[Bored chemist]

I understand what Hamdani is alluding to and it is something I have often thought about-permeability and permittivity are macroscopic properties derived fundamentally from the presence of charges in said material. Do they have a meaning at the atomic level?

You can calculate a refractive index from the relative permeability and permittivity.
That's a measure of how much light slows down as it passes through the material.
But light doesn't actually slow down,  simplistically, it gets "stuck" to the particles
So, on the microscopic level, a refractive index isn't well defined and thus nor is the permeability or permittivity.

On the other hand, I can say the plastic they make thin spectacle lenses from has a high refractive index because it's full of sulphur compounds and the sulphur is big and polarisable- the nuclei don't keep a very tight grip on the electrons so, a passing ray of light interacts strongly with the electrons and thus with the plastic.
That's a good enough model down to the atomic level or thereabouts

It's not a clear cut issue.

[hamdani yusuf]

I understand what Hamdani is alluding to and it is something I have often thought about-permeability and permittivity are macroscopic properties derived fundamentally from the presence of charges in said material. Do they have a meaning at the atomic level? Have to run now, working today, mv switchroom in a stinking meat plant-yuck.

Water has the same chemical composition, but different pressure and temperature can change its structure, which results in different electromagnetic properties, as shown in this article.

https://pubs.acs.org/doi/10.1021/jp105975c#
Dielectric Constant of Ices and Water: A Lesson about Water Interactions
J. L. Aragones, L. G. MacDowell, and C. Vega
Abstract

In this paper, the dielectric constant has been evaluated for ices Ih, III, V, VI, and VII for several water models using two different methodologies. Using Monte Carlo simulations, with special moves to sample proton-disordered configurations, the dielectric constant has been rigorously evaluated. We also used an approximate route in which proton-disordered configurations satisfying the Bernal−Fowler rules were generated following the algorithm proposed by Buch et al. (Buch, V.; Sandler, P.; Sadlej, J. J. Phys. Chem. B1998, 102, 8641), and the dielectric constant was estimated assuming that all configurations have the same statistical weight (as Pauling did when estimating the residual entropy of ice). The predictions of the Pauling model for the dielectric constant differ in general from those obtained rigorously by computer simulations because proton-disordered configurations satisfying the Bernal−Fowler rules can differ in their energies by as much as 0.10−0.30 NkT (at 243 K). These differences in energy significantly affect properties that vary from one configuration to another such as polarization, leading to different values of the dielectric constant. The Pauling predictions differ from the simulation results, especially for SPC/E and TIP5P, but yield reasonable results for TIP4P-like models. We suggest that for three charge models the polarization factor (G) in condensed phases depends on the ratio of the dipole to the quadrupole moment. The SPC/E, TIP5P, TIP4P, TIP4P/2005, TIP4P/ice models of water are unable to describe simultaneously both the experimental dielectric constants of water and ice Ih. Nonpolarizable models cannot describe the dielectric constants of the different condensed phases of water because their dipole moments (about 2.3 D) are much smaller that those estimated from first principles (of the order of 3 D). However, the predictions of TIP4P models provide an overall qualititatively correct description of the dielectric constant of the condensed phases of water, when the dipole moment of the model is scaled to the estimated value obtained from first principle calculations. Such scaling fails completely for SPC/E, TIP3P, and TIP5P as these models predict a completely different dielectric constant for ice Ih and water at the melting point, in complete disagreement with experiment. The dielectric constant of ices, as the phase diagram predictions, seems to contain interesting information about the orientational dependence of water interactions.

Note also that the permittivity shown here is the bulk value. It's not clear if local electric permittivity or magnetic permeability of a point in space closer to the Oxygen atom differ from another point closer to the Hydrogen atom, or another point between two water molecules.

[hamdani yusuf]

That's why they don't work well at microscopic scale.

citation needed
AFAIK any moving charge creates a magnetic field, and any changing magnetic field can induce a current in a conductor. I've only worked with atomic nuclei (in MRI systems) but BC may well have played with electrons (chemists like ESR measurements).

