Tässä hieman quartenioneista. Eivät ole helpoimpia asioita, mutta voivat osoittautua hyödyllisiksi.
Quaternion
https://en.wikipedia.org/wiki/Quaternion• "Time is said to have only one dimension, and space to have three dimensions. […]
The mathematical quaternion partakes of both these elements; in technical language it may be said to be "time plus space", or "space plus time": and in this sense it has, or at least involves a reference to, four dimensions. And how the One of Time, of Space the Three, Might in the Chain of Symbols girdled be." —
William Rowan Hamilton (Quoted in R.P. Graves, "Life of Sir William Rowan Hamilton").
• "Quaternions came from Hamilton after his really good work had been done; and, though beautifully ingenious,
have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell." —
Lord Kelvin, 1892.
• "I came later to see that, as far as the vector analysis I required was concerned, the quaternion was not only not required, but was a positive evil of no inconsiderable magnitude; and that
by its avoidance the establishment of vector analysis was made quite simple and its working also simplified, and that it could be conveniently harmonised with ordinary Cartesian work."
Oliver Heaviside, Electromagnetic Theory, Volume I, pp. 134–135 (The Electrician Printing and Publishing Company, London, 1893).
Utilizing Scalar Electromagnetics To Tap Vacuum Energy
http://www.cheniere.org/techpapers/swee ... 201991.htmIn 1837
Sir W.R. Hamilton said,
"The notion of time may be unfolded into an independent pure science... a science of pure time is possible."
As is well-known, the fundamental units utilized in physics are arbitrary. It is even possible to construct all of physics on a single unit, time. This oddity shows the truth in Hamilton's statement; it is even more odd, because quantum mechanically time is not an observable. This means that the observable world can be modeled completely in terms of the nonobservable, which is essentially what modern quantum mechanics is now doing.
Hamilton viewed his magnificent quaternions as essentially having accomplished the mathematical structuring of time. Maxwell's original EM theory, as is well-known, was modeled in Hamilton's quaternions, not in the highly curtailed Heaviside/Hertz vectors erroneously taught today as "Maxwell's theory."
Not a single one of the present so-called "Maxwell's" vector equations ever appeared in a book or paper by James Clerk Maxwell.
For some years the author has worked on an extended electromagnetics theory, involving
the scalar component of the quaternion.
In Maxwell's original quaternion theory, this scalar component often remains when the directional components zero. Further, it then enfolds vectors and functions of vectors inside, in a hidden variable manner. Specifically, the author has patterned a unified field theory concept upon the previously unnoticed but remarkable early work of E.T. Whittaker.
In two fundamental papers in 1903 and 1904, Whittaker showed that all present vector EM can be replaced by scalar potential interferometry, and that bidirectional harmonic EM plane wave sets could be used to produce a standing wave of force-field-free potential (Figures 1 and 2).
…
In modern terms, Whittaker showed how to turn EM wave energy into electrogravitational potential energy, then how to interfere two such scalar potential waves to recover electromagnetic energy, even at a distance.
This unrecognized work is of great importance: when applied to modern physics, it produces supersets of quantum mechanics (QM), classical electromagnetics (EM), and general relativity (GR).
E. T. Whittakerhttps://en.wikipedia.org/wiki/E._T._WhittakerWhittaker's pair of papers in 1903 and 1904 indicated that any potential can be analysed by a Fourier-like series of waves, such as a planet's gravitational field point-charge. The superpositions of inward and outward wave pairs produce the "static" fields (or scalar potential). These were harmonically-related. By this conception, the structure of electric potential is created from two opposite, though balanced, parts. Whittaker suggested that gravity possessed a wavelike "undulatory" character.
