I'm un-deleting this, but I want to say one thing: If it sounds like I was on methamphetamine while writing incoherent stream of consciousness… it's because I probably started having fever already and crashed shortly afterwards. Just bare in mind that while it's about problem solving and complexity, I feel a bit confused about it while reading it now.

It's even less good to know that scientists have some theories but ultimately aren't exactly sure why.

I'll argue this point. Aside of being of same mind as oyster on that one, I would like to have a try at showing how solving problems escalates. See, the main obstacles regarding solving complex problems are:

- Amount of people with the know-how and willingness/time (both dependant on money)

- Coordinating a group of experts and making them communicate efficiently (hard but underestimated task!)

- Incredibly steep rise in difficulty the more detailed your hypothesis/model gets

Here's a good way to show what I mean. Let's keep to electromagnetism and say that I am interested in the uniform, conducting, ideal disk in the external (constant) electric field and what I want to find is the behaviour of induced currents inside the disk and the charge distribution. If I were to add "the disk is neutrally charged before the electric field appeared" it's a problem that most high school students should be able of answering. However, real-life problem is going to be a coin in time-dependant electromagnetic field (microwave).

Now, let's assume that this is not a disk but something with actual width. Basically a coin-shaped ideal conductor without charge in a constant electric field. That's a bit more problematic, but doable by a freshman student. In a time-dependant electric field that is a fairly simple function (something like E(t) = E * sin(wt)) it's still doable on this level.

Getting more complex: we want to know about a real coin after all. Would there be a difference to solution if we don't polish coins? Intuition says yes and I can actually solve this problem for a uniform layer of dirt that can be assumed as having negligible depth. However, having to deal with polished and unpolished coins basically splits our research path.

If the coin is polished, and assuming above idealisation, let's now notice that depending on the surroundings of the coin we can find shapes of the box where anything interesting can't even occur. Why? Because we know that EM wave can be reflected, and if the surroundings can also reflect it… we get various interference relations. So we take the 'box' with coin inside and ask questions about positioning the coin. Size of the coin very likely matters (related to wavelength), but not as much as direction of electromagnetic wave!

For unpolished coin you have all of the above with additional questions regarding type of dirt, fraction of surface that was polished (hard!), and determining if unpolished case would be the same as polished coin with diminished reflection. It isn't, because depending on what the dirt is (let's be specifically-idealistic) and say that it's a uniform layer of oxide of the metal used for making the coin.

This problem is likely for a graduate student in physics. And we are still talking about fairly simplistic model of a coin without any features… in the vacuum! I can tell you that's it not a problem until you will start considering the surroundings to be either non-linear for EM wave and probably some other factors. Air, even with water vapour, is going to have a lesser effect than having the coin submerged in water.

Here is a place where a preliminary experiment would be in order. Coins made of pure nickel, copper and some copper-nickel alloy. Various sizes, all polished. Dirtying them done by applying various oxidising chemicals for set time duration (to allow building thicker, but uniform, layers that we can actually look-up in metallurgy tables). Boxes of various sizes and shapes. Now we can have a fairly lengthy experiment montage that ends with theorists being given a lot of data to coordinate the efforts in the direction set by intermediate experiment.

Of course this is a gross oversimplification on my part. We already know how oxides influence internal currents, why certain wavelengths would produce much stronger result etc. But it's a good way to show that something as simple as a coin in a microwave problem is really complex after adding more factors. This problem was at some point an undertaking that likely could conclude with someone getting a doctorate afterwards.

Now the problem mentioned at the beginning would make it worth to apply a group of specialists and research budget to solve this problem in detail… or maybe use them for slightly more pressing problems. ;)