| New Energy Technology |
T. E. Bearden
P.O. Box 1472
HUNTSVILLE, Alabama 35807
United States of America
It is revealing to discuss the basic genesis of modern electromagnetic theory starting with Maxwell's original theory expressed in quaternions (1) (2) (3).
Most of us are familiar with four fundamental equations of theoretical electromagnetics, universally taught in Western universities and colleges as "Maxwell's Equations". (See Table 1) It may come as somewhat of a surprise, at least to the casual scientist or engineer, that these equations never appeared anywhere in Maxwell's fundamental "Treatise". (4) (5). In fact, they are entirely due to the interpretation of a single brilliant man, Oliver Heaviside (6) (7).
The Early Struggle in EM Theory
Maxwell wrote his first paper on electromagnetics in 1864 - during the time of the US Civil War, and the paper was published in 1865 (8). At that time, the modern form of vector analysis had not yet been completed (9). The prevailing mathematics available for use in deeper electrical physics was the quaternion theory founded by Hamilton in 1843 (10). Hamilton's quaternion theory was the first significant nonarithmetic mathematical system (11).
Maxwell's original expression of his theory was written in quaternions and quaternion-like mathematics. It attracted singularly attention (12), and was considered only speculation until Heinrich Hertz discovered electromagnetic waves in 1885-1888 (13) (14).
Indeed, early on, mathematicians strongly attacked Maxwell for his - to them revolutionary and startling concept that energy could exist in a massless wave and travel through space (15). While that concept is considered self-evident to today's scientist and engineer, it was considered incredible and starting when Maxwell proposed it.
DIFFERENTIAL VECTOR FORM OF HEAVISIDE/MAXWELL EQUATIONS
Maxwell's equations (Gaussian units):
Combining these equations with the Lorentz force equation and Newton's Second Law of Motion is thought to provide a complete description of the classical dynamics of interacting particles, and electromagnetic fields.
a. Two vectors which are not interlocked by the medium (abstract vector space), simply pass through each other and do not interact. They cannot be said to have a common resultant, except fleetingly.
b. Two vectors which are interlocked by the medium (abstract vector space) do not pass through each other but do interact. They can be said to have a common translation resultant externally. However, internally they must be said to produce a stress in the medium (abstract vector space).
Figure 1: A serious flaw exists in the application of the abstract vector analysis to physical systems. Only when the local gravitational effects are fleeting or negligible, does this flaw become negligible - and the vector theory become a valid representation (model).
Maxwell himself was an excellent mathematician of the time (16) (17), of ability far beyond that of most of the contemporary electrical theorists and experimenters (18) (19). Possibly as a result, both his early lectures and writings were therefore difficult - or even nearly impossible - for his contemporaries to comprehend (20). It required the translation of Maxwell's theory (20) into the abbreviated and clearer, more readily understood vector mathematics of Oliver Heaviside (22), and the publication of clearer and much simpler expositions by Heaviside (23), before "Maxwell's theory" - or at least the Heaviside subset of it - began to capture the attention of leading university electrical scientists (24).
At the same time, the major expositor of the tough, obtuse and very difficult quaternion theory - Prof. Peter Guthrie Tait - was a stubborn, fiery, argumentative mathematician rather than a physicist. He also delayed preparing his exposition of quaternion theory until a number of years had passed and his mentor, Hamilton, had had time to rework his own obtuse, difficult book (25) (26). While Tait delayed, scientists and engineers beset with practical problems in the real world of industry were frantically seeking a simplified theory that: (1) could be readily grasped and understood, and (2) could immediately be applied to solve their practical problems of equipment design and building. The only available and accessible simplified theory of electromagnetism that fitted their urgent needs was the clear, simplified and imminently practical work of Oliver Heaviside - who himself held no degree and was self-educated.
Accordingly, the die was cast. Working engineers and leading scientists focused upon Heaviside's vector interpretation of Maxwell's difficult quaternionic expressions. In Heaviside's version the engineering calculations were enormously eased, and electrical engineers could get solutions to their pressing problems and get on with their business of constructing electrical devices and electrical machinery. Except for a very few mathematical scientists who could handle the heavy labours of quaternions, Heaviside's electromagnetics rapidly became the ipso facto standard.
A major schism developed between the increasingly isolated few quaternionists and the steadily multiplying vectorists, slowly growing to white heat in the literature A final duel to the death became inevitable.
The duel exploded before the turn of the century and a short, sharp debate occurred among about 30 or so scientists and in about 12 journals (27). The culmination was quick - complete victory by the vectorists. The quaternion EM theory was simply cast out, and the scientific community turned to Heaviside's limited vector subset of the Maxwell theory. The short "debate" only confirmed what had already become an accomplished fact: the Heaviside vector analysis translation of the EM subset of Maxwell's theory was already universally accepted and applied.
Vector Analysis Excised Electrogravitation
Ironically, in their great haste to seize upon Heaviside's simpler, clearer explanation of EM and get on with solving practical engineering problems, the nineteenth century scientists gave up something of far greater value: the unification of EM and gravity, and the ability to directly engineer gravitation itself.
Maxwell had actually written a unified field theory of electromagnetics and gravitation - not just the unification of electricity and magnetism as is commonly believed (28). Further, this can readily be shown by examining some significant even startling - elementary differences between quaternion mathematics and the present vector mathematics (29) (30) (31) (32).
Let us briefly look at one of these key differences, to show that the present vector mathematics expression of Maxwell's theory is only a subset of his quaternion theory (33).
What Heaviside's theory specifically omitted was electrogravitation (KG) - the ability to transform electromagnetic force field energy into gravitational potential energy, and vice-versa. And that has been omitted because of the assumptions of the vector theory in the nature of: (1) EM vector field combination, and (2) a zero-vector resultant of the interaction of multiple nonzero EM force vectors (34) (35).
Briefly, in Heaviside's vector mathematics, the abstract vector space in which the vectors exist has no stress nor consequent "curvature" in it. That is, the mathematical vector space does not change due to interactions between the vectors it "contains". This, of course is not necessarily true in the "real space" of the physical world. Thus when such an abstract vector space and its concomitant coordinate system are taken to model physical space (physical reality), the model will be valid only when the physical space itself has no appreciable local curvature, and is in a state of total equilibrium with respect to its interactions with observable charged particles and masses.
So abstract vector theory implicitly assumes "no locked-in stress energy of the vector space itself". By assumption, the only interactions are between the objects (the vectors) placed in/on that space. Therefore, when two or more translation vectors sum or multiply locally to a zero-vector translation resultant, in such an "unstressable" vector space one is justified in: (1) replacing the system of summing/multiplying translation vector components with a zero-vector, and (2) discarding the previous translation vector components of the zero-vector system. That is, one may properly equate the translation zero-vector system with a zero-vector, since the presence or absence of the combined vectors can have no further action. Specifically, axiomatically they exert no stress on the abstract vector space. Under those assumptions, the system can be replaced by its equivalent zero-factor alone.
Note that, applied to electromagnetics, this modeling procedure eliminates any theoretical possibility of electrogravitation (EM stress curvature of local space-time) a priori.
Force Vectors are Translations of Stress
Conceptually, a force vector is actually a release of some implied stress in a local medium. The force is applied to create stress in a second local region immediately adjacent to the primary region of stress. Of course the stress being thus "translated" by the force vector may be either tensile or compressive in nature, but a priori the force vector always represents the translation of that stress from its tail-end toward its head.
Consequently, an EM force vector is a gradient (inflow or outflow) in a scalar EM potential (stress), where the referent potential stress may be either tensile or compressive. Since modern Heaviside-type vectors do not distinguish between, or even recognize, the two "head and tail" scalar EM potentials involved in a vector, one needs to refer to Whittaker (36) to get it right. Whittaker, a fine mathematician in his own right, showed that any vector field can be replaced by two scalar waves. Unfortunately, the electrogravitational implications of Whittaker's profound work were not recognized and followed up, and their connection to Maxwell's quaternionic EM theory was not noticed nor examined.
So the idea of a vector EM force represents a release of a primary "tail-associated" scalar potential, and a bleedoff of that potential. It represents an increase in its primary "head-associated" scalar potential, and a bleed into that potential. Each scalar potential itself represents trapped EM energy density in the local vacuum, in the form of two or more (even an infinite number of) internal (infolded) EM force vector components (which may be either fixed, dynamic, or a blend of the two). The trapped energy density, however, may be either positive or negative with respect to the local energy density of the standard ambient vacuum, since the potential may be either compressive or tensile.
Maxwell's Electrogravitation Was Lost
Today we know that all potentials are gravitational and curve space-time; it is well-known in general relativity that gravitational curvature is simply the set of many potentials. One therefore can see that a vector EM wave represents a progressive translation wave in the vacuum EM potential - in the local EM-induced curvature of space-time. This EM change in local curvature of space-time moves away at the speed of light, producing only the most fleeting or momentary changes in curvature of any localized space-time region.
