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The Heaviside Signal
An alternative view of the transverse electromagnetic wave.
By Ivor Catt
Wireless World, July 1979
This article proposes a different picture of electromagnetic propagation from the familiar "rolling wave" idea in which electric and magnetic fields topple over and forward, continually changing into each other as they go. The author postulates “an unchanging slab of E x H energy current” travelling forward at the speed of light, and names it “The Heaviside signal” after a concept expressed in the writings of Oliver Heaviside. This process does not rely on a causal relationship between the electric and magnetic fields, which are seen as co-existent. I now (Oct 2012) realise that Heaviside did not describe it in his book .
Maxwell faced up to the paradox that whereas electric circuits, in order to function properly by allowing the passage of electric current, were thought to require a complete closed circuit of conductors, electric current still seemed to flow for a time when a capacitor (which of course is an open circuit) was placed in series with the closed loop of conductors. He “cut the Gordian knot” (according to Heaviside in his Electromagnetic Theory, 1893, London, p28 sect 30) by postulating that a new kind of current, which he called “displacement current”, leapt across the plates within the capacitor. This electric current, which was uniformly distributed in the space between the capacitor plates, could even flow through a vacuum.
Maxwell followed up this daring idea by suggesting that electromagnetic waves might exist in space. Scepticism about his postulated “displacement current” was silenced in 1887 when Hertz discovered the predicted waves in space. The classic pre-Popperian requirement of a good scientific theory seemed to have been met – the prediction of further results which are later confirmed by experiment.
There are two versions of the transverse electromagnetic wave, the “rolling wave”, and what we shall call here the “Heaviside signal.” We shall discuss only the wide variety of views among those who believe (with the relativists) that there is no instantaneous action at a distance.
The lack of action at a distance creates a fundamental difficulty for the wave in space if it is to be launched by a force in the direction of propagation. The key to the ability of a force to project a wave is that there is a pressure difference between two points along the line of propagation. However, knowledge of a difference in pressure between two points A and B which are separated by distance implies instantaneous knowledge at B of the pressure at A; that is, instantaneous action at a distance, which has been outlawed.
This dilemma seems to be overcome if it is postulated that the force which projects the wave is a lateral, shear, force. It seems that a shear force can act at a point, and so not contradict relativity whereas a longitudinal force cannot.
The above king of reasoning, combined with the postulation of displacement current, which seemed to flow at right angles to the direction of propagation, joined forces to create the notion of the rolling wave. The rolling wave contains alternating concentrations of magnetic energy ˝mH2 and electric energy ˝eE2 in the direction of propagation. It is useful to think of a road with alternate red trucks and white motor cars. The magnetic energy or flux (by Faraday’s law of induction) generates electric energy and displacement current ahead of itself, which in turn (by the Biot-Savart Law) generates magnetic flux, or energy, ahead of itself. Each type of energy, or flux, topples over and forward, changing as it topples into the other kind of energy. It is as though in the road containing the alternate red trucks and white cars, first the red trucks reappear as white cars a little further ahead while at the same time the white cars turn into red trucks a little further ahead; then the cars and trucks change back again, moving forward a little with each metamorphosis. The analogy with the pendulum has been proposed. One can think of a long line of pendulums, alternate ones having potential energy and kinetic energy, and communicating their energy forward step by step with a change of type of energy at each one.
The Heaviside Signal
Opposed to the rolling wave is what we have called the Heaviside signal. The most highly developed form of this view is that at any point in space, an electromagnetic signal contains one kind of energy only, which is equal to the product of E and H at that point, where
E/H = ./(m/e) Energy density = EH/c
Further, the Heaviside signal always travels forward unchanged at the speed of light c = 1/ [./(me)] , and never any slower. E, H and c are always mutually perpendicular.
The two men most likely to understand the “Heaviside signal” point of view and to oppose the “rolling wave” were Oliver Heaviside himself, in honour of whom it has been given its name, and Poynting, the man whose name is attached to the vector E x H. However, their writings show that neither man arrived at a full understanding of the Heaviside signal described in the previous paragraph.
