James Clerk MAXWELL

20 Quaternion Equations

James Clerk Maxwell, "A Dynamical Theory of the Electromagnetic Field" ( Royal Society Transactions, Vol. CLV, 1865, p 459 ); Orally read Dec. 8, 1864. [ MS-Word.doc ]

Andre Waser : On the Notation of Maxwell's Field Equations [ PDF ]

TOMBE, Frederick: Maxwell's Original Equations ~ Before Heaviside, et al., mangled them.

The 1873 edition of A Treatise on Electricity & Magnetism contains the 20 Quaternion Equations that later were rewritten --- censored --- by Oliver Heaviside, et al.. These equations reconcile relativity with modern quantum physics and help to explain "free energy" and anti-gravity.

Table of Contents:

Volume 1: 1 ~ 2 ~ 3 ~ 4 ~ 5 ~ 6 ~ 7 ~ 8 ~9 ~ 10 ~ 11 ~ 12 ~ 13

Volume 2: 1 ~ 2 ~ 3 ~ 4 ~ 5 ~ 6 ~ 7 ~ 8 ~ 9 ~ 10 ~ 11 ~ 12 ~ 13 ~ 14 ~ 15 ~ 16 ~ 17 ~ 18 ~ 19

Links to the complete copies in the Posner Collection at Carnegie Mellon University:

The complete copies also are included in Rex Research Civilization Kit.

Maxwell's Quaternion Equations

by Col. Tom Bearden

Maxwell's original theory was published as:

James Clerk Maxwell, "A Dynamical Theory of the Electromagnetic Field", Royal Society Transactions, Vol. CLV, 1865, p 459. The paper was orally read Dec. 8, 1864.

[ MS-Word.doc ]

It is also published in The Scientific Papers of James Clerk Maxwell, 2 vols. bound as one, edited by W. D. Niven, Dover, New York, 1952, Vol. 1, p. 526-597. Two errata are given on the unnumbered page prior to page 1 of Vol. 1.

In this paper Maxwell presented his seminal theory of electromagnetism, containing 20 equations in 20 unknowns. His equations of the electromagnetic field are given in Part III, General Equations of the Electromagnetic Field, p. 554-564. On p. 561, he lists his 20 variables. On p. 562, he summarizes the different subjects of the 20 equations, being three equations each for magnetic force, electric currents, electromotive force, electric elasticity, electric resistance, total currents; and one equation each for free electricity and continuity. In the paper, Maxwell adopts the approach of first arriving at the laws of induction and then deducing the mechanical attractions and repulsions.

A copy of the original Maxwell paper can easily be obtained for about $15 from Amazon etc. It is:

James Clerk Maxwell, The Dynamical Theory of the Electromagnetic Field, edited by Thomas F. Torrance, Wipf and Stock Publishers, Eugene, Oregon, 1996. This booklet, which sells for about $15, contains Maxwell's original 1865 dynamical theory paper and some additional commentaries.

Here's what Barrett --- a nationally known electrodynamicist and one of the co-founders of ultrawideband radar --- has to say about Maxwell's theory:

"In the case of electromagnetism, the theory was first simplified before being frozen. Maxwell expressed electromagnetism in the algebra of quaternions and made the electromagnetic potential the centerpiece of his theory. In 1881 Heaviside replaced the electromagnetic potential field by force fields as the centerpiece of electromagnetic theory. According to him, the electromagnetic potential field was arbitrary and needed to be "assassinated" (sic). A few years later there was a great debate between Heaviside and Tate about the relative merits of vector analysis and quaternions. The result was the realization that there was no need for the greater physical insights provided by quaternions if the theory was purely local, and vector analysis became commonplace.