We note here as an aside: Only in a standing EM wave and in phase waves of coupled EM waves is there any deviation from the "momentary and then lost" change in the local space-time curvature. In those cases, the "persistence" of the local change in potential is an adverse function of frequency; hence at extremely low frequencies EM potential change persistence is sufficient to produce some very small electrogravitational effects. The effect is still slight, however, since the normal concept of "standing EM wave" represents a standing force vector situation, which is actually a stabilized spatial bleedoff of the potential. If a standing scalar EM wave is produced as in the two opposing pump waves in nonlinear optics pumped phase conjugate mirrors - then the stress is not primarily spatial, but temporal. Spatial effects then occur by particle-coupling - either in the virtual particle flux of vacuum or from the nucleus of an atom to the electron shells, and out into the material lattice structure. In the case of a standing scalar wave, electrogravitational effects are highly magnified because of the conversion of the primary potential stress to the time component. This increases the EG effects obtainable by a factor up to 9x10exp16. For this situation, at ELF standing scalar EM wave frequencies, very appreciable electrogravitational effects can be locally obtained.
The "Bottom Line" of EM Force-Field Theory
Thus concentrating only on the force fields of Maxwellian EM theory is equatable to concentrating on the situation where any localized electrogravitational effect that is temporarily formed is instantly released at the speed of light. The EG-effect in such a system is so small and fleeting, that the possibility of any persisting or significant local gravitational effects may be ignored.
Because of this, in any EM theory based only on the force fields and focusing only on their effects, then: (1) EM forces and their derivative effects may be represented by elementary Heaviside/Gibbs vector theory, including the equivalence of the zero-translation vector and any zero summed/multiplied system of nonzero translation vectors, (2) a system of EM forces which sum or multiply to a zero resultant may be discarded outright and the zero-vector substituted, (3) the effect of an EM potential is only to serve as an accumulator from which an EM force may be produced, and only its nonzero gradient will be thought to have any physical significance, (4) translation of EM forces (i.e., of potential gradients) and their effects on charged matter will assume primary importance, and (5) the potentials themselves may be regarded as simply mathematical conveniences and of little importance. This is precisely the subset of Maxwell's electromagnetics extracted and written so clearly by Heaviside.
As was Hertz, Heaviside was adamantly opposed to attaching any sort of physical reality to the potentials, preferring that they should be excised and "murdered". An indelible imprint - that potentials were "mysticism" and at best only mathematical conveniences - was imposed upon physics by Heaviside and Hertz (21). This rigid mindset was not to lessen (at least in quantum mechanics) until 1959; it was not to be assuaged until the mid-1960's (22) (37).
How EM Potentials are Regarded Today
So in 1988, we have finally arrived at the state where the potentials are more-or-less understood by a consensus of quantum physicists as being the primary EM reality, while the force fields are now seen to be secondary effects generated from the potentials.
This understanding, however, still has a long way to go before it penetrates the main bastions of physics and electrical engineering. Most scientists and electrical engineers are still adamantly committed to the Heaviside version of Maxwell's theory, and are strongly conditioned that the EM force fields are the primary effectors in electromagnetics.
They are also nearly totally resistant to the idea that there may be a fundamental error in automatically replacing a zero-resultant system of EM translation force vectors with a zero factor, rather than replacing the system with the combination of a conditional zero vector (conditional for translation only) and a scalar stress potential. Consequently, most orthodox scientists and engineers are still strongly conditioned against quaternions, and erroneously believe that Heaviside's translation was complete. Seemingly it has never occurred to most mathematicians and scientists that zero-vectors are usually not truly equal. Stress-wise, zero resultant combinant systems of multiple translation vectors usually differ in: (1) magnitude, (2) polarization, (3) type of stress, (4) frequency components, (5) nonlinear components, and (6) dynamic internal variation (38).
Vectors Versus Quaternions: The Cross Product
In a conventional 3-dimensional vector, one may have three vector components, such as (in Cartesian coordinates):
Obviously if the vector components of vector
We shall be interested in the vector product of two identical vectors
where A is the length (magnitude) of vector
After Heaviside and Gibbs, electrical engineers are trained to replace the cross product
Now let us look at the comparable quaternion expression of this situation. First, in addition to the three vector components, a quaternion also has a scalar component, w. So the quaternion q corresponding to vector
The physical interpretation of equation (5) is that there locally exists a stress w in the medium and a translation change
When the quaternion is multiplied times itself (that is, times an identical quaternion), the vector part zeros, just as it did for the vector expression. However, the scalar part does not go to zero. Instead, we have:
There is a very good physical interpretation of this result. The zero translation vector resultant
Notice that the zero vector in equation (6) does not represent the absence of translation vectors, but it represents the presence of a system of multiple (in this case, two) vectors, one of them acting upon the other in such a manner that their external translation effect has been lost and only their stress effect remains (39). The quaternion scalar expression has, in fact, captured the local stress due to the forces acting one on the other, so to speak. It is focused on the local stress, and the abstract vector space, adding a higher dimension to it.
In other words, the
One sees that, if we would capture gravitation in a vector mathematics theory of EM, we must again restore the scalar term and convert the vector to a quaternion, so that one captures the quaternionically infolded stresses. These infolded stresses actually represent curvature effects in the abstract vector space itself. Changing to quaternions changes the abstract vector space, adding higher dimensions to it.
Artificial Electrogravitational Timestress
Let us assume for a moment that the two identical vectors
We now recall the modern quantum mechanical view that no "static" thing exists as such in the universe. A macroscopic "static" force - at quantum level - represents a continual constant rate of quantum change. In the case of an electrical force, it represents a continual constant rate of flux exchange of virtual photons.
The zero vector in equation (6) represents a constant exchange of macroscopically organized virtual energy into the local medium. Consequently, it represents continual internal work into and onto the local medium, but without translating it.
So a zero vector system of nonzero vector components represents internal or "infolded" constantly-working forces (internal to the medium) where the system does not cause translation of the point or region of application, whereas a nonzero vector and a nonzero vector system represent external forces which cause at least some translation of the point or region of application, unless this translation is nullified by other forces (40).
Physically, equation (6) may now be seen to state that: (1) internal forces (in the form of an internal stress) are present in the local medium but no translation force is present, and (2) these internal forces are continually performing internal work on the local medium without external translation. Since the translation vector component has spatially zeroed, then the scalar component that results may be taken to represent the time rate of expenditure of this internal work that is being done on the local medium - that is, it represents the extra internal power (which is simply the extra energy density of time) now being expended locally in and on the medium as a sink. If the vector components of the zero vector system are oriented outward, then the scalar stress component changes sign and it represents the extra internal power locally flowing out of the medium as a source.
Infolded Structuring is Dynamic and Complex
As can be realized, by changing the magnitudes, phasing, directions, rotations and dynamic frequencies of the vector components of the zero-vector stress system, very elaborate and sophisticated structuring of the local space-time medium (the local vacuum) may be deterministically constructed and controlled at will.
The continually performed internal work represents an increase or decrease in the local energy density of the medium, hence in the stress of the medium. However, note that this stress - either compressive or tensile is in and on the rate of flow of local time in the region. This timestress represents an artificial stress potential, where by "artificial" we mean that the timestress of the local medium is structured and macroscopically patterned (and controlled) deterministically; translation of that timestress is spatially radiating out over a finite macroscopic neighbourhood of the local point or region of application. This may be contrasted to a "natural" potential where the internal component stress vectors in the surrounding spatial neighbourhood are microscopic and randomly varying in all directions.
In equation (6), then, we have a local gravitational effect - a local increase in the energy density of a vacuum. Because the large EM force is utilized rather than the weak G-force, and because it is a timestress condition, it is a powerful local general relativistic effect. Because the local vacuum flux is significantly altered, we have a locally curved space-time which is significantly anisotropic, in violation to one of the fundamental (and crippling) assumptions of Einsteinian general relativity. Further, this is an electrogravitational effect. since it is a gravitational effect produced by purely electromagnetic means (41).
We have therefore produced a local curvature of space-time, and done so electromagnetically.
What is even more astonishing to the conventional relativist is that this local curvature startling enough in its own right - is also deterministically structured, and we can control the structuring at will. Hence we can engineer (structure) the vacuum itself (42).
But to return to equation (6).
The EG Sine-Squared Stress Wave
and this is a scalar EM stress wave, of variation of the local curvature of the vacuum. It is a powerful electrogravitational (scalar electromagnetic) wave, particularly if we produce it as a standing wave and use it to "pump" atomic nuclei in a rhythmically varying manner (43).
Briefly, a sine-squared wave has the appearance of a sort of "skinny" sine wave a near-sawtoothed wave that is now oscillating about an increased bias. In other words, the wave of equation (8) represents a scalar EM (an KG) wave that pumps the atomic nuclei of a targeted material, holding those nuclei at an excited average potential level. The wave has strong and very useful applications in - among other things - electrohealing. (44).
Example: Application to Explain Four-Wave Mixing
Now most modulations are represented by similar multiplication between two waves. Suppose we have two equal-amplitude, continuous monochromatic
This scalar wave will not appreciably react to the orbital electron shells of an atom of the dielectric, but will not pass through these outer "Faraday cages", reaching directly into the highly nonlinear nucleus itself.
We invoke the quantum mechanical picture of the nucleus as: (1) a region of local sharp curvature of space-time, (2) incredibly dynamic, with particles of every kind continually changing, transmuting, giving off other particles and waves, being absorbed, etc., (3) containing violent and dynamic charges and locally trapped fierce currents, and with field strength fluctuations reaching 10 and above, (4) in violent virtual particle exchange with the neighbouring vacuum, and (5) on the average, positively charged, so that it is -- on the average -- time reversed (46).
