## Ivor Catt and The Myth Of The Rolling Wave

The myth of the rolling wave is a term used by this writer to describe a problem in electromagnetic theory first raised by the English scientist Ivor Catt, in articles published in the English magazine Wireless World. The problem is referred to as a myth, since it has its source not in physics textbooks, but in popularizations of physics, designed for the general scientifically educated audience, but not for experts in the field of classical electromagnetic theory. The term rolling wave was used by Ivor Catt to describe the way in which science writers discussed the physics of the electromagnetic wave as an interaction between electric and magnetic fields of an electromagnetic wave, such that the fields were produced by a kind of self perpetuating interacting process of induction.

The reason the rolling wave is referred to as a myth, is because it has no formal justification within the logical structure of electromagnetic theory in terms of a mathematical interpretation. It arises as part of the hermenutic discussion found within the non-formal science popularization. Hermanuetic means how the formalized mathematical physics is to be interpreted so that it can be understood. This informal interpretation of the wave physics then found its way into the formal textbook formulations as a description of how electromagnetic waves work physically. It is therefore not a part of formal physical science, but an explanatory accessory incidental to the formal physics. This explains why it became the subject of criticism from Ivor Catt as part of his reformation of the formal electromagnetic wave theory.

The reason Ivor Catt attacked the rolling wave concept of interpretation has its roots in his attempt to revise thinking regarding the foundations of electromagnetic theory. That is he criticizes the foundations of the theory through attacks on its formalism in terms of Maxwell’s Equations. It is needless to remark that his criticisms were not appreciated and certainly not understood by the physics establishment. They certainly saw no need for a reformation of the Maxwell Equations formalism and were perfectly happy with the prevailing mathematical physics formalism. However, as an electrical engineer working in the development of digital computers, it was painfully obvious to Ivor Catt that the prevailing models of electrical physics were unsuitable.

The primary difference between engineers who deal with physical reality and mathematical physicists is that engineers have the legal responsibility of understanding physics so that the undertaking is successful. That means the airplane has to fly and the bridge does not fall down. In modern terms it must be “fit for purpose.” By the 1960s it was obvious that the electron flow model for electrical circuits was woefully inaccurate or not “fit for purpose” for use in high speed computer circuits. Hence engineers began using transmission line models for computer circuits. One place where the transmission line model proved superior to the electron model was in the modeling of capacitors as transmission lines. This became the subject for one of Ivor Catt’s articles in Wireless World.

According to Catt and his collaborators, Malcolm Davidson and David Walton, the correct model to use for the interconnection of logic gates is the two wire transmission line. However, there arises two difficulties in using a transmission line model for computer interconnection. First, the fact that transmission line textbooks primarily and almost exclusively discuss alternating current applications and second that Maxwell’s Equations appear to disallow the transmission of direct current electromagnetic waves because of the rolling wave interpretation. This interpretation found in many textbooks, after WWII says that a time varying electric field produces a time varying magnetic field, that is a displacement current, which is in turn linked back to the formation of the time varying electric field, through the Faraday Law, which asserts that a time varying magnetic field produces a time electric field. The difficulty here is that if these statements are correct, then it is impossible for the transmission line model to be applied to computer circuit interconnection, because computer logic uses DC electrical pulses. Since it was obvious to Catt and his collaborators that the transmission line model worked perfectly in the case of DC pulse circuitry, the conclusion was something had to be amiss in the electromagnetic theory textbooks. This caused Catt to focus his study upon electromagnetic theory and ways to correct this difficulty.

Catt, Davidson and Walton’s solution was to disavow the standard electromagnetic theory found in the textbooks and introduce a revised electromagnetic theory christened Theory C. The primary thesis of this new theory was that the curl equations of Maxwell’s electromagnetic theory, that had become the basis for the mythological rolling wave conception, were to be dispensed with, and removed from the physics textbooks. In hindsight this was a political mistake in that the academic establishment was not interested in agreeing with a theory being promoted by some unknown lumpen scientists, who were merely computer engineers. That is little more than unskilled technicians with little knowledge of mathematics and not members of the academic club of pure scientists.

An important aspect of the opposition that Catt encountered, that he did not appreciate or understand, was that the rolling wave was not a formal part of the Maxwellian theory. This misunderstanding resulted in the wrong approach in his criticism of the prevailing electromagnetic theory. He maintained that the Maxwell Equations, which were sacrosanct and unassailable, were “bogus”. To the academicians, this was outrageous heresy and had to be suppressed. It was certainly unacceptable that a lumpen scientist, a mere unskilled engineer, would be allowed to criticize a fundamental pillar of pure scientific knowledge. The inevitable reactions were predictable. Catt’s attempt to revise physical theory to include the new understanding of how computer interconnection circuits actually worked was vehemently opposed, with the result that now, many years later, the new understanding has not been incorporated into the textbooks. But more seriously, the myth remains in the textbooks and presents a serious difficulty to understanding the physics of electromagnetic waves.

