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CONTRIBUTIONS TO THE ELECTROMAGNETIC THEORY BY HENNING F. HARMUTH AND ONE ANALOGY IN THE HISTORY OF ELECTRODYNAMICS Lukin K. A. LNDES Usikov Institute for Radiophysics and Electronics National Academy of Sciences of Ukraine IRE NASU 12 Akad. Proskura St., Kharkov, 61085, UKRAINE. Tel. +38-057-7203349, Fax +38-057-3152105 e-mail: [email protected]; [email protected] http://LNDES.org

Abstract Considerable nontrivial contributions that have been done by Henning F. Harmuth to electromagnetic signal theory and UWB Radar and Communication systems are briefly described in the paper. An interesting historical analogy in scientific life of Henning Harmuth and Oliver Heaviside is traced. Keywords: electromagnetic signal propagation, modified Maxwell’s Equations, dipole currents, magnetic Ohm’s law.

1. INTRODUCTION This paper is devoted to Henning F. Harmuth, the outstanding scientist and electrical engineer who has been successfully working in the field of Electromagnetic Signal Radiation and Propagation, Radar and Communication close to 60 years. He has initiated research activity in several important fields of contemporary Radar and Communications, such as Carrier Free Radar that nowadays is known as Ultra Wide Band (UWB) Radar, orthogonal sequences in Communications, Large Current Radiator, electromagnetic signals propagation, quantum electrodynamics, etc. This paper is not a full description of the scientific contributions by Henning F. Harmuth, but just an attempt of proper evaluation of some most important of them, from the author’s viewpoint. That is why all statements are disputable and the author will be thankful to those who will send their remarks and critics for further discussions.

2. ON THE MODIFIED MAXWELL’S EQUATIONS If you take a look at textbooks on classical electrodynamics, especially, the old ones, you may easily find that Maxwell’s equations normally are formulated in such a way that they unify basic laws of electromagnetism discovered up to the date of the equations formulation (1860-65) and their publication (1873). Normally, so called constitutive equations are to be considered as an entire part of the set of electrodynamics equations to 978-1-4244-2738-3/08/$25.00 ©2008 IEEE

describe all electromagnetic phenomena in media. In particular, Ohm’s law was always considered as one of these constitutive equations for conducting media. Ohm’s law is present in the equations originally derived by James Maxwell. However, at that period very little was known about the microscopic structure of media. That is why these equations may be reasonably corrected in case of their failure in the adequate description of the phenomena that requires advanced knowledge of media microscopic structure. Publication of the three papers by Henning F. Harmuth [1-3] devoted to his modification of Maxwell’s equations and the necessity to revise the notion of group velocity when studying electromagnetic signal propagation through conducting media has caused more than 10 years contradictory discussion in the IEEE Transactions on Electromagnetic Compatibility (see for example [4-9]). Those who treated themselves as well educated experts in electromagnetic theory did not accept the necessity of Harmuth’s suggestion to modify Maxwell equations for conducting media, and this was the reason for the discussion. Actually the motivation to modify the well accepted Maxwell equations was their failure in describing electromagnetic signals propagation through a conducting medium in terms of non-divergent solutions within the formalism of initial-boundary-value problems with step-like initial conditions for these equations. It turned out that the associated magnetic field (but not the electric one) has a divergent term when electric excitation is applied. In other words, the classical problem on propa-