The presence of the sine-squared EG wave in the nucleus alters the nuclear potential by - on the average - the "DC" component potential amount. However, this delta in the potential is dynamic, varying as the sine-squared. This dynamically oscillating potential wave constitutes a pump wave on the nucleus itself, and it is rhythmically pumping the amplitude of the nuclear potential itself. We may think of the pumped nucleus as now conditioned to function as a parametric amplifier, ready to be given another "signal input" (47).
Now let us introduce yet another small sine wave into the nonlinear dielectric. It will modulate each of the two pump wave components, forming a scalar modulation upon the scalar sine-squared pump wave, and riding directly into the nucleus. In positive time, this now constitutes a "signal input" to the "parametric amplifier nucleus". The input is absorbed and amplified, up to the level of the pumping energy available in the pump wave that can be "scavenged up and gated".
Internal Absorption Can Be External Emission
However, the nucleus, being time reversed, also produces a time-reversed absorption which is seen spatially by the external observer as constituting emission! That is, in his own positive time, the external observer sees the time-reversed absorption as an emission event. Further, this is a time reversal - and hence an "emission" to the external observer of the entire parametrically amplified signal wave. (After all, in reversed time it is the pump wave that is modulating the signal wave - a principle of importance.)
So the powerfully amplified signal wave in the parametric amplifier is seen by the external spatial observer to be emitted from the nucleus. In short, a time-reversed and powerful scalar wave is emitted by the nucleus, passing back along the exact path taken by the original "signal wave". To a time-reversed entity, that invisible path is its path ahead of it in positive observer time. The external observer sees the emitted wave emerge as a powerfully amplified time-reversed EM wave, backtracking precisely back along the exact path taken by the signal wave, and appearing everywhere in phase spatially with the continuous signal wave.
In 4-space, of course, the time-reversed wave is out of phase in the fourth dimension, time.
Four-Wave Mixing is Like a Triode
This is the mechanism by which four-wave mixing provides a powerfully amplified time-reversed replica of the signal wave.
Note that the entire process can be compared to a triode: the signal wave constitutes the grid signal, the pump wave constitutes the plate voltage, and the nucleus of the atom in the dielectric provides the self-powered cathode.
We put in the signal wave (grid signal) and get out a 180-degree phase-shifted, amplified phase conjugate replica (amplified plate signal). The difference is that the PCR is phase-shifted in time, not space.
Negative Energy, Nuclear Binding and Transmutation
Note also that negative energy is already involved in the time-reversed nucleus of the atom, as in negative time (48). Excess "negative energy" in the nucleus means "additional binding energy", which will be expressed as additional inertia and coupled onto the electron shells. In this case the "inertial mass" of the pumped material increases, inversely as the pumping frequency. Less "negative energy" in the nucleus means "decreased binding energy", which places the nucleus in an unstable state. The nucleus can actually be transmuted by this means (in many cases toward barium, which apparently has the least binding energy per nucleon). Transmutation to an isomer appears easiest, though this is not always the case (49). It seems theoretically possible to design a complex pumping mixture of frequencies and power levels which will cause a specific radioactive nucleus to undergo transition to a harmless element or combination of elements. The main point is, scalar EM allows direct production of structured electrogravitational potentials in the nucleus, opening up the possibility of direct and controlled engineering of the nucleus itself.
Obviously, in this short paper we have only scratched the surface. We have presented only the barest illustration of how Maxwell's original quaternion theory was actually a unified field theory of electrogravitation, where gravitation deals with the stress (enfolded and trapped forces) of the medium, and electrogravitation deals with the electromagnetic stress (enfolded and trapped EM forces) of the medium.
Of course, a great deal more work is necessary, but at least this indicates the way to go to obtain a unified field theory of electromagnetics and gravity that is practical and engineerable (50). I can only state that the indicated approach works in the laboratory, and let it go at that without further elaboration.
Recapitulation: From Maxwell to 1900
In summary, Maxwell himself was well-aware of the importance and reality of the potential stress of the medium (51). However, after Maxwell's death, Heaviside - together with Hertz - was responsible for striving to strip away the electromagnetic potentials from Maxwell's theory, and for strongly conditioning physicists and electrical engineers that the potentials were only mathematical conveniences and had no physical reality. Heaviside also discarded the scalar component of the quaternion, and - together with Gibbs - finalized the present modern vector analysis.
The scalar component of the quaternion, however, was the term which precisely captured the electrogravitational stress of the medium. By discarding this term, Heaviside (aided by Hertz and Gibbs) actually discarded electrogravitation, and the unified EM-G field aspects of Maxwell's theory. However, the theory and the calculations were greatly simplified in so doing, and this excision of electrogravitation provided a theory that was much more easily grasped and applied by scientists and engineers - even though they were now working in a subset of Maxwell's theory in which gravity and EM remained mutually exclusive and did not interact with each other.
Shortly before 1900, the vectorists' view prevailed, and the Heaviside version of Maxwell's theory became the established and universal "EM theory" taught in all major universities - and erroneously taught as "Maxwell's theory"! Though gravitation had been removed, the beautiful unification of the electrical and magnetic fields had been retained, and so the rise in applied and theoretical electromagnetics and electromagnetic devices began, ushering in the modern age.
Impact on Einstein's General Relativity Theory
Unfortunately, however, the excision of electrogravitation from Maxwell's theory was later to leave Albert Einstein with a quandary: it seemed that the only way space-time could be curved measureably was by and at a huge collection of mass, such as the Sun or a star. Accordingly, in constructing his theory of general relativity, Einstein assumed that the local space-time was never curved (since obviously the observer and his lab instruments would not be sitting on the surface of the Sun or of a distant star). Consequently, he did not write an unrestricted general theory of anisotropic space-time, but instead he wrote a highly restricted sort of "special relativity with distant perturbations" - which, nonetheless, was a revolutionary and epochal achievement.
Ironically, Einstein then spent the remainder of his life vainly trying to find a way to reintroduce electromagnetic fields into his general relativity, and to provide a unified field theory of gravity and electromagnetics. He failed, because his own prior assumption of a locally flat space-time had already effectively ruled out the very thing he sought.
Effect on Western Search For a Unified Field Theory
Today the magical unified theory of gravitation and electromagnetics continues to elude Western scientists, because they nearly universally adhere to Einstein's rejection of a locally-curved space-time. In so doing, the West largely rules out any local, laboratory-bench development of, and experimentation with, general relativistic systems. And in turn, that relegates general relativity to a non-experimental theory and, except for cosmological observations, a sort of "special relativity with distant perturbations."
The "locally flat space-time" assumption saves the conservation laws - and Western scientists have now become nearly totally dogmatic in their subservience to conservation. To challenge the conservation laws - and Einstein's restricted general relativity - leads to ostracization by his peers and vigourous suppression (52).
Soviet Theory of an Anisotropic Space-time
Soviet scientists, on the other hand, regularly publish papers where Einstein's crippling "local flat space-time" assumption is removed and the anisotropy of space-time is unrestricted, strongly implying that they might have developed an experimental unified field theory (53). They also are quite frank to publish statements that in a general relativistic system, conservation laws do not apply (54).
In numerous previous papers and books, the present authour has presented extensive evidence of the Soviet weaponization of electrogravitation and hence of a unified field theory (55).
Impact on Science and Humanity
Thus a great irony now is evident in Western science. More than 120 years ago, Maxwell wrote the first paper in his unified field theory of electrogravitation. Had Western scientists and mathematicians given greater attention to Maxwell's quaternion theory, by 1900 we should have been developing antigravity propulsion systems and interplanetary exploration vehicles.
Certainly humankind could have been lifted to much greater heights than where we are today. And along the way, we just might have avoided two great and bloody World Wars and a host of smaller ones.
In the modern geometrodynamic view, all forces are considered to arise from, and be rooted in, the curvature of space-time - in gravitation. If the curvature of space-time itself can easily be engineered and controlled by electromagnetic means, the extensive application of our present advanced state of electromagnetic development and devices can lead to control of the world of physical reality on a scale heretofore only dreamt of in the minds of our greatest visionaries.
Consider such a vision by Albert Einstein: Quoting:
"It would of course be a great step forward if we succeeded in combining the gravitational field and the electromagnetic field into a single structure. Only so could the era in theoretical physics inaugurated by Faraday and Clerk Maxwell be brought to a satisfactory close."
With the mastery of electrogravitation and the control of physical reality itself in our grasp, the freeing of humankind from want, misery, and poverty would directly follow. The impact on mankind's development would be almost beyond present human conception. Consider this vision from Teilhard de Chardin of the mastery of physical reality and the elimination of man's inhumanity to his fellow man:
"Someday, after we have mastered the winds, the waves, the tides and gravity, we shall harness for God the energies of love. Then for the second time in the history of the world man will have discovered fire."
Like Prometheus of old, in his quaternion EM theory James Clerk Maxwell produced a blazing coal of fire, literally taking the fire of gravitation from Olympus and giving it to human beings. Uncomprehending, scientists heaped ashes over the fiercely glowing coal, and only warmed themselves with the tiny trickle of electromagnetic heat that escaped the dampening ashes. For over a hundred years, the fiery coal has been quietly lying there, buried under the ashes, still glowing brightly.
It is time to be bold. For the enrichment of all mankind, let us uncover Maxwell's long-dormant fiery coal and fan into full bloom the Promethean flame of power that lies sleeping within.
