Explaining Einstein's Finite Universe

with the Spherical Standing Wave Structure of Matter

The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. (Albert Einstein, 1954)

Can we visualize a 3D universe which is finite yet unbounded? (Albert Einstein, 1954)

The results of calculation indicate that if
matter be distributed uniformly, the **universe** would necessarily
be **spherical**.

I must not fail to mention that a theoretical argument can be adduced in
favour of the hypothesis of a **finite universe.**

The general theory of relativity teaches that the inertia of a given body is greater as there are more ponderable masses in proximity to it; thus it seems very natural to reduce the total inertia of a body to interactions between it and the other bodies in the universe, as indeed, ever since Newton’s time, gravity has been completely reduced to interaction between bodies. (Albert Einstein, 1954)

A human being is part of the whole called by us universe, a part limited in time and space. We experience ourselves, our thoughts and feelings as something separate from the rest. A kind of optical delusion of consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from the prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty… The true value of a human being is determined primarily by the measure and the sense in which they have obtained liberation from the self. … We shall require a substantially new manner of thinking if humanity is to survive. (Einstein, 1954)

Introduction - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - Top of Page

Einstein's General Relativity requires a finite spherical universe (it cannot be infinite because of Mach's Principle, with which Einstein strongly agreed, that the mass of a body is finite, is determined by all other matter in the universe, thus all other matter in universe must be finite).

Two problems;

a) What surrounds this finite spherical universe? (Einstein used his spherical ellipsoidal geometry of General Relativity to propose curved space - if you travel in any one direction you will curve around and eventually return to your starting point - subtle, clever, weird, wrong).

b) What stops finite spherical universe gravitationally collapsing (thus Einstein's Cosmological / Antigravity Constant).

2. Two discoveries, one theoretical, one empirical sent Cosmology down the path of the Big Bang Theory for the creation of our universe.

a) Friedman used Einstein's equations to show that an expanding universe was possible by the equations, and solved the problem of the collapsing universe and thus removed the need for Einstein's Cosmological constant. Einstein was reluctant - believing in a static (non-expanding universe).

b) Then Hubble
famously showed the relationship between distance and redshift. If Doppler
shift caused this redshift then it meant stars / galaxies were moving apart.

Einstein, swayed by this argument, changed his mind - thus his comment 'My biggest blunder' referring to the Cosmological Constant.

As we shall explain though, this is not the correct solution, in fact Einstein's 'cosmological constant is largely correct, but it is not caused by anti-gravity within the universe, but by the gravitational forces of matter outside our finite spherical universe within an infinite space. Further;

1. Redshift with distance is not Doppler effect, but caused by Huygens Principle (a wave can be treated as an infinite number of spherical wave sources). It is necessary that all other matter's out-waves must combine in a Huygens wave front, to form our spherical In-Waves. We absolutely are a part of the universe (not separate / discrete bodies) - our matter formed from all other matter in the universe. This explains Mach's Principle and redshift with distance (in the article, particularly equation of the cosmos, it shows the mathematical deductions from wave theory correctly deduce Mach's Principle (Milo Wolff) and Redshift with distance).

2. To understand Cosmology you must understand the relationship between the finite and the infinite. The big bang does not explain this, it was not until Milo Wolff applied knowledge of the Wave Structure of Matter to the study of the Cosmos that this problem could be solved.

a) Space is Infinite (one thing existing must be infinite) but our spherical universe is finite. Matter is finite. We unite these two finite things, matter and universe, by realising that matter, as a spherical standing wave formed by other matter's out waves, determines the size of our finite spherical universe. Matter and Universe are the same thing / are united.

b) Due to this sharing of waves, only a finite number (about
10^80) of other Spherical Standing Waves combine with our matter. The article
shows two separate deductions for this, one by myself (simple) and one by
Maths Physicist Milo Wolff (mathematical, logically equivalent).

Thus there are an infinite number of finite spherical universes within an infinite space.

Current Big Bang Cosmology defines **Universe**
as both;

i) All that exists (both Space and Matter)

ii) Finite and Spherical.

The Wave Structure of Matter Cosmology (being founded on One thing Space) requires that Space is Infinite, but that we only interact with a finite sphere of matter within that Infinite Space. Thus the current 'Big Bang' definition of Universe is wrong according to WSM.

So you can either re-define Universe by maintaining meaning one;

i) Universe is all that exists (both Space and Matter) which WSM says is Infinite - thus Universe is Infinite.

But then:

ii) Finite and Spherical Universe is wrong. The Universe is no longer finite and spherical, and effectively has the same meaning as Infinite Space / all that exists. And you then have no word for the finite spherical region of space that we interact with other matter (which causes our In-Waves). It also becomes very confusing when considering Mach's Principle and Einstein's General Relativity (see below).

Our other option is to re-define Universe as the Finite sphere of Space
(and other matter) we see and interact with (and that contributes to our
In-Waves, while Space itself is Infinite).