Contributions to the Electromagnetic Theory by Henning F. Harmuth and One Analogy in the History of … gation of the front of electromagnetic step-like (or pulse) waveform does not have a non-divergent solution if one is interested in obtaining a complete solution that supposes deriving and evaluating both electric and magnetic fields when studying such wave propagation through a conducting medium. When the magnetic analogue of the electric conducting current term has been inserted into Faraday’s law equation the above divergence disappeared even if one will put to zero the related magnetic conductivity coefficient in the obtained solution of the modified Maxwell equations [1, 2]. This has been shown by Henning F. Harmuth and approved by other researchers [8, 9] in terms of mathematics. Later on Henning F. Harmuth noticed that even though magnetic charges have not been discovered yet, there are many physical problems where one may consider dipole magnetic currents rather than monopole ones to make Maxwell equations symmetric. In particular, this model has been applied to describe interstellar propagation of electromagnetic signals [10] and propagation of signals in non-conducting media with electric and magnetic dipole currents [11]. It is typical for human beings to create a cult figure or idolize somebody in an area of their mental activity, and to follow his or her doctrine after that. This approach is reasonable and rather useful to a certain extent but, obviously, this can not last forever! Nevertheless, we may observe that many scientists and engineers are just afraid to touch some statements in contemporary science and engineering! Henning F. Harmuth does not belong to them. Moreover, he does not just follow the stereotypes in science, but work out his own ideas, if the facts and/or their knowledge contradict the old statements or theories extended beyond their limits. Very often these ideas are quite different from the well known and well accepted ones. That is why it is extremely difficult to follow them! Henning F. Harmuth is a rather brave scientist to be able to say that Maxwell’s equations may fail in a situation where all scientists consider them to be undisputedly correct. Moreover, he has enough will and moral power to keep following and defending his statements for more than 20 years! He deserves our respect for that reason as well! It’s worth of making two general comments related to the acceptance of Harmuth’s results by Soviet scientists and to the terminology concerning the modified Maxwell’s equations and the content of this modification. First, I would like to note that the scientific community in the Soviet Union was always open to new ideas. Moreover, the existent system of the Academy of Sciences encouraged initiating new research fields, considering this as one of the main objectives in its permanent developments. In this way, the Soviet scientific community was quiet open to accepting new ideas, and if such an idea originated from outside the country it sometimes provided even more motivation for decision makers to start that research in the Academy of Sciences. This circumstance

along with scientific merit of Harmuth’s ideas explains why his books translated into Russian were so popular among Soviet electrical engineers and has significant influence on the research in the related areas. Moreover, it may be the first time in the history of science that a scientific book written by an American scientist in English was translated into Russian and published in the Soviet Union first, and only a few years later in English, but not in the USA. This has happened not because the author wanted it, but because of tremendous difficulties faced by the author when he tried to publish in the USA a book containing new ideas on applying information theory to physics! My second comment concerns a slightly different reaction to Harmuth’s ansatz related to his modification of Maxwell’s Equations. We have been taught in Soviet Union that two of Maxwell’s equations, Ampere’s law modified by Maxwell and Faraday’s law of electromagnetic induction, are always valid for a medium containing no electric and magnetic charges either free or bound ones (the physical vacuum). At the same time, considering electromagnetic fields in a medium with electric charges one has to add so-called constitutive equations which establish relations between the fields and parameters of the medium. In this way, one may consider many modifications of the overall set of the equations governing electromagnetic fields in media. This is the commonly accepted standpoint in contemporary electrodynamics. However, there is the problem of lossy media. If one needs to consider signal propagation through a lossy medium, such as gas, seawater, or dielectric solids, with dissipation of the energy of the electromagnetic field, one will necessarily need to describe this dissipation, and the simplest way to do that is to use Ohm’s law connecting electric field and electric current density associated with the motion of free electrons or ions. This may be done because of the existence of electrons or dipoles as the carriers of electric currents. At the same time, nobody introduces a similar law to describe losses associated with the magnetic field because the existence of free magnetic charges has not been proven, but we know that magnetic dipoles exist just as electric ones. At this point it is worth to note that the electromagnetic field losses due to interaction with bounded charges or dipoles in dielectric and magnetic materials are usually described in terms of imaginary parts of dielectric permittivity and permeability associated with the electric and magnetic dipoles of the medium, respectively. Considering the propagation of electromagnetic signals in the form of rectangular pulses or step-functions through a lossy medium, Henning F. Harmuth faced the problem of singularity in the expression for the magnetic field if the pulse was exited by electric excitation. In order to go around this problem he suggested modifying the Maxwell’s equations for conducting media via introduction into Faraday’s law a term proportionate to the magnetic field, i.e. he suggested to introduce Ohm’s law for magnetic monopole or dipole current densi-


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Lukin K. A. ties. Surprisingly, this step eliminated the singularity mentioned above even if the medium’s magnetic conductivity will be put to zero in the solution obtained. This allowed him to investigate the propagation of signals through media with heavy losses. Henning F. Harmuth called the equations obtained in this way Modified Maxwell’s equations. Initially it was just a mathematical need which, by the way, changed the symmetry class of the equations under consideration (from U(1) to SU(2) as noticed by Terrence Barrett). However, in my opinion, there is at least one physical justification for the need of that modification which I would like to explain briefly here though it deserves more detailed investigation. For the above reasons, Maxwell’s equations with an added term for magnetic current density should be considered as one of the possible modifications of Maxwell’s equations, but because of the exceptional importance of the particular case of lossy media the term Modified Maxwell’s equations may be applied and reasonably used.

