The Crosstalk Photographs for Laymen.

The Significance of the Crosstalk Photographs.

Ivor Catt. 9 April 2010

Under Faraday’s Law, v = -d(phi)/dt , which forbids superposition but whose mathematics permits it, we end up with two electric currents travelling in opposite directions down the same wire. – 17 June 2010

This is an attempt to introduce the layman to the developments of the last three weeks.

We close the switches in Figure 3 and immediately reopen them. (If we did not reopen them, the result would be as in the animations .) All experts will agree that a very narrow spike of voltage and current (made up as in Figures 4 and 5 ) advances at the speed of light guided by the two conductors. Its four constituents are listed here . In the case of my work, the narrow spike, or pulse, was originally six inches long, lasting for one tenth of one billionth of a second. It was like a very short flash of light travelling down between the two conductors. This narrow spike, which had by now widened to half of one billionth of a second was introduced between the conductor and the copper plane below in the top of Figure 23 . Travelling in the epoxy glass board between the conductors, it narrowed down back to six inches wide. In the board, it travelled at half the speed of light in a vacuum or air. It gradually widened further, ending up 270 inches down between conductor and copper plane to a width of one billionth of a second, shown in the top trace in Figure 39 (shown upside down).

Next, we introduced the spike between the left hand conductor and the copper plane, see Figure 9.1 . The resulting voltages for the active and the passive (right hand) conductor are shown in traces 3 of Figure 9.2 and Figure 9.3 (and Figures 28 and 29 ). That is, a smaller voltage spike immediately appeared on the right hand conductor adjacent to the driven conductor.

This pair of conductors was very long, and the signals were inspected as they travelled along, 120 inches along (second trace) and 234 inches along (first trace). The initial spike, large on the line driven and one sixth of the height on the other line, had broken down into two spikes. The slowest (even mode) one was equal on each line. The faster (odd mode) one (arriving first) was equal and opposite. In Figure 33 , the second traces were widened to show this more clearly. Note that in the first trace of Figures 9.2 and 9.3 , having travelled twice as far, the two spikes are twice as far apart. The conclusion is compelling, that in the first trace they are on top of each other, making a large spike on the active line, Figure 9.2 , and a small spike on the passive line Figure 9.3 , because here they are opposite.

(I have drawn the field patterns for the even mode and  odd mode . Since a copper plane acts as a mirror for light or for electromagnetic waves, it is easier to think in terms of four conductors and omit the copper plane.)

Convincing proof that two TEM Waves of opposite polarity are travelling together near to the passive line on the right is provided by Figure 9.5 . Instead of a narrow spike, a step has been introduced into the active, left hand line , first trace of Figure 9.4 . This step is the same as a long series of spikes. In the right hand, passive line, we see, in the first trace of Figure 9.5 , a step, which is a series of small spikes. However, in the second and third traces, the first negative spike separates out by arriving fastest. After that, the step represents a series of small spikes, positive and negative, superposed, like the negative and positive spike in the second trace of Figure 9.3 , but largely cancelling each other out for our voltage measuring instrument.

The idea that two waves of opposite polarity can travel together in the same region as in the third trace of Figure 9.3 and the first and second traces of Figure 9.5 contradicts Faraday's Law , one of the earliest and most basic laws in the history of electromagnetic theory. 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” excludes the possibility of two independent fields at one point in space, which we see in trace 3 of Figure 9.3 .

Faraday's law is a fundamental relationship which comes from Maxwell's equations. It serves as a succinct summary of the ways a voltage (or emf) may be generated by a changing magnetic environment. “ Under Faraday’s Law, there is no possibility of two changing magnetic environments in the same place, as we see in the third trace of Figure 29 .

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Dear John (Foggitt)

I have just realised one implication of using the Principle of Superposition under classical theory.

