The Heaviside Signal

An alternative view of the transverse electromagnetic wave.
By Ivor Catt
(First published in 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.

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 rolling wave
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 ½mH2 and electric energy ½eE2 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.

(Ivor Catt kindly gave permission for this to be included here)

Please note this is Catt's theory because that is Ivor Catt's name - any connection with other cat states is purely coincidental and no humour is intended.

The point of particular interest (to me) is that the theory does away with the nightmare of sinewaves everywhere. When moving from a field description of EM to a photon description - Ivor Catt's theory removes the need to explain where a photon hides the 'wriggly bits' that arise from the 'sinewave' solution to Maxwell's equations.

One of the problems with the theory may arise from the way the normal 'first move' is to attempt to turn the wavefront back into a sum of sinewaves - thereby reintroducing gain and phase velocity as an artifact of the chosen method of analysis.

With luck Mr Catt will be willing to deal with any questions that may arise.

Many thanks to Ivor Catt for what I regard as a brilliant insight into the nature of EM phenomenon and for allowing me to present his theory here.


-Confused2.

My two cents: light is a dual wave; a wave of electricty at right angles to a wave of magnetism.

I believe light inflation and a changing form of light is the future of physics. Action at a distance becomes a problem when a very low energy photon is emitted. If light is to be local then light waves must form. The larger the light wave the longer it will take. Imagine a light year photon were emitted. It could not instantaneously appear if we do not believe in action at a distance. Such a large photon would take a year to form. This means there is pre-formed light. Light must grow and this growth I call inflation. Others might just as well call it light expansion.

The problem is in understanding that light's energy is always conserved even in this pre-form.

Light's energy density expands.

Well, the light spreading looks pretty much like the deformation of the soft massive foam, it's the easiest explanation of the tranversal electrical and magnetical field combination...
But it's required to be multidimensional, to explain things like the light wave spin.

Hello Nick, Zephir and possibly Ivor,

Nick - Imagine having a battery containing only sufficient energy to transmit a single light year long photon. We connect the battery to our light year long photon transmitter. To me it would seem that the photon cannot leave until all the energy is out of the battery and it cannot stay after that time - is it possible it just goes 'ping' after about a year?

Zephir - the sinewavey thing is what makes most sense to me - I hate to ask this but you have posted it here.. are you drawing a single photon here? Is it possible that the slow start and finish are a consequence of the way you created your pulse rather than the actual mechanism of transmission?

Best wishes, John.