NOTES AND REFERENCES
1. James Clerk Maxwell was born on June 13, 1831 in Edinburgh, Scotland. In 1847 he entered the University of Edinburgh, then transferred to Cambridge in the fall of 1850. After graduation, he stayed on at Cambridge in a research position. He was elected a Fellow of Trinity College and placed on the staff of college lecturers. In 1856 he returned to Scotland, where he took up a Chair of Natural Philosophy at Marshall College, Aberdeen. In autumn, 1860 he took a new position as Chair and Professor of Natural Philosophy and Astronomy at King's College, London (a position he held to 1865, at which time he resigned).
Maxwell was economically independent. He was elected to the Royal Society in 1861, while at King's College. From 1865 to 1871 he resided at his ancestral Scottish country home, Glenlair, developing his major ideas into book form.
Maxwell returned to Cambridge in 1871, where he became the first holder of the Cavendish Chair of Experimental Physics. There he also supervised the construction and operation of Cavendish Laboratory. His treatise on electromagnetism appeared in 1873. He held his position at Cambridge until he died on Nov. 5, 1879, at age 48, of a form of stomach cancer - the same ailment that had killed his mother when he was a child.
2. His famous treatise was J.C. Maxwell, "A Treatise on Electricity and Magnetism", Oxford University Press, Oxford, 1873. For an elegant and readable account of Maxwell's life and achievements, see I. Tolstoy, "James Clerk Maxwell: A Biography", Canongate, Edinburgh, 1981. Maxwell's compact and powerful quaternionic expression of the general equations of the electromagnetic field are given in Article 619, Vol. 2, p. 258 of his Treatise. See also 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 Whittaker, Vol. III, Third Edition, Chelsea Publishing Co., New York, 1971, p. 660. Just how much more powerful was Maxwell's quaternionic expression of EM theory than was Heaviside's vector interpretation, was succinctly expressed by Josephs: "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 its own special rules of operation and its own special theorems. A quaternion is, in fact, a generalized or hypercomplex number... " (Josephs, ibid., p. 660)
3. The prevailing view in physics - and in most physics textbooks - is that Faraday - himself uneducated and woefully ill-prepared mathematically discovered and formulated the concept of "lines of force", or field lines; and that Maxwell, his mathematical interpreter, then tinkered together the equations to explain electromagnetic radiation on the basis of Faraday's field concepts. However, there certainly can be serious ground for contesting this simplified view. As White states, ''The mathematics which Maxwell used to develop Faraday's results came out of a body of work which had as its implicit subject unified field theory. Leonhard Euler, Pierre-Simon Laplace, Joseph-Louis Lagrange, and Karl Friedrich Gauss prepared these mathematical and theoretical foundations, elaborated by Sir William Hamilton, which shaped the positive content of Maxwell's work... As the story goes, Maxwell first elaborated the equations which describe the magnetic effects of an electrical current and the ability of a magnet in motion to induce electricity, and then, by algebraic substitution, came on the wave equations. In fact, James MacCullagh, a collaborator of Sir William Hamilton and Franz Neumann, a collaborator of Gauss, Wilhelm Weber and Bernhard Riemann, produced these same equations between the years 1839 and 1848, at least a decade before Maxwell began his scientific career... Field theory, as it was developed through the work of Euler and Lagrange, elaborated by Gauss, and totally redefined by Riemann, depends upon the concept of potential energy," (Carol White, "Energy Potential: Towards a New Electromagnetic Field Theory", with excerpts from two original works by B. Riemann, Campaigner Publications Inc., New York, 1977, p. 19-20). White gives a critical discussion of the way in which standard textbooks have assigned credit for priorities and conceptual contributions in the foundations of theoretical electromagnetics. Extending Riemann considerations, White focuses strong attention on the potentials and on a new approach to electromagnetics.
There is certainly a great deal wrong with modern EM theory, as is well-known to a small but growing circle of scientists. As Dr. Domina Spencer of the University of Connecticut states, "Since the turn of the century there has been a lot of first class experimental and theoretical work that reveals problems with relativistic electromagnetic theory, but this work has been virtually ignored by the mainstream physicist". Dr. Spencer and her colleagues are embarked on a thorough review of all the experimental work that has been performed on electromagnetic phenomena since Ampere published his first results in 1824. (Note that Soviet scientists did such a review immediately after World War II.)
For more on the subject of what's wrong with the present foundations of EM theory, see particularly Peter Graneau and P.N. Graneau, "Ampere-Neumann Electrodynamics of Metals", Hadronic Press, Nonantum, Massachusetts 1985; P. Graneau and P.N. Graneau, "Electrodynamic Explosions in Liquids", Applied Physics Letters, 46, 1985, p. 468. See also H.E. Puthoff, "Ground State of Hydrogen as a Zero-Point-Fluctuation-Determined State", Physical Review D, 35 (10), May 15, 1987, p. 3266-3269; Puthoff, "Zero-Point Fluctuations of the Vacuum as the Source of Atomic Stability and the Gravitational Interaction", Proceedings of the British Society for the Philosophy of Science International Conference, "Physical Interpretations of Relativity Theory", Imperial College, London, Sept. 1988. Also see very important work by Dr. Henry Monteith, referenced elsewhere in this paper. See also Cynthia Kolb Whitney, "Electromagnetic Fields Near Dynamic Systems of Charged Particles", Hardonic Journal, 10, 1987, p. 299-301; Whitney, "Field-to-matter Energy Transfer", "Manifest Covariance in Relativistic Potential Theory", Physics Essays, 1 (1), 1988, p. 15-17; Whitney, "Generalized Functions in Relativistic Potential Theory", Hadronic Journal, 10, 1987, p. 91-93. For a lay description of some of the exciting work and problems of foundations of electromagnetic theory, see articles by Chappell Brown in Electronic Engineering Times: "Anomalies in Electromagnetic Law Spur Debate", Sept. 14, 1987; "Railgun Research Shoots Holes in Lorentz's Theory", Apr. 6 1987; "Electrons and Conduction: Not So Simple After All", Dec. 28, 1987. Finally, it is hoped that this present paper will help shed at least a little light on the subject.
4. J.C. Maxwell, A Treatise on Electricity and Magnetism, Oxford University Press, Oxford, 1873.
5. For confirmation that the Heaviside equations - which presently are erroneously called "Maxwell's equations" - are not to be found anywhere in any of Maxwell's books or papers, see Josephs, ibid., p. 647. See also Sir Edmund Whittaker, "Oliver Heaviside", Bulletin of the Calcutta Mathematical Society, 20, 1928-1929, p. 202. See also Paul J. Nahin, "Oliver Heaviside: Sage in Solitude", IEEE Press, New York, 1988, p. 9, note 3. Today - ironically - most engineers and scientists who study and utilize "Maxwell's equations" have examined neither Maxwell's original work nor the theory of quaternions.
6. Oliver Heaviside was born in poverty on May 18, 1850 in Camden Town, the youngest of four children. Young Heaviside was forced to drop out of high school and go to work. His aunt, however, had married well, to Professor Wheatstone of King's College, London - who was later to become Sir Charles Wheatstone, F.R.S. By his uncle's influence, Heaviside was appointed to a telegrapher's position at Newcastle in 1868. Gradually, he began to theoretically attack the problems in telegraphy, but was forced by increasing deafness to resign in 1874 and return to live with his parents in London.
Heaviside never possessed a formal university degree, but was much later in the early 20th century - to be awarded an honorary doctorate.
Studying mathematics on his own, Heaviside had begun to write improvements for telegraphy, and in 1873 began using calculus. He also studied differential equations and made regular contributions to the Telegraphic Journal, the English Mechanic, and the Philosophical Magazine, with seven papers by 1874.
Heaviside was astounded by Maxwell's "Treatise on Electricity and Magnetism", published in 1873, and Maxwell became his undying hero. Heaviside mastered the manuscript in two years - something few men have done to this day.
With the invention of the telephone in 1877, Heaviside began also to study telephonic transmission. Then Maxwell died in 1879. In 1885-87 Heaviside published in the Electrician a series of articles under the title "Electromagnetic Induction and Propagation", where for the first time he gave a clear and modern vector exposition of Maxwell's theory. Heaviside was violently opposed to the potentials, however, remarking that they were "metaphysical" and that it was even "best to murder the lot". He focused strongly on the EM force fields as the primary EM causative entities. This attitude was to spread and condition generations of electrical scientists -that the EM potentials were only mathematical conveniences.
Though self-educated, Heaviside was a true genius. He also developed the energy flow in the EM field, developed the skin effect, speculated analytically on faster-than-light charged particles, discovered the theory of distortionless signal transmission, and articulated the concept of inductively loaded circuits including self-induction. He had difficulty in getting his papers accepted for publication, since he made use of unusual methods of his own in solving problems. But in 1892 his collected papers were published in two volumes under the title of "Electrical Papers". Later his "Electromagnetic Theory" also dealt with a number of important problems.
Heaviside, followed by Gibbs, attacked the quaternionist expression of Maxwell's theory, though he held the highest regard for Maxwell himself. By 1892-3 the controversy between the multiplying vectorists and the few remaining quaternionists exploded into a duel to the death, and the vectorists quickly won. Interest in quaternions then dropped sharply, and vector EM theory in accordance with Heaviside's interpretation came to be universally accepted.
Heaviside also had his bitter opponents, and even his EM theory was very slow in being accepted by the mathematical physicists, many of whom snobbishly considered Heaviside crude and uneducated. In his writings Heaviside himself often subtly railed at the rigour demanded by the mathematicians, and sometimes essentially used brute force to get the correct results even though mathematical rigor suffered.
