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Chapter 10

Gravitation

Although "gravitation" comes from the Latin word gravebo, philosophers of Egypt, Greece, and Rome knew of gravitation only in relation to the ground-in terms of weight and falling. Sun, Moon, planets, and stars were borne on crystal spheres rotating about stationary Earth. True, Aristarchus had suggested in the second century B.C. that all turned about the Sun, but any idea of attraction by the Sun had not occurred to him, nor to Copernicus, who rejuvenated this model seventeen centuries later, nor to Galileo, nor to Bruno, who supported Copernicus. But, two millennia B.C. Aryan Indo-Iranians had recognized heliocentricity, and the role of the Sun in holding the Earth by its attraction. I quote from J. Arunchalan's translation of Sanskrit psalms from the Rig Veda:

This Sanskrit wisdom should have been transmitted through the Persians and Arabs to the Egyptians and Greeks, but it seems that they knew better.

Pythagoras to Copernicus

The early Indians had identified correctly the relative distances of the known planets from the Sun: Mercury, Venus, Mars, Jupiter, and Saturn, and they knew that the Moon was nearer to the Earth than was the Sun. The Vedas also recorded that the equinoxes came a little earlier each year, and gave the rate, rediscovered centuries later by Hipparchus.

It was obvious to the Egyptians and the Greeks that the Earth was flat. Until Pythagoras recognized the Earth's shadow on the Moon during an eclipse and concluded that the Earth was a sphere, which solved the problem why the pole star reached a higher altitude as one moved north, and why the masts of departing ships could be seen long after their hulls had disappeared below the horizon. But few of his contemporaries believed him, because everyone knew that the Earth was flat, until Aristotle, two centuries later, ended this debate.

Pythagoras had discovered that the harmonious intervals were simple integral ratios of the length of a stretched string, and jumped to the conclusion that this must be the ratio of the distance to the eight heavenly bodies, forming the melody of the spheres, which was generally believed for centuries thereafter.

But his spherical Earth was still motionless at the center of the Universe, which revolved daily about us, borne on transparent crystal spheres. With the Sun's path through the stars once a year, and the Moon's once a month, three independent crystal spheres were necessary. The five known planets also moved independently of the stars, and of each other, and needed individual crystal spheres (now eight). To complicate things further, even as far back as Babylonian times Mar Istar had observed that Jupiter sometimes went backward with respect to the fixed stars, and soon all of the planets were known to do so.

Eudoxus gave a mathematical solution with stars, planets, Sun, and Moon on twenty-seven coupled transparent spheres around a stationary Earth, which became the creed for a thousand years. Callipus removed some residual discrepancies, such as the summer period between equinoxes being longer than the winter period, adding seven more spheres as the five planets and Sun and Moon had to be corrected individually. Now there were thirty-four spheres.

Aristotle added still more to make fifty-six, including a divine outermost sphere, his primum mobile, which drove all the rest and produced day and night. There is a striking parallel between the way the stationary Earth model was patched up whenever a new fact emerged, and the patching up of the "big-bang" model every time new cosmic facts oppose it.

Even two thousand years later, Fracastoro of Padua, resuscitated the Eudoxus model with seventy nine crystal spheres, eight bearing the stars and planets (equivalent to the octave of Pythagoras), six for the daily rotation and precession, six each for Sun and Moon, ten for Saturn's motions, eleven for Jupiter, nine for Mars, eleven each for Venus and Mercury, plus the outer primum mobile.

He did this to revert to having all rotations centered on man's Earth (Homocentria, as he titled his work), eliminating the five epicyclic motions Hipparchus had meanwhile introduced to match the apparent "looping" motion of the planets caused by their heliocentric not geocentric motion.

The famous Egyptian astronomer, Claudius Ptolemaeus (126-161 A.D.), commonly known as Ptolemy, compiled and integrated the earlier works of the Arabs and the Greeks, particularly of Hipparchus. Because very little of the work he summarized has survived, Ptolemy is probably accorded greater status than he merits.

Ptolemy's system follows closely that of Hipparchus, but although all motions are circular, and all speeds are uniform, he made the centers of the primary circles slightly eccentric from Earth. His reconstruction was as perfect mathematically as was possible while holding to geocentricity, and had the blessing of the Christian Church, for it maintained the dogmatic prescription with Earth stationary under the vault of heaven, at the center of the Universe, with man as the ultimate creation.

This Ptolemaic system reigned supreme until the end of the fifteenth century. Other suggestions had been made, but in earlier times they had been scorned and ridiculed. After the rise of Christianity they became blasphemous heresies.

In the fourth century B.C., Heraclides, a pupil of Plato and contemporary of Aristotle, seems to have been the first to observe that if Earth rotated once a day this would explain the apparent motions of Sun, Moon, the planets, and stars. He also explained the motions and cyclic variations in brightness of Venus and Mercury by suggesting that they revolved around the Sun, which along with the Moon, the planets, and the stars, revolved around the Earth.

This would explain why Venus sometimes heralded the Sun as the morning star (Phosphorus) and at other times followed the setting Sun as the evening star (Hesperus), and between-times seemed much brighter and closer or fainter and more distant. These were brilliant observations, and significant steps towards heliocentricity. But contemporary establishment rejected such heresy because the asymmetry of his system was indigestible. The Pythagorean vision of universal harmony and symmetry was then the ruling creed.