This provides a better definition as then the finite spherical universe still makes sense with respect to Mach's Principle and Einstein General Relativity.

Thus in this Wave Structure of Matter Cosmology the **Universe** is defined as follows;

**Universe**: The Finite Spherical region of Matter and Space that we can see and interact with (within an Infinite Space). Only this other matter's Out-Waves contribute to the formation of our Matter's in-Waves. i.e. Huygens' Principle - and this is the cause of Mach's Principle, that the mass of our matter is determined by all the other matter in our finite spherical universe (because it is created by it!).

Introduction - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - Top of Page

We begin this section with a fairly long quote from Eric Lerner, though it is important, as it provides a historical analysis of Einstein’s Relativity, the birth of the 'Big Bang' and its influence on Society;

(On November 9, 1919 the New York Times, Page six) : ECLIPSE SHOWED GRAVITY VARIATION, and below, DIVERSION OF A LIGHT RAY ACCEPTED AS AFFECTING NEWTON'S PRINCIPLE, HAILED AS EPOCH MAKING. BRITISH SCIENTIST CALLS THE DISCOVERY ONE OF THE GREATEST OF HUMAN ACHIEVEMENTS. An observation of the May 29, 1919, solar eclipse had confirmed Einstein's prediction of the bending of light from a distant star by the sun's gravity. This vindication of his general theory of relativity was announced at a meeting of the Royal Astronomical Society.

Why was Einstein's theory, not even briefly described in this first article, so outstanding? One scientist noted that the effect on practical astronomy of the small differences from Newton's laws would not be very great. But 'it was chiefly in the field of philosophical thought that the change would be felt.' The Times reported, 'space would no longer be looked on as extending indefinitely in all directions. Straight lines would not exist in Einstein's space. They would all be curved and if they traveled far enough they would return to their starting point.'

Thus the first public announcement of Einstein's theory suddenly proclaimed the falsity of a basic cosmological tenet, that the universe is infinite. More surprises came the next day when a Times headline declared, LIGHTS ALL ASKEW IN THE HEAVENS, MEN OF SCIENCE MORE OR LESS AGOG. Not only was the new theory shocking in its implication, but it was incomprehensible as well: J. J. Thompson stated that it was useless to detail the theory to the man in the street, for it could only be expressed in strictly scientific terms, being ‘purely mathematical.’ In fact, the Times went on, Einstein himself had warned his publishers that there were not more than twelve people in the whole world who could understand his theory.

Einstein's new theory appealed to scientists, reporters, and editors because it brought a vision of the universe as a whole, a vision that appeared as a solace to a tormented society. The cosmology Einstein developed in 1917, two years after formulating his general theory, had, for many scientists, a terrific aesthetic and philosophical attraction. In part, this was based on the appeal of general relativity itself. As Alfven has written, ‘No one can study General Relativity without being impressed by its unquestionable mathematical beauty.’ And, moreover, it was demonstrated not only in its prediction that light near the sun would be bent by gravity, but by subtle variations in the orbit of Mercury which Newtonian gravitation had not been able to explain. Newton and other scientists had always been bothered that gravity appeared to act ‘at a distance’, a magical influence in empty space. General relativity eliminates this problem, showing that mass curves the space around it like a weight resting on a sheet pulled taut at the edges. It is this curvature of the space that results in gravity, not the direct action of one object on another.

But beautiful as it was, this change in gravitational theory was not what captured the imagination of scientists and the press. It was instead Einstein's cosmological speculations of a closed, finite universe. Gravity, Einstein argued, would curve the entire cosmos around into a four-dimensional sphere, finite, yet without boundaries. Einstein's spherical universe is static, eternally unchanging, ruled by his elegant equations.

To a society shattered by World War 1, this vision of a calm, ordered universe must have been tremendously reassuring. When mankind is progressing, the dynamic changing infinite universe, the ‘restless universe’, as Sir James Jean called it, seems exciting and challenging. But when human affairs are in shambles, and change no longer means progress but can mean upheaval and death, a finite and static universe like Einstein's can appear a balm to tortured souls, just as Augustine's hierarchical cosmos seemed to offer refuge from the confusion and misery of the fourth century.

As one of Einstein's biographers, physicist Abraham Pais, wrote, ‘Einstein's discovery appealed to deep mythic themes. A new man appears abruptly, the suddenly famous Dr. Einstein. He carries a message of a new order in the universe .. His mathematical language is sacred, ... the fourth dimension, light has weight, space is warped. He fulfils two profound needs in man, the need to know and the need not to know but to believe.’ In a time of death and uncertainty, ‘he represents order and power. He became the divine man of the twentieth century.’

Whatever the complex motives that produced the myth of Einstein and the general theory of relativity, it has had a profound impact on twentieth-century science. Nineteen nineteen became a fault line in the history of science, and in that year the main trends that were to lead to the acceptance of the Big Bang began.