Heaviside made major improvements in electrical transmission theory, propagation theory, and advanced the operational calculus to study transients. In "Electromagnetic Theory" (1893-1912), he postulated that the mass of an electric charge would increase as its velocity increased, anticipating one aspect of special relativity. In 1902, he predicted the ionosphere and the Earth-ionospheric duct. Eventually he was awarded an honorary doctorate and was once considered for the Nobel Prize.
Heaviside, ever the outcast and apart from his peers, died in a nursing home at Torquay on Feb. 3, 1925.
7. It is little known that, in his later years, Heaviside may again have turned to quaternion operations, and even developed a "unified" theory of electromagnetics and gravity. These papers were never published, but were reported found in 1957 where Heaviside had lived for some years (some electrical scientists, however, continue to dispute the authenticity of the papers). Little or no adequate review of this unified theory has been made, though several writers have not hesitated to express judgements pro and con as to its authenticity, its promise, or its usefulness (e.g., see Josephs, ibid.; H. J. Josephs, "History Under the Floorboards", Journal of the IEE 5, Jan. 1959, pp. 26-30; H.J. Josephs, "Postscript to the Work of Heaviside", Journal of the IEE 9, Sept. 1963, p. 511-512; B.R. Gossick, "Heaviside's 'Posthumous Papers"', Proceedings of the IEE 121, Nov. 1974, p. 1444-1446; Paul J. Nahin, "Oliver Heaviside: Sage in Solitude", IEEE Press, 1988, p. 305-307).
My own comment is that this (purportedly Heaviside's) unified theory should be examined experimentally, not just mathematically, to ascertain whether or not it works. Certainly Heaviside had long considered localization of energy: e.g., in 1893 ("Electromagnetic Theory", p. 455), he wrote: "To form any notion at all of the flux of gravitational energy, we must first localize the energy... whether this notion will turn out to be a useful one is a matter for subsequent discovery". At least he understood the requirement for a local change in the energy density of the medium by electromagnetic means.
Ironically, then, the man who almost single-handedly "slew" Quaternions and Maxwell's quaternion theory, may eventually have returned to them to try to capture the elusive gravity, which - by the present authour's thesis - inadvertently he had discarded earlier when he struck down the scalar component of the quaternion and converted it to a vector.
8. J.C. Maxwell, "A Dyamical Theory of the Electromagnetic Field", Philosophical Transactions of the Royal Society of London 155, 1865, p. 459512. (Presented in 1864).
9. For an excellent discussion of the Development of Vector Analysis, see M.J. Crowe, "A History of Vector Analysis: The Evolution of the Idea of a Vectoral System ", University of Notre Dame, Indiana, 1967.
10. IN 1835, Sir William Rowan Hamilton's memoir, "On a General Method in Dynamics", was published, expressing the equations of motion in a canonical form that captured the duality between the components of momentum and the coordinates. The deep significance of this duality was not fully appreciated until the rise of quantum mechanics nearly 100 years later. In 1843, Hamilton discovered quaternions, though his investigations in algebra had begun 10 years earlier. In 1853, his "Lectures on Quaternions" - a most difficult and awkward book - appeared. Hamilton spent the remaining 22 years of his life developing the algebra of Quaternions and its applications. His quaternion work was published posthumously in 1866 as "The Elements of Quaternions". The mantle for "quaternion champion" then passed to Professor Peter Guthrie Tait, who had patiently delayed publication of his own book on quaternion theory until after the book of Hamilton, his mentor, was published. See P.G. Tait, "An Elementary Treatise on Quaternions", Oxford Univ. Press, Oxford, 1875.
11. Hamilton's quaternion algebra was a landmark; for the first time, it freed algebra from the commutative postulate of multiplication.
12. See Paul J. Nahin, ibid., p. 100-101. See also Freeman Dyson, "The Maxwell Equations", in M.S. Berger, "J. C. Maxwell, The Sesquicentennial Symposium, Elsevier Science Publishers B.V., Amsterdam, 1984, p. 17-22. Quoting:
"... the mathematicians of the nineteenth century failed miserably to grasp the great opportunity offered to them in 1865 by Maxwell. If they had taken Maxwell's equations to heart as Euler took Newton's, they would have discovered, among other things, Einstein's theory of special relativity, the theory of topological groups and their linear representations, and probably large pieces of the theory of hyperbolic differential equations and functional analysis. A great part of twentieth century physics and mathematics could have been created in the nineteenth century, simply by exploring to the end the mathematical concepts to which Maxwell's equations naturally lead."
13. Heinrich Hertz discovered (proved) the existence of Maxwell's electromagnetic waves in 1888, almost a decade after Maxwell's untimely death.
14. In 1880 Hertz received his doctorate from the University of Berlin, where he had studied under the renowned physicist Hermann von Helmholtz. He began serious study of Maxwell's electromagnetic theory in 1883. While professor of physics at the Karlsruhe Polytechnic, between 1885 and 1889, he produced electromagnetic waves in the laboratory, just as predicted by Maxwell. In his lab, he was able to measure the wavelength and velocity of these waves, and he showed that their susceptibility to refraction and reflection was the same as that of light and heat waves. This established that light and heat are electromagnetic waves, which until then was only an unproved theory. With experimental confirmation by Hertz, Maxwell's theory especially as interpreted in a much simpler vector form by Oliver Heaviside and Hertz - became predominant.
15. See Roger Penrose, "Integrals for General-Relativistic Sources: A Development From Maxwell's Electromagnetic Theory", M.S. Berger, ibid., pp. 211-243. Quoting:
'With the notable exception of Faraday before him, no other major physicist of his day had apparently regarded the concept of 'field' as anything more than a convenient mathematical auxiliary to the prevailing point-particle-action-at-a-distance view of physical reality. The idea that 'disembodied fields' can propagate through empty space carrying energy as they go, was as startling and revolutionary an idea at the time as radio is commonplace to us today."
16. Maxwell had a distinguished academic background. He received a mathematics degree from Trinity College in 1854, became Professor of Natural Philosophy at Marshall College, Aberdeen, Scotland in 1856, and in 1860 was appointed to King's College in London. After a short retirement, he became the first Cavendish Professor of Physics at Cambridge.
17. See note 12 above with respect to the delay in physics occasioned by the leading mathematicians of Maxwell's day ignoring the impact of Maxwell's theory. For another cogent argument about what might have been discovered much earlier in physics if quaternions had not also been cast aside, see James D. Edmonds, Jr., "Quaternion Quantum Theory: New Physics or Number Mysticism?", American Journal of Physics, 42 (3), Mar. 1974, p. 220-223. For yet another argument about what quaternions might have had to say about gravitation and a unified field theory, see this present paper.
18. Of course there were exceptions, but most engineers of the day were little skilled in mathematics. Electrical theory, instruction, and knowledge was particularly primitive. Most electrical engineers desperately needed something as simple as possible, to solve their signaling and power transmission problems. Even many eminent electrical scientists, such as J.J. Thompson, themselves never quite grasped what Maxwell's theory was all about. Also, the prevailing electrodynamics theories of the time were action-at-a-distance models, such as those of Karl Friedrich Gauss and later by Wilhelm Weber. The mathematicians of Maxwell's time had developed a taste for quite different directions of endeavour, and those who had themselves lost touch with physics could not assess the merits of Maxwell's theory (see Dyson, ibid., p.21). Maxwell's own presentations were obtuse and difficult; since he used a mechanical model of the ether, his presentations were filled with clunking gears, ratchets, and distracting machinery - sufficient to route all but the hardiest theorists. Until Hertz proved Maxwell's EM waves in 1888, (over 20 years after Maxwell began publishing his theory), most scientists felt very constrained by the action-at-a-distance competition to Maxwell's theory.
19. Oliver Heaviside's clear and simplified vector exposition of Maxwell's theory began to be published in The Electrician. With Maxwell's untimely death, Heaviside became his tireless successor and unyielding advocate, though other brilliant scientists such as Gibbs, Hertz and Lorentz also made great contributions.
20. In "A Treatise on Electricity and Magnetism", Maxwell did not develop the analytical consequences of the energy concept. Instead, his paper is filled with descriptions of early Victorian ideas about the nature of electrical energy, expressed in a maze of symbols representing quaternion formulations of scalar and vector potential functions, etc. As a result, engineers of the day found Maxwell's chapter on the general equations of EM field theory quite unreadable.
Even years later in the 1880's, it was still almost impossible to find a teacher who comprehended Maxwell's electrodynamics. Michael Pupin, for example, travelled from the US to England in vain, seeking such a professor. Finally, in Berlin he found one Helmholtz - who was able to teach him Maxwell's theory (See Dyson, ibid., p.21).
21. In 1892, Heaviside's series of papers in The Electrician and elsewhere were published as his "Electrical Papers", MacMillan and Co., in two volumes. Much later, this book provided a basis for his "Electromagnetic Theory", The Electrician Publishing Co., London and New York, 1922. The second edition with an introduction by E. Weber was published at New York in 1950. The third edition with a foreword by Sir Edmund Whittaker was published by Chelsea Publishing Company, New York, 1971.
22. Heaviside railed at the elusive idea of the potential, and focused electromagnetics upon the force fields, as did Hertz and Gibbs. Scientists and the literature were strongly indoctrinated with the dogma that the potentials were only mathematical conveniences. (Before one censors Heaviside, Gibbs and Hertz too strenuously for their shortsightedness, one should recall that, classically, forces and force fields - not energy - had been uppermost in scientific theory.)