A century and a half later, Aristarchus Samos also declared that all the planets, including Earth, revolve around the Sun, that Earth rotates once a day, and that all the celestial motions are then simply explained without the multiplicity of imaginary crystal spheres. Aristarchus was a brilliant mathematician who deduced that the Sun was at least eighteen times farther away than the Moon, and was very much larger than the Earth.

He was probably also the first to estimate the diameter of the Earth, and Eratosthenes may have got the idea from him. Had the works of Aristarchus survived the sacking of the Alexandria library, he would probably now rank as one of the greatest thinkers ever.

But, alas, Aristarchus, whom we now know to have been wholly correct, was totally rejected, even by Archimedes. Just as today orthodoxy believes the so-called "big bang", everyone then knew that man and his Earth were the center of the Universe. This became firmly fixed by the rise of Christianity so Aristarchus' discovery was lost for another seventeen centuries.

At long last the heliocentric system was resurrected rather timidly and apologetically by Nicolaus Copernicus, canon of Frauenburg, more astronomer than priest. Copernicus realized the relativity of motion, and that a geocentric system with epicycles could give identical apparent motions as seen from Earth as would a heliocentric system.

Algebraically, it was like moving the center of co-ordinates from Earth to Sun, Copernicus also recognized that rotation and revolution of Earth could together explain many enigmatic features of the celestial motions. His monograph was circulated only privately for three decades, and although he received covert favourable comments, it was only published cautiously in 1543, virtually on his deathbed, and then not in his own country. But he still did not know about gravitation.

Although Copernicus gets the credit, he had not really discovered anything new. He was aware of the heliocentric arguments of Aristarchus, and also that Nicholas of Cusa had, a century before him, claimed that the Earth and the planets revolved in circular paths about the Sun in an infinite Universe (which solved the apparent absence of parallax from the extremes of the Earth's orbit). What had changed was
 that there were now some willing to listen and even to defend such heretic notions before the Church.

Brahe, Kepler, Newton

Tycho Brahe, who had spent two decades meticulously recording the position of Mars, died in 1601, and, notwithstanding the objections of Brahe's family, his records were acquired by his assistant, Johannes Kepler, who spent the next six years trying to make sense of the voluminous data, blinded by the universally held meme that all cosmic motions had to be perfect circles. Finally in 1607 all fell into place, and he announced three laws:

(1) each planet describes an elliptical orbit, with the Sun at one focus of the ellipse.
(2) the radius vector of each planet Sweeps out equal areas in equal times.
(3) the square of the orbital period is proportional to the cube of the major axis of the ellipse.

From Kepler’s laws, Newton deduced his Law of Universal Gravitation, first published in his Principia in 1686 (although he claimed that he had completed it twenty years earlier):

Attractive force = m1m2 G / d2 . . . ( 1 )

the gravitation constant G is added to make "proportional to" into "equal to"

Observe that there are six independent propositions in Newtonian gravitation:

(a) gravitation is a universal force between bodies

(b) the force between the bodies is along the straight line between the bodies

(c) the force is inversely proportional to the square of the distance between the bodies

(d) the law of inverse squares is universal

(e) the force is proportional to the product of the masses of the bodies

(f) the force is independent of all other Properties other than mass, such as density, temperature, charge, magnetism, and solid or gaseous state.

Newton showed that: Proposition (a) and follow directly from Kepler's third law because the Sun's attraction applies equally to all planets and ignores their nature and state. Proposition (b) follows directly from Kepler's second law. Propositions (c), (d), and (e) follow directly from Kepler's third law, because the acceleration of a planet =

    . . . (2)

where a is the major semi-axis of the ellipse, T is the period, and r is the distance from the Sun.

Proposition (f) also follows directly from Kepler's third law. The proposition (c), that the attractive force is inversely proportional to the square of the distance from the Sun, had already been suggested by Robert Hooke (whom Newton despised), and by Newton's close friend Edmund Halley, and also by Christopher Wren. It had even been contemplated, but not adopted, by Kepler.

Proposition (f), that the gravitation law was independent of the nature of materials, had been roughly confirmed by Galileo who is said to have dropped bodies of different density and weight from the leaning tower of Pisa. Newton confirmed it more closely using pendulums with bobs of different density. Early this century R. Eotvos of Budapest confirmed Newton's law to one part in 107, and most recently V I. Panov has confirmed it to an accuracy of 0.9 x 10-12.

Tension along a wire remains undiminished no matter how long the wire Tension exerted from a point in a film diminishes uniformly with distance from the point, because the tension is distributed around a circle whose circumference is 2ptimes the radius. In a three-dimensional medium centripetal tension diminishes according to the square of the radius because the tension is distributed over the surface of a sphere whose area is proportional to the square of the radius.

Therefore the tension at a point is directly proportional to 1/d2, or equal to m/d2. Insertion of a second mass adds its centripetal tension, resulting in a tension maximum proportional to m1m2 / d2 along the line between the two masses. Hence Newton's gravitation law. The acceleration of each body is determined by its mass and the magnitude of the tension gradient, which increases as the separation diminishes.

Action-at-a-Distance

Although Newton expressed Kepler's empirical findings in mathematical form as his law of gravitation, he could not conceive how and why a body acts on another distant body with no identifiable link between them, and what determines the magnitude of the gravitational constant, and what it means physically. Action-at-a-distance was a particular concern of Rene Descartes and others of the French Academy of Science during perennial feuds with the London Royal Society. Even Newton wrote in a letter to Richard Bentley:

Fundamentally, the fact that bodies accelerate toward each other could be due either to an intrinsic attraction or to their being pushed together by something else. Indeed, Le Sage argued that the impact of universal streams of particles could lead to mutual convergence directly proportional to their diameters and inversely proportional to their separation. But every known or postulated particle failed energy-wise by many orders of magnitude. Currently, a retired NASA engineer, Maurice E. Mitchell, advocates a similar gravity-push hypothesis by neutrino flux, with very low but not zero mass, and perhaps by other electromagnetic particles. This class of theory ignores the fact that bodies of similar diameter may differ in density, and hence in mass.