Before discussing the origin of the rolling wave myth, it is important for the reader to understand that Catt and his collaborators did not understand that the rolling wave was not a formal deduction of electromagnetic theory and surprisingly it appears that the critics of Catt et al were also unaware of the mythological origins of the rolling wave myth. Therefore, it seems that the participants on both sides of the controversy, could not understand what the argument was about. Hence, neither side was able to convince the other of the truth of their arguments. There is however, the following uncomfortable aspect of the debate. That is that the Maxwell curl equations, the Ampere Law and the Faraday displacement current law, do not have the empirical foundations that ought to be required of fundamental physical laws. There is a prevailing and unresolved controversy surrounding both of these Maxwell laws. But Catt really only aimed his criticism at the displacement current, which being Maxwell’s great achievement was, of course, sacrosanct.

Maxwell’s great discovery is the addition of the displacement current to the other previously existing electromagnetic laws. Therefore only that displacement current law can be said to be a physical law due to Maxwell. But because the entire fundamental set of equations are called Maxwell’s equations there is an historical error in thinking that Maxwell is responsible for all of them.

It is unfortunate that the formulation of the formal problem was not undertaken by Catt et. al., but instead Catt promoted his alternative theory C, which unfortunately has been ignored because of his criticism of the system of Maxwell’s Equations. The problem however, was real and persists today as an unsolved problem of electromagnetic theory. A formal statement of the problem, which appears as a contradiction within the mathematical formalism is as follows.

The Maxwell Equations are shown in physics textbooks to produce electromagnetic wave solutions of the form f(t-x/v), the forward wave, and f(t+x/v) the reverse wave, where t is time and x is position in the direction of wave motion, with motion increasing x, taken as positive for the wave. These wave solutions have no evident restrictions upon the frequency distribution of the Fourier analysis of the waveform that is the solution. The formal solutions allow waves that have a zero frequency. That is in other words, continuous DC waves of electricity along with DC pulses are allowed as solutions. But we know that such solutions are not allowed in the real world, since DC currents are not transmitted through space without wires. So wireless solutions are not permitted. On the other hand, functions with zero frequency solutions are permitted for guided waves on transmission lines. In this case the function can have a zero frequency component, while for wireless waves, zero frequency components are prohibited. There is no discussion of the physical reasons behind this dichotomy in any physics textbooks. However, they do present the rolling wave interpretation, and that implies that if the fields are not time varying, ie no DC or zero frequency component, then electromagnetic waves can not exist. So it is implied by the rolling wave interpretation, that DC current and DC pulses are prohibited on transmission lines, since such signals do have a zero frequency time variation in the frequency domain. Since there are no time varying fields they can not be electromagnetic waves.

The direct simple solution to this problem was to eliminate the rolling wave from all of physics, as being false and misleading physics. Additionally, because the rolling wave produced another serious difficulty, Catt reasoned that it was a serious flaw within electromagnetic theory. The additional difficulty is that if the rolling wave interpretation was accepted, it became impossible to make sense of the conclusion that the electric and magnetic fields are in time phase. If the time varying electric field was the cause of the magnetic field, then there had to be time difference such that the two fields must be out of phase in relation to each other. Although this was not a result evident in the Maxwellian formalism, there was produced a misunderstanding, because of the belief in the rolling wave interpretation found in textbooks.

The solution proposed by Ivor Catt in his writing was to dispense with the rolling wave and the associated curl equations, but the reasoning sounded like a personal ego trip, because he said Maxwell’s Equations are bogus, and because he promoted his Theory C as a replacement. Theory C proposed simply that the electric and magnetic fields were established at the source as energy current ExH and were related by the characteristic impedance of the transmission line and free space respectively. The same thing applied in free space so there was no need for the rolling wave according to Catt. Finally, since the rolling wave involved the applications of Maxwell’s curl equations, there was the need to remove them as well. The result of these proposals was a resounding, NO! Looking backwards in time, it may have been more politically correct if Ivor Catt had said that just the rolling wave was bogus, instead of the curl equations. But he was aiming at a complete reform and a replacement theory.