It was not until 1959 that scientists were goaded once again into facing the unpleasant fact that the potentials were the primary reality and the translation force fields were simply made from them by operations. See Y. Aharanov and D. Bohm, "Significance of Electromagnetic Potentials in the Quantum Theory", "Physical Review", Second Series, 115 (3), Aug. 1, 1959, p. 485-491.
Even so, this latter view was still not fully accepted until the mid-1980's, and it is only recently that the potentials - so beloved and emphasized by Maxwell himself - are once again accepted as the heart and soul of electromagnetics. See Bertram Schwarzschild, "Currents in Normal-Metal Rings Exhibit Aharonov-Bohm Effect", Physics Today, 39 (1), Jan. 1986, p. 17-20 for confirmation that the AB effect has been proven to the satisfaction of all but the most diehard skeptics.
Even so, the primacy of the potentials is still fully accepted only by a handful of scientists. See S. Olariu and I. Iovitzu Popescu, "The Quantum Effects of Electromagnetic Fluxes", Reviews of Modern Physics 57 (2), April 1985 for an exhaustive discussion of the Aharonov-Bohm effect (which proves the physical reality and primacy of the potential) and an extensive list of references.
23. Particularly in his earlier papers in The Electrician, and in his "Electrical Papers" in 1892.
24. In addition to being an excellent experimentalist, Heinrich Rudolf Hertz (1857-1894) was also a noted theorist - and one who also died at an untimely early age. Hertz also made a theoretical reformulation of Maxwell's theory, removing the potentials and focusing on the force fields, as did Heaviside. In his "Electrical Waves", (see Dover, New York, 1962, p. 196- 197; first published in English in 1893), Hertz stated:
"... I have been led to endeavour for some time past to sift Maxwell's formulae and to separate their essential significance from the particular form in which they first happened to appear. The results at which I have arrived are set forth in the present paper. Mr. Oliver Heaviside has been working in the same direction ever since 1885. From Maxwell's equations he removes the same symbols (the potentials) as myself; and the simplest form which these equations thereby attain is essentially the same as that (at) which I arrive. In this respect, then, Mr. Heaviside has the priority... "
25. For Tait's quaternion theory, see P.G. Tait, "An Elementary Treatise on Quaternions", Oxford University Press, Oxford, 1875, 1st edition.
26. For details of the long struggle Heaviside had with his adversary Tait, see "The Great Quaternionic War", Nahin, ibid., p. 187-215. See also M. J. Crowe, "A History of Vector Analysis", University of Notre Dame Press, Notre Dame, 1967, passim. See also A.M. Bork, "Vectors Versus Quaternions - The Letters in Nature", American Journal of Physics, 34, Mar. 1966, p. 202-211.
27. With the availability of excellent and extensive expositions of the vector interpretation of the translation force-field subset of Maxwell's theory by Heaviside and Hertz, and with the nearly insurmountable difficulty associated with the complex quaternions and potentials which few scientists understood, the rejection of the quaternionic form of Maxwell's theory and the acceptance of the vector subset was inevitable.
28. Again recall that even Heaviside, the mighty mouse of a man who, together with Gibbs slew quaternions, much later may have again turned to quaternions to grapple with the elusive gravity.
To deal with curved space-time, one must deal with potentials, for - in a strict sense - a potential is a curvature of space-time. It is also a trapped spatio-temporal stress, the nature of the stress being determined by the nature of the stressing fields comprising the potential. The stress may be either compressive or tensile, and may contain a complex infolded structure of infinite variability. Gravity is not determined by force fields (the escape of curvature of space-time), but by potentials (the stabilized presence of curvature of space-time).
In addition, one runs headlong into the need for negative energy and negative time. For example, if two like charges are brought together, energy is required to overcome the repulsion, and this energy "goes into the field" to give a positive energy density of space. Two masses, however, attract each other; it takes the exertion of energy to keep them apart - or, in other words, the field energy is negative in this case. Maxwell was much perplexed by this problem, as was Heaviside - and as has been most other physicists who struggled with it, down to and including the physicists of today.
Actually, if we accept the negative field energy requirement, we can expect to meet negative energy when time is reversed, since the fundamental quantum (photon) is composed of (
As early as 1898 Carl Barus - in a paper titled "A Curious Inversion in the Wave Mechanism of the Electromagnetic Theory of Light", American Journal of Science 5 (Fourth Series), May 1898, p. 343348 - showed an interpretation of Maxwell's electromagnetic wave equations that could "make the wave run backward". His paper was ignored, but it may have been the first indication of what today in nonlinear phase conjugate optics is known as the time-reversed EM wave.
In the early 1970's Western scientists discovered a strange thing in the open Soviet literature: the production of a time-reversed (TR) wave in nonlinear optics. Indeed, such a wave is a solution to the wave equation, and so the solution applies to all manner of waves (it has been accomplished, for example, with sound waves).
Time-reversed EM waves were controversial at first, since many physicists (even today!) naively equate time reversal with the science fiction notion of "traveling backwards in time". It is nothing of the sort, of course. For an object to travel backwards in time, the entire universe sans the object would have to be time-reversed to a previous state, so that the "present object" is seen as being present in a "past state of the universe". Time-reversing a single wave means that only the single wave is seen by the external observer to be affected by the reversal process. He sees (in his own forward time) a successive series of spatial positions of the reversing wave. He sees the rest of the universe moving forward in time in a normal fashion.
Since time is not observable, we simply see such a TR wave, not as time-reversed, but as spatially-reversed. (We see a time-reversed particle as both spatially-reversed and charge-reversed.) Though much is still unsure about time reversal, it is legitimate and has been in physics for decades. (See Robert G. Sachs, "The Physics of Time Reversal", University of Chicago Press, Chicago, 1987, for a broad and comprehensive coverage of the role of time-reversal in physics, and its clear distinctions from space reversal and velocity reversal. For an excellent introduction to the nonlinear optics time-reversed EM wave, see David M. Pepper, "Nonlinear Optical Phase Conjugation", Optical Engineering, 21 (2), Mar./Apr. 1982, p. 156-183.)
So today we are aware that a time-reversed EM wave can readily be produced. The present author has already pointed out that an EM wave carries both energy and time, and that a time-reversed EM wave has both its energy and time content reversed in sign. Such a TR wave carries negative energy and negative time. So a normal (forward-time) photon must be considered as comprised of (+
In an atom, normally photons are emitted by radiation from negative charges, while anti-photons are emitted by radiation from positive charges - such as the positively charged nucleus of an atom.
EM mixing stress and time reversal can be utilized to create an amplified time-reversed replica of a small input signal wave. When EM wave mixing stress is rhythmically applied to the atom, a scalar EM stress wave system is formed with zero E and B vector resultants. This wave passes through the electron shells and pumps the nucleus to an excited state. Input of another EM wave to the atom modulates the scalar pump wave, in turn modulating the pumping of the nucleus and accomplishing 4-wave mixing. The time-reversed (positively-charged) nucleus acts as a pumped phase conjugate mirror and emits a phase conjugate (time-reversed) EM wave, which travels out of the nucleus as a modulation upon the scalar pump wave "bridge to the outside".
As is well-known in four-wave mixing, the emission of a phase conjugate replica does not change the momentum of the mirror; i.e., it does not cause recoil. When it strikes another stressed atom, however, it modulates the stressing scalar waves and penetrates into the nucleus, where it is absorbed. Absorption of the negative energy/negative time wave in the nucleus does cause recoil negatively! Thus all atomic nuclei are continually being drawn to each other by negative recoil from four-wave mixing reactions. This is the genesis of gravity.
Of course, since time is not observable, we do not observe reversed time - we do not at all see any sort of "travel into the past", as explained previously. In a universe moving in positive time, we will simply see the time-reversed wave as spatially reversed - since time itself is not observable - and exhibiting very peculiar behaviour and negentropy by proceeding from disorder back to order. We will also see such a TR wave converging upon its path rather than diverging which characteristic itself is a move from disorder to order, and negentropic.
As can be seen, when we include TR waves, the second law of thermodynamics (which assumes only positive-time EM energy) must be reversed, so that it becomes the law of negentropy. This present second law is only half the case; addition of the law of negentropy completes the other half of it.
Note also that random time-reversed EM waves (time-reversed "heat") when added to normal heat, cools the region (reduces the algebraic size of the positive heat). It reduces the disorder of the region by multi-photon (multi-wave) mixing. Electrostatic cooling should be reexamined in light of this characteristic union of disordering and ordering.
29. The negative energy solutions and potentials of quaternion theory are particularly interesting, though they have been little pursued by theorists. It is also to be highly regretted that very early work on "reversed EM waves", such as the paper by Barus, ibid., was not vigourously followed up at the time.
30. As will be seen, the scalar component of the quaternion can infold and capture the stress energy of a zero-translation-resultant electromagnetic stress system, which constitutes the capture of an electrogravitational potential. Regular periodic oscillations (in magnitude, relative components, phase, etc.) of this potential constitute powerful standing gravitational waves of local curvature in space-time. Direct and significant local general relativity (GR) then exists in the laboratory, and direct GR experiments may readily be conducted.
31. In Heaviside EM theory, we are taught to discard zero translation resultant electromagnetic stresses. We are taught to discard those aspects of EM that: (1) form gravitational and inertial effects, and (2) are capable of directly reaching and engineering the atomic nucleus in a controlled fashion. Consequently, our present crude "engineering" of the nucleus is largely restricted to introducing a whole neutral particle or violently striking the atom with a speeding particle "hammer". With scalar EM we should be able to tune, change and control the nucleus like fine-tuning a precision watch.
