Physics and Maths

 About Classical Electrodynamics The above are the two key pictures, deriving from http://www.ivorcatt.co.uk/x0307.htm and http://www.ivorcatt.co.uk/x0357.htm   What is proven is that at one point in space there are two electric field densities and directions, and also two magnetic field densities and directions. This is totally revolutionary, and I should have noticed it 46 years ago. Dave Walton on the phone today confirms that he did not notice this either. The two fields are derived using Faraday's Law, and proven mathematically by me in my paper "Crosstalk (Noise) in Digital Systems”, which can be reached at http://www.ivorcatt.co.uk/x0357.htm . In that paper I then (wrongly) assume that superposition is permissible, and I show superposition at http://www.ivorcatt.org/digihwdesignp57.htm . What I show is illegal under classical electrodynamics, since we see two fields superposed at the same point in space. But Faraday's Law does not permit superposition. This is Faraday’s Law; "The induced electromotive force or EMF in any closed circuit is equal to the time rate of change of the magnetic flux through the circuit.[1]" .  You cannot have two changing magnetic fluxes in the same surface causing two different voltages around the periphery of the surface. Under conventional theory, you cannot have two electric fields or two magnetic fields at one point in space at the same instant in time.   Then I realised that we had already met this illegal situation many years ago when we sent two pulses from opposite directions down a coax, illegal when they overlap. When they overlap, there are two independent fields, electric and magnetic, at the same point in space at the same time. However, the case from crosstalk, http://www.ivorcatt.co.uk/x0362.jpg , when both travel in the same direction, is more grotesque (under classical theory). In contrast, "Theory C" makes no assertions for or against over this idea of two fields at one point in space. Since "Theory C"  excludes electric charge and current, Faraday’s Law no longer applies.   Ivor Catt       28 March 2010   .