I think any introduction to quantum mechanics mention some limitations of Maxwell's equations, that's why quantum mechanics was developed in the first place. Different sources may emphasize different limitations.

How microscopic did you have in mind? 

What about a point of space between hydrogen and oxygen atom in a water molecule?

[hamdani yusuf]

However, you weren't originally asking questions about high speed particles   (posts #148 through to #174 started with particles moving at ~ 1m/s and even the upgrade to Cathode rays had velocities ~ 0.1c).

My original question is about limitation of Maxwell's equations to describe point to point interactions between two electrically charged particles, similar to Newton's mechanics and universal gravitation. Coulomb's law is only good for non-moving charges. How their movements affects the interacting forces is not well defined yet.
For my example about slowly moving electrically charged particle is to show that B field and E field are not constant over time when measured at a specific point in space, and they affect each other, which may complicate the calculation further.

[Bored chemist]

Water has the same chemical composition, but different pressure and temperature can change its structure, which results in different electromagnetic properties, as shown in this article.

We know that snow looks different from rain, even without that article.

What about a point of space between hydrogen and oxygen atom in a water molecule?

We can certainly measure the electron density there and, from that , we can get a fair idea of the permeability and permittivity.

[alancalverd]

There is an underlying misunderstanding here.

The wavelength of visible light is orders of magnitude larger than an atom or molecule. When you walk on sand your speed depends on its bulk properties (wet, dry, compacted...) not the interaction of your foot with each individual grain, though the inter-grain mechanics (sharp, soft....) actually determine the bulk property. 

The fact that for instance μ_iron is sometimes enormously greater than most other materials is clearly a function of group (domain) behavior rather than that of a single atom.

As the wavelength of EMR approaches atomic dimensions so we need to model the interaction by quantum rather than wave mechanics, as I stated several posts ago.   At the other end of the scale we can measure μ and ε statically for any substance, and as we can see with the dispersion of white light in glass, these parameters vary with wavelength and with the nature of the transmitting medium, since bulk properties ultimately depend on atomic properties. 

So to address HY's problem: Maxwell's equations describe wave propagation. The wave model works well when considering propagation at wavelengths greater than an atom or molecule diameter and also describes diffraction from a crystal lattice (a bulk property), but does not describe the interaction of EMR with individual atoms, for which we have a particle model. 

Maxwell's equations don't "break down" any more than a train timetable "breaks down" when you want to catch a bus - they predict only and exactly what they say they predict.

[hamdani yusuf]

There is an underlying misunderstanding here.

OK.
In Maxwell's theory, speed of light in a medium depends on its ε and μ. But Maxwell didn't say how distribution of electrically charged particles in the medium affects the values of ε and μ. The change of speed when light propagate from one medium to another is commonly attributed to the cause of refraction. Observations show that change of direction in refraction depends on frequency, which in turn implies that ε and μ of the medium also depend on frequency.

I have uploaded three more videos investigating behavior of microwave. This time I use meta-material.
The first is constructing meta-material to demonstrate interference by partial reflector

Second, we emulate refraction in microwave using meta-material, which is a multilayer metal grating

Lastly, reconstructing prism for microwave using meta-material to demonstrate refraction and internal reflection.

NB: This is not an April fool

These are videos showing experiments on refraction of microwave using metamaterials.

The air between the aluminum tubes is the same in composition as the air outside of the meta-prism. Yet, it demonstrates significant difference in ε and μ in microwave frequency. It shows that Maxwell's equations are incomplete. They haven't described the relationships between distribution of particles and electromagnetic characteristics of space around them.

[Bored chemist]

But Maxwell didn't say how distribution of electrically charged particles in the medium affects the values of ε and μ.

It isn't just their distribution that matters.
How tightly held they are also maters.