32. See also James D. Edmonds Jr., "Quaternion Quantum Theory: New Physics or Number Mysticism?", American Journal of Physics, 42 (3), Mar. 1974, p. 220-223. See also his paper, "Maxwell's Eight Equations As One Quaternion Equation", American Journal of Physics, 46, Apr. 1978, p. 430-431.
33. See also Dyson, ibid. and Josephs, ibid. Also, Dr. Henry Monteith of Sandia National Laboratories has independently discovered that Maxwell's quaternion theory contained a unified field theory of gravitation and electromagnetics. See Monteith, "Dynamic Gravity and Electromagnetic Processes: Parts I and II", July 1988. See also Monteith, "Visualization and Duality in Mathematical Physics", Sandia National Laboratories, Albuquerque, April 15, 1986. Monteith has extended quaternion theory to include the hyperbolic quaternion, and has shown that his extended theory contains both spinor and twistor theory as subsets, and is a full theory of anisotropic space-time. Presently, he is preparing a major book on this subject, and he may very well be the scientist who writes the great new unified EM-G field theory so long sought by physicists.
34. See papers by T.E. Bearden, published by the Tesla Book Co., POB 1469, Greenville, Texas: "Comments on the New Tesla Electromagnetics: Part 1: Discrepancies in Present EM Theory", 1982; "Part III: Clarifying the Vector Concept", 1983; Part IV: "Vectors and Mechanisms Clarified", 1983; "Solutions to Tesla's Secrets and the Soviet Tesla Weapons", 1981; "Soviet Weather Engineering Over North America", 1-hr. videotape, 1985; "Star Wars Now! The Bohm - Aharonov Effect, Scalar Interferometry, and Soviet Weaponization", 1984; "Far-de-Lance: A Briefing on Soviet Scalar Electromagnetic Weapons", 1986; Chapter 4: "Extraordinary Physics" in "AIDS: Biological Warfare", 1988, p. 74-203. See also Bearden, "Tesla's Electromagnetics and Its Soviet Weaponization", Proc. 1984 Tesla Centennial Symp., International Tesla Society, Colorado Springs, Colorado 1984; Bearden, "Soviet Phase Conjugate Weapons: Weapons That Use Time-Reversed Electromagnetic Waves", Bulletin, Committee to Restore the Constitution, POB 986, Ft. Collins, Colorado 80522, Jan. 1988.
35. Of interest in EM theory is the appearance of closed circuital fluxes of EM energy in a region, which has bothered a very great number of physicists and electrical engineers including Maxwell and Heaviside. Heaviside's derivation of the Pointing vector with a vector G term describing these "close-loop energy traps" was published in The Electrician on Feb. 21, 1885. Heaviside wrestled with this G-vector, but dismissed it as an unnecessary and useless introduction of an auxiliary circuital flux. Actually, such a trapped closed-loop energy flow constitutes a special kind of dynamic structure internal to an electromagnetic potential, in the view of the present author. Further, since this EM potential has a definite deterministic pattern and structure, it may be regarded as an artificial potential, in contradiction to a normal potential with a random energy flux structure. If this view is correct, then Heaviside (and other electrical physicists, subsequently) may again have discarded one part of electrogravitation - because, after all, in modern general relativity, gravitation primarily consists of a number of potentials, trapped energy density of vacuum constitutes a curvature of space-time, and closed circuital fluxes of EM energy represent dynamic internal energy-density structures.
Such closed loop energy flows actually exist and are definitely real.
For example, the Earth's atmosphere experiences
36. E.T. Whittaker, "On an Expression of the Electromagnetic Field Due to Electrons By Means of Two Scalar Potential Functions", Proc. Lond. Math. Soc., Series 2, Volume 1, 1903, p. 367-372.
37. Even today it is still in vogue in physics and electrical engineering. Specifically, engineers almost never try to design equipment that utilizes potentials in the absence of the force fields. There are a few notable exceptions, of course. The author and Frank Golden did work in the 1970's with "free A-field" equipment developed by Golden, and Dr. William Tiller did important theoretical work in curl-free vector potentials (free A-field). See his US Patent No. 4,447,779, "Apparatus and Method For Determination of a Receiving Device Relative to a Transmitting Device Utilizing a Curl-Free Magnetic Vector Potential Field", fan. 31, 1981; US Patent No. 4,429,280, "Apparatus and Method For Demodulation of a Modulated Curl-Free Magnetic Vector Potential", fan. 31, 1984; US Patent No. 4,432,098, "Apparatus and Method For Transfer of Information By Means of a Curl-Free Magnetic Vector Potential Field", Feb. 14, 1984. For an exhaustive discussion of the Aharonov-Bohm effect (which establishes the reality and primacy of the potentials), see S. Olariu, "The Quantum Effects of Electromagnetic Fluxes", Reviews of Modern Physics, 57 (2), Apr. 1985, p. 339.
38. Indeed, so far as is known to the present author, there is still not a single EM textbook that even recognizes and addresses the issue of whether or not a zero-resultant force vector system can be exclusively equated to - and totally replaced by - a zero translation vector resultant. The reason may be that, unconsciously, physicists have wished to avoid the incredible implications of infolded and inwardly structured EM energy (as perhaps witnessed by the rather short shift given to David Bohm's fundamental and revolutionary "hidden variable" theory of quantum mechanics). Not only does one face the implications of the internal structuring of EM energy, but one also faces the implications of curving local space-time (violating Einstein's general relativity) and deterministically substructuring that curvature of space-time, vacuum potentials, and the very vacuum itself.
This profoundly affects one of the fundamental assumptions of quantum mechanics: that the nature of quantum change is totally statistical. With internally structured potentials and direct control and manipulation of "hidden variables", one can engineer quantum change itself, even before collapse of the wave function. That is, one can speak of engineering physical reality itself.
Indeed, one would now be dealing with physics on a notion of the "information content" of hidden physical processes, where the hidden informational content of interacting energies can produce startling and unusual phenomenology, including violation of all present macroscopic conservation and exclusion laws. Very strange effects are already known in quantum mechanics, which conceivably may be due to the interaction of such infolded information structures. For example, one can sometimes even influence or decide the outcome of at least one type of experimental interaction after it has apparently already happened. In the two-slit experiment, one can wait until after the interactions with the electron are completed, and still select whether the electron will exhibit a classical particle or a quantum interference (wave) nature in the interaction. See, for example, John Archibald Wheeler, "The 'Past' and the 'Delayed-Choice' Double-Slit Experiment", in A.R. Marlow, ea., "Mathematical Foundations of Quantum Theory", Academic Press, N.Y., 1978.
Soviet scientists have particularly focused on the infolded structure of electromagnetic waves, referring to this structure as the "information content" of the fields. They have intensely applied this approach to the study of biological systems; for example, see N.D. Devyatkov and M.B. Golant, "Prospects for the use of millimeter-range electromagnetic radiation as a highly informative instrument for studying specific processes in living organisms", Soviet Technical Physics Letters, 12 (3), Mar. 1986, p. 118-119; See also N.D. Devyatkov (ed.), Applications of low-intensity millimeter-wave radiation in biology and medicine (in Russian), IRE Akad. Nauk. SSR, Moscow 1985. Further, each type of cellular disease has its particular EM radiation structure; it has been shown that the EM radiation structure (the EM information) emitted by diseased cells are capable of inducing that same disease physiology and symptomology in distant cells. See Vlail Kaznacheyev, "Electromagnetic bioinformation in intercellular interactions", PSI Research, 1(1), Mar. 1982, p.47-76. It follows that time-reversing (phase-conjugating) the mitogenetic "disease" information signal could provide a "healing" signal for a specific cellular disease condition (See Bearden, "AIDS: Biological Warfare", 1988 for an extended discussion, and appreciable details of the Priore device which utilized such an approach to demonstrate nearly 100% cures of terminal cancers, leukemias, and other diseases in laboratory animals).
The weapon implications using modulated electromagnetic carriers are obvious, and it is significant that: (1) over-the-horizon (OTH) beams from Soviet giant microwave OTH radars continually intersect over North America, (2) the world's greatest expert in EM induction of cellular disease at a distance V. Kaznacheyev - is associated with two secret institutes in the outskirts of Moscow which produce microwave-directed energy weapons, and (3) extensive health changes have occurred over the decades in personnel in the US Embassy in Moscow, where weak microwave radiation has been beamed against the building since the early 1950's. Actual measured EM field data inside the Embassy reveals a strong correlation between the locations where induced health problems in Embassy personnel occurred, and the locations where the EM force fields from the Soviet microwave radiation were minimal or zero. Note that the areas where EM force fields are absent or minimal represents those areas where the potentials are strongest. The high correlation of disease induction to those specific areas, strongly indicates that the Soviets have deliberately used structured EM potentials in the microwave radiation to induce diseases in Embassy personnel. It is obvious that this has been a continuing test stimulus to see (by US response at the site or lack of it) whether or not we are knowledgeable in scalar EM and in structured EM potential disease induction technology and weapons. Installation of aluminum screens over the windows merely decreased the force field components, not the potentials. Obviously we have continually certified our ignorance of scalar EM.
