Text: Just how much more powerful was Maxwell's quaternionic expression of EM theory than was Heaviside's (i.e., the modern view) vector interpretation, was succinctly expressed by Josephs as follows: "Hamilton's algebra of quaternions, unlike Heaviside's algebra of vectors, is not a mere abbreviated mode of expressing Cartesian analysis, but is an independent branch of mathematics with is own rules of operation and its own special theorems. A quaternion, is in fact, a generalized or hypercomplex number..." (H.J. Josephs, The Heaviside papers found at Paignton in 1957, Electromagnetic Theory by Oliver Heaviside, Including an account of Heaviside's unpublished notes for a fourth volume, and with a foreword by Sir Edmund Whitaker, Vol. III, Third Edition, Chelsea Publishing Co., New York, 1971, p. 660. For example, one difference between vectors and quaternions is of particular interest. In multiplication, when the multiplied vector components of two quaternions produce a zero vectorial resultant, the product of the quaternions may still produce a nonzero scalar resultant. Further, this scalar resultant has a hidden variable internal structure of infolded functions of the component vectors that have vectorially "zeroed" or "cancelled". When the interacting zero-summed vector components of the quaternions are EM force vectors, the nonzero scalar component of the quaternion resultant - with its deterministic, infolded, zero-summed (and so oppositively paired) vectors represents a trapped EM stress of spacetime, and hence it is a deterministically EM-substructured scalar potential. Further, this scalar potential's deterministic, infolded EM vector structure is vector zeroed, hence constitutes a force-free field, with its presence and its infolded EM structure completely hidden from normal "electron translating" detectors. This structured quaternionic force-free potential represents a patterned change in the local stress energy density of vacuum. If the infolded vectors are functions of time, then each infolded component of the structured potential is time-varying. One can even produce standing waves of, and determinsitically structured dynamic patterns in, the locally trapped energy density of vacuum. These changes/waves in the local vacuum stress energy density represent very strong, engineerable, electrogravitational changes/waves in the local rate of flow of time, and in the local curvature of spacetime/vacuum itself. This directly extends present Einsteinian general relativity, making it an empirical engineering science, and adding in the missing electromagnetics as well. In short, Maxwell's original quaternion theory was already a unified field theory of gravitation and electromagnetics - it was a testable and engineerable theory of elctrogravitation. Oliver Heaviside abhorred the quaternion, since it linked together a scalar component and a vector component, or "apples and oranges" in his view. When he excised the scalar component of the quaternion to produce his vector mamthematics for translations of Maxwell's theory, Heavside threw away electrogravitation. As is well-known, Maxwell prepared his EM model based on his mechanical model of the etheric medium. Also, Maxwell himself was well aware o fthe inportance of EM stress in the medium, although he had apparently not realized that this represented gravitational "charge" or gravitation potential. He knew that vectors alone could not express EM stress effects, but quaternions captured them. For example, quoting from Maxwell's A Treatise on Electricity and Magnetism, Vol. 1, 3rd Edition, New York, 1954: "There are physical quantities of another kind 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 refraction. Quantities of this class require for their definition nine numerical specifications. They are expressed in the language of quaternions by linear and vector functions of a vector." Unfortunately the internal structure of atoms was not known at the time, so Maxwell had no way of arriving at the activation charging of atomic nuclei by EM stress. Note that Maxwell's book was first published in 1873. [A few years later, Keely said Maxwell was substantially correct in is ideas. Keely had direct access to atomic nuclei and fully substantiated the fundamental idea of quaternions in his concepts of energy/matter actions and interactions. See his Law of Oscillating Atomoles and Law of Vibrating Atomolic Substances.] See also R. Chen, Cancellation of Internal Forces, American Journal of Physics, 49(4), Apr. 1981, p. 372 for a discussion of summation vectors and internal vectors. Internal forces occur in equal and opposite pairs (i.e., as stresses), so they contribute nothing to the vector sum (i.e., to external translation). [Their potentials, however, remain latent.] Note, however, that just this sort of stress in the medium or in the system is what was captured by the non-disappearing scalar component of the resultant in quaternion multiplication, even when the vector translation component of the interaction resulted in a zero translation (vector) resultant. The scalar component of Maxwell's quaternions captured and retained the internal vectors that result from zero-vector summations of non-zero EM force fields. Oliver Heaviside (and to a lesser extent, Williard Gibbs) discarded the entire internal EM vector region when he excised the scalar component of the quaternion. The internal EM vector region is the electrogravitational region, and that is what was discarded - all those parts of Maxwell's theory where EM forces turn to gravitational potential. Accordingly, Heaviside only captured a subset of Maxwell's unified EM/G field theory; he captured only that small subset where gravitation and electromagnetism are mutually exclusive. In the vacuum, this internal or infolded EM stress energy constitutes a change of the local gravitational potential, hence a curvature of the local spacetime. Further, a deterministic structure of these equal and opposite pairs of internal EM forces can be and is infolded within the potential [there held latent], and hence "hidden" within a structured change to the local vacuum/spacetime.

See Also: ELECTROGRAVITATION; OUTREACH; GRAVITY; SPACE; TIME; FULL HARMONIC CHORD; TRIUNE POLAR FLOWS; LATENT; LAW OF OSCILLATING ATOMOLES; LAW OF VIBRATING ATOMOLIC SUBSTANCES; GRAVITOBIOLOGY

Source: 134