The vast applications of electromagnetic theory since then were made using vector analysis. Although generations of very effective students were trained using vector analysis, more might be learned physically by returning, if not to quaternions, to other mathematical formulations in certain well-defined circumstances. As examples, since the time when the theoretical design of electromagnetism was frozen, gauge theory has been invented and brought to maturity and topology and geometry have been introduced to field theory. Although most persons view their subject matter through the filter of the mathematical tools in which they are trained, the best mathematical techniques for a specific analysis depend upon the best match between the algebraic logic and the underpinning physical dynamics of a theoretical system." [Terence W. Barrett and Dale M. Grimes, Preface, p. vii-viii, in Advanced Electromagnetism: Foundations, Theory and Applications, Terence W. Barrett and Dale M. Grimes (eds.), World Scientific, Singapore, 1995.]

Maxwell died in 1879 of stomach cancer.

In the 1880s, several scientists --- Heaviside, Gibbs, Hertz etc. --- strongly assaulted the Maxwellian theory and dramatically reduced it, creating vector algebra in the process. Then circa 1892 Lorentz arbitrarily symmetrized the already seriously constrained Heaviside-Maxwell equations, just to get simpler equations easier to solve algebraically, and thus to dramatically reduce the need for numerical methods (which were a "real bear" before the computer). But that symmetrization also arbitrarily discarded all asymmetrical Maxwellian systems - the very ones of interest to us today if we are seriously interested in usable EM energy from the vacuum.

So anyone seriously interested in potential systems that accept and use additional EM energy from the vacuum, must first violate the Lorentz symmetry condition, else all his efforts are doomed to failure a priori.

We point out that quaternion algebra has a higher group symmetry than either vector algebra or tensor algebra, and hence it reveals much more EM phenomenology and dynamics than does EM in vector or tensor form.

Today, the tremendously crippled Maxwell-Heaviside equations --- symmetrized by Lorentz --- are taught in all our universities in the electrical engineering (EE) department. Note that the EE professors still dutifully symmetrize the equations, following Lorentz, and thus they continue to arbitrarily discard all asymmetrical Maxwellian systems. Hence none of them has the foggiest notion of how to go about developing an "energy from the vacuum" system, which is asymmetrical a priori.

The resulting classical electromagnetics and electrical engineering (CEM/EE) model taught in all our university EE departments also contains very serious falsities. Most of modern physics, such as special and general relativity, quantum field theory, etc., has been developed since the 1880s and 1890s fixating of the symmetrized Maxwell-Heaviside equations. A paper gathering together a listing these serious flaws and giving proper citations, is T. E. Bearden, "Errors and Omissions in the CEM/EE Model," available for free downloading at: .

This paper also shows a magnetic Wankel engine (suppressed from the world market) that can be built by any electrical engineering department or physics department, and then tested at COP>1.0 to one's heart's content. The magnetic Wankel system is also easily close-looped for self-powering (where all its input energy is freely furnished by the vacuum, and the operator need furnish none of the input energy at all --- thus providing fuel free, continuous use of the energy from the vacuum, at will.

In the hard physics literature, rigorous proof that eliminating the arbitrary Lorentz condition provides systems having free additional energy currents from the vacuum is given by M. W. Evans et al., "Classical Electrodynamics without the Lorentz Condition: Extracting Energy from the Vacuum," Physica Scripta, Vol. 61, 2000, p. 513-517. Evans' own O(3) model is very advanced, and it also directly specifies mechanisms for an EM system receiving and using excess energy freely from the vacuum.

Fortunately, today some scientists have turned again to higher group symmetry algebras in which EM is expressed. These higher group symmetry electrodynamics theories then show far more EM phenomenology than the standard CEM/EE model used in electrical power engineering.

Anyway, that gives you a brief overview of the Maxwell theory, and the rather sharp curtailment of it that has become the accepted but very crippled model for electrical engineering. Specifically, it is that crippled model and its continued propagation and use that is directly responsible for the increasing energy crisis worldwide, and our dependence on conventional fuels etc.

We do point out that the original Maxwell quaternion and quaternion-like theory of 1865 also contained errors, by the physics that has been learned since then. One of those errors was Maxwell's assumption of the material ether, an ether which was falsified experimentally in 1887 after Maxwell was already dead. But the present CEM/EE model still assumes that same old material ether, more than a century later.

