Paul S. wrote:...and, no, I'm not suggesting "Maxwell's Silver Hammer" for the soundtrack...
But we *are* quizzical, studying pataphysical science in the home...
I am talking about the assertion that we have seen here in the forums -- that I cited when I opened my talk in Las Vegas, that I referred to in the "Response to RHull" also posted elsewhere in the forums -- that James Clerk Maxwell's fundamental formulas of electromagnetic theory are ... incomplete.
The thing about Bearden is, sure people laugh at him... but he may actually be a crackpot. I've struggled with his assertions in this regard before and got not very far. But my classical electromagnetics knowledge is slim, beyond a vague high-school understanding that 'voltage is pressure' and the right-hand rule.
I've done a little digging about quaternions, and though I don't really grok the subject at all, I find William Rowan Hamilton a very interesting chappie. http://en.wikipedia.org/wiki/William_Rowan_Hamilton
As I understand it, he basically invented complex analysis as we understand it, and saw quaternions as the next obvious step of treating 3D coordinates as numbers. Only, this is the fun bit, the maths didn't work in 3D, he had to take it to 4D. Basically inventing spacetime before Einstein did. He spent I think his next 40 years trying to evangelise quaternions as The Answer To The Universe and nobody much listened. The problem with quaternions is they are noncommutative under multiplication: ie, the *order* you multiply them is significant. This was seen as a problem, so vectors were used instead in physics. They're less elegant, I think, but you can do almost anything with them. However, *maybe* the restrictions that appear using quaternions actually reveal some deep structure about the way spacetime works? Possibly using them would stop us from going down too many mathematical dead ends? Hamilton believed so. Doug Sweet - http://world.std.com/~sweetser/quaterni ... index.html
- is another amateur physicist who is trying to restate Einsteinian physics in quaternions. It's still an open question, I think, if it will get anywhere.
Peter Guthrie Tait among others, advocated the use of Hamilton's quaternions. They were made a mandatory examination topic in Dublin, and for a while they were the only advanced mathematics taught in some American universities. However, controversy about the use of quaternions grew in the late 1800s. Some of Hamilton's supporters vociferously opposed the growing fields of vector algebra and vector calculus (from developers like Oliver Heaviside and Willard Gibbs), because quaternions provide superior notation. While this is undeniable for four dimensions, quaternions cannot be used with arbitrary dimensionality (though extensions like Clifford algebras can). Vector notation largely replaced the "space-time" quaternions in science and engineering by the mid-20th century.
Today, the quaternions are in use by computer graphics, control theory, signal processing and orbital mechanics, mainly for representing rotations/orientations. For example, it is common for spacecraft attitude-control systems to be commanded in terms of quaternions, which are also used to telemeter their current attitude. The rationale is that combining many quaternion transformations is more numerically stable than combining many matrix transformations. In pure mathematics, quaternions show up significantly as one of the four finite-dimensional normed division algebras over the real numbers, with applications throughout algebra and geometry.
I still can't yet get my head around what they are, geometrically. My math-fu is not strong. I can visualise complex numbers as a rotation and extension in a polar-coordinate plane space; if 'i' is a 90 degree out-of-plane rotation, then 'j' and 'k' presumably also are too, and one would think a quaternion would be three rotations in space and an extension in time, but that doesn't account for the noncommutativity, or does it?
Interestingly Hamilton develops the idea of mathematical sequence as primarily indicating *time*, not linear space, and the '90 degree rotation' of i,j,k as being spatial dimensions. Interesting to me that he prioritises time like that; it's the opposite of the normal intuition.
I think the 'Hamiltonian' which shows up in quantum mechanics has nothing to do with quaternions, but I'm not sure. The seem to have permeated Hamilton's thought pretty deeply.
http://www.zpenergy.com/modules.php?nam ... e&sid=1656
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.
Guess who wrote that? Bearden, of course.
Yes. However, Aspden argues much the same as Bearden does, only using different terms, about asymmetry being important. So I suspect there is something behind what they're both talking about, but it needs to be translated. That's probably a lot of work by people who understand the relevant math and science. And it's definitely in contradiction of some fairly fundamental assumptions of electromagnetics, so it's only crackpots or amateurs with no career to lose who will be open to doing it, but it's only well-trained scientists who stand a chance of constructing experiments to prove it.
The basic claim is something like 'electricity is not really caused by electron flow, rather it is caused by an underlying energy of space which is merely triggered by the electron flow' and that in particular visualising electron flow like water in a pipe, requiring a closed loop, is the Wrong Metaphor, and that creating closed electrical circuits actually mostly cancels out the underlying energy. I don't understand what the Right Metaphor is, however. Both Aspden and Bearden seem to be interested in circuits with 'free-floating grounds' and 'making the vacuum ring' by hitting it with a short resonant EM pulse and then looking for 'echoes' which manifest as alternating positive/negative charges on different sides of a circuit which we then extract as power. Sort of like the production of 'virtual particles' from cosmic rays, I think, but at much lower energy levels (where conventional theory would consider such virtual interactions impossible). There's a huge lack of fundamental theory here to explain their intuition.
