Seems that maxwell's
four equations, famously used in every text book on physics and
serving as the mathematical underpinning of all electromagnetic/static
applications, are not the original Maxwell equations. They are,
instead, simplifications by Oliver Heaviside. Simplifications
he made after cropping out the quadternions which removed the
scaler potential component because "It was too mystical"
A detailed report is found at http://www.enterprisemission.com/hyper1a.html
or better yet, let's
use Bearden's citation of Maxwell - "There are physical quantities
of another kind [in the aether] which are related to directions
in space, but which are not vectors. Stresses and strains in solid
bodies are examples, and so are some of the properties of bodies
considered in the theory of elasticity and in the theory of double
[rotated] refraction. Quantities of this class require for their
definition nine [part of the "27-line"...] numerical
specifications. They are expressed in the language of quaternions
by linear and vector functions of a vector ..."
-- J.C. Maxwell, "A Treatise on Electricity and Magnetism,"
(Vol.1, 3rd Edition, New York, 1954)
Bearden says that the
three physical theories are subsets and that they each ignore
the subset of the other-dimension, the inside dimension. Each
of the three physical theories lack this subset, and to unify
them into one, each would require this subset be added, or re-added.
PHYSICAL SPACE AS A QUATERNION STRUCTURE - I:
MAXWELL-EQUATIONS: A Brief Note.
by Peter Michael Jack
ABSTRACT: We show how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. Then, a new field component is discovered, which reduces part of the degree of freedom found in the guage, but which can then be used to explain thermoelectricity, suggesting that the theory of heat has just as fundamental a connection to electromagnetism as the magnetic field has to the electric field, for the new theory now links thermal, electric, and magnetic phenomena alltogether in one set of elementary equations. This result is based on an initial hypothesis, named "The Quaternion Axiom," that postulates physical space is a quaternion structure.
Quaternions were introduced by William Rowan Hamilton of Ireland in 1843. Hamilton was looking for ways of extending complex numbers (which can be viewed as points on a plane) to higher spatial dimensions. He could not do so for 3-dimensions, but 4-dimensions produce quaternions. According to the story Hamilton told, on October 16 Hamilton was out walking along the Royal Canal in Dublin with his wife when the solution in the form of the equation
i2 = j2 = k2 = ijk = -1
suddenly occurred to him; Hamilton then promptly carved this equation into the side of the nearby Brougham Bridge (now called Broom Bridge). This involved abandoning the commutative law, a radical step for the time. Vector algebra and matrices were still in the future.
Not only this, but Hamilton had in a sense invented the cross and dot products of vector algebra. Hamilton also described a quaternion as an ordered quadruple (4-tuple) of real numbers, and described the first coordinate as the 'scalar' part, and the remaining three as the 'vector' part. If two quaternions with zero scalar parts are multiplied, the scalar part of the product is the negative of the dot product of the vector parts, while the vector part of the product is the cross product. But the significance of these was still to be discovered. Hamilton proceeded to popularize quaternions with several books, the last of which, Elements of Quaternions, had 800 pages and was published shortly after his death.
Even by this time there was controversy about the use of quaternions. Some of Hamilton's supporters vociferously opposed the growing fields of vector algebra and vector calculus (developed by Oliver Heaviside and Willard Gibbs among others), maintaining that quaternions provided a superior notation. While this is debatable in three dimensions, quaternions cannot be used in other dimensions (though extensions like octonions and Clifford algebras may be more applicable). Vector notation had nearly universally replaced quaternions in science and engineering by the mid-20th century.
James Clerk Maxwell described in the "A Dynamical Theory of the Electromagnetic Field" the interrelated nature of electricity, magnetism, and electromagnetic fields in a set of twenty differential equations in quaternions. The theory was the first paper in which Maxwell's equations appeared. Maxwell's 1865 formulation was in terms of 20 equations in 20 variables, and, in 1873, he attempted a quaternion formulation. Quaternions have a vector and a scalar part and have a higher topology than vector and tensor analysis. The theory unifies two kinds of force — the electric and the magnetic.
Oliver Heaviside reduced the complexity of Maxwell's quaternion equations, creating the four vector-based differential equations we now know collectively as Maxwell's equations. Some people claim that Maxwell's original quaternion equations describe certain physical effects that cannot be explained by the simplified vector equations
Evidence of a Fourth Dimension
Let us now leave this supposition of framework and threads. Let us investigate the conception of a four-dimensional existence in a simpler and more natural manner in the same way that a two-dimensional being should think about us, not as infinite in the third dimension, but limited in three dimensions as he is in two. A being existing in four dimensions must then be thought to be as completely bounded in all four directions as we are in three. All that we can say in regard to the possibility of such beings is, that we have no experience of motion in four directions. The powers of such beings and their experience would be ampler, but there would be no fundamental difference in the laws of force and motion.
The model above is
that of multi-perspectives independantly arrived at by Hal Linstone
And Zinchang Zhu of ISSS. Banathy would liken these to spectacles.
TOP is Hal's. Technical-Organizational-Personal is mirrored by
Zhu's matter, relational, personal Li model.
It is an adaptation
of a more general model using three circles and a triangle. We
can use that same model to denote the forces of nature and how
they are to be unified.
Notice how there is
a center point, and how the small triangle is curved