Faraday cages are one of the most basic tools in electrical anything. They're based on the principle that if you place a hollow, conductive container inside an electromagnetic field, then no matter what that field is on the outside, the container shields it: inside the container, the field is zero. These also work in reverse: if you put a field source inside
a conductive container, the container will prevent that field from getting out.
This is pretty useful if you want to do something that could produce dangerous fields, like use microwaves to heat food. By wrapping it in a Faraday cage, you make sure that the resulting fields don't also heat everything in their vicinity.
Now, most Faraday cages aren't solid, conductive containers; it's been known for a long time that a wire mesh works just as well. Except it turns out that it doesn't.
Faraday invented the cage in 1836. From then until roughly the 1940's, the correct functioning of mesh cages has been a combination of lore and practical engineering: if you really care that your cage works (like in a microwave oven), you build it and measure what happens. The theory of them was worked out by Feynman in the 1940's – except it turns out that Feynman simply did it wrong. (In particular, he looked at wire meshes with constant charge
on them, not constant voltage;
the math was right, it simply solved the wrong problem)
According to Feynman's solution, what matters for a working Faraday cage is the proximity of the wires. Roughly, the depth into the cage at which it provides the needed field suppression drops exponentially as the wires move closer together. It turns out this isn't right: fields decay only linearly with wire spacing. What really matters is the thickness
of the wires: the suppression does
scale exponentially with that.
In practice, this explains a lot of open mysteries, like why your cell phone works inside an elevator, but not inside an underground parking garage. Elevators, under the old theory, should have been pretty good Faraday cages; how do the radio signals, which are just EM fields, get out? It turns out they aren't very good Faraday cages at all. Likewise, garages don't tend to have deliberate EM shielding on them, but they do
have lots of rebar, and windows which are often grated. Put those together and the new theory tells you that you have a great Faraday cage.
Also in practice, this team now has a good method for calculating how Faraday cages will actually work ahead of time. It's not rocket science; it's simply solving the differential equations of electrodynamics for a cage. You can see some of the results in pictures below, where the density of lines indicates the field strength. (In all of those pictures, an EM source is to the right of the cage)
The moral of this story: if everyone assumes that there's a good theory for something, but nobody can actually find it worked out in detail, there's a good chance that there actually isn't