As Alfven points out, it is quite ironic that a triumph of science led to the resurgence of myth. The most unfortunate effect of the Einstein myth is the enshrinement of the belief, rejected for four hundred years, that science is incomprehensible, that only an initiated priesthood can fathom its mysteries. Alfven wrote sixty years later, ‘The people were told that the true nature of the physical world could not be understood except by Einstein and a few other geniuses who were able to think in four dimensions. Science was something to believe in, not something which should be understood. Soon the best-sellers among the popular science books became those that presented scientific results as insults to common sense. One of the consequences was that the limit between science and pseudo-science began to be erased. To most people it was increasingly difficult to find any difference between science and science fiction.’ Worse still, the constant reiteration of science's incomprehensibility could not fail to turn many against science and encourage anti-intellectualism.

Einstein had first formulated his conception of a static, finite universe in 1917, two years after developing the general theory of relativity. But he soon saw its flaws. A static, closed universe could not remain static, because its own gravitation would cause it to collapse.

Clearly, Einstein reasoned, something prevents the collapse of the universe, something like the centrifugal force of rotation, but not rotation itself. This force must somehow increase with distance: it had never been observed on earth or in the solar system, but it must be strong enough at cosmological distances to overcome gravity. He introduced a new term into his equations of gravity, ‘the cosmological constant,’ a repulsive force whose strength increases proportionally to the distance between two objects, just as the centrifugal force of a rigidly rotating body increases proportionally to its radius. But this force, he thought, acts in all directions equally, like gravity, so it does not disturb the symmetry of the universe.

To preserve his conception of a static universe, Einstein set the cosmological constant to a level that would balance gravity exactly, so that its repulsive force neutralized the tendency of the universe to collapse.

In 1924 new observations changed the picture radically. For a decade, astronomers had been measuring the spectra of stars in nearby galaxies. In nearly all cases, the spectra shifted slightly toward the red. Scientists had long known the simplest explanation of these redshifts is that the galaxies are moving away, shifting the frequency of light to the red (an analogous phenomenon makes the pitch of a train whistle rise as it approaches and fall as it recedes). It seemed strange that, rather than moving randomly, the galaxies all seemed to be moving away from each other and from us.

Lemaitre developed a new cosmological theory. Studying Einstein's equations, he found, as others had before him, that the solution Einstein proposed was unstable; a slight expansion would cause the repulsive force to increase and gravity to weaken, leading to unlimited expansion, or a slight contradiction would, vice versa, lead to collapse. Lemaitre, independently reaching conclusions achieved five years earlier by the Russian mathematician Alexander Friedmann, showed that Einstein's universe is only one special solution among infinite possible cosmologies- some expanding, some contracting, depending on the value of the cosmological constant and the ‘initial conditions’ of the universe.

Lemaitre synthesised this purely mathematical result with
Wirtz's and Hubble's tentative observations, and concluded that the universe
as a whole must be expanding, then any of the cosmological scenarios that
led to expansion could be a valid description of the universe. But cosmic
repulsion and gravity are not delicately balanced- repulsion predominates
in an expanding universe.

Lemaitre put forward his hypothesis of an expanding universe in a little-known
publication in 1927, and within two years his work and Friedmann's had become
widely known and accepted in the tiny cosmology fraternity. By this time,
1929, Hubble had published the first results showing the redshift relation,
apparently confirming Lemaitre's idea of an expanding universe.

But if the universe is finite in space, then it must be finite in time as well, Lemaitre argued. Thus the non-singular solutions that Lemaitre found- in which the universe has no beginning- were unacceptable. The only ones that corresponded to Lemaitre's philosophical views were closed in space and limited in time. Eddington gave him a further rationale for looking at singular solutions- the second law indicates that the universe must have originated at a state of low entropy.

From these two philosophical premises, Lemaitre developed his concept of the ‘primeval atom’, the first version of the Big Bang. At a 1931 meeting of the British Association on the Evolution of the Universe, he put his ideas forward for the first time. Beginning from the idea that entropy is everywhere increasing, he reasoned, quantum mechanics (developed in the twenties) shows that as entropy increases, the number of quanta - individual particles in the universe - increases. Thus, if we trace this back in time, the entire universe must have been a single particle, a vast primeval atom with zero radius. He identified this instant with the singularity of some relativistic solutions. Just as uranium and radium atoms decay into subatomic particles, so this giant nucleus, as the universe expanded, explosively split up into smaller and smaller units, atoms of the size of galaxies decaying into atoms the size of suns and so on down to our present-day atoms. (**Eric J. Lerner**, The Big Bang Never Happened, 1991)

With this summary in mind let us now turn to the ideas of Albert Einstein;

If we ponder over the questions as to how the universe (space), considered as a whole, is to be regarded, the first answer that suggests itself to us is surely this: As regards space (and time) the universe is infinite. There are stars everywhere, so that the density of matter, although variable in detail, is nevertheless on the average everywhere the same. In other words: However far we might travel through space, we should find everywhere an attenuated swarm of fixed stars of approximately the same kind and density. (**Einstein**, 1954)

Einstein thought it sensible that space was infinite, as the concept of a finite sphere of Space with a center and a boundary seemed unreasonable. As we have explained, Einstein's (and many other philosopher's) belief in an infinite Space and time as being the most obvious and sensible universe is correct, this being a necessary consequence of the Spherical Standing Wave Structure for Matter.

