An Exact Classical Mechanics leads toward Quantum Gravitation
Ronald D. Pearson (October 1997; revised May 2003; revised September 2005)
This pamphlet suggests that misconceptions in classical mechanics are responsible for blocking progress in physics. Refinements are described which spill over into quantum theory and appear to provide answers to vexed questions. For example, it leads to alternatives to both special and general relativity which match the achievements of both. Unlike relativity, however, the new solution is fully quantumcompatible, being consistent with the concept of the quantum vacuum. It needs critical analysis to judge the value of the changes made and promote three experiments in orbit for verification/falsification.
An Exact Classical Mechanics leads toward Quantum Gravitation  A foreword to show why this derivation was required (added September 9, 2005)
Some critical correspondence originating from a dialogue on the
"BBC Science and the Séance" message board has shown that an introduction to the theory called "Exact Classical Mechanics" (ECM) is required. What was omitted was the reason for the derivation of this theory. This reason is actually provided in the copy of "Consciousness as a SubQuantum Phenomenon" (CSQP) also available on the website of the Campaign for Philosophical Freedom. The brief summary I now provide ought to have been included in the introduction so that the rest makes sense.
Cosmologists are, to this day, still struggling, unsuccessfully, to solve the problem of the "cosmological constant" (CC) that arises from big bang theory as the prediction of a universe expanding at a rate 10^120 times greater than is possible. ECM theory was developed to provide a solution and does so very successfully. The logical basis can be summarised as follows:
The quantum level of reality is based on wave mechanics in which subatomic particles sometimes behave like little billiard balls bouncing off one another (particle nature) and sometimes act like waves spread over a large volume of space. This is known as "waveparticle duality". A socalled "quantum vacuum" exists as a seething mass of "virtual particles"  sonamed because each keeps popping out of nothing to vanish again shortly afterwards. On this basis accurate predictions emerge for the nature of electrodynamics (QED) and nuclear phenomena QCD as explained very lucidly by the late Richard Feynman in his book QED. The quantum vacuum seems to have superseded the old "ether" as the ultimate background medium.
The solution for the CC demanded that neither of these are the ultimate levels of reality. Instead they are regarded as emergent from a deeper and ultimate level of reality that is truly real: the basis of all that exists. To prevent confusion with the old ether or aether, which had now to be considered emergent, this was called "ither". This was required to provide the organised waves needed at the quantum level: waves whose nature or source is not even considered in quantum theory. The ither could not be based on wave mechanics since then an even deeper level would then have been required to make its waves. An unsatisfactory infinite regression would be implied.
The most probable basis applicable was chosen as a slightly revised Newton's classical mechanics. This needed to obtain at both the ither and macroscopic levels with the quantum level sandwiched in between. Einstein's relativity theories could not be used since the observer was assumed as the "frame of reference" making it incompatible with both the existence of any background medium and the concept of kinetic energy. This is why ECM theory was required. If it could be shown to replicate the achievements of relativity theory at the macroscopic scale then strong justification for its validity at the level of ither could be claimed, especially if it also led to a solution no other theory could provide. The ECM theory achieves these aims.
It is encouraging that the Cambridge physicist, Professor Stephen Adler, has copied this lead in his book, "Quantum Theory as an Emergent Phenomenon" published in May 2004 by Cambridge University Press. The synopsis contains the phrase:
"quantum theory is not a complete final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level are taken to be an extension of classical dynamics...."
This must surely add considerably to the credibility of ECM and its application that had appeared by 1990 in my book (6) Intelligence Behind the Universe and its inclusion in Russian conference proceedings (9) of 1991.
ECM theory is used to provide a solution to the creation problem. To permit pure creation from the void of zero energy the ither had to exist as a mixture of real particles, to be called "primaries", some made of positive energy but with the remainder made of a negative kind, the latter defined by interchanging the forces of "action" and "reaction" in Newton's laws. Then the two forms could mutually annihilate to leave nothing. Pure creation could then be permitted as the converse case. Published in Russia in 1993 (Pearson 10)
Creation required both positive and negative primaries to be made of the arithmetic sum of two kinds of energy: rest energy and kinetic energy. As shown in CSQP, when pairs collide, as a result of the conservation of momentum (actually and more basically due to the force of action on one being equal and opposite that on the other) the kinetic energies of both increase in equal and opposite amounts so that the sum of the gains is zero, so complying with the law of conservation of energy. The result is a flawfree theory for creation but gives an excessive creation rate. Fortunately as densities increase instability is predicted since the entire fluid so formed, can self organise into microscopic flow cells, of lower energy, in which primaries converge to a point or line at the centre of each cell. Here the conservation of momentum dictates annihilation instead of creation and this provides the solution for the CC problem.
The ither now appears as a tangle of solidlike filaments and blobs where annihilation proceeds. These have a fine mesh even compared with the size of subatomic particles, so that nothing except the fluid component of primaries could move. At first matter in motion seems disallowed and would be if subatomic particles were real little objects travelling along. However, the tangle of filaments and blobs can be arranged to look like neural networks similar to those of our brains and the theory shows the net would then be able to provide power in the form of organised waves.
Now chaos theory shows that if highly organised configurations are possible then, in the fullness of time and by the power of randomness, such configurations will arise. If these also have the power of replication then the whole flow field can selforganise.
Although a speculative feature of the theory, if accepted as possible, then the whole of quantum theory and the reason it has to work on wave mechanics now makes sense. This emergent level now appears to have been deliberately contrived to make it appear, at the next emergent macroscopic level, as if large objects can travel, even though nothing can actually move through the filamentous network. Subatomic particles have to be wavegenerated spikes built as sequences joined end to end in time but not in position. Each new position has to be specified as probability functions so that each new position is most likely to be chosen proportional to the square of the amplitudes given by wave interference patterns. All the properties of each subatomic particle represented need to be carried in the memory banks of ither in a form similar to numbers. Many of these "particle properties" cannot be real. For example, electrons have an unimaginable double kind of spin and carry an anomalously high angular momentum that can only be represented by numbers.
This model provides a highly satisfactory interpretation for the enigma of waveparticle duality and fits very well into Richard Feynman's QED and QCD approaches (quantum electrodynamics and quantum chromodynamics the latter relating to the atomic nucleus). He shows for example that a photon moving from a source to a mirror jumps about at random though only as a potential of superpositions of all possible states and does not appear as a real particle until it hits the mirror. So an ephemeral and nonreal quality is implied.
Also at the quantum level kinetic energies do not need to be considered real. Indeed, even the four forces of nature no longer appear real. They now appear as mathematically contrived because motion is produced like the successive illumination of the pixels on a TV screen: the pixels do not move at all.
The only inconsistency I found in Feynman's approach was his use of the "negative coupling" in theories explaining the mutual attraction between certain particles. Mediators are emitted from one particle to be absorbed by the other and forces arise due to momentum exchange. But this only explains repulsion. The negative coupling is a negative sign that reverses the direction of the forces. Clearly a gross violation of the law of conservation of momentum is implied.