Controversy has always surrounded the term Maxwell's equations concerning the extent to which Maxwell himself was involved in these equations. The term Maxwell's equations nowadays applies to a set of four equations that were grouped together as a distinct set in 1884 by Oliver Heaviside, in conjunction with Willard Gibbs.
The importance of Maxwell's role in these equations lies in the correction he made to Ampère's circuital law in his 1861 paper On Physical Lines of Force. He added the displacement current term to Ampère's circuital law and this enabled him to derive the electromagnetic wave equation in his later 1865 paper A Dynamical Theory of the Electromagnetic Field and demonstrate the fact that light is an electromagnetic wave. This fact was then later confirmed experimentally by Heinrich Hertz in 1887.
The reason that these equations are called Maxwell's equations is disputed. Some say that these equations were originally called the Hertz-Heaviside equations but that Einstein for whatever reason later referred to them as the Maxwell-Hertz equations. see pages 110-112 of Nahin's book
These equations are based on the works of James Clerk Maxwell, and Heaviside made no secret of the fact that he was working from Maxwell's papers. Heaviside aimed to produce a symmetrical set of equations that were crucial as regards deriving the telegrapher's equations. The net result was a set of four equations, three of which had appeared in substance throughout Maxwell's previous papers, in particular Maxwell's 1861 paper On Physical Lines of Force and 1865 paper A Dynamical Theory of the Electromagnetic Field. The fourth was a partial time derivative version of Faraday's law of induction that doesn't include motionally induced EMF. 
Of Heaviside's equations, the most important in deriving the telegrapher's equations was the version of Ampère's circuital law that had been amended by Maxwell in this 1861 paper to include what is termed the displacement current.
Confusion over the term "Maxwell's equations" is further increased because it is also sometimes used for a set of eight equations that appeared in Part III of Maxwell's 1865 paper A Dynamical Theory of the Electromagnetic Field, entitled "General Equations of the Electromagnetic Field"  (page 480 of the article and page 2 of the pdf link), a confusion compounded by the writing of six of those eight equations as three separate equations (one for each of the Cartesian axes), resulting in twenty equations in twenty unknowns. (As noted above, this terminology is not common: Modern references to the term "Maxwell's equations" usually refer to the Heaviside restatements.)
These original eight equations are nearly identical to the Heaviside versions in substance, but they have some superficial differences. In fact, only one of the Heaviside versions is completely unchanged from these original equations, and that is Gauss' law (Maxwell's equation G below). Another of Heaviside's four equations is an amalgamation of Maxwell's law of total currents (equation A below) with Ampère's circuital law (equation C below). This amalgamation, which Maxwell himself originally made at equation (112) in his 1861 paper "On Physical Lines of Force" (see above), is the one that modifies Ampère's circuital law to include Maxwell's displacement current.
We could start, I guess, by looking at 'General Equations of the Electromagnetic Field' and trying to see whether these eight (or twenty) equations are in fact identical to the modern Heaviside versions.
Bearden points at Lorentz as introducing the symmetry he hates. Deyo points at the Lorentz force as being crucial to the operation of flying discs. Lorentz force is also the component shared by toroidal magnetic field systems such as cyclotrons, magnetrons, calutrons and tokamaks. Is there something about this force which is misunderstood in the modern interpretation?
Hendrik Lorentz introduced this force in 1892. However, the discovery of the Lorentz force was before Lorentz's time. In particular, it can be seen at equation (77) in Maxwell's 1861 paper On Physical Lines of Force. Later, Maxwell listed it as equation "D" of his 1864 paper, A Dynamical Theory of the Electromagnetic Field, as one of the eight original Maxwell's equations.
Although this equation is obviously a direct precursor of the modern Lorentz force equation, it actually differs in two respects:
* It does not contain a factor of q, the charge. Maxwell didn't use the concept of charge. The definition of E used here by Maxwell is unclear. He uses the term electromotive force. He operated from Faraday's electro-tonic state A, which he considered to be a momentum in his vortex sea. The closest term that we can trace to electric charge in Maxwell's papers is the density of free electricity, which appears to refer to the density of the aethereal medium of his molecular vortices and that gives rise to the momentum A. Maxwell believed that A was a fundamental quantity from which electromotive force can be derived.
[/quote]Despite its historical origins in the original set of eight Maxwell's equations, the Lorentz force is no longer considered to be one of "Maxwell's equations" as the term is currently used (that is, as reformulated by Heaviside). It now sits adjacent to Maxwell's equations as a separate and essential law.[/quote]
Hmm. Interesting. If the Lorentz force is not part of the Maxwell equations, maybe we have a chance at splitting it off and attacking it separately.
Interesting also that Maxwell was working from an ether conception of a 'vortex sea'. If we return to that kind of idea, do we get closer to understanding something he saw which has been lost in the modern restatements? Why did he not have a concept so fundamental as electric charge?
It's a big ball of wibbly-wobbly timey-wimey stuff.