Unfortunately for Einstein, limited understanding of Mach's Principle and
lack of knowledge of how Matter exists in Space and is interconnected with
other Matter in the Space around it (The Wave Structure of Matter) prevented
this from being possible at the time, and led to the current confusion and
paradox of modern cosmology. So let us now explain (using the ideas of Einstein)
how the Wave Structure of Matter, and particularly the Huygens' combination
of In-Waves and Out-Waves, solves these problems and paradoxes.

Einstein continues;

This view of an infinite space is not in harmony with the
theory of Newton.

The latter theory requires that the universe should have a kind of center in which the density of stars is a maximum, and that as we proceed outwards from this center the group-density of the stars should diminish, until finally, at great distances, it is succeeded by an infinite region of emptiness. The stellar universe ought to be a finite island in an infinite ocean of space. (**Einstein**, 1954)

Clearly Einstein thinks this 'island' universe unreasonable, nonetheless, it is a logical consequence of Newton's force laws as he explains below;

According to the theory of Newton, the number of 'lines of force' which come from infinity and terminate in a mass m is proportional to the mass m. If, on the average, the mass density Po is constant throughout the universe, then a sphere of volume V will enclose the average mass Po V. Thus the number of lines of force passing through the surface F of the sphere into its interior is proportional to Po V. For unit area of the surface of the sphere the number of lines of force which enters the sphere is thus proportional to Po V/F or to Po R. Hence the intensity of the field at the surface would ultimately become infinite with increasing radius R of the sphere, which is impossible. (**Einstein**, 1954)

Einstein correctly argues that as the radius R of the spherical universe tended to infinity then if this infinite matter in distant Space contributed to the mass of our matter, our matter would necessarily have an infinite mass - which it clearly does not. The solution is to realize that matter is a SSW that shares its waves with other SSWs in Space, so once the radius increases past a certain radius (the size of our Finite Spherical Universe) then we can no longer consider the contributions of Out-Waves from this farther distant matter - We have already counted and used their wave contributions which make up the SSWs of closer matter. (Otherwise we would be counting the same waves twice, three times etc. etc.)

As we have explained (sorry for the repetition but it is important!), it
is this solution (of the sharing or Huygens’ combination of waves)
that enables SSWs to exist with a finite mass-energy density, mass and size (the
size of our universe) within an infinite Space.

Without this knowledge though, the problem of matter having a finite mass and yet being part of Infinite Space was impossible to explain. As Einstein writes;

Newton included the infinity of space and time in his fundamental principles and speculated on the question of whether or not the stars were finite in number and filled only a finite part of the infinite space. He came to the conclusion that the number of stars must be infinite and spread rather uniformly through space, for a finite number would collapse in consequence of their mutual attraction. Later it turned out that this argument led to mathematical difficulties of so severe a kind that even modifications of the Newtonian law of gravitation for large distances were contemplated. (**Einstein**, 1954)

In order to escape this dilemma, Seeliger suggested a modification of Newton's law, in which he assumes that for great distances the forces of attraction between two masses diminishes more rapidly than would result with the inverse square law. In this way it is possible for the mean density of matter to be constant everywhere, even to infinity, without infinitely large gravitational fields being produced. We thus free ourselves from the distasteful conception that the material universe ought to possess something of the nature of a center. Of course we purchase our emancipation from the fundamental difficulties mentioned, at the cost of a modification and complication of Newton's law which has neither empirical nor theoretical foundation. (**Einstein**, 1954)

While Seeliger's solution is in fact correct, without knowledge of the Spherical Wave Structure of Matter and the Huygens' combination and sharing of waves, he had no theoretical foundation for this solution. We can now clearly understand the solution to this problem of infinite mass by realizing that distant SSWs contribute less and less to our In-Waves with increasing distance (hence their contribution to our mass-energy density and mass diminishes) and their gravitational effect upon us likewise diminishes.

Thus the Spherical Standing Wave Structure of Matter in an infinite three dimensional Space now provides this new theoretical foundation which deduces exactly what Einstein and Seeliger required! There is no 'island' of masses in an infinite empty Space. Instead, matter is distributed uniformly throughout an infinite Space, but it contributes less and less to our In-Waves, and thus our mass, with increasing distance thus preventing our mass from becoming infinite, and also preventing our finite universe from collapsing on upon itself due to gravitational forces.