Heaviside vacillated between the two views , the rolling wave and the Heaviside signal. He always applauded the idea of displacement current, which appears to put him on the side of the rolling wave. Further, on page 6, art. 453 of volume 3 of his “Electromagnetic Theory”, when he says that the curl of E, not E itself, is the real source of the waves, he is again arguing for the rolling wave. Curliness is obviously a bid for shear, vorticular forces, a concept intrinsic to the rolling wave. However, elsewhere he seems to stand firmly for the Heaviside signal. For instance (ibid, art. 451, page 4), he says, “It carries all its properties with it unchanged,” which is a clear statement of the Heaviside signal. Heaviside mentions the slab elsewhere in his writings. One does not conceive of slabs rolling, or generating shear forces or stresses. Almost by definition, a slab, like a slab of heavy granite, moves forward unchanged at constant velocity.
Professor Poynting, who first suggested that energy was distributed in space with a density E x H, also had a partial vision of the Heaviside signal. He definitely did not know that E is always perpendicular to H, and that the x in ExH means simply multiplication. (He had a term sinq for the angle between them.) Poynting was writing before the general agreement that light is electromagnetic, and so he did not know that this Poynting energy always moved forward (in the third dimension) at a constant speed, 1/ [./(me)], the velocity of light in the medium.
Poynting had a very good grasp of the direction of energy flow and its magnitude, but did not seem to understand the importance of reflections at a change of medium, which leads one to think of energy current ExH flowing backwards along the previous path, passing through the next portion of forwards travelling energy current. This superposition of forward and backward energy currents (implicit in the phrases “phase velocity” and “group velocity”) has prevented a clear understanding of the electromagnetic wave.
For fifty years, technology did not give us the power to drive the medium with an electromagnetic signal. With the low power at our disposal, all we could do was resonate the medium with periodic (sinusoidal) excitation in the same way as we move a child on a swing. In a resonant medium, energy is necessarily flowing in both directions; most of the forward energy returns to aid the source on the next cycle.
Our inability to drive a medium except periodically insinuated itself into our group psyche, until we came to assert that nature was periodic (and even that it was sinusoidal). Implicit in this view were the wrong beliefs that
(1) electromagnetic energy is necessarily contrapuntal,
(2) E/H = ./(m/e) is not always true, (e.g. when two waves are passing through each other so that H cancels but E does not, so that E/H = infinity ), and
(3) Signals can travel slower than the speed of light 1/[./(me)] .
The absurdity of this third idea is easy to demonstrate if we consider a two directional highway. If all cars move at 60 m.p.h. but some (A per hour) move eastwards and some (B per hour) move westwards, no one would argue that the total passage of cars eastwards per hour pas a reference point, that is, (A-B), would help us to determine the velocity of cars by the formula
Flow of cars = (A-B) per hour
Distance between cars = L
Therefore velocity of cars = (A-B)L m.p.h.
However, this seems to be done, at least subconsciously, with phase velocity and group velocity. The very terms imply some such calculation.
Some ten years ago the successful manufacture of high speed (1ns) logic elements capable of driving a 100 ohm load made it possible, for the first time for fifty years, to drive a medium rather than gently resonate it, as a matter of normal routine. Those driving a high speed logic step could clearly see it travelling at the speed of light for the dielectric (never any slower) and remaining unchanged on its journey. For the first time for seventy years, high speed digital engineers were privileged to see the Heaviside signal, an unchanging slab of ExH energy current guided between two conductors from one logic gate to the next. Reflections were prevented by proper termination at the destination, so that notions of phase velocity and group velocity evaporated. We saw a slab of energy launched from one pint, travelling unaltered, to be absorbed by the terminating resistor at the destination.
