Can the polarization bound charge density be expressed in vacuum by a wave function?

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Discussion Overview

The discussion centers around the concept of expressing polarization bound charge density in vacuum through a wave function, particularly in the context of electromagnetic wave propagation. It explores theoretical aspects of electromagnetic fields, including the electric field, magnetic field, and electric displacement field.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the feasibility of expressing polarization bound charge density in vacuum, noting that there are no bound charges in vacuum.
  • Another participant elaborates on the theoretical framework involving monochromatic plane electromagnetic waves and the solutions to the wave equation.
  • The discussion includes the relationship between the electric field $$\vec{E}$$, magnetic field $$\vec{B}$$, and electric displacement field $$\vec{D}$$, particularly regarding their wave equations and the potential for complex exponential solutions.
  • There is a proposal to consider the possibility of linear harmonic polarization in vacuum, with a caution against prematurely dismissing it without thorough analysis.
  • Participants seek clarification on terms like "disruptive polarization" and "non-disruptive polarization," indicating a need for definitions and proof of claims made about the differences between $$\vec{D}$$ and $$\vec{E}$$ in vacuum.

Areas of Agreement / Disagreement

Participants express differing views on the existence of bound charges in vacuum and the implications for polarization. There is no consensus on the definitions of disruptive and non-disruptive polarization, nor on the validity of the claims regarding the wave equations for $$\vec{D}$$ and $$\vec{E}$$.

Contextual Notes

The discussion lacks clear definitions for key terms and concepts, which may lead to misunderstandings. There are unresolved questions regarding the nature of polarization in vacuum and the mathematical treatment of the fields involved.

south
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TL;DR
I ask the question assuming that vacuum polarization does not always require the presence of large potentials or large energy densities.
Can the polarization bound charge density be expressed in vacuum by a wave function?
 
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Maybe you can give some more background on your question. In vacuum, there are no bound charges. So it is not clear what you mean.
 
Thanks DrDu for your help. I'll try to expand.

Nothing practical. Just theory. Monochromatic plane EM wave propagating in vacuum. The wave equation in this case admits a sinusoidal solution, a cosinusoidal solution, and a complex exponential solution.

In EM propagation, the electric field $$\vec{E}$$, the magnetic field $$\vec{B}$$, and other fields, such as the electric displacement $$\vec{D}$$, which interests me particularly, undulate.

When there is no circular or elliptical polarization, the wave equations of $$\vec{E}$$ and $$\vec{B}$$ do not admit the complex exponential solution. Does the wave of the field $$\vec{D}$$ admit this solution?

The answer depends on considering vacuum polarization impossible or possible for any frequency greater than zero. Vacuum disruptive polarization does not occur at any frequency. And what about a non-disruptive polarization, let's say linear harmonic polarization?

I don't dare to deny in advance the possibility of a linear harmonic polarization of the vacuum, without analyzing the subject carefully and in sufficient detail.
 
south said:
When there is no circular or elliptical polarization, the wave equations of ##\vec{E}## and ##\vec{B}## do not admit the complex exponential solution. Does the wave of the field ##\vec{D}## admit this solution?
Why do you believe this is true? Can you prove it? What exactly do you think the difference is between ##\vec{D}## and ##\vec{E}## in vacuum?
south said:
Vacuum disruptive polarization does not occur at any frequency. And what about a non-disruptive polarization, let's say linear harmonic polarization?
Please define "disruptive polarization" and "non-disruptive polarization".
 
renormalize said:
Why do you believe this is true? Can you prove it? What exactly do you think the difference is between ##\vec{D}## and ##\vec{E}## in vacuum?

Please define "disruptive polarization" and "non-disruptive polarization".
The conversation has veered into demands that are beyond my reach. I beg your pardon for not being able to continue. Thank you very much and best regards.
 
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