James Clerk Maxwell: A Treatise on Electricity and Magnetism

**[rexresearch.com](index.htm)**

---

**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](maxwell1/maxwell1864.doc)
> ]**
>
> **Andre Waser : On the Notation of Maxwell's Field Equations
> [ [PDF](maxwell1/20equations.pdf)
> ]**
>
> **>> [TOMBE, Frederick: Maxwell's Original
> Equations](maxwell1/1MaxwellOrigEq.pdf) ~ 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](maxwell1/contents-1.jpg)
> ~ [2](maxwell1/contents-2.jpg)
> ~ [3](maxwell1/contents-3.jpg)
> ~ [4](maxwell1/contents-4.jpg)
> ~ [5](maxwell1/contents-5.jpg)
> ~ [6](maxwell1/contents-6.jpg)
> ~ [7](maxwell1/contents-7.jpg)
> ~ [8](maxwell1/contents-8.jpg)
> ~[9](maxwell1/contents-9.jpg)
> ~ [10](maxwell1/contents-10.jpg)
> ~ [11](maxwell1/contents-11.jpg)
> ~ [12](maxwell1/contents-12.jpg)
> ~ [13](maxwell1/contents-13.jpg)**
>
> **Volume 2: [1](maxwell2/contents-1.jpg)
> ~ [2](maxwell2/contents-2.jpg)
> ~ [3](maxwell2/contents-3.jpg)
> ~ [4](maxwell2/contents-4.jpg)
> ~ [5](maxwell2/contents-5.jpg)
> ~ [6](maxwell2/contents-6.jpg)
> ~ [7](maxwell2/contents-7.jpg)
> ~ [8](maxwell2/contents-8.jpg)
> ~ [9](maxwell2/contents-9.jpg)
> ~ [10](maxwell2/contents-10.jpg)
> ~ [11](maxwell2/contents-11.jpg)
> ~ [12](maxwell2/contents-12.jpg)
> ~ [13](maxwell2/contents-13.jpg)
> ~ [14](maxwell2/contents-14.jpg)
> ~ [15](maxwell2/contents-15.jpg)
> ~ [16](maxwell2/contents-16.jpg)
> ~ [17](maxwell2/contents-17.jpg)
> ~ [18](maxwell2/contents-18.jpg)
> ~ [19](maxwell2/contents-19.jpg)**
>
> **Links to the complete copies in
> the [Posner
> Collection](http://posner.library.cmu.edu/Posner/books/book.cgi?call=537_M46T_1873_VOL._1) at Carnegie Mellon University:**
>
> **<http://posner.library.cmu.edu/Posner/books/book.cgi?call=537_M46T_1873_VOL._1>**
>
> **<http://posner.library.cmu.edu/Posner/books/book.cgi?call=537_M46T_1873_VOL._2>**
>
> **The complete copies also are
> included in
> [Rex Research
> Civilization Kit](index.htm).**
>
> ---
>
> **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](maxwell1/maxwell1864.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:**
>
> **http://www.cheniere.org/techpapers/CEM%20Errors%20-%20final%20paper%20complete%20w%20longer%20abstract4.doc**.
>
> **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***
>
> ---