 ...An Exact Classical Mechanics leads toward Quantum Gravitation... Contents
4.9 Gravity as a Negative Buoyancy ForceThe derivation began by assuming the presence of a force producing flux φ without specifying what this could be. Now that the energy density has been found to vary with ψ, however, it is worth pursuing the idea that the force might be generated by energy density gradients instead. Energy density ε will vary inversely as the cube of L and so, incorporating equation[37] we can write:  | [50] |
Differentiating both equations[36] and [50] with respect to r we have:  | [51] |
This author's previous publications(6 to 11) have shown that the i-ther has to exist as a composite of positive and negative energy states. This is because attractive forces cannot be modelled, without freedom from paradox, unless the gauge particles which mediate such forces carry negative momentum. This means that the arrow, representing momentum, needs to point in a direction opposite that of motion. The accelerating force of action needs to be reversed so that negative work is done in acceleration: so specifying a negative inertial mass. It follows that such particles are constructed from negative energy. If then a mixture of particles, called, "primaries" is considered, all moving close to the speed of light and constantly colliding, it was shown, by the author's publications (7,8,10&11) (historical order) that curious effects appear. (Note that the primaries were first called, "cosmons". Since this name was already in use for a model by Adolphe Martin, which did not include negative energy states, it had to be changed). A mathematically-based solution showed, that in order to conserve momentum at each pair collision, each primary gained energy in an equal but opposite amount to its partner. Collisions of opposites therefore result in a breeding effect so that the i-ther tends to grow continually in both size and density! Most of this is cancelled by mutual annihilation at centres where high density prevails, resulting in a filamentous structure. This had the ability to store energy imbalances, later released to generate quantum waves of real energy. Energy conservation meant that the positive and negative phases of the mixture needed to co-exist in a close balance. An asymmetry of rest-energies between opposite types of primary also had to be present . The positive kinds needed to have the greater rest-energy and, to preserve conservation of energy, the negative primaries needed to be produced with the greater kinetic energies. Without this asymmetry the filaments could not generate the required quantum waves. It is useful to define ε as a reference energy density: the value which would obtain if rest energies were zero. Then if the average speed of positive primaries is v+ the corresponding energy density will be ε+. The kinetic theory of gases can be refined to yield the pressure P+ as a function of the number n+ of primaries per cubic metre, the total energy per primary E (equal for both positive and negative kinds) and v+ yielding:  | [52] |
Since the rate of production of primaries is equal for both phases it follows that the number crossing unit area per second ξ must also be equal for both. Now the positive primaries can be imagined as at the centres of cubes of side L filling a cubic metre so that their number n+ = 1/L3. If these all move toward a surface at speed v+ there will be 1/L2 rows in motion and the number crossing per second in each row will be v/L. Allowing for three-dimensional motion it follows that:  | [53] |
Since v will be close to the speed of light c it is convenient to write: Then noting that we obtain:  | [54] |
A similar expression applies for the negative phase and ε is the datum value common to both. Hence by addition the net pressure Pn becomes:  | [55] |
It being assumed that δ+>δ-. Then equation[55] can be differentiated and equated to [51] to yield:  | [56] |
Now the buoyancy force F on a particle of volume Vp when combined with equation[56] becomes:  | [57] |
The sub-atomic particle of volume Vp will have a net energy density which is the sum of two values differing from ε so the net value will be εp+ - εp- yielding a mass m equal to:  | [58] |
Then the gravitational acceleration g = F/m is given by dividing [57] by [58]. It is also given by dividing equation[31] by E/c2 . Then with r0 given by equation[32] it follows that:  | [59] |
Equating equation[59] with [57]/[58] the result becomes:  | [60] |