However, this serves to augment the case for these forces being abstract since in this case the inconsistency is of no consequence. No real forces are needed if the particles are sequences governed by wave interference patterns.
Even the entire quantum vacuum will now be seen as a contrived phenomenon. It no longer appears as a seething mass of virtual particles. They are now better described as abstract ones: just numbers appearing and vanishing again to provide the effect we describe as the nuclear forces. The quantum vacuum can therefore flow like a fluid.
Such a basis permits several universes to coexist, interpenetrating yet not interfering with one another, but with all of them supported by a common itheric reality. This can be effected by tuning each to a narrow band of matter waves of the quantum.
Survival Physics also appears from this model since it is clear that our minds can be considered as structures of the background medium. Then the entire spectrum of socalled "paranormal phenomena" can readily be found scientific explanation as real effects. For example, the itheric mind can tune into one of these parallel universes at a time for a while and then switch to another. The need no longer exists for trying to find alternative explanations as delusion or fraud for psychic phenomena.
This explains why ECM theory needed to be developed. Since Chapter 4 shows it matches the achievements of Einstein's general relativity very well, provides a solution that solves the CC problem and correctly predicts that the expansion of the universe is in a state of acceleration, it is hoped that the reader will not try to discredit the approach on grounds that it has not arisen from any department of physics.
One critic suggested the theory could not explain nonlocality: the phenomenon where two "entangled" particles arise together and move apart, still behaving as if coupled whatever the separating distance. ECM on its own is a classical theory and is unable to address quantum problems. However, the complete theory provides a mechanism in terms of the filaments. These have a mass density that is proportional to the sum of opposite energies that are in a state of mutual annihilation. Consequently their net density is zero or close to zero. Zero mass density is the condition for the propagation of waves at infinite speed. So the theory is not wanting in this respect: and no other mechanism has appeared from any other theory. Hence a very strong case can be proposed for the validity of Survival Physics of which ECM is an important feature.
A "quantumwave theory of gravity" also appears from the complete solution that fits the experimental observations. It does not invoke "gravitons". This is the only place any excursion into quantum theory is made except for a reinterpretation of the vexed question of waveparticle duality. The mathematics of quantum theory is not changed in any way. That theory is regarded as fully proven and satisfactory except for gravity. Since there is no satisfactory theory of quantum gravity, as yet, this is of no consequence.
Please ignore the "rotating dumbbell" included in section 2 since this contains features needing modification. This was a speculative part open to critique and misrepresentation. It was an attempt to explain by ECM the lifetime increase of cosmic rays that special relativity predicts as a consequence of "time dilation". Since now the quantum and macroscopic levels appear as emergent and contrived it is quite reasonable to consider relativity theory valid at this level being organised by the itheric mathematics as a slight modification of the ECM operating at the level of ither. 
Contents
The AuthorRonald Pearson started his career as a Scientific Officer at the N.G.T.E. Whetstone assisting in the development of jet engines. He invented a "gas wave turbine" and demonstrated a working prototype. The rest of his career was spent as a university lecturer, first at Liverpool and finally at Bath, in the fields of thermodynamics and fluid mechanics. These specialisations formed the ideal springboard for tackling problems in Cosmology where misconceptions in classical mechanics have, as will be shown, prevented gravitation being incorporated into quantum physics.
An Exact Classical Mechanics leads toward Quantum Gravitation, October 1997 Ronald D. Pearson BSc(Eng)(Hons. London Ext.), C.Eng.M.I.Mech.E prior to retirement and switch to physics. ISBN 0 9517558 8 9 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top 1.0 IntroductionNewton's classical mechanics are only applicable at speeds low compared with that of light and so have to be regarded as inexact. Einstein developed what physicists consider to be an exact alternative in his theories of relativity and these have become established. For over sixty years, however, theoreticians have been trying to match Einstein's general relativity, his theory of gravitation, to quantum theory: they have not succeeded. Worse still, a clever analysis by H. Aspden(1) of the interferometer experiments of Brillet and Hall(2) have shown that absolute speeds can be measured: something which the postulate of special relativity forbids! This apparatus, unwittingly, included a novel feature which Aspden showed to be responsible for what the experimenters considered a "persistent anomaly". They were actually measuring the surface speed of the Earth about its axis and the latter, as will be shown, was comoving with a background fluid, something incompatible with relativity theory. It seems prudent, therefore, to return to Newtonian concepts and revise them to remove false aspects. The changes need to lead to a theory which replicates all the achievements claimed to be unique to both classical theories of relativity. They also need to match up with quantum theory at appropriate interfaces. This pamphlet summarises part of a study which began in 1984 after an article had appeared in New Scientist by Professor Tryon(14). He proposed that, since gravitational potential energy was negative, it could balance the massenergy of the universe. Then everything could have arisen exnihilo. However, this depended on taking the datum for gravitation at infinity, merely because this was customary. Clearly the massenergy would remain at infinity where the gravitational energy had been fixed as zero: so completely invalidating the concept. If such a simple misconception had been accepted, as it had, by the system of peerreview, then clearly a close look at other aspects of classical mechanics needed to be initiated. A number of other misconceptions were soon discovered and it is the aim of this presentation to highlight some of these and offer, for the critic, what appear to be paradoxfree alternatives. It should be noted that in previous publications by this author(6,7,8,9,10&11) a modified background substrate had always to exist. To differentiate it from other concepts, such as space, quantum vacuum, ether or aether, it has been called the "nuether". Unfortunately this has been found too clumsy and so the name has now been changed to "ither", pronounced eyether and short for "intelligent ether". That it has the potential to evolve a conscious intelligence has already been justified in previous publications(7,8,10&11). It comprises a seething mixture of primary particles to be called, "primaries" and this replaces the name "cosmons" used previously(7). In these publications, the ither was shown to have a simple basis assumed as the ultimate reality where electromagnetism gravitation and nuclear forces do not exist. The aether is generated by waves from the ither to produce the observed complexity, matter and the four forces of nature. The new approach, to be presented, is steadily gaining acceptance by physicists. It has been peerreviewed by the Russian Academy of Sciences and Arts and appeared in three publications of their conference proceedings two of which are quoted(9&10). A further 4,500 word article by this author(11) has also appeared in the scientific journal "Frontier Perspectives". This received a commendation from the editor. A start will be made by extending Newtonian physics to replace special relativity. The critic should note that the resolution of problems to do with the null result of the Michelson and Morley experiment will appear late in the derivation. This experiment was responsible for discrediting the idea that an allpervading medium, called "ether", existed. Michelson himself never agreed with this deduction. 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top 2.0 An Alternative to Special Relativity2.1 The radiation pressure of light redefines Inertial Mass
