How can we define material properties using Maxwell's equations?

[Stretto]

There are certain properties of materials that are "artificial" in the sense that they have no direct physical basis but are sort of added into the evolution equations to get the right effect. I don't mean to sound like they are arbitrary but that they are more empirical and not directly derivable from first principles.

What I mean by intrinsic is that all "properties" of ordinary matter that we encounter in our everyday lives on the macroscopic level must be due to the electrical forces between the atoms and molecules of the material. That is, they are governed by Maxwell's equations.

But these properties generally are not derived from the microscopic Maxwell's equations but "artificially" inserted into equations that are suppose to govern the materials behavior. Take Viscosity. It's obviously due to the local electrical forces at the microscopic scale.

Is there a way to rewrite Maxwell's equations so that the macroscopic properties of a material "pop out" and one can cover the whole spectrum of macroscopic behavior? e.g., by expanding some factor in Maxwell's equations in a Taylor series and saying that this term goes with this macroscopic property, this term with that, etc...

That is, we know the macroscopic properties are "inside" Maxwell's equations(or should be) but they are not obvious in most cases.

Suppose we have a material that we know the exact atomic configuration of. Suppose we model it using Maxwell's equations and setup some type of simulation using it. Suppose that we know empirically that it is the color "red". When we model it we should see it as being "red"(Although it might take a little more than Maxwell's equations to deal with color). Now this property of "color" in the material surely has some term in Maxwell's equations that one can modify to change the color in the simulation(although this might effect some other properties too).

Obviously to be able to completely define all the properties of a material macroscopically is a pipe dream and usually terms are defined as properties by a lot of hard work. But because all the macroscopic properties that we experience have something to do with the EM field(and usually mostly if not all) it would seem that we might just have to rewrite Maxwell's equations in a specific way for all these properties to pop out.

By properties I mean the common ones such as color, viscosity, compressibility, permeability, capacitance, etc... These are all intrinsic as they are due to the atomic configuration(nothing global such as vorticity which would be an extrinsic property of the system).

It seems that a "property" of a material is something that has some certain type of invariance in that depends on the atomic level and macroscopically it doesn't change if the material is in some kinda state of equilibrium. It's kinda hard to define but "properties" seem to be static and independent of the equations they are used in. If they are not then possibly they are not true properties of the material. Obviously in some cases we do have "properties" that are not static so possibly the definition I'm trying to get at is not adequate or these are not true properties or simply properties cannot be perfectly defined. After all, at the atomic level we can ultimately rearrange atoms and particles to get any other material and property.

In any case I'm just curious about how we can define "properties" of materials in a meaningful way and which most likely should come from QM and Maxwell's equations(or rather QED) and how they present themselves in Maxwell's equations and if there is a natural way they can do it(as if there were a "property operator" that would return a property).

 

[Drakkith]

There are certain properties of materials that are "artificial" in the sense that they have no direct physical basis but are sort of added into the evolution equations to get the right effect. I don't mean to sound like they are arbitrary but that they are more empirical and not directly derivable from first principles.

I don't believe this is the case. The macroscopic effects are directly a result of the combination of the microscopic (quantum) effects. In addition, Maxwell's equations do not describe the interaction of matter and light.

Also, most of your examples are NOT examples of fundamental properties.

By properties I mean the common ones such as color, viscosity, compressibility, permeability, capacitance, etc... These are all intrinsic as they are due to the atomic configuration(nothing global such as vorticity which would be an extrinsic property of the system).

This is not correct. Color has very much to do with the way matter is formed on the macroscopic scale. For example, Gold is actually a green color at very small sizes. The same is true for viscosity, compressibility, permeability, and capacitance. For example, Graphite is very easy to break, compress, ETC, yet Diamond is MUCH harder even though both are made of Carbon.

It's kinda hard to define but "properties" seem to be static and independent of the equations they are used in.

If you take the same system and don't change it at all then yes, no matter the equation the property you use in it will be the same as long as it represents the same property. IE if you use the mass of something in an equation, another equation that uses mass will use the same number as long as the mass of the system is the same. But the properties are only the same if they system is unchanged.

 

[Studiot]

There is already a scientific distinction betwen extensive and intensive properties.

Extensive properties are additive in a system, they depend upon the quantity of matter. Examples are mass, inertia, volume etc.

Intensive properties are not additive, although they may vary from point to point within a system.
Examples are temperature, density etc.

go well

 

[Stretto]

@Drakkith: I think I mentioned this somewhere. By "property" I mean a macroscopic property. This is because I'm trying to describe them. As I said/implied color is due to QM but macroscopically it is a simple "property".

On the macroscopic level one doesn't ordinarily encounter phenomena that cannot be described by Maxwell's equations alone. This means, whatever "creates" the properties(QM or beyond) is irrelevant because macroscopically we won't be able to observe it. The only thing that comes to mind where this fails is the interference involved in thin films as now it depends on the thickness of the material which automatically means that it is not a macroscopic property.

@Studiot: Um, yes, but I'm specially talking about extracting them from equations(specifically Maxwell's equations).

Generally the method of defining a property is to look at an equation for a few years and realize "Hey, that term represents some property!" or even simpler just decide arbitrarily that some term in the equation can be measured and is somewhat constant(in some sense even though ultimately it can't).

http://en.wikipedia.org/wiki/Navier–Stokes_equations

For example, look out viscosity is defined. It is simply defined as a term or part of a term usually that has a proportionality constant in front of it. Note that in this case viscosity is defined from the u*grad^2(v) term(which further came from a simplification of the stress term).

For it to be an inherent property of the material at the very least it shouldn't depend on position. Hence if we had some position term in the equation it wouldn't represent a property(directly at least).

If we were to expand an equation in terms of velocity then we could get a "properties" that were velocity dependent if they didn't have any direct dependence on position(and possibly other things). If they did we might have to factor them or figure out how we can remove the dependence on position.

So, position dependence is a big deal. A property is not really a property if it depends on position(if it does the material is not homogeneous and more of a "compound").

Next, things that depend on velocity generally are properties but who's values tend to be describable in terms of other more intrinsic quantities. Take viscosity. We know it is dependent on velocity but it's "value"(proportionality constant) per material is dependent on intrinsic properties of the material. Viscosity is not some innate property of the material but simply the macroscopic effect of things that happen at the microscopic level which is due some to QM and some to Maxwell's equations.

So possibly viscosity's value for a material can be further factored into terms that are more intrinsic and fundamental.

Ultimately is about how you write the equation in the most useful form. It is more mathematics than physics so this might be the wrong place to ask.

What I do know is that "properties" that depend on mass and/or position are not properties in the sense I'm talking about(because then a "material" is not really a material as it is too complex to describe and seems to be more of a combination of more fundamental materials).

 

[DrDu]

Maybe you would like to google "emergent properties"?