Cosmologists latched onto Einstein's curvature of space as having solved the action-at-a-distance paradox. Each mass distorts the space about it. Masses do not attract each other. They merely move down the local gradient in the distorted space. But what is curved or distorted? Empty space? Does this exert a force on bodies to move? Einstein's curved geometry is merely a convenient notation. Action- at-a-distance is not really solved. But cosmologists conveniently bury their problem in it, and happily go on to something else.

Šther, The Discredited Universal Medium

Newton knew that his gravitation law was purely kinematic, completely describing the motion of the planets, but saying nothing about the mode of copulation of the mutual forces. It had not removed the action-at-a-distance "absurdity". So he reverted to the Šther of Roberval and Descartes. Rene Descartes in his Principia philosophae (1644) thought that space without matter could not exist.

Newton's German rival, Gottfried Leibnitz, required an Šther, probably as a very tenuous but not massless medium, permeating all matter, responsible for gravity and elasticity. Immanuel Kant, in 1755, considered such an Šther essential to explain action-at-a-distance and the radiation of light and heat. Michael Faraday thought that an all-pervasive Šther transmitted electric and magnetic waves, and James Clerk Maxwell agreed that it was inconceivable that a wave motion should propagate through empty space.

Šther was essential to Nernst as a recipient of energy. A mass imposes a quasi-elastic static radial tension (strain energy) in the Šther which diminishes directly with distance. An electric charge and a magnetic pole imposes static strains in the tangential plane, mutually normal to each other, and likewise diminishing with distance. If oscillating, such a strain propagates through the Šther as an energetic wave. Likewise an oscillating mass would imply a longitudinally oscillating gravity wave, but such has not been detected. An impulsive change of mass would imply propagation of a single peak soliton, but such has not been observed.

The massless medium which transmits gravity and electromagnetic waves has been called Šther, space-time, vacuum, Mach’s medium, and field. I could proceed with this discourse with any of these terms, but return to the term "Šther" because Šther has historical priority, and no other meaning than the medium that pervades all space (so to invent a new term would be redundant). "Space", "vacuum", and "field" have their own specific meanings, both technically and in common language, so it is undesirable to extend their meanings to cover Šther with its intrinsic empirical properties, which I [will now] proceed to define:

[ Definition of Šther ]

(1) Šther has no mass (hence no density), nor has it charge or spin. Indeed, these properties are *strains1 of the Šther itself, which is therefore more fundamental than these properties.

(2) The mass of an entity is expressed uniquely by the state of *strain it imposes on the Šther, directly proportional to the magnitude of the mass, and diminishing inversely as the square of the distance from that mass.

(3) Every mass is subject to an acceleration directed in the direction of the maximum *strain gradient in the Šther, directly proportional to the Local *strain gradient in the Šther. But bodies do not move relative to the Šther.

(4a) Šther is all pervasive, hence does not have position (such as co-ordinates), nor velocity, nor acceleration, nor rotation. These are properties of bodies, relative to one another. But Šther may be *strained by bodies, and such *strains may propagate through the Šther, like the propagation of strain through rock as seismic waves.

(4b) Šther behaves as though every charge or magnetic pole imposes a *strain on it, directly proportional to the magnitude of the charge or magnetic pole, and diminishing inversely as the square of the distance from that charge or magnetic pole.

[ 4a and 4b are used due to a numbering error in the draft ]

(5) Every charge or magnetic pole is subject to an acceleration directed in the direction of the maximum *strain gradient in the Šther, directly proportional to the local *strain gradient, tending to draw it toward the other body if the charges or magnetic polarity are opposite, or tending to repel it if the charge or magnetic polarity are similar.

(6) Electromagnetic waves propagate through the Šther in a manner geometrically similar to the propagation of shear waves through an elastic medium.

(7) Extensional *strain exists everywhere throughout the cosmos, which causes continuous pervasive expansion.

(8) The velocity of propagation depends only on the state of tensile *strain in the Šther. Hence the velocity is slower in the proximity of mass, which adds its additional *tension to the universal *tension.

(9) Wave frequency is invariant through the Šther, but the frequency appears to increase (blue-shifted) if the emitter and receiver are converging, and to decrease (red-shifted) if the emitter and receiving are diverging, irrespective of which is the emitter. This is simply a Doppler modification.

(10) Bodies move with respect to each other, and with respect to waves propagating through the Šther, but not with respect to the Šther.

Commencing with James Bradley in 1727, physicists, assuming that Šther should be an absolute frame of reference, attempted to measure the movement of the Earth with respect to it.

The most famous was the Michelson-Morley 1881 experiment (using the interference between light deflected along and transverse to the Earth's motion). The laboratory moves with the Earth's rotation, and Sun's galactic motion, and the galaxy's motion, but none of these define absolute motion. But if the Earth had motion relative to the Šther, there should be a direction where one path should be faster than the other. No such difference has been found.

Kennedy and Thorndyke also used interference, Fizeau passed light through moving water, and most recently Towns used ammonia-laser microwaves, but none found movement with respect to the Šther, nor should such relative movement have been expected.