39. The physical interpretation of the zero vector is interesting. To the external observer, a zero translation vector applied to an object or point merely means the absence of observed translation of that object or point. If, in addition, no infolded finite vector components exist in the zero-vector, then no internal stress due to the zero-vector exists internal to the object or point. If, on the other hand, infolded finite vector components exist in the zero-vector (that is, if it is a zero-vector-resultant system of multiple non-zero translation vectors), then internal stress due to the zero-vector system exists internal to the object or point. In other words, there are two kinds of zero-translation vectors: (1) those that have no infolded internal finite structure, and (2) those that do have an internal, infolded finite structure. One of these zero vectors is stress-free, while the other is a stressing system. The latter class of zero translation vector constitutes a potential, contains a massless charge, and represents a direct curvature of local space-time with a deterministic, infolded structure that affects a surrounding region of space-time.
40. 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 sum (i.e. to external translation).
41. Unfortunately Einstein studied the prevalent Heaviside version of Maxwell's electromagnetic theory in university. Therefore he studied only a subset, and one in which EM and G are mutually exclusive a priori. Since potential with curvature of space-time, that meant that he would of necessity assume that EM forces did not curve local space-time. After all, EM forces simply radiate away as EM radiation, fleeing at the speed of light. So no EM force was going to be around long enough to warp space-time.
Accordingly, Einstein was left with the weak gravitational force between masses as the only force with which to curve space-time. The mass-attraction G-force is so weak that only adjacent to a stupendous collection of mass - such as the Sun or a star - would there be sufficient space-time curvature to even detect. Einstein reasoned that the observer and the laboratory would never be on the surface of the Sun or at the surface of a star; consequently, he assumed that - where the observer and the laboratory were located - the local frame would be a Lorentz frame and local space-time would never be curved. In other words, Einstein did not write a general theory of curved (anisotropic) space-time at all. Instead, he wrote a severely restricted subset of such a theory. He wrote a sort of special relativity with distant perturbations, where all the "general" relativity occurs at an appreciable distance from the observer, and then only at or near a huge collection of mass.
This had several results (considered advantages by orthodox scientists). (1) it strongly implied that one would never have a direct experimental science of general relativity on the laboratory bench. After all, if the local space-time is uncurved, it means there is no local general relativity. (2) it assumed that it was impossible to utilize the far stronger EM forces (which are some 10exp36 to 10exp42 times as strong as the G-force) to make gravitational potential. And with the denigration of the EM potentials as having no physical reality, Heaviside's force field-oriented EM theory diverted one directly away from considering the constitution of EM potentials as having any relevance to anything physical. (31 it saved the sacrosanct conservation laws, which had been raised to a dogma.
Ironically, after assuming that local space-time was never curved, Einstein spent the rest of his life futilely striving to get electromagnetics back into general relativity fold, to form a unified field theory. He failed - never realizing that it was his own assumption of a locally-uncurved space-time that doomed all his efforts to failure.
In the West, Einstein's severely restricted general relativity has itself become tantamount to dogma, and any challenge to the sacrosanctity of the conservation laws results in immediate alarm. This is not true at all in the Soviet Union, where leading academicians regularly publish papers detailing aspects of an unrestricted general relativity, where local space-time can be curved and where all conservation laws can be violated.
For example, see A.A. Vlasov and V.I. Denisov, "Einstein's formula for gravitational radiation is not a consequence of the general theory of relativity", Theoretical and Mathematical Physics, 53 (3) June 1983 (English translation; Russian publication Dec. 1982), p. 406-418. Quoting: "... in general relativity there are no energy-momentum conservation laws for a system consisting of matter and the gravitational field."
See also V.I. Denisov and A.A. Logunov, "New theory of space-time and gravitation", July 1982, p. 3-76. This paper (p.3) points out that "... the gravitational field in general relativity is completely different from other physical fields and is not a field in the spirit of Faraday and Maxwell.".
A 1984 Soviet paper by senior Russian physicist C. Yu. Bosgoslovsky, "Generalization of Einstein's Relativity Theory for the anisotropic space-time", is also very relevant. See also V.I. Denisov and A.A. Logunov, "The inertial mass defined in General Relativity has no physical meaning", preprint p. 0214, Institute of Nuclear Research, USSR Academy of Science, Moscow, 1981.
For documentation of a near-conspiracy in the West against refutation of Einstein's restricted general relativity, see Ruggero Maria Santilli, "Ethical Probe on Einstein's followers in the U.S.A.: An Insider's View", Alpha Publishing, POB 82, Newtonville, MA 02160, 1984.
The assumed mutual exclusion of EM and G can be theoretically shown to be false. See R.M. Santilli, "Parsons and Gravitation: Some puzzling questions", Annals of Physics, 83 (1), Mar. 1974, p. 108-157. It can also be experimentally proven to be false.
For some years John Hutchison of Vancouver, Canada has performed experiments where he places a sample (material or object) between two giant Tesla coils, then violently activates the coils. The two coils provide "strong bucking EM force fields" into and onto the sample, with many, many frequencies and randomly varying multi-wave interactions. The irradiation also produces strong, fluctuating ELF components, in and on the central object. Gravitation in a mass varies as a function of the magnitude of the
When phasing conditions and target internal conditions are just right, nonlinearities in the central target object act to a certain degree as a nonlinear medium of sufficient reflectivity to be considered a pumped phase conjugate mirror (though certainly one of very low efficiency). Under fortuitous conditions, the object is levitated, since its nuclei are being pumped with an ELF scalar wave and forced to produce a great deal of excess negative time. In negative time, masses repel rather than attract; hence the more
While Hutchison's experiments are relatively uncontrolled, he has produced verifiable results: for example, a major German laboratory has found alterations in the metal of his sample that are previously unknown, and which cannot be duplicated by any other known procedure. His approach is essentially no cruder than the "get a bigger hammer" approach of high energy physics; he just does not have the facilities, funds, and team of supporting scientists to meticulously instrument his results and stabilize his fields. And he certainly has suffered great derision from orthodox engineers and scientists who do not at all understand the principles utilized in his experiments. Nevertheless, Hutchison is right and all the deriding pundits are wrong.
42. Utilizing the microstructure of the vacuum is something which orthodox scientists have never even tried. For confirmation, see Tsung Dao Lee, "Particle physics and Introduction to Field Theory", Harwood Academic Publishers, N. Y., 1981, Second printing with corrections, 1982, p. 1957.
43. The sine-squared wave is of extraordinary importance. Its characteristics were independently discovered by John Bedini experimentally, as a special means he discovered and utilized to greatly enhance and control EM effects on cells and cellular structures. In a nonlinear medium such as living tissue, an ordinary EM sine-squared wave of appropriate frequency causes generation of its own phase conjugated replica in the body. The two waves are locked together by the modulation effect, and form a sine-squared scalar EM wave which penetrates widely throughout the body, even to the atomic nuclei, with greatly decreased power levels required. By modulating this wave with specific "healing photons" designed for a specific disease, internal EM healing via structured EM potentials (i.e., by the specifically-tailored information content of the EM potentials) can be introduced throughout the body's own "cellular information system". Photobiology, little known in the West, nevertheless has great promise and offers a potential for healing a great many diseases presently impossible or difficult to cure.
44. Along the lines developed in Bearden, "AIDS: Biological Warfare", Tesla Book Co., 1988.
45. For a comprehensive engineering overview of the theory of four-wave mixing, see David M. Pepper, "Nonlinear Optical Phase Conjugation", Optical Engineering, 21 (2), Mar./Apr. 1982, p. 150-183.
46. For a detailed, cautious overview of time-reversal in physics in general, see Robert C. Sachs, "The Physics of Time Reversal", University of Chicago Press, Chicago, 1987.
47. For a useful discussion of the theory of parametric oscillation, see V.V. Migulin et al, "Basic Theory of Oscillations", Ed. V.V. Migulin, translated from Russian by George Yankovsky, Mir Publishers, Moscow, 1983 (revised from the 1978 Russian edition).
48. See Bearden, "Extraordinary Physics", ibid. for a discussion of negative time.
49. A close associate, John Bedini, has accomplished such transmutation of elements in the laboratory in proprietary experiments. Indeed, transmutation can be accomplished by scalar EM means at extremely low power and energy - at levels so weak that living systems can and do accomplish limited transmutation of elements. Louis Kervran was a Nobel nominee in 1977 for proving just that. For example, see his "Biological transmutations", Crosby Lockwood, London, 1972; "Transmutations Biologiques", Libraire Maloine, Paris, 1962; "Transmutations a faible energie (naturelles et biologiques)", Libraire Maloine, Paris, 1972.
50. For an extended discussion, the reader is again referred to Bearden, "Extraordinary Physics" in "AIDS: Biological Warfare", 1988.
51. Maxwell himself was well aware of the importance of EM stress in the medium, though he had apparently not realized that this represented electrogravitational potential. For example, quoting from his "Treatise", Vol. 1 3rd edition, (New York, 1954), p. 10: "There are physical quantities of another kind which are related to directions to 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."
Note that, since Maxwell assumed a material ether, he obviously assumed it to have such stress and strain characteristics, and knew that this situation was captured by the quaternions.
52. Santilli, "Ethical Probe... ", 1984.
53. Denisov and Logunov, "New Theory... ", ibid.; Vlasov and Denisov, ibid., Bosgoslovsky, ibid.
54. Denisov and Logunov, "The Inertial Mass... ", ibid.
55. See the several weapons references by Bearden, previously listed above.