Introduction - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - Top of Page

How the Distant Stars Determine Our Inertial Mass

Einstein himself started with the conviction that Ernst Mach was correct. But at the end of the day he had to sadly admit that his equations were not Machian and that general relativity was a 'local' theory. But we have seen that the equations were not wrong (after all they just represent conservation of mass-energy and momentum). It was the fact that **particles realized their mass by communication within their creation light sphere that made the physics Machian** - and that had been omitted in the conventional solution.

This becomes terribly important from another aspect, namely quantum mechanics. In the small mass-energy regime, discrete rather than continuous phenomena are encountered. Empirically this is a well-validated physics. But to the despair of generations of physicists, it appears impossible to unify general relativity and quantum mechanics. Perhaps the outstanding aspect of quantum phenomena, however, is that they involve non-local physics. If we make classical dynamics a non-local theory then we open the prospects of unifying these two branches of physics. (**Arp**, 1998)

Halton Arp makes some very good observations, and the solution to these
problems can now be clearly understood. Matter is 'nonlocal' and is in fact
a Spherical Standing Wave Structure that determines the size of our finite
spherical Universe.

And as Einstein confirms, general relativity requires that the universe be finite and spherical;

I must not fail to mention that a theoretical argument can be adduced in favour of the hypothesis of a finite universe. The general theory of relativity teaches that the inertial mass of a given body is greater as there are more ponderable masses in proximity to it; thus it seems very natural to reduce the total inertia of a body to interactions between it and the other bodies in the universe, as indeed, ever since Newton’s time, gravity has been completely reduced to interaction between bodies. (**Einstein**, 1954)

It is true that the mass (inertia) of a body is affected by other matter in the Space around it. This is because mass is related to mass-energy density of space of the In-Waves (the greater the mass-energy density of space, the greater the mass) so the more matter around a body, then the more their Out-Waves are contributing to that body's In-Waves and thus increasing its mass-energy density of space and inertial mass. As the inertial mass of our matter is finite (not infinite), therefore, either matter and/or Space must be finite; or the matter (Out-Waves) which contribute to our In-Waves must be finite within an infinite Space. As explained above, it is this latter option which we now realize to be the correct solution.

A similar argument about inertial mass was made in 1883 by Ernst Mach (who Einstein greatly respected and agreed with). Mach boldly stated that, Newton's law of Inertia **F=m.a**, was established by all the matter of the universe . At that time the unknown origin of Newton's inertia law attracted frequent attention. Mach (very cleverly) saw the connection between inertia and distant matter in the universe from considerations on the following experiment, which produces two fundamentally different ways of measuring a body's rotation in Space:

First, without looking at the sky, one can measure the centripetal (inertial) force on a rotating mass m using Newton's law in the form **F=ma=mv ^{2}/r** to find circumferential speed

The second way is to compare an object's angular position and circumferential speed v relative to the distant fixed stars.

Remarkably, both methods give exactly the same result and this was a great mystery at the time. Mach realized that the inertia law required a means to link the inertial behaviour of each body with all other matter (the stars) of our universe. Mach is reputed to have said, 'When the subway jerks, it is the distant stars which throw us down.' Einstein agreed.

Although most scientists have been intrigued by Mach's Principle, its truth was not recognized by most scientists because a paradox, termed instant 'Action-at-a-Distance' was seen in it by persons who declared that it is impossible for all the distant matter of the universe to instantaneously act upon a moving body here on earth. We now understand that their error was to regard matter as discrete 'Particles'.

This paradox is completely resolved by the Wave Structure of Matter (WSM) which shows that all distant matter establishes its presence throughout the universe by their In-Waves and Out-Waves which produce a nearly uniform mass-energy density of space throughout Space. Thus the 'presence' of distant matter from our universe already exists at each point in our Space. There is no need for instant action-at-a-distance. Accelerated Wave-Centers interact with the Space around them whose mass-energy density of space is determined by all the matter in our universe. Nothing is instantaneous. Waves only travel at speed c, which is determined by the mass-energy density of space. (The velocity of waves in Space, c, is slower in Space of higher mass-energy density of space as per the WSM Principle.)

It should be noted here though, that Mach was only partly correct. Mach,
like Einstein, believed that all matter interactions could be considered
relative to other matter, thus the concept of Space was largely ignored.

In fact it is the other way around (Newton was correct) and it is Space which exists and causes Matter, and the mass-energy density of space determines the behaviour of matter (SSWs) in this Space. This then explains how distant matter contributes to the mass-energy density of space of our In-Waves and thus our inertial mass.

Using the hindsight of the Wave Structure of Matter (WSM) it is now clear that not only was Mach largely correct for inertia but his concept applies to all the other natural laws as well. Each of the laws and the natural constants is determined by the inherent properties of Space, and in particular the mass-energy density of space which is established by the other matter of our universe. We live in a universe in which each part depends on the whole. Again we emphasize that the modern paradoxes were largely produced by the ancient concept of discrete 'Particles' and these paradoxes are now resolved by abandoning the 'Particle' concept and replacing it with the Spherical Standing Wave Structure of Matter whereby the Wave-Center causes the observed 'Particle' effect.