The quanta of light, the photons, are emitted instantly when electrons drop from higher to lower orbits in atoms. However, for the present analysis it will be imagined that it would be possible to apply a force in some way in order to increase the kinetic energy of a photon from zero, measured from local space, (ither) to some finite value E_{K}. If a force F is applied at constant velocityc, then Newton's second law must be changed from:
 [1] 
The energy supplied by force F moving distance dx will be Fdx equal to dE, so multiplying equation[1] by dx and expanding by the standard method of differentiation by parts the first result yields the factor dx/dt which is velocity v: so we obtain:  [2] 
Here dv = 0 and v = c so we can write the integral:  [3] 
Since all the work ∫Fdx is supplied at constant speed c it is entirely absorbed as kinetic energy i.e. E_{K} and clearly there is an equivalent "kinetic mass" m_{K}. Furthermore each photon of mass m_{K} will carry momentum m_{K}c and so if there is a flux per unit area z in numbers of photons per second falling on unit of absorption area, then the resulting rate of change of momentum per unit area will exert a pressure P_{r} given by:  [4] 
This is the radiation pressure formula which has been fully confirmed by experiment, so proving that light carries momentum and therefore carries the kinetic mass m_{K}. From this point it is possible to take two alternative approaches for obtaining an equivalent energy corresponding with rest mass m_{0} and a revised inertial mass. 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top 2.2 Method 1: By Linear AccelerationAn undefined object of rest mass m_{0} is to be considered accelerated from rest with respect to a fluid ither to a speed v so that its inertial mass increases to m. Equation[4] for radiation pressure has already established that kinetic mass m_{K} is equivalent to kinetic energy E_{K} as given by [3]. A massive object, when accelerated from rest, also acquires kinetic energy and so its inertial mass must increase as speed increases. It is reasonable to assume that this inertial mass m is directly proportional to a total energy E though with a constant of proportionality needing to be determined. This assumption will be seen fully justifiable after method 2, based on the conservation of angular momentum, has derived the identical end equation. No other assumption could have provided this consistency. With B as the constant of proportionality to be determined, we can write:  [5] 
Also Newton's second law, for accelerating force F with mass as an extra variable has to be expressed as the "rate of change of momentum", which can now be written in two forms:  [6] 
Expanding [6] using differentiation by parts:  [7] 
Now the work done by force F in an element of distance dx is Fdx and is equal to the gain in kinetic energy dE of the object. Hence multiplying both sides by dx we have:  [8] 
Putting v = dx/dt this becomes:  [9] 
Rearranging & noting that E = E_{0} when v = 0:  [10] 
Now this is a standard form of integral readily solved by putting: z = 1  Bv^{2}, so that dz = 2Bvdv. Integration yields:  [11] 
Which can be rewritten:  [12] 
Clearly as v is increased so E increases according to equation[12] until Bv^{2} = 1. At this point E becomes infinite and so no further increase in v is possible. Let this limit be defined as the speed of light c. Hence B = 1/c^{2}. Substituting for B in equation[5] & [12] results in:  [13] 
Note: The author has been informed that this method was at least partly anticipated about 100 years ago by Whittaker. Where c = 2.997925 X 10^{8} m/s. The kinetic energy of the moving object is clearly given by:  [14] 
With E given by equation[13]. So light must have E_{0} = 0 and m_{0} = 0. It is necessary to see how well these predictions are supported by observation and compare them with the achievements of an alternative classical approach. 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top 2.3 Method 2: Restenergy Assumed to BE Kinetic Energy (Independent of Method 1)It seems possible that the universe could be constructed entirely from kinetic energy E_{K}. For example, two particles connected by a weightless chain can be imagined in orbit about one another. Each could be made of pure kinetic energy so that it moved at the speed of light, as proved in method 1. The pair would, however, appear as a single stationary particle possessing a rest energy corresponding to the sum of the kinetic energy of the components. A pion might be modelled in this way. The quantum model will not be the same but the hope is to see if this (incorrect) classical model can provide the required classical/quantum interface; just as the classical Bohr radius of the hydrogen atom forms such an interface for electromagnetism. Bohr proposed a model in which the electron orbited the nucleus like a planet going round the Sun in a circle. This was later replaced by the quantum model due to Schrödinger, in which electrons existed in a spherical "orbital" with a random distribution. It had a probability of being found at any radius which increased with distance from the nucleus up to a certain value and then fell off again. However, the peak of the probability curve coincided with the Bohr radius. In this way it seems reasonable to consider the Bohr radius as a classical/quantum interface because a residue of classical theory can be said to have a useful existence. A pion consists of a pair of quarks, to be imagined rotating about one another like a spinning dumbbell, each at radius r about a common centre. Then the orbiting pair will be observed as a single stationary particle having rest mass m_{0}. In a first simplified model, to be refined later, each quark will be assumed made entirely of photonlike orbiting kinetic energy E_{K}, where E_{K} = m_{K}c^{2}, moving at the speed of light. The pair is now assumed accelerated to a speed v by a force directed along the axis of rotation. Modelled as a rotating dumbbell the orbital speed of each quark (shown as small spheres) falls from c, when the pion is at rest, to v_{orb} as the linear speed is increased to v. The condition needing to be satisfied is that each member moves at unchanged speed c. (This is for the unrefined model in which each quark has no restenergy) The combined rest energy will be:  [15] 
If the pion is accelerated bodily to a linear speed v, with the axis of rotation in line with the direction of acceleration, then the orbital speeds will fall to to v_{orb} as shown in FIG.1. It will be assumed that the orbital radius remains constant, a condition which Method 1 will later show to be justified.  [16] 
This derives purely from the geometrical theory of Pythagoras. Each member of the pair will follow a helical path at a speed c, directed along this path, since as shown in Method 1, when m_{0} = 0 absolute speed = c. Conservation of angular momentum p_{r} given by p_{r} = mvr then dictates that, assuming r to remain constant:  [17] 
Then substituting for v_{orb} from [16] in [17] yields:  [18] 
Since this is identical with a rearrangement of equation [13] derived by method 1, the assumption that r remains constant is justified. Furthermore an expression for the angular velocity ω for the orbiting quarks can be compared with the rest value ω_{0} and, since r is constant becomes, since ωr = v_{orb}:  [19] 
A more refined model would make the orbital speed of each quark of the stationary pion equal to ηXc where η<1 to allow for nonorbital components of energy, such as a spinning motion of each quark about its own axis. For example, a quark could be made up of subquarks of pure kinetic energy orbiting at speed v_{q} about the centre of gravity of the quark. Then:  [20] 
This simplifies to:  [21] 