Nevertheless, because of the Michelson-Morley result, the Šther concept has been abandoned for the past half century in favour of relativistic geometry, which is still only kinematic. Even the word Šther has become a "dirty" word, not used by respectable scientists! Modern physics sequesters the action-at-a-distance dilemma in the "field" concept, which begs the question. [Is this physics?] This is not physics but metaphysics.

The "vacuum" of space (i.e. the Šther) has been endowed by particle physicists with a property of spontaneous creation and annihilation of electron- positron pairs and other particles, along with other bizarre properties, including the role of banker. The particle physicist, Paul Davies, writes:

According to particle physicists, a W-messenger particle "borrows" a large amount of virtual energy from the vacuum, but has to pay it back in less than 10-24 second when its "message" is discharged. Surely... the classical definition of a vacuum as a space in which there are relatively few atoms or molecules, (the perfect vacuum, unattainable in practice, containing none) could not be applied to such a medium! The properties of Šther are empirical and specific. Like Newton, Descartes, Kant, Faraday, and Maxwell, I find it unacceptable to endow the words space, vacuum, or field with such empirical properties.

Einstein's equations virtually assign an "elasticity" to space, whereby masses distort the rectangular co-ordinate grid of space. This is a valid mathematical model. Newton expressed gravitation as mutual attraction between bodies. But a single body induces its own gravitational field irrespective of the presence of any other body. The force implied by the observed "action-at-a-distance" is an empirical intrinsic property of the Šther.

The Šther has no density nor viscosity. Its most significant property is the one implied by "action-at-a-distance" phenomena, namely that it reacts with all bodies as though it were a strictly Hookean substance. But Hookean elasticity is caused by the forceful displacement of the mutual equilibrium positions of atoms, and viscous strain results from atomic diffusion biased by applied force, whereas, in contrast, Šther has no atoms.

Another empirical difference between Hookean elasticity and Šther *elasticity is that Hookean stress cannot exceed the attraction between adjacent atoms where failure and separation occurs, whereas no limit has been observed or hypothesised for Šther *stress (gravitational attraction) even in such phenomena as neutron stars and black holes. Nor has any limit been observed for charge.

Mass of a body is defined as the amount of matter it contains; or its resistance to acceleration; or the amount of centripetal *strain it imposes on the Šther. *Strain and mass mutually cancel. The total mass of the Universe is equal to the total *strain energy of the universal Šther caused by that mass. One cannot exist without the other. Annihilation of the mass would cancel the energy, both to zero.

Gravitational and Electromagnetic Fields

Einstein devoted many years of his life trying to combine his gravitational field equations with the electromagnetic equations established by Maxwell. Modern theoretical physicists have laboured to establish the GUT (Grand Universal Theory), which would combine the whole of physical phenomena in a single grand equation-in vain. I suggest that this is impossible!

Fire and water may combine through plasma theory, but not gravity and electromagnetism. Electromagnetic theory combines radio, heat, infrared, light, ultraviolet, X-rays, and gamma rays into a single continuous spectrum, but not gravity - like soul and body, or real and imaginary numbers.

A body may radiate at any part or parts of this spectrum at any conceivable strength, or may emit no radiation whatever, without in any degree influencing its gravity field. Gravity and electro-magnetic fields coexist and overlap without any mutual interference or synergism. The force of attraction between two charged particles is modified by the intervening medium and also by their relative motions, but no conditions to which matter may be subjected affects its gravitation. Gravitation is unique.

Man is aware of gravity, and of the many aspects of the electromagnetic spectrum, because these are accessible to his senses of sight, sound, and touch. Could there be other fields not accessible to our senses? Oriental mystics and advocates of telepathy believe that there are. The Šther, through which both gravity and electromagnetic strains are propagated, is another medium which is not accessible to our human senses.

Newton, Einstein, and most cosmologists work in the gravity medium, although gravity is extremely weak compared with electromagnetic forces (the gravity attraction between a proton and an electron is 5x10-40 weaker than their electromagnetic attraction). Moreover 99.9 % of the observed matter in the Universe is in the plasma state, so plasma physics should dominate in our study of the cosmos.

Extension of Newton's Law to the Cosmos

Notwithstanding its elegance, Newton's Law has a logical flaw, an "Achilles' heel", which was destined to be fatal in modern cosmology. He assumed his law to be universally true far beyond the scale of his empirical data - the orbit of Mars.

Kepler's laws, and their derivative, Newton's law of universal gravitation, are laws based an Brahe's decades of observations of the motion of Mars to an accuracy of one arc-minute. Newton's law was still satisfactory when applied to binary stars but these distances were roughly on the scale of the solar system).

No empirical law can be safely applied beyond the scale of the observations on which it, is based, lest there be a minute additional term too small to be detected on the scale of the empiricism but which increases with scale until it dominates, or terms with exponents that alter the balance of the equation with change of scale.

For example, the Spitfire was a most successful aircraft; but if an aircraft were built from the same plans except that every part was doubled in size, it could not fly at all, because its mass would increase eight-fold, while the wing area to support it would only increase four fold.

Unfortunately, physicists and astronomers, mesmerized by the towering authority of Newton, assumed the validity of Newton's gravitation law far beyond the solar system, on which it was based, to the whole cosmos, not merely doubling the scale as in the Spitfire example, but by a million million times, without any confirmation whatsoever! Such an extension might have been valid, but, sadly, it wasn't.