In the second and first traces of the photographs in http://www.ivorcatt.org/digihwdesignp57.htm , we see first of all a negative spike on the passive line, trace 2 of Figure 9.3 Thus, to terminate the electric field lines as shown in http://www.ivorcatt.co.uk/x0362.jpg or http://www.ivorcatt.co.uk/x0361.jpg we need, first, when the odd mode passes by, negative charge density on the surface of the passive (top right) line; and then shortly afterwards when the even mode passes by we need positive charge on the passive (top right) line.

Now initially, at the third trace of Figure 9.3 , when the two modes have not yet separated out, you thought there could be two superposed electric fields. However, we now see that the third trace of Figure 9.3 shows that initially there has to be on the surface of the passive (top right) line superposed negative and positive charge. That is, at one point on the surface of the (top right) conductor there are two charges, one negative and the other positive, until the odd mode and the even mode separate out. The negative charge terminates the electric flux field at its negative end, and the positive charge terminates the electric flux field at its positive end.

Can two charges of opposite polarity exist at the same point, one terminating positive electric flux and the other terminating negative electric flux? This is much more dubious than the idea that two electric fields can exist at one point, and superposition of their effects (or their causes) applied.

Ivor Catt  14 April 2010

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We need a thorough analysis of the work I did on crosstalk in the 1960s, the mathematics I developed to prove the limitation to two modes, and the photographs showing a third, illegal mode.

In my paper "Crosstalk (Noise) in Digital Systems" I wrote on page 761 , Appendix I;

“Assume that a current voltage step i, v, is travelling down the [pair of] parallel lines from left to right .... ” . Note that I did not say “Assume a single current voltage step .... ” [Note 1]. I was trapped in the reigning framework, deriving from Faraday’s Law, which I proceeded to base the argument and the mathematics on. I concluded that only one wave-front pattern could travel in such a way at only one velocity. Then on page 762 I used similar arguments giving “Proof that only two types of wave-front pattern can be propagated down a system of two wires and a ground plane [i.e. a symmetrical four wire system].” I (wrongly) began; “Now assume that a [single] wave front involving current steps ia and ip is travelling down the lines with a velocity c.” Note the missing, but implied, word “single”. Here is the fatal flaw in the whole discussion (leading to the fatal flaw in Faraday’s Law, which assumes a single field at one point), leading to the “proof” by the pictures . However, close inspection of  the pictures shows us that although traces 2 and 1 appear to confirm the calculations, and thus Faraday’s Law, traces 3 disprove it by showing a third (asymmetric) mode, which is not permitted under "Theory N" , but acceptable under "Theory C" .

Of course, an apologist for Establishment Electromagnetic Theory may want to argue that the small spike in the bottom trace of Figure 9.3 is not the combination of two spikes which separate out later in traces 2 and 1. But only a “scientist” deeply committed to defending theory a century old would do so. That means, of course, virtually every one of today’s scientists. However, it is likely that, rather than defending archaic theory, they will merely ignore the whole of this matter – both the mathematics and the pictures.

The inadequacy of mathematics as a language, and the too great faith in it by myself as well as others, for instance in my 1967 paper , is discussed by me in my book at 1 and 2 . Elsewhere I illustrate the multifarious problems by taking x, squaring it, finding the square root and deducing that the value is now x or –x. Even within mathematics there are obscurities, even when mathematics is divorced from physical reality. It is not surprising that I fell into a trap in 1964 when they were combined.

Note 1. I did not have to say “Assume that a single current voltage step i, v, is travelling down the [pair of] parallel lines” because under Faraday’s Law two steps in the same place at the same time would be illegal. I was then and for decades later a conscientious follower of Faraday. Now the truth is that if two pulses travelling in opposite directions down a coaxial cable pass through each other, there are then two current voltage pulses at the same point for a time, admittedly not both travelling “from left to right”. Thus, such a situation already defies Faraday’s Law, and nobody has ever noticed. (Elsewhere I assert that no professor or text book writer has ever considered {and never mentioned} two pulses travelling through each other, of course, so they could not confront this defiance of Faraday’s Law. One can only think about what one thinks about.)