Hence η will appear on both sides of equation [17] and so will cancel leaving the value of m/m_{0} unchanged. A quantum description would show that, instead of orbiting, the quarks would seem to jump about over the surface of a sphere of radius r. The pion would then be spherical instead of discshaped but the foregoing classical approach should yield the required classical/quantum interface. 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top 2.4 Special relativity versus the revised NewtonianEquations [13] and [18] are effectively identical and replicate the famous Einstein equation obtained from special relativity, but here it has appeared, from both Methods 1 and 2, without any reference to relativity at all. Both have been entirely derived from our first refinement of Newtonian physics  the need to incorporate the mass equivalent of kinetic energy in the definition of inertial mass. Method 1 depended on acceleration, which can be regarded as following Whittaker. In relativity these equations arise as a direct result of its postulates without reference to acceleration. Indeed, accelerated states are outside the scope of special relativity theory. The mathematical similarities mean, however, that most experimental verification of special relativity will support the revised Newtonian equally well. The mathematical similarities are, however, illusory because v is now the speed of any object relative to the local ither: not the observer as in relativity! The consequence is that other differences are inherent. In relativity an observer moving with any object only sees the rest mass m_{0} and rest energy E_{0} of that object, because no absolute frame of reference is permitted. In the extended Newtonian such an observer sees the full inertial mass m and total energy E because these now have absolute, not relative values. Furthermore, in relativity, the observer judges the kinetic energy of any other object in terms of its observed speed. Hence the kinetic energy of a given object will be accredited different values by observers in different frames of reference, i.e. in motion relative to each other. Hence in relativity theory, kinetic energy, total energy and inertial mass, take on an illusory quality, whilst for the revised Newtonian this is not the case. This removes the uncertainty concerning the actual energy of any object and permits, in principle, the total energy of the universe to be assessed. Relativists have said this quantity is impossible to define! 2.5 Time dilationMuons resulting from the impact of cosmic rays in the upper atmosphere are detected at ground level. Muons moving slowly decay with halflives of 2.2 X 10^{6}s and it is estimated that their lives need to be extended about nine times to explain ground level observation. For this reason they have been used to verify Einstein's prediction of time dilation. The muon is structured more like an electron, however, and so is not a good example for our purpose: so we will study the pion we modelled in Method 1 instead. Charged pions have the shorter halflife of 1.8 X 10^{8}s. The analysis given in Method 2, using Newtonian theory, could equally apply to relativity with v now defined as relative to the observer. For simplicity we will assume η = 1. If the observer moves with the pion differences in these theories now appear. The relativist expects exactly the same mechanics to apply and so sees the quarks orbiting at speed c, just as if both observer and pion were stationary. However, observing a pion moving at relative speed v the quarks would be seen orbiting at speed v_{orb}. The way these are reconciled, in relativity, is by assuming time has dilated in ratio c/v_{orb} for the observer moving with the pion. The Newtonian moving with the pion would, however, observe exactly the same orbiting speed v_{orb} as he did when he was stationary (observing the pion in linear motion at speed v). He would, however, use his Brillet and Hall interferometer to measure his absolute speed and find it was v. Then he would add v to v_{orb} vectorially and discover the vector sum to be c: equal to the orbiting speed with both observer and pion stationary. No time dilation is now required. However, the angular velocity of the orbiting quarks would reduce with speed according to equation[19]. If the lifetime of an unstable particle is measured in the number of rotations before decay, then both theories will predict the same life extension. For mechanisms based on atoms a different approach is needed and this will now be considered. This time the vibration of a hypothetical matter clock will be investigated. 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top 2.6 Vibration of a hypothetical matter clock  Fig. 2 Magnetic force on current elements 
 Fig. 3 Hypothetical matter clock 
For the revised Newtonian, it is necessary to define two kinds of clock: "light clocks" and "matter clocks". Light clocks will depend on photons, generally involving laser beams, whilst matter clocks will depend on mechanical vibrations, such as those of quartz crystals. Vibration of crystals is made complex by an induced motion, perpendicular to the direction of main excitation caused by the socalled "Poisson's ratio". A hypothetical matter clock, which is mathematically less complex, will therefore be considered in detail. A special clock is to be imagined built from three identical spheres arranged in a straight line, as shown in Fig. 3. The outer spheres are fixed to a frame and the centre one is allowed one degree of freedom so that it can vibrate only along the line of centres. Its rest position is centrally located at distance A from each end sphere. All spheres carry identical electrostatic charge Q and, at absolute rest, a restoring force is produced proportional to the net electrostatic force. Additional magnetic forces, caused by the linear motion of all charges, will come into play at absolute speed v. When the central sphere vibrates it will generate electromagnetic waves, so the resulting motion will be a damped oscillation. Forced at resonance, however, this energy loss can be offset so that the effect of wave generation can be completely ignored. The magnetic force for each of two short lengths of wire dl and dl_{1} carrying currents i and i_{1} is illustrated in Fig.2. Each reacts to the magnetic field produced by the other so that forces are perpendicular to motion. It is interesting to note that Newton's third law, action and reaction are equal and opposite, is apparently violated when the line joining these elements have angles θ and θ_{1} relative to directions of current flow. It is restored when reaction against the background medium is considered. For complete circuits there is not even apparent violation. The motion of the charges relative to the ither is equivalent to a current such that current i = vQ/δl. Furthermore since the magnetic μ_{0} and electrostatic ε_{0} constants are linked to the speed of light c such that:  [22] 
It is convenient to convert entirely to electrostatic units so that the magnetic force F_{m} on the upper moving charge can be expressed as:  [23] 
The arrangement of the clock is illustrated in Fig. 3 together with its absolute motion at speed v, at an angle θ with respect to the inline direction and in which the centre sphere has displacement x. The net force F on this sphere, after binomial expansion with second and higher order terms ignored, becomes:  [24] 
If the mass of the centre sphere is m then, together with equations [8] & [24] a simple harmonic motion is specified which yields the angular velocity ω:  [25] 
By putting v = 0 the value ω_{0} for the vibration of the clock at rest is obtained and this can be divided into equation [25] to yield ratios for finding how frequency changes with linear speed v, i.e.:  [26] 
This expression can be used to investigate the way the clock will change frequency as it is accelerated to a higher speed. It has been derived from a Newtonian basis but is equally applicable to special relativity since, in the latter case, the observer can always be considered at rest. It is convenient to define β = v^{2}/c^{2} . The two cases are compared below for v<<c: Special relativity for θ = 90° then A/A_{0} = 1 and Q/Q_{0} = 1 has to be assumed. For θ = 0 the Lorentz contraction has to be applied so that A/A_{0} = 1  1/2β . The two results yield Δ ω /ω _{0} of 3/4β and 1/2β respectively so that the arithmetic mean is 1/4β. Revised Newtonian. In both cases A/A_{0} = 1 = Q/Q_{0} is assumed giving: Δ ω/ω_{0 } = 3/4β and Δ ω/ω_{0} = 1/4β respectively. In this case, for v<<c an integration yields an exact average for a smoothly rotating clock which becomes 1/2β. Only this value is consistent with experimental observation. For the case of special relativity an inconsistency is evident because, from a time dilation prediction, the result has to be Δ ω/ω_{0} = 1/2β. No practical clock could be expected to show the full anisotropy suggested by the revised Newtonian case. For caesiumbeam clocks the atoms would be rotating and so only the average would appear. The nearest approximation to the hypothetical clock analysed would be a quartz crystal oscillator. It could not be expected to give the complete anisotropy, however, owing to Poisson's ratio. When materials are compressed they expand laterally by between 1/4 and 1/3 of the direct strain and this will tend to reduce the anisotropy. It will not be eliminated, however, and so a new experimental check has emerged! It could only be measured for an experiment in orbit because terrestrial speeds would not give adequate resolution. A pair of identical quartz crystals with axes arranged mutually perpendicular would be required with output signals added to produce a beat frequency. They could be mounted on a rotating table and then the beats should cycle when the clock is in Earth orbit. Calculations show that at an absolute speed of 7.79 km/s and using 460 MHz oscillators, a beat frequency of .155 Hz should be returned. It is known that such clocks