Since EXP(-3Ψ) is close to unity in weak fields like those in the solar system it follows that the differential density inside the particle boundary must equal that outside to provide the observed gravitational acceleration. When the properties of a mixture of positive and negative energies are analysed they are found to be unlike those of fluids of everyday experience. Focused quantum waves enhance the breeding effect to produce density humps in both phases on which the waves are superimposed. Close to the focus the ultimate density can readily be approached: the i-theric liquidus state in which the primaries occupy about one quarter of the total volume. At lower densities creation slightly exceeds annihilation but at higher values the converse is true: because multiple collisions favour annihilation. The liquidus is the "black hole" condition of this theory, even though the speed of light never falls quite to zero. It is black because light and matter will simply dissolve as they enter. It is, however, totally unlike the black hole predicted by relativity, in which an elevated event horizon appears and a central singularity exists. Our black hole has a fuzzy edge but otherwise behaves like a solid object in the field of force generated by the external pressure gradient. This is because impinging primaries cannot penetrate and are reflected back. In the external fluid, where primaries are well-separated, pair-collisions result in the partners passing through one another without change of momentum in their directions of incident motion. Transverse scatter occurs with both moving in the same direction and this effect is responsible for breeding. However, the net negative pressure does not cause the positive primaries to move toward increased density: only the filaments or our black holes are accelerated in this direction. In a companion publication16, under preparation, it is shown how focused quantum waves can produce the required density increases for sub-atomic particle formation: as the new black holes. What this analysis shows is that gravity could be produced entirely as a result of the density gradients of the i-ther acting as a negative buoyancy force. There seems no need of any supplementary force produced by the hypothetical graviton. There seems no need for the vast mathematical sophistication which has developed over the last sixty years in efforts to integrate general relativity with quantum gravitation. There are two bonuses from the solution just advanced. Any graviton absorption model would inevitably involve the formation of gravitational shadows. For example, there would be a change in gravity within the shadow of the moon during an eclipse of the Sun. Efforts have been made to detect such shadows but none have been found which exceed the resolution of the apparatus used. Buoyancy forces do not produce shadows. Furthermore absorption models would generate tangential forces on planets. The gravitons would stream out radially from the near-point source of the Sun but the planet is in orbital motion. It will run into the gravitons, just as moving vehicles run into vertically falling raindrops: the latter appear to slant. A tangential force equal to radial force X vorb/c will add energy to the moving planet, causing it to continually gain energy and spiral out of orbit. No such phenomenon has been observed. 4.10 Further RefinementsThe formulation presented here was ultimately found not to be exact due to two effects which had not been taken into account. One of these was the space taken up by the primary particles of which the i-ther is composed and the other is more subtle. However, an exact solution was finally obtained using an energy-creating quantum-wave approach. This will be published in a companion volume(16). A mechanism for generating the energy-density gradients of the i-ther is now provided and, even more satisfying, as a by-product of the maintenance of sub-atomic particles. The Novikov equation also now appears as a prediction and also shows the previous formulation accurate to 10-8 in fields as strong as those at white dwarf stars. It shows that the density of the i-ther at the surface of the neutron star is about 1.68 times that at the Earth. This is a very small ratio as compared with the relevant matter densities. The matter density of a neutron is a bout 3 x 1014 that of water. What is important at present is that Aspden's analysis has already shown that absolute speeds can, after all, be measured. The hope is that the barriers in communication can be overcome so that NASA is made aware of the huge new field of exploration which is now opening. If a Brillet and Hall interferometer could be flown on every deep space mission the velocity structure of the i-ther could be mapped. It would be particularly interesting to find out if an i-theric vortex was centred on Saturn. No Earth-centred vortex could exist otherwise Brillet and Hall would not have observed their "anomaly". It follows that a critical mass for vortex formation must exist and Saturn might exceed criticality. If the first orbital flight also carried a Michelson Morley apparatus and gave a confirmatory result then there could be no Lorentz contraction, as required by special relativity. The more advanced apparatus depends on an asymmetry of reflection at a mirror, caused by absolute motion, and this is not affected by the Lorentz contraction. Finally a pair of mutually perpendicular quartz crystal vibrators need to be tested in orbit to detect the predictions given here for anisotropy of vibrational frequency caused by absolute motion. This apparatus would weigh only a few grams. So three new experiments have arisen as spin-off from the analysis. There are others but they will not be considered here. | 