3. ON THE MAGNETIC OHM’S LAW Let recall the microscopic picture of the electric Ohm’s law. The current density in a conducting medium is proportionate to the electric field strength because the electrons being accelerated by the electric field experience multiple inelastic collisions with heavy atoms, transferring portion of their kinetic energy to heating of the crystal lattice or separated ions. However, the process of heating is the consequence of a huge number of microscopic (individual) processes of transforming the energy and shape of non-polarized neutral atoms or ions due to those collisions which leads to varying of their dipole momentum in time. This implies the generation of additional microscopic currents in the lossy medium, and the magnetic component of the field will necessarily interact with these currents (eventually transferring portion of its energy to them) which may be interpreted and described as Ohm’s law for a magnetic current density. In this way, the conventional Ohm’s law in a lossy medium is to be always supplemented with a magnetic Ohm’s law! This is another reasonable problem, how strong will be this additional current? Normally, the related losses should be much less compared to the losses associated with the electric Ohm’s law and therefore in many cases they may be ignored. Another reason why may ignore these currents is explained by very short relaxation time from the deformed shape o the atom to its normal state. That means very short time of existence of such dipole currents which does not affect signal propagation in case of slow varying fronts of the pulse. However, this is not the case when studying the propagation of step-like signals through lossy media. The main reason for that lays in the fact that step-like idealization of an electromagnetic pulse implies infinitely fast varying of its fronts. In reality this means that we will have to take into account Ohm’s law for magnetic field whenever the raising time of a pulse will be comparable with the above relaxation time. Another situation that requires 278

taking into account the above losses occurs when studying pulse propagation over extremely long distances since small effects will be accumulated during the long distance of propagation, and sooner or later they will make an appreciable contribution to the solution. General approach to calculation of the dipole electric and magnetic currents induced by electron collisions is given in [21].

4. ELIMINATING INFINITIES Henning F. Harmuth suggested not one, but several innovations in physics based upon eliminations of infinities. Actually we do not very often think about the fact that infinity is an irrational abstraction, most likely given to us by the devil, and we have to remember that any kind of infinity introduced into a theory explicitly or implicitly will give us also infinity in the solutions. Nevertheless, the infinity concept in all its manifestations possesses such magic power of attraction via its convenience, seeming simplicity and even self-evidence that it forces us to resist new theories that are suggested just to avoid the above infinites! All this takes place in contemporary physics even in spite of impressive successes in the creation of Quantum Physics and the Special Theory of Relativity which were results of the elimination of two well known infinities. We still have several hidden infinities in today’s theories describing and exploring nature. In his paper, Henning F. Harmuth summarizes his long-term research into this issue and draws our attention to infinity hidden in the continuum of spacetime normally used as a self-evident supposition, and also to the infinity associated with the infinity of information contained implicitly in many theoretical descriptions of nature. Henning F. Harmuth not just draws our attention to the problem, but also suggests and elaborates the related theoretical approaches to eliminating these infinities when solving new physical problems. Special attention deserves his idea to formulate quantum electrodynamics based on the Modified Maxwell equations since it looks like his approach enables to go around all the divergences which means elimination of another infinity. Henning F. Harmuth gave his vision of very important problems in physics that have not been solved so far: “… a. Introduction of the Modified Maxwell Equations and difference equations to Quantum Physics, in particular to the Klein-Gordon and Dirac’s Differential Equations (I am working on this). b. Studying the use of the Modified Maxwell Equations and difference equations for the unification of the General Theory of Relativity and Quantum Theory. c. The unification of the electromagnetic force, based on Maxwell’s Equations, and the weak interaction force needs to be reworked for the Modified Maxwell Equations and finite differences”. Henning F. Harmuth.