can achieve stabilities better than 10^{10} s/s when in temperature controlled environments but this is about equal to the signal. At least a tenfold improvement is required but this only applies to the difference signal and so should not pose an insoluble problem. Unfortunately a problem arises for both relativity and the Newtonian in that the value of A will vary in direct proportion to the size of atoms and this size cannot be assumed fixed simply by assuming electric charge invariant. Indeed the Bohr radius can be investigated. Fitzgerald made a similar study on atoms. He found that a lateral expansion Δ x/x equal to 1/2β would occur taking the magnetic force into account. He suggested this could be the reason for the null result given by the Michelson Morley experiment. Michelson and Morley had used an interferometer to measure the absolute speed of the Earth, expecting a value of at least 30 km/s to be shown. This depended on the speed of light appearing different for two mutually perpendicular directions and the theoretical difference would be 1/2β. Hence the Fitzgerald expansion would just cancel the effect. (Lorentz had suggested a contraction in the direction of motion to do the same and this idea, despite the lack of any theoretical basis, was adopted: presumably because it fitted in better with the predictions of Special Relativity) When this expansion is allowed Δ ω/ω_{0} becomes 3/2β for the transverse direction. If this were accompanied by a Lorentz contraction then the correct average value would arise but the anisotropy is still further increased. Such a contraction is not disallowed by the revised Newtonian but will apply only to objects built of atoms: it will not apply to empty space, in addition, as it does in relativity. To keep A constant Q has to increase as speed increases. If e is the electronic charge then Δ e/e_{0} = 3/4β. Some basic quantum analysis along the lines of the Schrödinger wave model seems to be required backed by experiment to discover exactly what really happens. No such modifications can be accommodated by the relativistic approach because this has to maintain A constant in the transverse direction and ignore the inconsistency with charge also remaining invariant. The Lorentz contraction must also be accepted in the direction of motion. This inflexibility is due to the absence of preferred frames of reference, with the consequent need for the observer to see the same mechanics whether travelling with a moving object or not. Fortunately for the revised Newtonian, not needing this constraint, some flexibility is allowable and any changes needed could be accommodated in this case. For adequate sensitivity only experiments in orbit could resolve the issue, using a practical version of the electromagnetic clock previously analysed. If transverse charge does in fact vary it could have serious implications for high energy physics and so its investigation would be worthwhile. To achieve a high enough clock vibrational frequency, however, the charged spheres (Fig.3) would need to be about the size of c_{60} buckyballs. The next problem to be resolved, however, is the manner in which restenergy varies with potential. This will take us into a minefield of misconception. 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top 3.0 Does restenergy vary with potential energy? Does it vary with binding energy?An electron accelerated by an electrostatic field provides a useful initial example. Any potential change Δψ_{e} is given by the work done in moving an object distance x against a field of force F from one position to another: i.e. Δψ_{e} = ∫ Fdx. If it is then released and allowed to accelerate freely in the field its potential will be lost as kinetic energy is gained. For example, an electron of m_{0} = 9.1091 × 10^{31 }kg is assumed falling through 10^{6} volts. (1 electronvolt = 1.6021 × 10^{19} joule) Equation[20] then shows energy ratio E/E_{0} = 1.957 and the electron will reach a value of v/c = .85958. It is now to be imagined that this high speed electron is allowed to slow down without change of electric potential. This can be done by allowing it to pass through a cloud chamber, for example, where it loses energy by knocking electrons off atoms to produce a trail of ions. We will suppose the electron is stopped. Its maximum kineticenergy was E E_{0} equal to Δψ_{e} but all this kinetic energy is subsequently lost. The final rest energy will be E  (EE_{0}): the original restenergy has been recovered! Overall the restenergy has not changed but potential has been lost: so restenergy cannot be affected by electrostatic potential! A similar argument can be applied to the gravitational field. An elastic object is allowed to fall freely onto a rigid deflector inclined at 45 degrees to the horizontal. Its initial vertically downward velocity is converted to a horizontal one without change of kinetic energy. Its total energy E is then E_{0} + E_{K}. Then it is stopped gradually by friction so that all E_{K} is lost. Clearly the original restenergy must be recovered. The same conclusion is reached if an object is considered lifted on a cable. The force of gravity is cancelled by the force on the cable so that, in lifting, zero work is transferred to the object. Its restenergy must therefore remain invariant even though potential has increased. It follows that restenergy must remain invariant in the gravitational field. Now we come to the nub of the issue. The foregoing conclusions mean that no binding energies, whether gravitational, chemical or nuclear, can be reflected as differences between the restmasses of separated particles and their combined masses! It is true that atomic nuclei have different masses from the sum of the protons and neutrons of which they are composed. The difference, however, has to be due to loss of particles like photons or neutrinos associated with nuclear reaction: they cannot be equated with potential change! And binding energies are potential change. It follows that gravitational binding energies, contrary to established opinion, cannot be equated with change of mass. For example, Clifford Will(15), says on page 24 (of The New Physics edited by Paul Davies) when referring to the neutron star, "...the observed mass is less than the total mass of all the neutrons in the star, because of the sizeable negative gravitational binding energy". He was referring to the theory of general relativity which does not accept the existence of any real force of gravity. Instead objects move along geodesics in curved spacetime and accelerate toward ponderous masses without a force being involved. On this theory it is true that some restmass has to transmute into kinetic energy as gravitational potential is lost. In this case, however, gravitation must be treated as totally different in nature from electromagnetism or the strong nuclear force because, as already proved, there can be no loss of restmass due to loss of potential if real forces are involved. Unfortunately theorists attempting to match general relativity to quantum theory obviously consider gravity as a real force as Chris Isham^{3} indicates. On page 87, of the same book, he shows how gravitons and gravitinos are postulated which interact with matter and themselves to produce a real gravitational force. They are copying the methods, developed so successfully by the late and famous Richard Feynman in his theory of quantum electrodynamics (QED), which considers electromagnetism as a real force. Clearly a total incompatibility exists which does not appear to have been recognised! In fact, if a neutron star were built entirely from accreted hydrogen, it would be heavier than its initial constituents owing to degeneracy pressure increasing electron velocities. If these fuse with protons to make neutrons, then a mass increase is again involved. This time it is because energy has to be added. This would derive from part of the excess kinetic energy which the hydrogen needs to shed on impact. Another concept needing to be assessed is the idea that, for the universe as a whole, its massenergy is cancelled by its "negative gravitational potential energy". Clearly this idea is invalidated by the forgoing argument and something else needs to provide the balance. It is necessary to deduce the basic mechanics behind the concept of any type of potential energy but with curved spacetime geometry disallowed, since it is not necessary, as §4 will demonstrate. In engineering mechanics, for example, total energy is defined as the sum of kinetic and potential energy, a useful concept because total energy can then be considered to remain constant. Potential energy is simply regarded as energy stored "somehow" in space due to the position of an object in the field of force. But how is it stored? Nobody ever