In looking for the justification or formal mathematical proof of the rolling wave, it is easily found by doing an internet search for “the inductive chain of electromagnetic waves”. The results in the images section show a chain of circles interconnected at right angles to each other, where the first circle represents a magnetic field, the second circle at right angles is a circle of electric field, and this connects to a circle of magnetic field, also at right angles to the circle of electric field. The interconnecting circles represent the chain of induction. The changing magnetic field of the source creates an electric field, shown by a circle linked to the magnetic field, and this is followed by a magnetic field circle linked to the electric field. Each circle representing an induction by Maxwell’s curl equations. It is easy to see that this chain of induction forms a wave, since the disturbance beginning at the source is propagated by successive inductions through the links of the chain of causality.

A search of electromagnetic theory textbooks shows that this conception is not presented as part of the formal mathematics of electromagnetic waves. For example it is not found in Introduction To Electrodynamics by David Griffiths, or in the older Classical Electrodynamics by John D. Jackson. Nor is it to be found in any of the older classic textbooks. Thus the chain of induction is not a formal part of electromagnetic theory despite its being found in abundance in Internet sources. The first appearance of the chain of induction occurs in the popular science book, Einstein’s Theory Of Relativity, by Max Born. It can be found in both the modern Dover Revised Edition of 1965 and in the English Edition of 1924. In the 1965 Dover Edition the chain of induction appears on page 185 as Figure 98, Electric and Magnetic Fields Linked by induction. This is essentially the same diagram as can be found on the Internet. Hence, it is reasonable to assert that Max Born’s book is the source of the rolling wave myth.

Prior to the appearance of Born’s book, explanations of electromagnetic waves were based upon the concept of an aether medium. One example is as follows from J.A. Fleming, The Wonders of Wireless Telegraphy : Explained in simple terms for the non-technical reader Society for promoting Christian Knowledge, 1913, page 78. “Since moving electric lines give rise to magnetic lines at right-angles to themselves, it is clear that the wire is embraced by a pair of circular expanding lines of magnetic force which accompany the expanding lines of electric force.” This is as close as Fleming gets to anything that sounds like the currently popular rolling wave. On the other hand George Pierce does come a little closer when he says this in Principles of Wireless Telegraphy, 1910, page 39: “The magnetic field produced by the displacement current…being oscillatory in character, will induce displacement currents in the medium farther out from the oscillator and the latter current will lag somewhat behind the former…so that we have the condition of things that exists in a wave motion…” The reader will agree that these are not really the modern conception of a rolling wave, although they just hint in that direction. The full rolling wave is not needed, because the aether medium is what is carrying the oscillations in the form of displacement currents.

The rolling wave appears again in 1938 in The Evolution Of Physics, a science popularization by Albert Einstein and Leopold Infield. In Chapter III, there is the section titled: The two pillars of the field theory, beginning page 142. There it is stated that: “The Change of an electric field is accompanied by a magnetic field….The change of a magnetic field is accompanied by an electric field.” In 1940 this statement appears in a textbook for the first time. In Introduction To Electricity and Optics by Nathaniel H. Frank, page 171, he says this”…the changing magnetic vector inducing an electric field and the changing electric vector (the displacement current) inducing a magnetic field.” After this the rolling wave myth appears in many introductory and elementary physics textbooks, despite its lacking a formal mathematical justification. Its justification being that it is useful as a pedagogical aid, or a teaching aid, to further understanding the physics of electromagnetic waves.

Unfortunately as a teaching aid it is probably misleading for the student rather than aiding in his understanding. That is because when we compare the statements that in the electromagnetic wave the magnetic and electric fields are in phase, the diagrams of the wave that are presented don’t match the diagrams of the chain of induction. The conclusion to be drawn from the chain of induction diagrams is that the electric and magnetic fields are out of phase, or out of step with each other, while the official textbook diagrams of the wave show that the fields are in phase. Hence, there is an inevitable misunderstanding for the student. In the book, The Principles of Electric Wave Telegraphy, 1910, page 349, J.A. Fleming, after stating that the electric and magnetic field vectors are in phase, apologizes in a footnote for making the mistake of saying they were out of phase in a previous publication. Hence even a renowned physicist and wireless radio expert fell into the error of believing that the electric field and magnetic field vectors are out of phase or out of step with each other.