Three centuries later, Edwin Hubble, observing the motion of galaxies on a scale more than 10-2 times as large as the solar system, found that distant galaxies, instead of attracting each other as Newton's law required, were receding with velocities which increased with distance. In hindsight, both phenomena are expressions of a single gravitation law.

In the vicinity of a galaxy, a unit mass suffers Newton gravitational attraction toward the galaxy. At the same time the unit mass is attracted by all the surrounding galaxies. This attraction away from the original galaxy has been integrated as Hubble's law which states that matter recedes from other matter with a velocity of ~50 km / sec / megaparsec, but the 50 (adopted by Sandage, Hubble's successor) depends on the validity of measurement of galactic distances, which is still uncertain by as much as 100%.

In my l976 Johnston Memorial Lecture, I combined the two into a single Newton-Hubble law, the acceleration of unit mass:

Acceleration = mG [(I/d2) - f (d,H,c)] ... (2)

which, by omission of the second term in the brackets, reduces simply to Newton's law. Omitting the first term, expresses Hubble's law, a function of the Hubble constant, H, the distance, d, and the velocity of light, c. By balancing the dimensions of the exponents of H, c, and d the expression becomes

Acceleration = mG [(1/d2) - (ad2H4/c4)] ... (3)

i.e.

Acceleration = Newton Term (left)  -  Hubble Term (right)

A scaling factor, a (a pure number), must be included because dimensional analysis only controls the exponents, not numerical equalities. The scaling factor is the ratio of the mass of the knowable Universe to the mass of the galaxy.

The Newton term begins large, but declines with the square of the distance. In the Hubble term, H/c is an extremely small positive fraction of the order of 10-13 km2 (in fact it is the squared inverse of the radius of the physically knowable Universe). Dimensionally the Hubble term is l/L2, the same as the Newton term, and when raised to the fourth power it is inconceivably small.  On the scale of the solar system it is quite undetectable; but it is real and positive, and increases indefinitely with the square of the distance, so that a distance must be reached (about 1012 times the size of the Mars' orbit) where the Hubble term first cancels the Newton term. This is the Newton- Hubble Null (Figure 127)This concept of an additional term, a function of distance added to Newton's law, was first introduced by me in the 1976 Johnston Memorial Lecture (Carey, 1978), several lectures in India, and in Carey (1988), and also by Ghosh (1993).
 

What is the Hubble term?

Imagine a rubber balloon with a pattern of spots on its surface. As the balloon is inflated, each spot sees that the adjacent spots recede from it. Spots two rows away recede twice as fast, and the speed of recession increases directly with distance from the observer. Each spot is surrounded by tension from the pull of the others. This tension is constant throughout the surface of the balloon. This model is a two- dimensional surface deployed in three dimensions.

Extend this mental model to three dimensions deployed in four dimensions of space-time, and the Hubble's extension is modelled. Replace the spots on the surface of an inflating balloon by an infinite array of galaxies, each attracting to itself, and a universal cosmic tension results, constant throughout the cosmos, which balances a galaxy's attraction at the Newton-Hubble null.

The distance to the null depends on the ratio of the galaxy's mass to the mass of the knowable Universe. The greater the galaxy, the greater the distance to its Newton-Hubble null. This is the meaning of the scaling factor a [i.e.] each galaxy is surrounded in all directions by tension, attracting inward toward itself, but there is no unique point to which all tension is directed. Perhaps gravitational attraction from a single galaxy may be balanced by orbital rotation, but this cannot be applied to the knowable Universe or to an infinite field of attracting galaxies.

Statistical Size of Galaxies

within this Newton-Hubble null distance from a galaxy, a free body moves toward the galaxy. Beyond this null distance, a free body moves away, with the Hubble term. This determines the maximum size of a galaxy. The million million galaxies in the Universe form a gaussian size-distribution with average of 1010 to 1012 times the mass of the Sun.

Why this mean size, and not a million times smaller or a million times larger? The mass-density of the cosmos (the Hubble term) determines the minimum distance between galaxies, and the statistical size of galaxies. Neither is, explained by classical physics.

Van Flanders (1995) has pointed out that as galaxies have a gaussian size distribution, the smaller end of the distribution would first fade from visibility with increasing distance, biasing the remainder toward the larger brighter galaxies. But this would not affect the increase of redshift with distance.

When the dimensionless number a in the above expression is 1020 (Dirac's "large cosmic number") the distance of the Newton-Hubble Null for the Milky Way is a little less than 166,000 light-years. The nearest neighbour of our Milky Way galaxy is the Large Magellanic Cloud 180,000 light-years away. Originally part of our galaxy, it has budded off and is receding very slowly from our galaxy, and from its next nearest neighbour, the Small Magellanic Cloud, which budded off earlier. The nearest spiral galaxy to our Milky Way galaxy is M31, the great spiral in Andromeda, which is about two million light years away, also receding slowly from our galaxy.

Observe also that although equation (3) was deduced solely from dimension analysis, Einstein's cosmic term c2/H2, and Dirac's "large cosmic number" 1020 pop out unsolicited, and also c4/H4 which is the space-time volume of the physically knowable Universe, and c/H, the radius of the knowable Universe: 1.66 x 1010 light years (5 x 109 parsecs). Such is the predictive power of equation (3).

Genesis of Clusters

1Milky Way, Large and Small Magellanic Clouds, the Andromeda spiral M3l, the Triangulum nebula M33, NGC6522, the small praco galaxy, IC16I3, possibly the Sextans systems, and several small ecliptical galaxies.