seems to know: so let us probe deeper. A clue was given in my previous books(6, 7 & 8) and article(10 & 11). These showed how a subquantum fluid, now to be called the "ither" (intelligent ether), has to exist as a balance of positive and negative energies. These each comprise a seething mass of primary particles (primaries) constantly colliding like the atoms of a noble gas. An asymmetry has to exist in that the restenergy of the positive primaries exceeds that of their negative partners with the latter having the greater kinetic energy (see §4.9). In consequence a small net negative pressure of the vacuum remains. Any density gradients result in net negative pressure gradients which act on positive matter to produce negative buoyancy forces. These are the source of the universal attractive force of gravity according to §4.9. For such a mixture the existing first law of thermodynamics is inapplicable. It is not wrong but has to be considered as a special case of a more general law which now reads, "Energy can only be created or destroyed in equal and opposite amounts". Hence both creation and destruction can proceed but only in such a way as to leave the net energy of the universe unchanged. Our special case has seemed to be universally applicable only because in most processes, such as chemical reactions, the negative component is not altered. But it does alter in freefall! On this basis when a ball is thrown into the air it is losing energy by pure annihilation of amount equal to the product of the force of action of gravity and height moved. An equal positive force of reaction acts on the net negative kinetic energy of the ither and so does positive work on that fluid. But positive work done on negative energy is equivalent to reducing the quantity of negative energy. Hence both the object and the ither lose energy of their own kind in equal amounts by mutual annihilation. When the ball falls back again, mutual creation occurs, so restoring initial values. This, according to the present theory, is the real explanation for changes in potential not being reflected in changes of an object's restenergy. Potential energy is not stored at all: it does not really exist! It has to be regarded as a pseudoenergy form: an artifice useful only for calculation purposes. The "total energy" of an object will, henceforth, be defined as the sum of rest and kinetic energies alone. Clearly, this sum will not be conserved in the potential field. 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top 4.0 Quantum Gravitation4.1 A preliminary formulation of basic equationsSince kinetic energy and kinetic mass have been shown equivalent it follows that kinetic energy as well as matter will couple with the gravitational force. The photons of light are pure kinetic energy: it follows that light must fall, just like matter, in a gravitational field. If a horizontal beam of light of depth dr is considered, bent by gravity, then clearly the photons will need to travel further on the outside of the bend than on the inside in order that its waves will always be normal to the direction of propagation. This is illustrated in Fig.4 showing how the change in light speed dc with dr arises due to gravitational acceleration g acting for time t. This results in the following equation:  [27] 
(A totally rigorous deprivation yields exactly the same result.) Clearly as the distance from a ponderous object is increased, so c must increase. At some datum level, suffix D, its value will be c_{D} and it will be c at another level. Then since restenergy is a constant E_{0} = m_{0}c^{2} = m_{0D}c_{D}^{2}. In consequence it follows that:  [28] 
The equivalence between energy and mass is now clearly restricted to constant gravitational potential, to be designated ψ. Rest mass now appears as a variable with respect to ψ! Clearly only energy can now be regarded as the constructional material of the universe. Mass now appears as only a convenient property of energy; something which helps govern motion by providing inertia.  Fig. 4 Gravitational light bending 
Inertial mass is now to be defined as:  [29] 
In consequence, and since kineticenergy as well as restenergy feel gravity, total energy E must couple with any gravitational flux φ so that a force F = φ E is produced. Furthermore, by simple Euclidean geometry φ must satisfy an inverse square law of intensity when emanating from some massive point object at distance d and so, with d_{D} as some chosen datum distance, it must obey the expression:  [30] 
By symmetry this flux must itself be proportional to the value E_{S} the total energy of that massive object. So when a constant of proportionality G_{C} is introduced the law for quantum gravity becomes:  [31] 
Where, by comparison of equations[30] & [31] it can be seen that another useful constant, the "gravitational radius" r_{0} emerges, given by the identity:  [32] 
The constant of gravitation is now G_{C} whose value is 8.2615 X 10^{45} Nm^{2}J^{2} when determined from the Newtonian constant G as shown by equation[31]. It differs from the Newtonian gravitational equation in two ways. Firstly G_{C} has to be the true constant not G! The latter must vary as c^{4} varies so that G_{C} remains constant. Secondly E varies with speed w and so replaces the constant restmass of the Newtonian. (w is the vector sum of u an v where u will be used for the field component and v the velocity component transverse to the field i.e. horizontal) These two effects go part way to giving the same predictions as general relativity. For example, F no longer obeys an exact inverse square law: it is slightly steeper. This difference produces precession in the orbits of planets. Next it is necessary to find how both c and E vary with gravitational potential ψ. It is best to obtain a general expression assuming ψ to have any profile, then:  [33] 
Used with equation[27], putting φc^{2} for g, since g = F/m = Fc^{2}/E, the variation in light speed can be found by integrating across an infinite number of elements such as that illustrated in Figure 4. A precise definition of ψ now emerges which is:  [34] 
Since dE = Fdr then dE =  φE dr. So the variation in E with ψ becomes:  [35] 
Equation[34] is universally valid, but [35] is valid for freefall only. For the special case of a single massive attractor with φ defined by equations[30] & [32] the value of ψ becomes:  [36] 
The radial distance r has replaced d since the massive attractor is assumed so large that its orbital motion can be ignored. 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top 4.2 Compressibility of the itherSo far only "flat" space has been considered, meaning that the ither is assumed to be of exactly uniform density. This is, however, incompatible with an expression from quantum theory given by Novikov(5) who says that space is filled with virtual particles which, on average, occupy cubes of side L given by the expression: L = (h/2π)/(m_{0}c). Substituting from [28] this gives L = (h/2π)c/(m_{0D}c_{D}^{2}): so L/L_{D} = c/c_{D} showing that the ither has nonuniform density. Then combining with [34] and [35] it follows that the general expression for motion in freefall in a compressible fluid ither is:  [37] 
4.3 The true speed of light c_{T} in the compressible itherThe propagation speed of light will be affected by the change of L with ψ as will now be shown. It is best to imagine the photons moving as if in instantaneous jumps of distance L followed by a dwell of time Δt before the next jump where c = L_{D}/Δt and c_{D} = L_{D}/Δt_{D}. If then c_{T}, the true light speed, is defined as c_{T} = L/Δt then its ratio with c_{D} becomes:  [38] 
Series expansions show that for flat space the change in light speed in weak gravity will be almost equal to ψ whereas in the compressible ither it will be 2ψ. This means that the bending of light will be doubled from the original Newtonian prediction and so will accord exactly with that of general relativity. Velocities are also affected so that the energy equation becomes modified to:  [39] 
4.4 The gravitational redshift Two Methods1.  The energy E of a photon is given by E = (h/2π)v where v is its frequency. Then from[35] E = E_{D} EXP(ψ): ((h/2π) = Planck's constant). Hence the redshift can be expressed as v/v_{D} = EXP(ψ): i.e. Δv ≈ ψ × v_{D} So the photon reduces in v as it rises from low level.  2.  A pair of equal masses connected by a spring have a vibrational frequency inversely proportional to the square root of their restmasses. It also follows by substituting for c/c_{D} from equation[34] in [28] that rest mass m_{0} = m_{0D}EXP(2ψ). It follows that Δω/ω_{D} ≈ ψ. This means that the object will vibrate at lower frequency when lowered in the gravitational field. This is consistent with method 1 and both are identical with general relativity. 