The concept of the 'curvature of space' is a mathematical construction of Einstein's general relativity. In reality Space is not curved, instead, the mass-energy density of space varies dependent upon the nearby proximity of matter (SSWs), and this causes a variation in the velocity of waves/light (as the central Principle of the WSM states) which is the cause of the curved path of matter and light in Space. This slowing of waves in higher mass-energy density of Space is the cause of gravity and explains, for example, why light curves past the sun, and why the earth orbits the sun.

Now it seems that many people do not correctly understand the meaning of the four dimensional space-time continuum, but it simply means that three spatial dimensions and a time dimension are required to define the motion of bodies and the path of light in three dimensional Space.

The non-mathematician is seized by a mysterious shuddering when he hears of 'four-dimensional' things, by a feeling not unlike that awakened by thoughts of the occult. And yet there is no more common-place statement than that the world in which we live is a four-dimensional space-time continuum. Space is a three-dimensional continuum. ... Similarly, the world of physical phenomena which was briefly called 'world' by Minkowski is naturally four dimensional in the space-time sense. For it is composed of individual events, each of which is described by four numbers, namely, three space co-ordinates x, y, z, and the time co-ordinate t. (**Einstein**, 1954)

Einstein is absolutely correct, if we wish to define the location of successive Wave-Centers (motion of ‘Particle’) of the In-Waves of a Spherical Standing Wave in Space then we require Three Dimensions for the Spherical Wave Structure in Space, and One Dimension for the Motion of the Waves. Thus we could number the Spherical In-Waves 1,2,3,4 ... counting out from the center, and thus plot successive Wave-Centers for each successive In-Wave (e.g. (x1,y1,z1,1) (x2,y2,z2,2)) and these four dimensional plots would describe the apparent motion of the Wave-Centers (‘Particle’) through Three Dimensional Space. (Thus we see how Time is caused by Wave Motion).

It is important to realize though, that Matter's Curvature of the 'Four Dimensional Space-Time Continuum' is Only Mathematically True. For Matter moving past a massive body in Three Dimensional Space (e.g. an asteroid moving past the Earth) then it is the relationship between the high mass-energy density of space of the Earth, which slows the In-Wave-Velocity (and shortens the Wavelength and stretches the Spherical In-Waves into an Ellipsoidal Shape) that causes the Resultant Wave-Center's of the asteroid to Move in a Curved (Accelerated) Path (which Einstein Mathematically and correctly Describes using Four Dimensions of Space and Time, as is necessarily required to determine the Motion of an object in Three Dimensional Space!).

But the path (of general relativity) was thornier than one might suppose, because it demanded the abandonment of Euclidean geometry. This is what we mean when we talk of the 'curvature of space'. The fundamental concepts of the 'straight line', the 'plane', etc., thereby lose their precise significance in physics. In the general theory of relativity the doctrine of space and time, or kinematics, no longer figures as a fundamental independent of the rest of physics. The geometrical behaviour of bodies and the motion of clocks rather depend on gravitational fields which in their turn are produced by matter. (**Einstein**, 1919)

Now this is very important, for it is this 'curvature' that largely led to Einstein's early fame. As we have explained, the measurable properties affected by the presence of spherically spatially extended Matter in Space is that the path of nearby light and matter is caused to be curved. It was the prediction by Einstein that light curved as it grazed the sun (subsequently confirmed by observation during a solar eclipse on the 29th May 1919) that resulted in his General Theory of Relativity becoming widely accepted and very famous! Just like an asteroid, the curved path of light is simply caused by the higher mass-energy density of space near Matter and the resultant slower Wave-Velocity. Einstein is largely correct when he writes;

The particle can only appear as a limited region in space in which the field strength / energy density is particularly high.

But we now understand his error of representing matter as spherical force fields and realize that it is actually the Wave-Amplitude and mass-energy density of space of Spherical Standing Waves in Space which is particularly high at the Wave-Center/’Particle’. His general principle is correct though, matter does determine the geometric properties of Space;

According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. (Albert Einstein)

Thus very tiny differences of Wave-Medium Density occur near very large
masses such as the Sun due to this cumulative effect of many trillions of
high mass-energy density of space Wave-Centers. This increasing mass-energy density of Space slows
the velocity of the wave fronts and causes them to curve slightly when passing
massive bodies like our sun.

Further, an infinite Space that has matter distributed uniformly must be 'flat' rather than ‘curved’ when considered over large scales of distance.

As our finite spherical universe is part of this infinite Space then this uniform distribution of matter (on the large scale) explains our 'flat' universe. In the derivation of Newton's Law of Inertia, the finite range of matter whose Out-Waves contribute directly to our In-Waves, and thus contribute to our inertial mass, required that the density of matter have the value **3H ^{2} / 8piG**, (See Wolff references) that is, of a 'flat' universe in general relativity.