 If the Hubble expansion is reversed, our "local group" of galaxies1 diverged from a single galaxy more than 1010 years ago. They budded off one-by-one, as their primitive parent reached its Newton-Hubble null. The primitive parent was only a normal galaxy, not the sum of their present masses (because all bodies increase in mass with time), and still further back evolved from a star cluster like the Sun's local cluster, the derivative of a nova explosion of a small star (see Chapter 5).

The tight group, NGC4395, 4399, 4400, and 4401 is another dispersed galaxy group like our local group of galaxies, having not long ago budded off beyond the Newton-Hubble null of their parent. The arms of the large spiral galaxies seem to be budding off from their parents at the Newton-Hubble null, but as they recede with the rotation velocity inherited from their secession radius, they lag behind as spirals.

The existence of galaxies and galaxy clusters is an unsolved problem of the current big-bang hypothesis, but given that all galaxies are growing and budding, it follows that galaxies should occur in clusters, each cluster having budded from an earlier single galaxy.

Allan Sandage, who succeeded Edwin Hubble as master of Palomar, had actually realized the failure of the Newton term at super-galactic distances in 1972, but dismissed it. I quote from Overbye, 1991, p.173:

Sandage's analysis was not correct. The Virgo cluster, indeed every body in the Universe does exert its gravity attraction, exactly as Newton thought, diminishing to zero at infinite distance. But at the Newton-Hubble null for that cluster its gravity attraction merges with the Newton attractions of all the bodies in the infinite Universe, the Hubble term of universal expansion.

 The centrifugal acceleration of orbiting bodies must balance the gravity attraction of the central body at their radial distance to maintain a stable orbit. The velocity curve radially from the galaxy center should rise steeply at first, then moderate, and finally fall steeply from the outer edge of the galaxy.

When Kent Ford and Nora Rubin in 1970 plotted this curve for M31, the great spiral in Andromeda, the curve was flat and did not fall steeply at the outer edge of the galaxy. Rubin and Ford then studied several other spiral galaxies, each of which yielded similar anomalous velocity curves.

What was wrong? It seemed that either Newton's law had broken down, or there was a lot of unseen matter in the outer part of galaxies. In fact they were applying Newton's law derived empirically on the scale of the solar system, to phenomena on the scale of galaxies, where the Hubble term [equation 3] and perhaps other terms should have been included.

Einstein's cosmic term, Lambda

Einstein's 1917 benchmark paper was published at a time, when the Milky Way system was believed to be the whole Universe, an eternal, stable, closed lens of stars. Einstein laboured in vain to generate such a Universe from his general relativity equations, because no derivatives were stable, they either continuously expanded or contracted.

He could only model the stable Milky Way "Universe" by adding an extra term to his general- relativity equations, his "cosmic constant", which did produce a stable, closed Universe. But he was never satisfied with it, and ended his following paper with the caveat,

In his 1922 and 1924 papers Alexander Friedman derived several Universe model solutions to Einstein's equations, some with the cosmic term, and some without it.

By the late 'twenties and early 'thirties, Hubble and his successors had found that the "nebulae" were not in the Milky Way system, but were far beyond it, and had established beyond doubt that the Milky Way Galaxy, far from being the whole Universe, is but one of billions of similar siblings, and that this galactic family is dispersing with velocities proportional to their separation, in accord with the general relativity equations. without the cosmic term. Einstein later described his earlier introduction of the cosmic term as "the greatest blunder of my life".

But did Einstein really blunder? I don't think so. In equation (3), a is a pure number that determines the scale. If a is set at 1020, d is the radius of a galactic domain, less than 105 light years. It is stable and constant and eternal, which is what Einstein had sought, the Milky Way realm. If a is set at unity (which virtually abolishes the cosmic term from the general relativity equations) d is the radius of the physically "knowable" Universe, about 1011 light-years.

This Universe is constant in radius (to the distance at which galaxies appear to us to be receding at the velocity of light), constant in mass, because galaxies disappearing beyond the limit of physical knowability are balanced by new matter continuously added between galaxies (like the constant mass of water in a stretch of river flowing before us).

So Einstein did not really blunder. He solved correctly the problem he set out to solve. What the cosmic term gave him was the radius of a galactic domain, that is the limits of the Milky Way system, which was his initial input datum. The general relativity equations without the cosmic term extend to the cosmos beyond our physically knowable Universe. We could try putting a at the next step in a Dirac hierarchy, 10-20, perhaps yielding a closed cosmos of a billion billion Universes but we have no way of knowing about that.

Dark matter in the Universe

In the early 'thirties Jan Oort, a Netherlands astronomer, reported that the visible stars had insufficient mass to account for the motions of stars in the vicinity of the Sun. It seemed, however, that Jupiter-like planets, invisible brown dwarfs, and gas clouds could perhaps make up the deficiency. But the Swiss astronomer, Fritz Zwicky, concluded that the apparent mass deficiency in distant galaxies and galaxy clusters was much too great to be explained in this way.

Kinematic studies of our own galaxy and of the Andromeda spiral, plotting orbital velocity against distance from the center, suggests significant mass deficiency. Even more so do the kinematics of the local group of galaxies, of galaxy clusters, and of binary galaxies. Spiral galaxies seem to contain five times as much unseen matter as visible matter, larger elliptical galaxies between ten and twenty times as much, small galaxy clusters twenty to fifty times, and large clusters (such as the Coma cluster of about a thousand galaxies) require a hundred times.