4.5 The conservation of angular momentumFor freefall equation[37] shows m/m_{D} = EXP(3ψ) . However, all velocity ratios u/c_{D}, v/c_{D} & w/c_{D} are altered in ratio L/L_{D} i.e. in ratio EXP(ψ). These can be combined to yield the following expression for the new law of conservation of angular momentum. Exhaustive checks have been made using trajectories computed in Cartesians: an example is illustrated on the cover. The following equation has been found to hold exactly:  [40] 
When equations[28],[37],[38],[39] and [40] are combined, exactly the same equation for the precession of the perihelion of planets arises as is given by general relativity. The original solution presented in the book(6) involved many pages of algebra but the mathematician John Day wrote to say he had found a simple solution which will now be presented. 4.6 The first contribution of John Day M.Sc.  The perihelion advance of planetsPlanets move in elliptical orbits about the Sun according to the original Newton inverse square law of gravity. The modified law causes the axes of the ellipse to rotate slowly and, measured from the line joining the point of closest approach to the Sun, this defines the perihelion advance. It is necessary to start, for the case of freefall, by combining equations[37] and [39] and rearranging to yield the following equation quoted from page 278 of the book(6):  [41] 
A "secondary datum", suffix 1 is used taken at the perigee and this replaces D. At this datum w_{1} is the speed of the planet and, being tangential, can be replaced with v_{1}, which changes to w at potential ψ. John's first letter arrived dated May 13, 1993. He graduated with first class honours in mathematics at the University College in London in 1952 and held three M.Sc's. In this letter he stated that he had devised a much simpler method than the one I had used. This solution will now be presented based only on energy and angular momentum. Hence it starts from equations[40] & [41]. He defines u = 1/r, then, puts h = v_{1}r_{1} to define dθ from the above equation[40] as:  [42] 
Then he quotes from standard works:  [43] 
Now by substituting from equation[41] the result is: The solution of this must be a precessing conic. Constants A + B govern only the size and shape, which can be found on evaluation to be only the conventional values with only minute correcting terms. The constant C alone governs the rate of precession (omitting from consideration of course the higher order evanescent terms of + ...). On evaluation the result is:  [44] 
This will give a precession per orbit of πC, i.e. 6π(Gm_{S}/(hc))^{2} The lightspeed c varies by a negligible amount within the solar system and so an average value of c_{1} can be used without significant error in equation[44]. The value of v_{1} can be obtained from Newtonian mechanics to adequate accuracy. The radius of closest approach, at "perigee" is r_{1} and the radius at greatest distance is r_{2} at "apogee". A slightly more refined version of equation[44] is:  [45] 
The result is identical with that given by General relativity. 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top 4.7 The Shapiro Time Delay  Fig. 5 Radar reflections from Venus to Earth 
The Shapiro time delay needs a special mention. Equations[36] and [38] show that c_{T} will reduce as light, including radar beams, approaches the Sun. A radar beam bounced from a planet like Venus will therefore take slightly longer to return than if it moved at constant speed: this excess is the Shapiro Time Delay ΔT_{S}. The extended Newtonian yields by simple integration:  [46] 
Nomenclature is defined in the lower diagram of Figure 3 showing the Earth and Venus orbiting the Sun. The plot shows equation[46] as solid line N, in close agreement with the plot marked GR called the Schwarzschild solution of general relativity and quoted by Shapiro(12) prior to his experimental programme. After the tests he(13) quotes the upper chain dashed curve marked "Shapiro Empirical?". It is this, not the others, which fit the experimental observations! Since only an unpublished source was given it seemed that this curve must be just an empirical match, which is why it is so marked. I found that if the ither rotated in a vortex motion centred on the Sun, then a further extra time delay would arise. This was due to light being helped on one path but hindered more on the other, resulting in a small net extra "vortex delay". To fit the discrepancy a velocity distribution was computed described by:  [47] 
Consequently, since the centre of the Earth is moving at the same speed as the ither the null observations of Michelson and Morley no longer seem inexplicable. Furthermore the stellar aberration observed by the astronomer Bradley can also be accommodated. His observations showed stars to move in small circles with annual periodicity. This was consistent with light appearing to be deflected by the orbital motion of the Earth about the Sun, at a speed of 29.7 km/s. The effect was similar to the apparent deflection of raindrops as viewed from a moving vehicle. The Earth would have no apparent speed relative to a comoving fluid but would be in orbital motion relative to any star. On Christmas Eve 1996 a letter arrived from John Day. It contained a mathematical proof showing he had derived the "Shapiro empirical?" equation from the fundamental metric equation of general relativity. So the latter can provide two solutions but only one is satisfied. 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top 4.8 The MetricLetter from John Day dated January 8, 1997 He starts off, "You might need reminding it is possible to reconcile the different points of view and make yours an explanation of relativity rather than a contestant". Then he goes on to show how a metric can be obtained from the revised Newtonian equations starting with the Lorentz form as follows. ds^{2} = dt^{2 } (dx^{2} + dy^{2} + dz^{2})/c^{2}r from the centre of a spherical centre will be equivalent to: (dX,dY,dZ) distance r from the same centre where: (dX,dY,dZ) = EXP(ψ)(dX,dY,dZ) & ψ = r_{0}/r_{1}  r_{0}/r We also note that it is reasonable to assume time is affected so that everything at r is slower than at r_{1} by a factor EXP(ψ) i.e. if (dx,dy,dz) = 0 then we would have simply ds =EXP(ψ) dt. So we can now see that if (dx,dy,dz) are nonzero then: This should be sufficient for determining formulae for all four tests of general relativity. The three involving photons for which ds = 0 are straightforward of course and involve only first order approximations of type EXP(ψ) = 1 + ψ Day then mystifies me by going on to say this yields:  [48] 
Where ψ is given by equation[36] He then says, "This is a remarkably good approximation to relativity's isometric form":  [49] 
John Day never explained to me the last two equations[48] and [49] and some assistance from a mathematician is needed to resolve this issue since, unfortunately, John passed away early in 1997. However, it is highly likely that the sophisticated tensor mathematics is giving solutions for both a stagnant and a vortex case. More theoretical work is needed to fully resolve this question. A Suncentred vortex implies the existence of a multiplicity of starcentred absolute frames embedded in galaxycentred frames. All will be energyrelated to a single primary reference frame. Only a single value for the total positive energy of the universe is then implied. It does not appear that there can be an Earthcentred itheric vortex otherwise the absolute surface speed of the Earth would not have been detected by the Brillet and Hall interferometer. There must be a minimum critical mass for vortex formation and this requires further study. It would be most informative if an absolute speed measurement could be made close to the planet Saturn to see if an itheric vortex existed around this object. It seems that a whole new field of space exploration could be opening. Unfortunately certain physicists contacted have dismissed the anomaly found by Brillet and Hall on the grounds that nobody seems to have repeated their experiment. It would be advantageous to carry out this repeat near the equator where Earth surface speeds would be about 30% greater than at Boulder. Then it is very likely that NASA would be interested in mounting the first orbital flight of a Brillet and Hall device. 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top The 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 ither 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 mathematicallybased 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 ither 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 coexist in a close balance. An asymmetry of restenergies between opposite types of primary also had to be present . The positive kinds needed to have the greater restenergy 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/L^{3}. If these all move toward a surface at speed v_{+} there will be 1/L^{2} rows in motion and the number crossing per second in each row will be v/L. Allowing for threedimensional 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 P_{n} 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 V_{p} when combined with equation[56] becomes:  [57] 
The subatomic particle of volume V_{p} will have a net energy density which is the sum of two values differing from ε so the net value will be ε_{p+}  ε_{p} 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/c^{2} . Then with r_{0} 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 itheric 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 wellseparated, paircollisions 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 publication^{16}, under preparation, it is shown how focused quantum waves can produce the required density increases for subatomic 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 ither 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 nearpoint 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 v_{orb}/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 ither is composed and the other is more subtle. However, an exact solution was finally obtained using an energycreating quantumwave approach. This will be published in a companion volume(16). A mechanism for generating the energydensity gradients of the ither is now provided and, even more satisfying, as a byproduct of the maintenance of subatomic 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 ither 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 10^{14} 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 ither could be mapped. It would be particularly interesting to find out if an itheric vortex was centred on Saturn. No Earthcentred 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 spinoff from the analysis. There are others but they will not be considered here. 