Contributions to the Electromagnetic Theory by Henning F. Harmuth and One Analogy in the History of … Young scientists, I believe, will consider these problems as a challenge in their scientific career to solve them and make thereby an appreciable contribution to contemporary physics.

5. HISTORICAL PARALLELS Let’s come back to the story of publications of Harmuth’s papers [1, 2] and some consequences of that. As I mentioned above, these papers have initiated more than 10 years discussion whether it is necessary or useless to modify Maxwell’s equations for conducting media: some authors supported H.Harmuth’s ideas, while others noted that the idea is not a new one since many other authors used fictitious magnetic currents in Maxwell’s equations to introduce symmetry and make solutions finding much easier. Finally, there were those who were very much against this modification of Maxwell’s equations, considering it not just useless, but also unacceptable. They opposed that idea as strongly as did those” leading experts” mentioned in the very first page of this Issue. I think just those experts were insisting on punishing the person who allowed the publication of those papers: Richard B. Schultz the Editor of IEEE Transaction on Electromagnetic Compatibility. He was retired as Editor of the above journal shortly after those publications because of “…lack the invaluable secretarial support necessary for the job” [19]. This is not the only such case in the history of physics and may be not only of physics, but also other fields of human mental activity. However, it is interesting to recall briefly that a similar story happened to Oliver Heaviside 100 years before Harmuth’s publications. Nowadays we respect Oliver Heaviside for his amazing and remarkable contributions to electromagnetism, and consider him as a well-recognized scientist and ”telegraphist” [20]. He was well ahead of his time in many issues of electrodynamics and signal propagation in telegraph cables. He was the first who formulated Maxwell’s equations in the form we use it now; he created the theory of signal propagation in cables; he predicted Cherenkov’s radiation and much more. At the end of the 19-th century, telephone and telegraph communication was a big business which also stimulated the related research focused on the increase of communications distance and the enhancement of its quality. All experts of that time widely believed that signals transmitted through a cable were nothing else but electric currents flowing in its conducting wire similar to a liquid in a pipe. O. Heaviside was the first who figured out, that an electromagnetic signal in a coaxial cable is not a current flowing in a conducting wire, but an electromagnetic field concentrated between the wire and the shield. This helped him to understand how to enhance distortionless propagation of EM signals in cables and to increase the distance of the telephone communications. However, in 1887 when he ”...first suggested adding extra inductance to telephone lines the idea struck most engineers as absurd” [20, p. 137]. Heaviside’s attempt to publish his

idea in the Electrician Journal faced the problem of getting clearance for publication from his boss W.H. Preece, chief of the Post Office telegraph engineers, who stopped this paper from publication since he disagreed with Heaviside’s idea. As a leading expert in W. Thomson’s theory of electric signal propagation in the conducting wire (which was wrong as we know now) he considered Heaviside’s idea as completely wrong and absurd. However Heavisde managed to publish his paper by parts with the support of Mr. Biggs, the editor of Electrician who published Heaviside’s articles ”in spite of most strenuous opposition by proprietors and every member of the staff” [20, p. 142]. It happened in the period between April and September of 1887, and ”early in October 1887 he was abruptly removed as Editor of the Electrician” [20, p. 142]. A familiar story, is it not? It is also interesting to recall that ”...when loading coils were finally introduced commercially around 1900 in America, their success helped make a number of scientists, engineers, and corporations, - conspicuously not including Heaviside - very rich. There is thus a special irony in the fact that when Heaviside first proposed inductive loading in 1887, British telephone engineers rejected his suggestion outright” [20, p. 137]. I would recommend to read Harmuth’s books rather carefully with keeping in mind the above story. To those who are interested in the details of interesting and not easy work of the ”Maxwellians” in the 19th century I would strongly recommend reading the book [20].

ACKNOWLEDGMENTS I am grateful to Henning F. Harmuth for cooperation, consultations and hospitality when I was visiting him in Washington, DC and Destin, Florida. My special thanks to him for inviting me to work on the book [10], which was very instructive and informative for me. I also would like to thank Dr. Gerry Kaiser who gave me as a gift an excellent book by Bruce Hunt “The Maxwellians” (when attending the NRT-2003 Conference in Kharkov): not having this book I would not be able to write the “Historical Parallels” section.

