The second advance in March 2010.

Comment on

Ivor Catt; pub. IEEE Trans. Comput., vol. EC-16, no. 16, December 1967

(The first March 2010 advance.)

Ivor Catt. 12th March 2010.

This realisation took 46 years to come to me. (The 1964 paper, once written, was

blocked for three years. ) First please realise that the practical case , of two parallel lines, one active and one passive, above a ground plane, is equivalent to the case where, using the fact that a copper plane is a mirror, we use the “method of images”, and replace the two lines and plane by four lines . In the paper, it is asserted that it is impossible for a signal to travel down one pair of wires and leave an adjacent pair of wires unaffected. It says that two modes can exist; one mode where it is as if the top wires in each pair are shorted together and the bottom two wires shorted together (Figure 39 in http://www.ivorcatt.co.uk/4_1.htm ), called "The Even Mode" . The other possible mode, called "The Odd Mode" , is as if pairs of wires are shorted together in a diagonal fashion (Figure 40). The paper then says, in http://www.ivorcatt.co.uk/4_2.htm ;

It is not possible for a current voltage signal to travel from A1G1 to A2G2 and leave the line P1P2 unaffected. Two fundamental TEM modes can exist on a pair of parallel conducting strips between parallel ground planes.

Further on, the possibility of superposition of the two modes is assumed, but not discussed.

I ask anyone reading this to print  http://www.ivorcatt.org/digihwdesignp57.htm and refer to it while reading. The two possible modes are mathematically proven in my paper, http://www.ivorcatt.org/x0330.jpg and my 1995 book , enlarging on the proof for a two wire system at  http://www.ivorcatt.org/x0329.jpg , again in my book . They are illustrated in at http://www.ivorcatt.org/digihwdesignp57.htm . However, the whole exercise is based partly on Faraday’s Law of induction. See http://www.ivorcatt.co.uk/4_1.htm “Properties of a Transmission Line”

Faraday’s Law states that changing magnetic flux through a surface causes an emf around its circumference. Superposition – a positive changing magnetic flux causing a positive emf and at the same time a negative changing magnetic flux causing a negative emf – is not permitted. It defies the assumed physical reality, that one point in space can only have one magnetic flux density. That is, the superposition of odd mode and even mode is not permitted as a result of the application of Faraday’s Law. Note that in the diagram, the energy entering the paper in the green square for the even mode has the electric field dropping from positive towards negative from right to left. In the case of the odd mode , the energy entering the paper in the green square has the electric field dropping from positive to negative from left to right. That is, one energy current (even mode) is upside down compared with the other energy current (odd mode) travelling in the same direction. Pace Faraday’s Law, the photographs are convincing evidence that there really are two different electric fields at one point in space. However, work on high speed digital electronics led to the realisation that Faraday’s discovery of electromagnetic induction was misunderstood by him and by everyone else. Space certainly has physical properties, 377 and 300,000, and it can accomodate energy. However, the way it accomodates energy is discovered more deeply during the last two weeks.

Now for the practical case where two Energy Currents, or TEM Waves, of opposite polarity are travelling at the same point in time and space, both supposedly (according to Einstein and Feynman ) partly caused by changing magnetic flux. Look at the pictures in my book "Digital Hardware Design" . In Fugure 9.3 the key trace is the third trace. This is because the other two traces see the single spike breaking up into two spikes, one positive and one negative. The idea that the two spikes are superposed in the third trace is compelling. Since they travel at different velocities, they later separate out, see traces 2 and 1.

I presume that we agree that the energy travels as a TEM Wave (or approximately TEM Wave) through the dielectric guided by the conductors. (As an example, see http://www.ivorcatt.co.uk/x0336.jpg for a single pair of conductors. The amount of energy flowing through the red cross section, or square, equals the amount of energy flowing through the blue cross section.) The greatest energy density is in the space close to the conductors. Close to the passive line, we see from the third trace that two energy currents of opposite “polarity” are superposed. One has vertically upwards voltage, or electric field, and the other has vertically downwards voltage. Similarly, the magnetic fields associated with each independent spike are opposite. The total energy involved is not indicated by the spike in the third trace, but by the sum of the two spikes in the second or first trace.

