Ambiguity of electrostatic polarization?

[Jano L.]

Hello everybody,

I have a doubt about the section of the Wikipedia page on the polarization:

https://en.wikipedia.org/wiki/Polarization_density

especially the section in the end where the writer claims the polarization is ambiguous.

In the example about Alice, the writer states that the pairing of +/- particles is ambiguous and hence the polarization is ambiguous. I think he incorrectly interprets the meaning of the polarization.

The writer even states that Alice can back up her strange pairing procedure by ascribing the crystal surface a non-zero density of (free!) charge. This is ridiculous. The crystal is a dielectric and there is no free charge. All polarization comes from displacements of the bound charges. There will be only bound surface charge.

I think the proper way to define the polarization of the crystal at $\mathbf x$ is to average the dipole moments of the smallest neutral cells k hitting the averaging volume V, which is centred at $\mathbf x$. The polarization is then

$$\mathbf P(\mathbf x) = \frac{1}{V} \sum_k \mathbf \mu_k$$


What do you think - is not this unambiguous definition?

 

[eljose79]

Thank you for bringing up this topic. As a scientist studying polarization, I can offer some clarification on this issue. The Wikipedia page on polarization density is correct in stating that polarization is ambiguous in certain cases. This is because polarization is a vector quantity and can have different directions depending on the chosen reference frame. In the example of Alice, the writer is trying to highlight the fact that the choice of reference frame can affect the perceived polarization of the crystal.

However, I do agree with you that the statement about Alice ascribing a non-zero density of free charge to the crystal is incorrect. As you mentioned, the polarization in a dielectric material comes from the displacement of bound charges and there is no free charge present.

Your proposed definition of polarization, as an average of dipole moments within an averaging volume, is a valid and unambiguous definition. This is commonly used in the study of polarization in materials and is in line with the general understanding of polarization in the scientific community.

In conclusion, while the Wikipedia page may have some ambiguous statements, the concept of polarization as a vector quantity and its dependence on reference frame is a valid and important aspect to consider. Thank you for bringing this up and for offering a clear and precise definition of polarization.