According to these results, by far the greater part of the mass of the Universe is unseen dark matter, a truly startling conclusion! Through all this theoretical fog, Newton's law has been applied to cosmic distances without the Hubble term, so of course the deficiency magnifies with scale!

Much discussion has sought the nature of this non-radiating matter. As the visible matter is nearly all baryons (the substance of atoms or atomic nuclei), most have thought that the theoretical dark matter must be in baryonic form, such as black holes, or cold planets like Jupiter. Apart from the improbability of such a vast population of black holes, brown dwarfs, or Jupiters, this answer has been rejected because of incompatibility with current beliefs in the early genesis of matter following the "big bang".

Excluding baryons leaves leptons, of which the only plausible candidates are neutrinos, which had been believed to be massless. Experimental evidence had only established that their mass could not exceed 20 electron-volts. As the "big bang" theory allowed 100 neutrinos /cm3 of space, even this minuscule mass could not account for the overwhelming unseen mass of the Universe.

But this suggestion also conflicts lethally with other aspects of the "big bang" theory. So particle physicists have turned to a hypothetical category of particles, namely photinos and gravitinos, which symmetry theory postulates must pair off with photons and gravitons; theory suggests that these could be quite massive (up to a billion electronvolts per particle).

The solution to this apparent paradox is simple. The alleged dark matter does not exist! It results from applying the naked Newton law to trans-galactic distances, without the Hubble term, and possibly other relevant terms.

Cosmic expansion

The analogy of the mutual recession of spots on an expanding balloon is only kinematic. The tension in the balloon does separate the spots, but the tension is caused by the increasing pressure within the balloon. To approach a dynamic analogy, consider an elastic film across a rigid ring, and place on the film many point objects each of which exerts a tension toward itself.

The result will be tension everywhere in the film and around the bounding ring, but no expansion. But if the film is infinite, the tension never reaches a boundary to contain it, the tension is universal and unbounded, and the film expands indefinitely. With the Šther concept, cosmic expansion is predictable and inevitable.

Pervasive *tension of the Šther implies an energy state throughout the Šther (space) that is the direct result of mass distribution through the Universe. Schwatzwald (1989) has stated that adding the cosmological constant l to the Einstein Field equation has the same effect as assigning an energy density lc4 / 8pG to the vacuum of space.

Einstein's general relativity describes the effect of mass as curvature of four-dimensional space-time, which correctly represents the accelerations acting on a particle and the bending of light rays, just as a parabola correctly represents the path of a ball thrown in the air. But neither curved space-time nor the parabola have any physical existence - they merely abstract the geometrical and kinematic aspects of reality, - in contrast to the radial *tension induced by a mass and the pervasive *tension of the cosmos.

Physical meaning of the gravitational constant

The gravitational constant came into being simply as the constant necessary to convert Newton's law (that force is proportional to the product of the masses and inversely proportional to the square of their separation) into an equality. Physically, it is a function of the pervasive *tension in the Universe and hence is inversely proportional to the density of the Universe. If there were significantly less matter in the Universe, the gravitational constant would be greater, because the attraction of the other matter in the Universe would be proportionally less.

Restating Newton's law, Force = m1m2 G/d2

in dimensional terms, MLT2 = M2GL-2

that is G = M-1 L3 T-2

that is GT2 = 1/density

Hence the gravitational constant is proportional to the inverse of the density of the Universe. Numerically, the gravitational constant is 6.6732 x 10-11 S.I. units (or newton meter squared per kilogram squared).

Physical meaning of Planck's constant

Radiation energy propagates through the Šther by cyclic *stress oscillation in the Šther at the frequency of the propagating wave. A minimum energy limit must be reached when the *stress corresponding to one cycle equals the pervasive *tension in the Šther and resonates with it. A lower *stress level cannot be transmitted. At twice, thrice any number of cycles above the fundamental frequency the propagating wave resonates with the pervasive medium. At intermediate points, resonance falls away on a sine curve.

The stress of the resonant fundamental wave is the pervasive *stress of the Šther. This is Planck's constant h, which is constant for all frequencies (being
 the pervasive *stress of the Šther). Energy at any frequency necessarily peaks at whole multiples of this constant.

The quantum concept was invented in 1900 by Max Planck, then Professor of experimental physics in Berlin. Earlier, Kirschoff, under whom Planck had studied, had shown that in a "black body" enclosure where all the objects are at the same temperature, the heat radiation at different frequencies is independent of the nature of the objects.

Planck set out to discover the precise relation between frequency and energy, which differed significantly from the expectation of classical physics. He tried the improbable (to him) assumption that the energy emitted by any radiator did not vary continuously, as had been taken for granted, but in discrete jumps in multiples of a fundamental unit or quantum. Planck himself was surprised that this suggestion worked, and passed empirical tests quite precisely.

So he announced what came to be known as Planck's Law, that the energy of electromagnetic radiation occurs in small individual packets, each of energy hn (where n is the frequency); he defined the fundamental unit of action h, now known as Planck's constant (which has been found to have the value 6.626075x10-34 joule / second or 4.135692x10-15 eV.s). The mysterious quantum, the energy at unit frequency, is a measure of the *elasticity of the Šther.

The implication to Planck was that electro-magnetic radiation was not waves but particles (photons). Geometrical optics, regarding light as transverse waves, adequately solves most phenomena, such as propagation, reflection, refraction, diffraction, interference, and polarization, throughout the spectrum from near infinitely long wavelength to the near infinitesimally short.

