Interaction between TEM pulses.

  fig14-Pulse enters junction

We start with an infinitely wide input (i/p) pulse delivered at the speed of light between perfectly conducting parallel plates into a four way split (Figs.14,15).


fig15- Pulse enters parallel junction

The i/p pulse splits up into four half sized pulses as shown. (Energy is conserved because energy is proportional to .)

A pulse coming from the east will behave similarly (Fig.16).

fig16- Pulse from east

Experience shows that superposition applies for pulses travelling down transmission lines[1].

Dissimilar pulses.

fig17- Dissimlar pulses collide

Send two pulses towards a junction (Fig.17). These pulses are called 'dissimilar' for reasons which will become clear[2]. The west pulse ('west wind') breaks up into the four pulses as shown in Figure 15. The east pulse breaks up similarly as in Figure 16. The combined result is that pulses exiting north and south cancel. Pulses exiting west and east add. Thus, dissimilar pulses help each other across the gap.

Dissimilar pulses hug.

Similar pulses.

fig18 - Negative pulse from east

Now consider the case when the east pulse is negative. The result is that pulses exiting east and west cancel, while pulses exiting north and south add.

fig19 - Similar pulses collide

Our model for the behaviour of TEM pulses and their interaction is not disputed. It is unfamiliar because of the gulf between academic electromagnetic theory, which is awash with complex mathematics, and the practical engineering of high speed logic systems. When assembling high speed logic systems, I necessarily investigated and ruminated on the situations discussed above. However, any academic who investigated the subject would come to the same conclusions about the interaction of pulses.

We are now in a position to develop our thoughts in two directions; the car headlight beam and the structure of the crystal.

The car headlight.

As previously asserted (Ref.9), Maxwell's Equations give us no information beyond the numbers 300,000 and 377. Into that knowledge void enters the situation above where dissimilar pulses hug.

We also know that a pulse P1 which departs from the open circuit end of a transmission line reflects back towards the line[3]. If this  returning pulse were followed by a (positive) pulse P2, then being dissimilar, they will hug. Therefore an alternating (perhaps sinusoidal) sequence of TEM pulses attempting to exit from the end of a transmission line will be helped in its forward progress by the portions of earlier (downstream) cycles recoiling (returning) back towards the source[4].

Synthesis.

The question arises as to the merits of the above model compared with other  models for the car headlight beam. However, first we have to discover the other models. Do they exist in any coherent form?

My impression is that competing models, if they exist, are hopelessly immersed in arcane mathematics and 'Modern Physics', which includes wave-particle dualism, the photon, and so on. There is no real competitor for the model/theory above for the car headlight beam[5].

The Crystal.

fig9 - The Crystal model

In our attempt to build the interior of a crystal (Fig.20) we concatenate an array of Figures 19.

fig19- Similar pulses collide

Whenever a pulse reaches a junction, it splits into two half pulses, each of which continues at right angles to the incident direction, accompanied by half of the colliding pulse. A subsidiary model for the flat surface (or edge) of our crystal is compatible. When a pulse attempts to exit from a transmission line it reflects without inversion (generating gravity by inspecting a nearby crystal). This indicates the possibility that a second superposed array of pulses which travel in the opposite direction, may be passing along the same array of paths shown. The sum of electric currents on the surfaces of the squares is thus zero, leading to zero I2R losses. (This means that the {copper?} surface need not exist.) The pulses in the second array, being dissimilar, might hug the pulses in the first array, and so not interfere. The only effect of the second array is to reduce  I2R losses to zero, and so enable us to get rid of the conducting surfaces.

Note that at the start, we may have only pulses (1), which then circulate around the squares in time periods 1,2,3,4. Alternatively we may start off with pulses (1) and (3), which chase each other round the squares. And so on.

Difficulties with the Crystal Model.

1) We live in a 3D universe, and a crystal is 3D. The above model is only 2D. This leads us to our second system. Whereas all of the above was premised on a transmission line terminated by three resistors in series, we can develop an equivalent scenario where those terminating resistors are in parallel. However, the reader is advised to keep the above system central in his mind, and regard what follows as merely subsidiary.

The perforated capacitor.

Following Figure 11, we moved to Figure 12, where a pulse travelling down a transmission line was confronted by three lines in series. We see another example in Figure 13 and beyond. In this section we address the inverse situation, which is closer to the reality of the charged capacitor.

Figures 12 and 13 become figures 21 and 22, where the path splits into three paths in parallel.

fig21- Coax parallel junction fig22- Parallel plate parallel junction

Under this new parallel regime;

Dissimliar pulses repel.

Similar pulses hug.

We first construct a capacitor with an array of square holes in it, Figure 23 , and then reduce the size of the holes to zero. We will thus begin to see how the energy current vacillating across a charged capacitor travels both east-west and north-south at the same time.

Summary of interactions.

Definitions.

Driving into three resistors in series is called a series split (Fig12etc.).

Also called vertical.

Driving into three resistors in parallel is called a parallel split (Fig.21etc.).

Also called horizontal.

For a series split, dissimilar pulses hug and similar pulses repel.

For a parallel split, dissimilar pulses repel and similar pulses hug.



[1]
However, the curious exception is in the matter of forces, which suddenly appear when TEM waves are superposed, see my letter in Electronics and Wireless World, feb85. Also Ref.18(b), p166.

[2]
The situation is essentially one in the style of Polar Co-ordinates. A 'positive' voltage is positive in a clockwise direction.

[3]
Figure 11
shows how any change of characteristic impedance in the space ahead of a pulse causes part of the pulse to reflect. When a pulse attempts to exit from the end of a transmission line, it sees a rapid sequence of small changes in characteristic impedance as the cross section approached continues to change, each of these changes causing some of the pulse to reflect.

[4]
Light is of course a sinusoidal TEM wave, and so contains the requisite sequence of positive and negative pulses.

[5]
This is a good place to point out the clash between Bohr's Correspondence Principle (which says that after 1927 no spring cleaning in science is allowed) and Ockham's Razor, which says that unnecessary clutter must be jettisoned. The decision is based on loyalty not on logic, with the entrenched academic wanting to retain all his hard-learned clutter, and continue to earn good money teaching it, however obsolete. This is the deep meaning of Bohr's Correspondence Principle (Ref.11). If read honestly, T.S. Kuhn sides with William of Ockham. "Though logical inclusiveness remains a permissible view of the relation between successive scientific theories, it is a historical implausibility." (Ref.12).