
Sorry, I meant cos(k'x'). I this moving reference frame the new frequency ω'=0, isn't it?
No. Omega' is given by the usual relativistic Doppler in terms of v/c, which in your case would be 1/n.
 
Meir Achuz said:
No. Omega' is given by the usual relativistic Doppler in terms of v/c, which in your case would be 1/n.

Strange. As soon as ω and k are connected via c and n>1, there should be the reference frame with the zero frequency ω'.
 

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