But the wave model did not seem to be able to explain the bonding of frequency to energy through steps of h, nor the photoelectric effect observed by Einstein (the kinetic energy emitted by incident light is hv - f, n being the frequency and f the binding energy holding the electron), nor the Compton effect (where X rays are scattered with energy peaks at hn), so that light seemed to come in packets, like the vending machine that could deliver chocolate bars but not partial bars.

So began the schism between the wave theory and particle theory of light. Nevertheless, the conclusion that light is both particles and waves was anomalous and remains anomalous [in standard theory].

Kelvin remarked in another context, "Paradoxes have no place in science". Max Planck, who initiated the quantum theory, never came to accept its peculiarities in full. Einstein, who agreed that the quantum theory neatly explained his photoelectric  observation, nevertheless found it so preposterous that he resisted it to his death. Steven Weinberg, who shared the 1979 Nobel Prize with Salam for their l967 formulation of the electro-weak equations, wrote:

General-relativity theory remains immiscible with quantum theory.

Niels Bohr said:

Professor Warren K. Green, Professor of Astronomy at Amherst University wrote: Brian Martin has written: Einstein, Schrodinger, and De Broglie believed that the statistical character of quantum predictions merely reflected our ignorance of the underlying infrastructure.

Clearly, we must go back to Planck's 1900 guess and seek a different model that reconciles all the phenomena of electromagnetic radiation. Planck's mistake was to seek the explanation of the radiation, rather than in the medium which transmits it.

What Planck was really measuring was the rigidity modulus of Šther (or whatever else you choose to call the medium through which light is transmitted). This determines the oscillation time of each frequency of light. Light of that frequency, or any integral multiple of that frequency, resonates. Any other frequency damps out.

All harmonic motion (such as a swinging pendulum, water waves, seismic waves, vibrating piano wires, a pumping heart, and electromagnetic waves) implies a restoring force, which opposes any disturbance from a neutral equilibrium position. In pendulums and water waves the restoring force is gravity; in seismic waves it is the elasticity of the rock; in pianos it is the tension in the wire; in the pulsing heart it is the tension in the myocardium; in radiant light it is the *rigidity of the Šther.

In all cases, increasing the frequency of the oscillation increases the energy. For any particular frequency there is an implied energy. When the 'black box' reaches equilibrium with all surfaces at the same temperature, light absorption and light emission of any particle are equal. The radiant energy emitted by an oscillating electron depends only on the frequency of the emitted radiation. That is, energy E = n x where x is a constant and n is an integer. That constant is h, Planck's unit of action, the *rigidity of Šther.

Notwithstanding repeated attempts, the quantisation of gravity has not been achieved. Nor have gravity waves [been detected], which should be longitudinal, with an *elastic constant different from Planck's constant, a function of bulk modulus and shear modulus, rather than shear modulus alone.

[Unfortunately] The sub-microscopic billiard-ball concept of electrons, protons, and other subatomic particles still persists, ultimately, solid little balls of matter, of something, or of nothing (!) which may materialize spontaneously from vacuum, and vanish when their function is done.

Physical meaning of the velocity of light

Transverse waves propagate through an elastic medium with a velocity of the square root of the shear elasticity over the density, never any faster. Their velocity does not depend on their frequency or intensity, only on the physical properties of the medium. As I have indicated before, Šther behaves mathematically like a Hookean elastic medium, and light waves, which have the same geometric form as elastic transverse waves, have a maximum velocity determined by the *elasticity of the Šther (2.99792458xl08 m/s), which is the same for any frequency of the electromagnetic spectrum, from the longest radio waves to the shortest gamma rays.

If the ray passes through another medium, be it solid, liquid, gas, or plasma, the velocity is less, hence refractive index. If a ray passes near a massive body on whatever scale (molecule, planet, star, or galaxy) the Šther is "stiffer", so the velocity is locally less,  hence a galaxy may act like a glass focusing lens. If a ray passes through a crystal, such as mica, a ray, polarized transverse to the cleavage passes much closer to the atoms than a ray polarized parallel to the cleavage, hence birefringence.

Hence the velocity of light is determined by the *elasticity and *density of the Šther. The motion of an emitter of light may affect the phase, amplitude, and frequency of the light, but never its velocity, as the Michelson-Morley experiment proved. In fact, I was always surprised that physicists had expected the velocity of light to be affected by the velocity of the emitter! After all, in an earthquake, the direction of the impulse which triggered it is recorded in the direction of first motion, but never in velocity, which is determined by the propagating medium. The pitch of a train whistle is affected by the speed of the train relative to the observer, but not the speed of the sound waves.

The velocity of light is the measure of the rate of expansion of Šther (or of space). Empirically, this rate is linear. For the mean density to remain uniform, matter would have to be created at the rate of c3, the cube of the velocity of light, where it is lacking as suggested by Stothers (1966).

In summary

Planck's constant h, the gravitational constant G, and the velocity of light c and of all other electromagnetic radiation, are uniquely determined by the physical properties of the Šther, and are wholly independent of temperature, pressure, charge, magnetic intensity or orientation, or of solid liquid gaseous or plasma state.

The velocity of light is commonly stated as a velocity, but Dr W D. Parkinson, and probably others before him, have recognized that the "velocity" of light is dimensionally a pure number. Rather than repeat his argument here, I have reproduced it as Appendix 2.

The fundamental constants, the velocity of light c, the relation of diameter to circumference, and the exponential constant, e, the base for natural logarithms, are dimensionally pure numbers.



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