[16feb01. Now hyperlinked in from my index. - IC]

Addition to orphan on my website

www.electromagnetism.demon.co.uk/11120.htm

Confidential to Dave, Malcolm Davidson, Nigel Cook, Mike Gibson. 14jan01 from Ivor Catt

See below; "but next day it came right when I found the error in my factual input."

This was wrong, in the sense that seemed to concern Dave Walton in a very brief telephone discussion close to 1jan01.

F = Bil, as below, was used by me using for I the current in the 377 terminating resistor. B came from the ExH energy current travelling down the cable at the speed of light, because B=uH.

Dave mentioned that the field was in the wrong direction, presumably thinking of the magnetic field caused by the electric current in the two parallel wires. Draw a 2 wire transmission line going from left to right. The magnetic field is into the paper, which makes it at right angles to the current in the terminating 377 ohms, which is down the paper. However, the problem is that the magnetic field is only to the left of the current in the resistor. In order to use Fleming's rule, the current down the 377 resistor would have to be immersed in a constant magnetic field B, both to the left and to the right of the 377 ohms.

I felt confident that I could immerse the 377 ohms in a steady field by, for instance, having TEM waves travelling towards the resistor both from the left and from the right. So I thought I was near to success. However, I have so far failed to devise a way in which the 377 will see the equal B field both to its left and to its right.

I am stuck. Ivor Catt 14jan01

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Confidential to Dave, Malcolm Davidson, Nigel Cook, Mike Gibson.

http://www.electromagnetism.demon.co.uk/catanoi.htm

Ivor Catt. 19.00, 1jan01

I feel it necessary to record what happened during the last 24 hours. I will make it an orphan on my web site http://www.electromagnetism.demon.co.uk/

On page 63 of my jan87 C.A.M. Pubs. Book "Death of Electric Current" I attempt to build a crystal out of TEM waves (= energy currents). I discuss this again on p8 of my nov94 (Westfields Press) book "Electromagnetism 1". Re Gravity. Somewhere, I write that TEM waves exit the crystal structure, to return rapidly when they confront an increase in characteristic impedance. If two such crystals are close together, such TEM waves will sidle down between the crystals before returning back inside. When returning, a TEM wave moves back through itself, always creating a force of attraction between the two crystals. I speculate that this may be gravity. Unfortunately, the idea is rudimentary because my crystal model is only 2D. However, any such briefly escaping TEM waves will cause a force of attraction between the two crystals, which explains why gravity is always a force of attraction, never of repulsion. This is because the energy currents (= TEM waves) always reflect without voltage reversal; they always see an open circuit, not a short.

Recently Nigel Cook has been emailing and phoning me on the following. He does not want his email to be included here because he thinks there may be errors in it. However, since this is only an orphan, I may include it. [14jan01. I did not. IC]

Nigel has the concept of a TEM wave in my crystal reaching the end / edge of the crystal, and then seeing a nearby crystal as looking a bit like a short across the TEM wave's travel. This leads us to the idea of a force on a wire which shorts the end of a transmission line, and so stops a TEM wave from proceeding. The blocked TEM wave then pushes at the short. (Nigel later dropped this idea. - IC, 16feb01)

Dave Walton told me long ago that light hitting an absorbing surface puts a pressure on the surface.

Yesterday I phoned Dave about the two views; the TEM wave sidling between the crystals, and the TEM wave treating the other crystal as somewhat of a short in its path. I said we did not know what was the mass of the TEM wave.

Dave said e=mc2. I had never thought of this formula in the context of TEM waves. That set the scene for my rumination for some hours.

Last night, because of an error in a footnote of my Wireless World sep84 article, wrongly giving energy density as B.D, when it is properly EH/c, I could not get e=mc2 to come out of my calculations (below). However, today, I found the correct formula by deducing it from Cullwick p231. This difficulty; the fact that I did not force-fit the results like the prince's shoe, gives more credence to the validity of my work next day. First of all it would not come right because of faulty informational input, but next day it came right when I found the error in my factual input. (The error in my article is repeated as a footnote on p137 of my jan87 book "Death of Electric Current".)