Now we have to think about why the mathematics in my paper predicts a result which defies Faraday’s Law. This is because at the start of the mathematics, the possibility of superposition was assumed. In http://www.ivorcatt.co.uk/4_1.htm , it says;

Crosstalk in digital systems, or;

Proof that only two types of wave-front pattern can be propagated down a system of two similar wires and ground plane[2].

There follows no discussion about superposition, which is assumed in the rest of the paper, but obviously illegal (as I only now realise, 46 years later). Thus, the third trace of Figure 9.3 (leading to the second and first races) refutes the whole tradition of classical electromagnetism. Where did it all go wrong? The answer is, right at the beginning. Faraday did not discover electromagnetic induction, and changing magnetic field does not cause electric field. http://www.electromagnetism.demon.co.uk/images/7877.jpg . Faraday did not introduce electric current into the primary of his transformer in his famous experiment;

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]

Faraday’s Law breaks down in the case discussed at http://www.electromagnetism.demon.co.uk/images/7877.jpg

Faraday introduced a TEM Wave, involving both electric and magnetic flux, and what came out of his transformer and travelled to his galvanometer was also a TEM Wave involving both electric and magnetic flux. The way in which the energy current gets into the secondary of a transformer is indicated in Mike Gibson’s work reached via http://www.ivorcatt.co.uk/4_6.htm at http://www.ivorcatt.co.uk/2631.htm and http://www.gibsonridgesoftware.com/physics/two_turn_inductor/tti_derivation.htm . Here we have the mathematics of how a TEM Wave enters the primary of a transformer and then gets into the secondary. Throughout, what is involved is TEM Waves, not electric fields or magnetic fields in isolation.

Earlier above, I stated; “The two possible modes are mathematically proven in my paper at http://www.ivorcatt.org/x0330.jpg .” This raises questions. Was a mathematical approach incapable of distinguishing between a case where superposition applies, and one where superposition does not apply? The answer is, “Yes.” Mathematics is like a shorthand; an inadequate language lacking precision and detail. The second question is, “What replaces classical theory, growing from Faraday’s Law and Oersted’s discovery for the next century or two?” The answer to this is that waiting in the wings is "Theory C" . Whereas classical theory makes two electric field densities at one point illegal, Theory C makes no assertion either way. We failed to notice that, using Einstein and Feynman’s description of a TEM Wave as "The Rolling Wave" , it is illegal for two pulses to travel from opposite directions down a coaxial cable and pass through each other leaving each other unaffected, since during their overlap there is no magnetic field. This predates today’s realisation that in the case of crosstalk , two different (upside down) TEM Waves of energy current travelling in the same direction at a point.

Another approach is interesting. A paper recently rejected for publication by Proc.IEEE (as virtually all my writings have been rejected by all journals for 40 years) discusses the relationship between mathematics and physics in the context of electromagnetic theory. The subject began with Faraday and Oersted, and further embroidery and mathematical enhancements gathered apace from then on. My rejected paper pointed out that the mathematics of physics, unlike that of chemistry, which has arrows instead of = signs, ignores causality. I wrote that had we originated with light, which we all knew about, we could have worked backwards through the same mathematics and ended up with Faraday’s Law etc. It was a historical accident that we started with steady and slowly changing fields, and ended up with the TEM Wave and light – rapidly changing. We could have started with the light and ended up with the conventional starting point. In that case, the justification for electric current and electric charge (and  Faraday's Law ), part of the conventional starting point, would not have been there, and under Occam’s Razor we would not have included it in our arsenal of theory. Of course, "The Catt Question" , combined with Figure 30 , obviates the need for electric charge and electric current (and therefore of Faraday's Law , which requires electric current). Now, as a result of my at last realising that two opposite TEM Waves of energy current travelling in the same direction at the same point in space can exist together, it becomes absolutely necessary to begin with light, the TEM Wave and the nature of space, and work back through mathematics and theory to those parts of conventional theory which remain valid and useful.