REFERENCES 1. Harmuth H.F. Nov.1986, Correction of Maxwell’s Equations for Signals I, IEEE Trans. on Electromagnetic Compatibility. EMC–28, #4, 250–8. 2. Harmuth H.F. Nov.1986, ‘Correction of Maxwell’s Equations for Signals II’, IEEE Trans. on Electromagnetic Compatibility. EMC–28, # 4, 259–6. 3. Harmuth H.F. Nov.1986, ‘Propagation Velocity of Electromagnetic Signals’, IEEE Trans. on Electromagnetic Compatibility. EMC–28, #4. 267–72. 4. Wait J. R. May 1992, The ”magnetic conductivity” and wave propagation’, IEEE Trans. on Electromagnetic Compatibility. EMC–34, # 2. – P. 139 5. Harmuth H.F. Aug. 1992, ‘Response to a Letter by J.R.Wait on Magnetic Dipole Currents’, IEEE


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Lukin K. A. Trans. on Electromagnetic Compatibility, EMC– 34, # 3, 374–5. 6. Lakhtakia A. Aug.1992, ‘Comments on a Letter by J.R.Wait on Magnetic Resistivity’, IEEE Trans. on Electromagnetic Compatibility, EMC– 34, #3, 375–6. 7. Afsar O.R. Aug.1990, Riemann-Green Function Solution of Transient Electromagnetic Plane Waves in Lossy Media IEEE Trans. on Electromagnetic Compatibility, EMC–32, #3, 228–31. 8. Hillion P. May 1991, ‘Remark on Harmuth’s ”Corrections of Maxwell’s Equations for Signals I”’ IEEE Trans. on Electromagnetic Compatibility, EMC–33, #2,144. 9. Barrett T.W. May 1989, ‘Comments on Solutions of Maxwell’s Equations for General Nonperiodic Waves in Lossy Media’, IEEE Trans. on Electromagnetic Compatibility, EMC–31, #2, 197–9. 10. Harmuth H.F. and Lukin K.A. 2000, Interstellar Propagation of Electromagnetic Signals. N.-Y.: Kluwer Academic/Plenum Publishers. 11. Harmuth H.F. and Lukin K.A. 2002, ‘Propagation of Short Electromagnetic Pulses through Nonconducting Media with Electric and Magnetic Dipole Currents’, Radiophysics and Radioastronomy. 7, # 4, 362–3. 12. Klimontovich Yu.L. 1982, Statistical Physics. M.: Fizmatgiz. 608 p. (In Russian).

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13. Harmuth H.F. 1986, Propagation of Nonsinusoidal Electromagnetic Waves. New York: Academic Press. 14. Harmuth H.F., Barrett T.W., and Meffert B. 2001, Modified Maxwell Equations in Quantum Electrodynamics. – Singapore: World Scientific. 15. Harmuth H.F. and Hussain M.G.M. 1994, Propagation of Electromagnetic Signals. Singapore: World Scientific. 16. Harmuth H.F., Boules R.N., and Hussain M.G.M. 1999, Electromagnetic Signals: Reflection, Focusing, Distortion, and Their Practical Applications. New York: Kluwer Academic/Plenum Publishers. 17. Harmuth H.F. and Meffert B. 2003, Calculus of Finite differences in Quantum Electrodynamics. Amsterdam: Elsevier/Academic Press. 312 p. 18. Harmuth H.F. and Meffert B. 2005, Dogma of the Continuum and the Calculus of Finite Differences in Quantum Physics. Amsterdam: Elsevier/Academic Press. 317 p. 19. Schulz R.B, Feb.1988, ‘Editorial Reminiscences of an Editor’, IEEE Trans. on Electromagnetic Compatibility, EMC–30, #1, 1. 20. Hunt B.J. 1991, The Maxwellians. Ithaca and London: Cornell University Press. 266 p. 21. Lukin K.A. 2007, ‘On the Description of Electromagnetic Signal Propagation through Conducting Media’, Electromagnetic Phenomena, 7, #1, 180-5.