We begin with a very nice (and important) quote from Halton Arp on Einstein’s famous ‘Cosmological Constant (which is really just an assumed anti-gravity force);

Like most people, I grew up with the received wisdom that
Einstein's General Relativity was so profound and complicated that only
a very few people in the world understood it. But eventually it dawned on
me that the essential idea was very simple, and it was only the elaboration’s
that were complicated. The simplest mathematical expression of General Relativity
is; G = T

The T represents the energy and momentum of a system of particles. In order to describe their behaviour in great generality, they are considered to be in a space whose geometrical properties (e.g.. curvature of space-time) are described by G. Now the solution to this equation tells us how these particles behave with time. The important feature of this solution is very simple to visualize, either the initial energy is large and the ensemble continues to expand or the energy is small and the ensemble collapses under the force of gravity. This is the unstable universe which distressed Einstein and caused him to introduce the cosmological constant (a special energy term) which just balanced the universe.

But in 1922 the Russian Mathematician, Alexander Friedmann, put forth a solution in which the spatial separations of the particles expanded with time. At first reluctant, Einstein later embraced the expanding universe solution so enthusiastically that he renounced his cosmological ‘fudge factor’ as ‘the greatest blunder of my life’. The Lundmark-Hubble relation was in the air at the time, and it seemed an ideal synthesis to interpret the redshifts of the extragalactic nebulae as the recession velocity of their expanding space-time reference frame. But basically, the theory was that the galaxies at our time were expanding away from each other, and therefore must have all originated in a ‘Big Bang’- that is, the universe was created instantaneously out of nothing. (**Arp**, 1998)

Let us now consider Einstein's thoughts on the subject of his famous Cosmological (Anti-Gravity) Constant;

My original considerations on the Structure of Space According to the General Theory of Relativity were based on two hypotheses:

1. There exists an average density of matter in the whole of space (the finite spherical universe) which is everywhere the same and different from zero.

2. The magnitude (radius) of space (the finite spherical universe) is independent of time.

Both these hypotheses proved to be consistent, according to the general theory of relativity, but only after a hypothetical term was added to the field equations, a term which was not required by the theory as such nor did it seem natural from a theoretical point of view ('cosmological term of the field equations'). (**Einstein**, 1952)

Einstein is largely correct with his two hypotheses - his problem was that he had to assume that the universe was finite and spherical (because of Mach's Principle and that matter’s mass is finite), and this necessarily meant that gravity would cause it to collapse upon itself. Thus he required a 'cosmological constant' (effectively a repulsive or anti-gravitational force) to prevent the matter in a finite spherical universe from collapsing upon itself.

With the WSM though, we realize that our finite spherical universe is in fact only part of an infinite Space that continues to be filled with an average distribution of matter. Thus this matter external to our universe gravitationally attracts our matter and thus prevents the matter in our universe from collapsing.

This explains Einstein's need for a cosmological constant - but it is not a gravitationally repulsive force as Einstein imagined (and which we do not observe), rather, it is simply the normal gravitational attraction of matter outside our finite spherical universe which prevents our universe from collapsing.

But as chance would have it Einstein found another explanation and thus famously renounced his cosmological constant as ‘my greatest mistake’. As it turns out, this error has led to 80 years of confusion, and to the rather mystical belief that our universe arose from nothing (no Space or Time) in a 'Big Bang' about fifteen billion years ago. In hindsight it is now clear to us that the 'Big Bang' theory is a human construction which satisfies our natural human instincts for spiritual/mystical (creation) explanations of things we don't yet understand.

So let us now further explain how the chance discoveries of others led
to this error, and in so doing finally move beyond creation theories and
realize that the spatial world we see around us is what exists - and has
always existed.

Einstein continues his argument;

Hypothesis 2 (a static finite spherical universe which requires a repulsive cosmological constant to prevent it collapsing) appeared unavoidable to me at the time, since I thought that one would get into bottomless speculations if one departed from it.

However, already in the 'twenties, the Russian mathematician Friedman showed that a different hypothesis was natural from a purely theoretical point of view. He realized that it was possible to preserve hypothesis 1 (average density of matter) without introducing the less natural cosmological term into the field equations of gravitation, if one was ready to drop hypothesis 2. Namely, the original field equations admit a solution in which the 'world radius' (radius of the finite spherical universe) depends on time {expanding space}. In that sense one can say, according to Friedman, that the theory demands an expansion of space. (**Einstein**, 1952)

So Einstein realized that if the universe was expanding (i.e. remove hypothesis 2) then there was no longer any need for his cosmological constant to prevent the universe from collapsing. Now initially Einstein had rejected this idea, but then a remarkable coincidence occurred which caused him to change his mind, and led to the current confusions of Cosmology. Einstein continues;

