shiv wrote:
Well you are the one who should be telling us about cloak tech
. I am the clock tech expert around these parts.
I shall try. First Shiv I claim you know as much as anyone else. Tomography that you encounter as a surgeon and invisibility that everyone's uncle and aunt are talking about are the reverse and obverse of the same coin.
Now when waves strike an object, lets say electromagnetic waves strike an object they scatter. So for a given frequency
there is some part that is transmitted, some reflected and so on. Suppose I make a list of this for every frequency say.
Then this is called the scattering data. Now there is an object that encodes the scattering data. It is called the Dirichlet to Neumann map in my article and in the other article by Gunther and Allan. Engineers call it the voltage to current map.
That is for every applied voltage on the boundary measure the corresponding current flux. All the scattering data I allude to above is caught in this voltage to current map. So what I show is that if I know the voltage to current maps for two bodies, then I have completely reconstructed the internal conductivity INSIDE. So boundary information tells me if you have an LCA hidden inside or your pet dog or your girlfriend. There is a small caveat let me explain this later.
If you look at my article, you will see how I construct the scattering solutions via an old inequality of mine.
Okay now the cloaking business. The idea is can I find two different objects that have the same scattering data.
Then I will not know if its your girlfriend hidden or your nasty boss. The answer yes! But then you will ask why is my theorem not violated. The answer is In my theorem I also assume that at each point inside the body if I look at all directions the conductivity of the material looks the same. Off course the conductivity changes point to point but at every single point things look isotropic, i.e same in all directions. The point that Gunther and Allan make is that
if the conductivity is non-isotropic then two objects can have the same scattering data. This is exactly how Pendry and company built their materials, they are highly non-isotropic and have different conductivities in different directions
at a given point. Its weird material but the mathematics already predicted the phenomena oh 15-20 years ago.
So there you go now....