Does the student really understand the purpose of the rolling wave as a teaching aid and not an actual physical reality? That is not clear, but is is also not clear whether the teachers and textbook writers understand this to be a teaching aid and not a formally true fact of the formal mathematical structural logic of the classical electromagnetic theory. In The Feynman Lectures On Physics, Volume II page 18-8, Feynman gives the following explanation regarding the process of wave propagation. “How can this bundle of electric and magnetic fields maintain itself? The answer is by the combined effects of the Faraday Law,…and the new term of Maxwell, (displacement current)… They cannot help maintaining themselves. Suppose the magnetic field were to disappear. There would be a changing magnetic field which would produce an electric field. If this electric field tries to go away, the changing electric field would create a magnetic field back again. So by a perpetual interplay – by the swishing back and forth from one field to the other – they must go on forever. It is impossible for them to disappear.” According to Feynman, the process of the rolling wave, the swishing back and forth, now has become an essential part to the maintenance of the wave and its physical reality. This is far from being a teaching aid and approaches mysticism.

It is the type of reasoning, as just given by Feynman, that Catt, et. al., objected to in their criticism of the textbook version of electromagnetic theory. For them this mysticism of Feynman is no longer physics that exists within reality. In particular, as pointed out above, the reasoning of Feynman means that the time varying nature of the induction process has become essential to the existence of the wave itself and so borders on the absurd, particularly in light of the fact that it rules out DC waves on transmission lines, which have a manifest empirical justification, through the experience of building high speed digital computer circuits. Additionally, it creates a contradiction to the formal mathematical theory where the electric and magnetic fields are mathematically shown to be in time phase.

The reader should notice a particularly important aspect of the justification of the rolling wave. That is the need to provide a physical mechanism for the propagation of the wave in the absence of any physical medium such as the aether. Here we see the way the rolling wave arises within the context of popular books discussing Einstein’s special theory of relativity. In the popular relativity books, it is important to stress the fact that in the electromagnetic theory of Maxwell, the induction laws arise from actions within the aether. This is particularly true for the displacement current, which was a polarization of the aether medium. But ironically, it was Einstein who was first to question the Maxwellian concept of an aether, in his 1905 paper. Ironically, Einstein did not question the existence of displacement current, but the justification of the Faraday law of the production of electricity from a changing magnetic field. The irony arises from the fact that Einstein did not criticism the displacement current, as Catt et al, but removed the aether by criticism of the other curl equation, from which it is speculated that Maxwell deduced his displacement current concept as an analogy by interchanging electricity and magnetism within the formal curl equations. Thus by taking the Faraday law and exchanging electricy and magnetism in the equations, he arrived at the displacement current law. But the irony is that the Faraday law was criticized by Einstein as a justification for the banishment of the aether.

The perceptive reader will notice that Einstein’s success in banishing the aether now required that the curl equations be justified without an aether to sustain the propagation of electromagnetic waves. In Maxwell’s theory, the aether provided an elastic medium through which electromagnetic disturbances were propagated as electromagnetic waves. However, now that there was no aether. Following Einstein’s banishment of aether, there needed to be a physical mechanism for propagating the waves. Hence, Max Born proposes the chain of induction as the new physical mechanism. This is later adopted by Einstein and Infeld and then copied by textbook writers in textbook after textbook. However, this idea never made it into the advanced formal mathematical textbooks and remained orphaned as a pedagogical aid occuring mainly in elementary textbooks.

This brings us to one of the important aspects of the Catt theory. The Catt theory says that there is no need for any physical mechanism to sustain the electromagnetic wave disturbance. The curl equations are to be abolished. This innovation appears at first to be fantasy, but upon reflection it resolves the difficulty of the absurdities produced by the rolling wave as well as giving a more easily understood theory, once the aether is dispensed with. That is to say it differently, the teaching aid of the rolling wave had become an impediment to understanding, in the opinion of Catt et. al., instead of being an aid to understanding.

In the innovation of Catt’s theory, the electric field and magnetic field vectors are coexisting, that is they are parts of the unity of the new concept of an energy current. An idea Catt derived from Oliver Heaviside. This energy current is a wave, but it is not a rolling wave in the usual sense of being a sinusoidal wave, as a water wave, but a wave by virtue of the fact that it moves through space at the velocity c, the speed of light. In transmission lines and wave guides this wave is guided between the wires or walls of the guiding device. There is no problem of sustaining the wave by the time variation of the wave’s fields, and so DC waves are possible on transmission lines. By starting with this new primitive of the energy current defined as the Poynting vector S, the wave of energy current is defined as the cross product ExH=S. When using the International Standard system of units the magnitudes of the vectors E, electric field, and H, magnetic field, are related by the equation E=ZH, where Z is the characteristic impedance of the medium. In Gaussian units the magnitudes of the vectors E and H in free space are equal as discussed in many textbooks like Feynman’s and Jackson’s.