...An Exact Classical Mechanics leads toward Quantum Gravitation... top 5.0 ConclusionA longheld view, that Newtonian mechanics has been permanently overturned by Einstein's relativity theories, was shown to be a misconception: the predictions of both special and general relativity can be paralleled when Newtonian mechanics is sufficiently refined. This does not mean the idea of time dilation is supported. Instead equivalent frequency shifts, caused by either high speed motion or change in gravitational potential, are produced in a universal time frame. These effects are caused by changes of inertial mass. The latter is the sum of rest and kinetic masses but the equivalence with total energy is limited. This is because, although E = mc^{2} is derived from purely Newtonian principles, c increases with gravitational potential. Then the inertial mass of an object becomes a variable even when its total energy remains constant. This showed mass to be only a property of energy which controls dynamical behaviour. Total energy alone, probably entirely kinetic in the ultimate analysis, turned out to be the only true constructional substance of space, (the ither) matter and motion. Used to explore the meaning of "potential energy", the new approach proved that the restenergy of an object is unaffected by changes of potential as it moves in any field of force, nuclear, electromagnetic, or gravitational. This meant that another misconception was highlighted: binding energies cannot be equated to changes in restmass or restenergy. These paradigmshifting changes need critical appraisal because they appear to solve the major difficulties of producing a satisfactory theory of quantum gravitation. This is important because general relativity is recognised by theorists to be incompatible with quantum theory. The new approach led straight to a quantum solution which needed no gravitons. This meant it predicted a complete absence of gravitational shadows. It was also fully consistent with the existence of a background compressible fluid medium, as required for explaining certain socalled anomalous phenomena. The latter are considered elsewhere (6,7,8,10&11). Finally three new experiments in orbit were proposed. Two of them would use proven interferometers, one having already detected absolute speeds. They could open up a whole new field of space exploration which might dwarf, in scientific importance, anything yet attempted by NASA.
6.0 AcknowledgementsThe contributions of the late mathematician and ardent relativist John William Robert Day M.Sc. proved invaluable: he became a most valued critic. His first letter, dated May 13, 1993, gave in a few lines, a solution for the perihelion advance derived from my basic equations. He had obtained these from my book(6) which effectively gave the same solution but had involved many pages of algebra. Mostly his efforts were directed to turning me into a relativity convert: to turn the theory into some kind of relativity/Newtonian hybrid. This was fiercely resisted. However, his critiques triggered new insights as recorded in the above text. The author is also indebted to Michael Roll, who heads "The Campaign For Philosophical Freedom", and to his many supporters for their untiring efforts in helping break through the barriers preventing communication.
7.0 References1  Aspden, Harold: Laser Interferometry Experiments on Light Speed Anisotropy Physics Letters 85A,No.8,9:19 October 1981  2  Brillet, A. & Hall J.L.: Improved Laser Test of the Isotropy of Space Physical Review Letters, Vol.42, No.9, 26 February 1979  3  Isham, Chris J.: Quantum Gravity: pp7093: The New Physics Cambridge University Press 1989: Edited by Paul Davies  4  Guth, Alan & Steinhardt, Paul: The Inflationary Universe: pp3460: The New Physics (as above)  5  Novikov,I.D.: Evolution of the Universe Cambridge University Press, 1983  6  Pearson, Ronald D.: Intelligence Behind the Universe Dec.1990: 370 pages Maths in Technical Supplement included.  7  Pearson, Ronald D.: Origin of Mind: Dec.1992: 72 pages Maths in Appendix for theory of breeding primaries & itheric structure.  8  Pearson, Ronald D.: Key to Consciousness: Quantum Gravitation: March 1997 24 pages; Explains breeding more simply.  9  Pearson, Ronald D.: Alternative to Relativity Including Quantum Gravitation Second International Conference on Problems in Space and Time St.Petersburg, Petrovskaja Academy of Sciences & Arts 1991  10  Pearson, Ronald D.: Quantum Gravitation and the Structured Ether Sir Isaac Newton Conference: St. Petersburg March 1993  11  Pearson, Ronald D.: Consciousness as a SubQuantum Phenomenon Frontier Perspectives: Vol.6,No.7,Spring/Summer 1997, pp7078 Refs. 68 Direct from publisher: see page 2  12  Shapiro, Irwin I.: Fourth Test of General Relativity Phys.Rev.Lett.Vol.13,No.26,[28 Dec.1964] p.789  13  Shapiro, Irwin I. et al: Fourth Test of General Relativity: New Radar Result Phys.Rev.Lett. 26, pp113235 [1971]  14  Tryon, Edward P.: What made the World?: New Scientist, 8/3/1984,pp1416  15  Will, Clifford: The Renaissance of General Relativity pp733(page 24) The New Physics: Edited by Paul Davies: As Ref.3  16  Pearson, Ronald D.: Survival Physics Survival Physics includes a paradoxfree "QuantumWave theory of Gravity" based on the work given here. The quantum waves produce the required itheric density gradients after being first focused to produce the subatomic particles of matter. The waves are generated by the "Opposed Energy Dynamics" of the ither. All is created by the background mind of ither (intelligent ether) which spontaneously forms from a filamentous structure described by the mathematical model. This theory of everything predicts the survival of consciousness after death and so supports the totally convincing experimental evidence now available. 