Everything that follows is classical theory - Theory N.

First consider Approach !.

If a transformer develops a shorted turn, it explodes outwards.

If electric current is sent round a wire circle, there is an outwards force.

If electric current is sent down one wire, causing magnetic field in the region of another, parallel wire, then if that wire carries current, a force Bil results, where;

B = magnetic field i = electric current l = length of wire.

Now send a TEM ExH wave step (slab of energy current) down a two wire transmission line. The line is perfectly terminated, and the termination absorbs the energy current.

The Zo and r, the termination, are 377 ohms.

From Ohm's Law, The electric current in the 377 ohms is E/r = E/377

The B field (= uH) is given by the H of the TEM wave. (B=uH)

The force F resulting is Bil = uH,(E/377).l

Length l = 1, so the force F = EHu/377 = EH u/ (sqrt u/e)

= EH u (sqrt e/u) = EH (sqrt ue) = EH/c (since c=sqrt ue)

We conclude that F = EH/c {1}

Approach 2

A TEM wave step 300,000 Km long approaches a short down a transmission line. Energy density e is EH/c [Note 1]. The total energy W in the 1 sec (or 300,000 km) long step is ExH. W = EH

From Approach 1, the force F required during one second to bring energy EH to rest is

F = EH/c {1}).

Now consider a mass m (density m/v) travelling at velocity v, brought to rest by this same force lasting for one second. Let us calculate the mass. From Newton's Second Law,

F x t = m x v. t=1, v=c, so F = mc.

So (using the result {1} from Approach 1,) EH/c = mc, or W/c = mc.

It follows that energy W = mc2. This formula, usually written e=mc2, is claimed for Poincare and later for Einstein. Here it is derived from the TEM wave in a transmission line, using only classical electromagnetic theory (Theory N).

Note 1.

My 1984 Wireless World paper footnote wrongly gives energy density as ExH. The correct figure EH/c can be derived from E G Cullwick, "Electromagnetism and Relativity", pub. Longmans 1957/61 p231. "Energy Density[W] in an e-m wave is ED or HB." Take ED. We know that E/H = sqrt u/e, so E = H (sqrtu/e). Put W = ED = EeE = E e H (sqrt u/e) = EH (sqrtue) = EH/c

The above shows that e=mc2 can be derived from the TEM wave solely using classical electromagnetism. Today (1.1.01) Dave told me that that was (well) known. However, I did not know it. Dave mentioned that Maxwell said so.

The Cullwick book that I cite above, p231, says, in a section entitled "Electromagnetic momentum"; "It was first shown by Maxwell(Treatise, vol 2, pp 792-3,) that this pressure, according to the electromagnetic theory of light, should be equal to the energy per unit volume of the incident wave." I have not yet (1.1.01) looked this up in Maxwell, although I have bought the 2 Maxwell volumes 2 months ago. I hope to add the relevant Cullwick and Maxwell sections to this orphan site.

Ivor Catt 2.1.01 01.00

In WW jan88 p54 I wrote that one could have a system containing velocity and momentum but lacking mass, which could sidle around hidden in the maths. The system could be made to function, produce results, and correlate with reality. The necessary parameter m, like the rabbit in the hat, could go about its business, the hat being in this case momentum and a fog of mathematics.

The present discussion is different. I think that the TEM is a necessary primitive, and so also is the force. However, when a TEM wave runs into obstruction, a force results. Thus, we have as primitives energy, e, TEM, and also force. Perhaps we need a third primitive, momentum, although I think that in a single-velocity universe we do not. We certainly do not need mass as a primitive.

Note that when I side with wave and against particle, mass is very much on the side of particle. So the move away from mass towards TEM/energy and force as primitive comes very much in the wake of favouring wave against particle in wave/particle duality.

I ought to add Cullwick to this website, and the bit in Maxwell's Treatise.

I have now (2.1.01) added Maxwell, Einstein and the Ether, the last part of Conquest of Truth. WWjan88, on p54, which is important.

Ivor

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16 August 2007. More thoughts