The idea that the vectors for E and H are coexisting, was really not a new innovation, in as much as that concept was already present within the formal mathematical theory. The problem with that theory was that it was difficult to understand how the electric and magnetic fields co-existed together when they had to be mutually induced. Max Born resolved that problem by the chain of induction. But that implied a time sequence of causal induction, which is clearly incorrect. The induction needed to be simultaneous. Some writers tried to resolve this difficulty by explaining that the mutual induction was like a feedback loop, such that an instantaneous change in one field immediately produced a similar change in the other field.

This aids the reader in understanding what F.H. Read says in his book Electromagnetic Radiation, 1980, page 14. “The concept of propagation in the absence of a medium is much more difficult. How can a… field E propagate itself if it has nothing on which to act if there is no medium which can react back on it? The answer to this question lies, in the case of electromagnetic waves, in the existence of the two fields E and B, and in the inter-play between them. We can see from Maxwell’s free space equations that a time-dependent electric field gives rise to a magnetic field, and if this is itself time-dependent it in turn gives rise to an electric field, and hence gives the possibility of propagation of the electric field. This same elasticy exists for the accompanying magnetic field, and the two fields are so closely related that the propagation can only be described as that of an electromagnetic field.” So it is the unity of the mutual elasticy of the fields that binds them together into the electromagnetic wave. According to Read the electric and magnetic fields react upon each other simultaneously as in a feedback loop to create a wave in perpetual motion. This is certainly less fantastic than the Feynman explanation, but it is far more complicated than the Catt theory which asserts the vectors E and H simply move through space with the speed of light as one unified wave of energy current.

The feedback loop notion is only a nascent concept within the explanation presented by Read. His description still seems to read like Born’s chain of induction, which is a causal process that takes time to occur. Read seems to be aiming at the idea that the fields are mutually supporting, such that a change in one field is accompanied by an instantaneous change in the other, which is exactly what is deduced from the formal mathematics and is described in the standard diagrams of the electromagnetic wave found in textbooks. The concept of instantaneous feedback provides the mechanism for the time varying electric and magnetic fields being in phase, instead of out of phase as we would expect for the causal chain of induction as proposed by Max Born.

The current Wikipedia article on Electromagnetic Radiation takes the instantaneous feedback idea one step further and banishes the induction idea altogether. They say that changes in the spatial electric field of the wave as viewed in space, with time fixed, are accompanied by time changes in the magnetic field and vice versa. These changes being in phase such that the variation of the fields in space and time are coincident in space and synchronous in time. However, nothing is said about how the fields are related in a DC pulse waveform. If we assume that the association exists in the same way for DC pulses as for AC waves, then the fields are related as Catt says by the characteristic impedance of the medium, and the description becomes equivalent to the Heaviside energy current S=ExH. The Catt description therefore avoids all of the confusing rhetoric and difficult mathematics in addition to correcting the mistake that DC pulses are disallowed as electromagnetic waves on transmission lines.

In this paper, the Catt, Davidson, Walton criticism of the Maxwell curl equations was investigated in light of the rolling wave concept found in textbooks and the Internet. The rolling wave is described as a myth, because it doesn’t have a solid foundation within formal mathematical theory. The source of the rolling wave was identified as Max Born’s book on Einstein’s relativity theory and is an attempt to justify the physics of the electromagnetic wave in the absence of an aether medium. Although the exact physical discussion of the rolling wave mechanism has evolved through time, the concept does not satisfy as a physical concept. In the final analysis, the rolling wave does not succeed in its purpose of replacing the aether as a physical mechanism so it is not “fit for purpose” as a physical concept. The fact that the rolling wave implies that DC pulses, in the form of electromagnetic waves, can not exist on transmission lines is a final nail in the coffin of that concept.

The reader may want to know exactly why the rolling wave is not fit for purpose. The conception arose from being a teaching aid in popular science books, which simplified the physics behind the difficult mathematical formalism. Ivor Catt objected to the formalism of Maxwell’s Equations as “due to the obscurantism of the fancy maths in which they are dressed..leading to a head spinning brew”. The Catt opinion on the rolling wave is as follows: “The cross linkage of electric and magnetic fields E and H only obscures the issue. There is no interaction between E and H… They are co-existent, co-substantial, co-eternal.” The Catt proposal that the student ought to be taught electromagnetic theory from the simplified point of view of the Oliver Heaviside energy current, was therefore an attempt to bypass the confusion created by attempts to bypass the historical method of mathematical derivation based upon the aether, which involved numerous pitfalls arising from false assumptions, ie the aether, and dubious mathematical methods involving numerous divs and curls.