But, while Maxwell didn't go into this aspect, others did.
https://en.wikipedia.org/wiki/Clausius%E2%80%93Mossotti_relation
And, once again, it looks like you didn't study before asking.

[hamdani yusuf]

Maxwell's equations don't "break down" any more than a train timetable "breaks down" when you want to catch a bus - they predict only and exactly what they say they predict.

Did Maxwell mention anything about the limitations of his model, or in what conditions was his model expected to fail in explaining observations?

[hamdani yusuf]

But Maxwell didn't say how distribution of electrically charged particles in the medium affects the values of ε and μ.

It isn't just their distribution that matters.
How tightly held they are also maters.

But, while Maxwell didn't go into this aspect, others did.
https://en.wikipedia.org/wiki/Clausius%E2%80%93Mossotti_relation
And, once again, it looks like you didn't study before asking.

How tightly held they are also depends on the distribution of the particles, i.e. protons, electrons, and neutrons.
The article you cited doesn't work for metamaterials, as shown in my experiments.
Which question did you try to answer?

[Bored chemist]

Maxwell's equations don't "break down" any more than a train timetable "breaks down" when you want to catch a bus - they predict only and exactly what they say they predict.

Did Maxwell mention anything about the limitations of his model, or in what conditions was his model expected to fail in explaining observations?

He probably thought that they were too obvious to mention.

Which question did you try to answer?

I was answering your misunderstanding.

[alancalverd]

Maxwell's equations have no known limitations. AFAIK they describe the propagation of EM radiation at all frequencies and in all materials.

They do not purport to describe attenuation, diffraction, interference, or any other interaction with anything, any more than a train timetable purports to predict the arrival of buses. (Toronto residents may disagree on that point, but few other cities are  as efficiently coordinated).

[paul cotter]

Maxwell's crowning achievement was to show that electric and magnetic phenomena were the result of one phenomenon, namely electromagnetism and that electromagnetic waves travel at the speed of light. It was never intended to be a TOE. Ferrimagnetic materials often display a variable μ dependent on the frequency and intensity of an applied MAGNETIC field but these materials are opaque to em radiation. Any material that is transparent to em will have a μ extremely close to that in vacuo. ε is a material bulk property and does not vary with frequency, to the best of my knowledge. PS alancalverd beat me to it, by 1.5 mins.

[hamdani yusuf]

Maxwell's equations have no known limitations. AFAIK they describe the propagation of EM radiation at all frequencies and in all materials.

Do they describe photoelectric effect?
Refraction of X-ray in glass?

[hamdani yusuf]

He probably thought that they were too obvious to mention.

Or he didn't know their limitations, and seemingly, you don't either.

[hamdani yusuf]

I was answering your misunderstanding.

So, you were talking to yourself.

[hamdani yusuf]

They do not purport to describe attenuation, diffraction, interference, or any other interaction with anything, any more than a train timetable purports to predict the arrival of buses. (Toronto residents may disagree on that point, but few other cities are  as efficiently coordinated).

Those exclusions would make Maxwell's equations not very useful.
So why did Kelvin confidently say that physics was almost complete back then?

[hamdani yusuf]

Ferrimagnetic materials often display a variable μ dependent on the frequency and intensity of an applied MAGNETIC field but these materials are opaque to em radiation.

Gamma ray is also em radiation, and it will likely pass through ferromagnetic materials to a significant depth.

[paul cotter]

Yes, point taken, I was generalising. Also I was talking about ferrimagnetic materials, not ferromagnetic. But the most important point is not to assume Maxwell's equation explain everything, ie a TOE.

[alancalverd]

Those exclusions would make Maxwell's equations not very useful.

Like a train timetable, eh? Or the periodic table, which doesn't predict the winner of a horse race.

So why did Kelvin confidently say that physics was almost complete back then?

Because he was wrong. Kapitza said the same thing in 1964 (I was there). As they say in aviation
after 100 hours you know everything
after 1000 hours you know you don't know everything
after 10,000 hours you know you can't know everything.