A few years later Hubble showed, by special investigation of the extra-galactic nebulae, that the spectral lines emitted showed a red shift which increases regularly with distance of the nebulae. This can be interpreted in regard to our present knowledge only in the sense of Doppler's principle, as an expansive motion of the system of stars in the large - as required, according to Friedman, by the field equations of gravitation. Hubble's discovery can, therefore, be considered to some extent as a confirmation of the theory. (**Einstein**, 1952)

One thing that is very interesting (and disturbing) is how knowledge gets corrupted over time. This particularly applies to the idea that '**Hubble discovered that the universe was expanding**'. He did no such thing, **Hubble discovered a relationship between redshift and distance **- one possible cause of this is the Doppler shift due to matter moving away from other matter (an expanding universe). Now this is a profoundly different thing to say, and yet it is simply amazing as to the number of respected scientists who say that Hubble discovered that the universe was expanding (which is not science!) As Eric Lerner correctly notices;

In one of its several variations the big bang cosmological theory is almost universally accepted as the most reasonable theory for the origin and evolution of the universe. In fact, it is so well accepted that virtually every media article, story or program that touches on the subjects of astronomy or cosmology presents the big bang (BB) as a virtual proven fact. As a result, the great majority of the literate populace of the world, including most of the scientists of the world, accepts big bang theory (BBT) as scientific fact. (**Lerner**, 1991)

It should be pointed out that Hubble himself was not convinced that red shift was exclusively due to Doppler effect. Up to the time of his death he maintained that velocities inferred from **red shift measurements should be referred to as apparent velocities**.' (**Mitchell**, 1997)

Below we quote a few scientists who have made this error, simply because we wish to strongly make the point about how we begin to assume things to be true, above and beyond what the observation tells us;

About 1929 the American astronomer Hubble demonstrated the existence of a strange correlation **between distance and speed of the nebulae: they all move outwards, away from us, and with a velocity which increases proportional to the distance**; or, in other words, the system of the spiral nebulae is expanding - just as the primitive comparison of this system with a gas had suggested to earlier thinkers. Now if one regards the expansion to have been the same in the past as it is today, one is led to the idea that the whole system must have had a beginning when all matter was condensed in a small 'supernucleus,' and one can calculate the time interval since this 'beginning of the world' and the present instant. The result obtained from Hubble's data was 2000 to 3000 millions of years.

Meanwhile the relativistic cosmology initiated by Einstein and De Sitter began to ripen in the hands of Friedmann, Lemaitre, Tolman, Robertson and others. A series of new possible models of the world were discovered between the extreme cases found by Einstein and De Sitter, and the question arose which of them fitted the empirical facts best, in particular those facts established by Hubble. Today there are many ramifications and refinements of the theory and there has been so enormous an increase of observational material that it is difficult to judge the actual situation. **Earlier ideas which seemed to be most fertile have turned out to be too narrow or even wrong**. (**Born**, 1964)

In the years following his proof of the existence of other galaxies, Hubble spent his time cataloguing their distances and observing their spectra. At that time most people expected the galaxies to be moving around quite randomly, and so expected to find as many blue-shifted spectra as red-shifted ones. It was quite a surprise, therefore, to find that **most galaxies appeared red-shifted: nearly all were moving away from us!** More surprisingly still was the finding that Hubble published in 1929: even the size of a galaxy's red shift is not random, but is directly proportional to the galaxy's distance from us. Or, in other words, the farther a galaxy is, the faster it is moving away! And that meant that the universe could not be static, as everyone previously thought, but is in fact expanding; the distance between the different galaxies is growing all the time.

**In 1929, Edwin Hubble made the landmark observation that wherever you look, distant galaxies are moving rapidly away from us**. In other words, the universe is expanding. This means at earlier times objects would have been closer together. .. Hubble's observations suggested that there was a time, called the big bang, when the universe was infinitesimally small and infinitely dense. (**Hawking**, 1988)

Only after the astronomer Edwin Hubble had studied the motions of galaxies and independently discovered that the universe was expanding. (**Wertheim**, 1997)

I am quite simply amazed that these good scientists can write such loose 'science'. Hopefully this will be an important lesson to Humanity – that we must always distinguish between empirical observations - and theories / interpretations founded on those observations!

Unfortunately for Einstein, and for science in general, they did not possess the correct knowledge of how matter finitely exists within an Infinite Space. If they had then they would have realised two profound things;

i) That Einstein’s Cosmological Constant is largely correct, but is caused by the gravitational forces of matter outside our finite spherical universe which prevent our universe from gravitationally collapsing.

ii) Thus there is no need for an expanding universe, and then they would have realised, from the correct WSM, that the redshift is caused by decreasing Wave interactions with distance.

Explaining Einstein's Finite Universe

with the Spherical Standing Wave Structure of Matter

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"When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter. ...

Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning. ... The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high. ...The

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