Also, after Maxwell published the first edition of his famous "Treatise.", not much happened. He was soundly criticized for using the quaternion approach, and even his own editor chastised him rather unmercifully for it. His attachment to the potentials as primary was also roundly criticized, since almost all theorists of the day believed that the potentials were simply mathematical conveniences having no physical reality whatsoever. To them, the force fields were the only physical reality in Maxwell's theory. Today, of course, we know in the quantum theory that it is the potentials that are primary, and the fields are derived from changes in the potentials.

The history of Maxwell's famous treatise is as follows: The publications are James Clerk Maxwell, A Treatise on Electricity and Magnetism, Oxford University Press, Oxford, 1873, Second Edition 1881 (Maxwell was already dead), Third Edition, Volumes 1 and 2, 1891. Foreword to the second edition was by Niven, who finished the work as Maxwell had dramatically rewritten the first nine chapters, much new matter added and the former contents rearranged and simplified. Maxwell died before finishing the rest of the second edition. The rest of the second edition is therefore largely a reprint from the first edition. The third edition edited by J. J. Thomson was published in 1892, by Oxford University Press, and later was published unabridged, Dover Publications, New York, 1954. J. J. Thomson finished the publication of the third edition, and wrote a "Supplementary Volume" with his notes. A summary of Maxwell's equations is given in Vol. II, Chapter IX of the third edition. However, Maxwell had gone (in his second edition) to some pains to reduce the quaternion expressions himself, and not require the students to know the calculus of quaternions (so stated on p. 257). We note that Maxwell did not finish the second edition, but died before that. He actually had no hand at all in the third edition as to any further changes. The Second edition (unfinished by Maxwell) was later finished by Niven by simply adding the remaining material from the previous first edition approved by Maxwell to that part that Maxwell had revised. The printing of the first nine chapters of the third edition was already underway when J. J. Thomson was assigned to finish the editing of the manuscript.

Indeed, as an example of a major error in the present CEM/EE model, we know today that matter is a component of force, and therefore the EM force fields prescribed in matter-free space by Maxwell and his followers (and by all our electrical engineering departments today), do not exist. The EM field in massless space is force-free, and is a "condition of space" itself, as pointed out by Feynman in his three volumes of sophomore physics. Specifically, speaking of the electric field Feynman states:

"...the existence of the positive charge, in some sense, distorts, or creates a "condition" in space, so that when we put the negative charge in, it feels a force. This potentiality for producing a force is called an electric field." [Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures on Physics, Addison-Wesley, Reading, MA, Vol. 1, 1964, p. 2-4].

He further states:

"We may think of E(x, y, z, t) and B(x, y, z, t) as giving the forces that would be experienced at the time t by a charge located at (x, y, z), with the condition that placing the charge there did not disturb the positions or motion of all the other charges responsible for the fields." [ibid, vol. II, p. 1-3.]

But the CEM/EE texts still teach that old force field in empty space. However, Jackson --- a superb classical electrodynamicist of international reknown --- at least points out that this dramatic error in the model is just ignored. Jackson states:

"Most classical electrodynamicists continue to adhere to the notion that the EM force field exists as such in the vacuum, but do admit that physically measurable quantities such as force somehow involve the product of charge and field." [J. D. Jackson, Classical Electrodynamics, Second Edition, Wiley, 1975, p. 249].

Jackson does admit it and point out that this logical problem is just ignored, for which he is to be highly commended. Most textbooks simply do not even discuss it.

So at his death in 1879, Maxwell had already laboriously simplified some 80% of his "Treatise" himself, to comply with the severe demands of the publisher. The second edition of his book thus has the first 80% considerably changed by Maxwell himself. The third edition contained the same theory as the second edition essentially, but just with additional commentary. It is this third edition that is widely available and usually referred to as "Maxwell's theory".

Today, there is still a widespread belief that the third edition represents Maxwell's original EM work and theory, in pristine form just as created originally by Maxwell.

It doesn't.

Best wishes,

Tom Bearden