At this point we just had to unburden ourselves at the theoretical level of implicit contrapuntal notions. A beautiful vision resulted, of a lateral strain ExH (where E/H = ./(m/e) which by definition travelled forward at velocity 1/ [./(me)].) As it travelled forward it filled (or probed) the space ahead of it in the same way as the ripples on the surface of a pond will fill the space (surface) as they come to it. Logic designers maintained a near constant aspect ratio in the space ahead, because whenever this slab came to a change in aspect ratio ( = change of characteristic impedance, better termed characteristic resistance) some of the energy could double back on its tracks according to the well-known laws of reflection. However, this did not lead back to the old “phase velocity” and “group velocity” notions; rather, the slab of energy current split into two slabs, one to continue forward and the other to return, both slabs continuing to probe, or fill, the space presented to them on their journeys.
The Heaviside signal offers us a dramatic simplification of our view of the fundamentals of electromagnetic theory.
[For the rest of the article, see Wireless World, July 1979. This copy typed by Ivor Catt on 22apr02.]
Complete article is at pdf version
Einstein teaches "The Rolling Wave".
Albert Einstein and Leopold Infeld, "The Evolution of Physics" , pub. CUP 1938, p154 (sometimes p148);
" .... What kind of changes are now spreading in the case of an electromagnetic wave? Just the changes of an electromagnetic field! Every change of an electric field produces a magnetic field; every change of this magnetic field produces an electric field; every change of ...., and so on. As field represents energy, all these changes spreading out in space, with a definite velocity, produce a wave. The electric and magnetic lines of force always lie, as deduced from the theory, on planes perpendicular to the direction of propagation. The wave produced is, therefore, transverse." Analysis ; The smoking gun.
In contrast, Heaviside says, see above; “It carries all its properties with it unchanged,” which is a clear statement of the Heaviside signal.
Ido Yavetz, From Obscurity to Enigma. The Work of Oliver Heaviside, 1872-1889, pub. Birkhauser Verlag, Basel
P6, footnote 17
“In many ways the most remarkable and most revealing account of Heaviside’s life is continaed in G.F.C. Searle’s "Oliver Heaviside, The Man" , edited by Ivor Catt (1987). …. The full document was published for the first time only in 1987 under somewhat mysterious circumstances (see Catt’s introductory note).”
Feynman teaches “The Rolling Wave”
What follows is the key item among those quotes from Feynman very helpfully quoted by Forrest Bishop below. It is a clear statement of "The Rolling Wave". This subject is extremely well covered in my article http://www.ivorcatt.com/2604.htm . The decription of "The Rolling Wave" in my article mirrors that of Feynman's TEM Wave.
“Now let us ask what happens if we suddenly stop the motion of the charged
sheet after it has been on for a short time, *T*…
[Note 1. By Ivor Catt. But in the TEM pulse, or even more in the TEM step in Figure 9.4 , Feynman's "Suppose the magnetic field were to disappear." (above) cannot be supposed, because behind the step, for a very long time, E field and H field are constant. Do the E field and the H field suppose that the other might disappear? This is obviously nonsense in the context of a steady TEM step, as in Figure 9.4 .]
J. D. Jackson seems to say that displacement current creates magnetic field, and is necessary for radiation to be possible. He propounds “The Rolling Wave”. On page 218 of his *Classical Electrodynamics* (2nd ed.), which is the leading graduate textbook in the US, he writes; “Maxwell called the added term … the *displacement current*. This necessary addition to Ampere’s law is of crucial importance for rapidly fluctuating fields. Without it there would be no electromagnetic radiation, and the greatest part of the remainder of this [848 page] book would have to be omitted.” So we see that the math term is indeed the Prime Cause of physical phenomena."
Ivor Catt. 18june02
Scandals in Electromagnetic Theory http://www.ivorcatt.com/28scan.htm
Turning to the conflict between The Rolling Wave and The Heaviside Signal, the animation on
illustrates the dilemma beautifully. Keeping your eye on the left hand side of the animation, you will see the Rolling Wave. However, looking only on the right, you will see the Heaviside Signal, a slab of stationary energy current moving forward at the speed of light. Ivor Catt 6feb03