In particular, this realisation of mine means that space is more sophisticated than we thought. Starting with space accommodating energy current, we can proceed to discover more and more about the nature of physical reality. As it is stated at present, Faraday’s Law will not be part of it, because it involves electric current, which disappears under "Theory C" .

Ivor Catt. 12th March 2010.

14th March. Yesterday I made the curvilinear diagram and discussed it. Only then came the further realisation that, whereas for the two modes, even and odd, the polarity of the passive conductor is opposite, it does not follow that close to this conductor the cross sections of the two energy currents at a point are exactly opposite. The electric and magnetic dimensions of the ExH energy currents are not at exactly 180 degrees to each other. Rather, the two TEM Energy Currents are at an oblique angle to each other, tending towards 180 degrees. This makes the nature of space even more extraordinary. Ivor Catt. 14th March 2010

Later on 14th March. I have just talked to Dr. David Walton, my co-author, on the telephone. He agrees that for the historical record, it is valuable for us to record exactly who thought/realised what when. He confirms that he also had not realised that the crosstalk pictures http://www.ivorcatt.org/digihwdesignp57.htm , with which he is familiar (as co-author) contradicted the requirement of classical electromagnetic theory that one point in space could only have one value of field (electric or magnetic) at one instant in time. He agreed that we already knew this, because of the case when two TEM pulses travel through each other in opposite directions down a coaxial cable. When the pulses overlap, the two fields at one point in the dielectric are independent of each other – they coexist. However, the case discussed in this page, of two energy currents travelling in the same direction with independent values for E and H, is more extreme. He also agreed that until I pointed it out to him, he had not realised that the two energy currents at a point – from even mode and odd mode – were not (in cross section) at exactly 180 degrees to each other, but were oblique to each other. (Possibly at some points the angle is exactly 180 degrees.) Two days ago, both of us fell into the trap of thinking that since the two signals in the passive conductor were opposite to each other, the energy currents were exactly opposite to each other, which we now realise they are not. – Ivor Catt

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Analysis

Figure 9.3. The bottom trace is what appears on the passive line when a spike (Figure 9.2) is introduced into the parallel active line. ( See diagram. ) The voltage amplitude of the bottom spike is an indication of the amount of energy it contains. However, it breaks up into two spikes, trace 2, which total more than the original spike. This forces us to accept the obvious, that the two spikes, trace 2, previously combined to camouflage each other in the first spike, trace 3. Also note the gradual degradation between trace 2 and trace 3 (but perhaps near to constant area). This means that the original two superposed spikes making up the small spike, trace 3, if treated separately, were very much larger. In fact, since the two spikes in trace 2 of figure 9.2 derive from the very large spike of trace 3, Figure 9.2, it is obvious that the two superposed spikes given by trace 3 in Figure 9.3 are large, containing much more energy than the small visible spike, trace 3 of Figure 9.3, indicates. Thus, consideration of conservation of energy forces us to conclude that the third trace, Figure 9.3, is two large spikes superposed. Now under classical theory, each superposed spike contains not only energy but also magnetic and electric field, of opposite polarities. This is illegal under classical electromagnetic theory, which derives from Faraday’s Law et al. Classical theory only permits one electric field density and one magnetic field density at one point in space and time. Analysis of these pictures forces us to migrate away from classical theory, perhaps to "Theory C" .

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Crosstalk (Noise) in Digital Systems

Pages 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , some of which is in two of my books. The argument starts at page 30 of one book , and at page 4 of the other book , continuing on page 55 . Here in figure 9.2 we see “a very narrow pulse introduced at the front end of the active line. If there were no parallel passive line nearby, this pulse would travel down the active line (at the speed of light for the dielectric) more or less unchanged,” in a TEM mode. “However, as the other two traces show, the presence of the passive line caused the original narrow pulse to break up into two similar pulses.”