Cosmology
The Metaphysics of Space and the Wave Structure of Matter (WSM) explains how our Finite Spherical Universe Exists within an Infinite Eternal Space

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. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them. (Albert Einstein, 1918)

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. (Albert Einstein, 1954)

And since, as history abundantly shows, people's views of the universe are bound up with their views of themselves and of their society, this debate has implications far beyond the realm of science, for the core of the cosmological debate is a question of how truth is known. How these questions are answered will shape not only the history of science, but the history of humanity. The emerging revolution in science extends beyond cosmology. Today the study of the underlying structure of matter, particle physics, is intimately tied up with cosmology - the structure of the universe, theorists argue, is the result of events in the first instants of time. If the Big Bang hypothesis is wrong, then the foundation of modern particle physics collapses and entirely new approaches are required. Indeed, particle physics also suffers from an increasing contradiction between theory and experiment. Equally important, if the Big Bang never occurred our concept of time must change as well. Instead of a universe finite in time, running down from a fiery start to a dusty, dark finish, the universe will be infinite in duration, continuously evolving. (Lerner, 1992)

I live in hazard and infinity. The cosmos stretches around me, meadow on meadow of galaxies, reach on reach of dark space, steppes of stars, oceanic darkness and light. There is no amenable god in it, no particular concern or particular mercy. Yet everywhere I see a living balance, a rippling of tension, an enormous yet mysterious simplicity, an endless breathing of light. And I comprehend that being is understanding that I must exist in hazard but that the whole is not in hazard. Seeing and knowing this is being conscious; accepting it is being human. (Fowles, 1964)


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Introduction: WSM Cosmology

I realise that there are a lot of links (above) that go to headings on this page! However, the Wave Structure of Matter (WSM) Cosmology, being founded on One thing existing (Space), is actually very simple sensible and logical once known. I have just broken the page up into a number of smaller parts to try and make it easier to follow (so don't be put off).
With respect to the Big Bang Theory of Cosmology (which many Scientists now believe is wrong) there is another page on our website that has three very good articles from famous 'dissident' Scientists Halton Arp, Eric Lerner and William Mitchell. Please see; Problems / Errors of the Big Bang Theory of Cosmology

A Very Short Summary of the WSM Cosmology

When we look around us in space we see that we are surrounded by other matter (planets, stars, galaxies, galaxy clusters, etc.). The WSM cosmology deduces that this is true wherever you are in infinite space. However, we only see a finite region of infinite space and other matter, which we call the finite spherical universe. i.e. WSM cosmology is founded on the most simple solution - describing an infinite eternal space full of matter, but matter only interacts with other matter in a finite spherical region of space (which we call universe).

This Differs from the Big Bang Theory in Two Ways

1. WSM cosmology describes an infinite eternal perpetual system. There is no beginning or end to space and its wave motions that form matter.

2. While the universe is still finite, in the Big Bang theory the universe is all there is, whereas in WSM cosmology the finite spherical universe is just part of infinite space.

What does the Wave Structure of Matter (WSM) Cosmology Explain?

1. The universe does not gravitational collapse, as it is surrounded by other matter in infinite space. This is the equivalent of Einstein's Cosmological / Antigravity constant, but it is just normal gravity of matter outside our finite spherical universe within infinite space. This negates the need for an expanding universe.

2. Mach's principle (the mass of a body is determined by all other matter in the universe) is deduced for the first time. A common question asked of the spherical standing wave structure of matter is;
"Where do the In-Waves come from that form our matter?".
The answer is simple, from the Out-Waves of all the other matter around us within our finite spherical universe (which is a direct consequence of Huygens' Principle). Thus our mass / mass-energy density is finite because it is determined by a finite amount of other matter. See the Equation of the Cosmos (link to heading on this page).

3. Most significantly, this also deduces the redshift with distance as being caused by decreasing wave interactions with distance (rather than as a Doppler shift due to an expanding universe). See;
The Cosmological-Redshift Explained by the Intersection of Hubble Spheres
This article shows that each wave center 'particle' is the center of its finite spherical universe (Hubble Sphere), thus as two wave center 'particles' move apart there is less overlap of common spheres / universes, thus less wave interactions, thus less energy exchange, thus redshift with distance.

4. The Cosmic Microwave Background Radiation (CMBR) is sensibly explained due to radiation from cold matter in interstellar space.

5. Finally, the WSM cosmology predicts that motion of distant galaxies will behave as if there is matter all around them, whereas in the big bang cosmology there would only be matter on one side (the inside, as there is no 'outside').

Basically summarised - the current big bang definition of universe is 'all that exists' which is finite. IN WSM it is more correct to define universe as 'all that we can see and interact with', which is finite, whereas Space itself is 'all that exists' and is infinite. So effectively each wave center 'particle' is the center of its own finite spherical universe as part of infinite space.

The Wave Structure of Matter is the most simple science theory of reality and it clearly works (so it would be strange to dismiss this WSM Cosmology, given that it matches empirical facts very well).
The only difficulty is that it is new, and most people have been brought up with 'particle' physics and the Big Bang theory, so it takes a while for our minds to adjust to this new way of seeing things. But the Wave Structure of Matter in Space is simple, sensible and obvious once known.
Geoff Haselhurst.


Metaphysics: Reality & Cosmology must be Founded on One Thing Infinitely & Eternally Existing

While this may surprise some people, both ancient Indian and Greek Philosophy & Metaphysics realised that matter interacts with ALL other matter in the Universe, thus there is clearly a connection between the Structure of Matter and the Structure of the Universe. The roman stoic philosopher king, Marcus Aurelius explains this beautifully, though many philosophers and mystics have realised this interconnection of matter within the One Universe (which is the founding principle of ancient Greek & Indian Philosophy).

Frequently consider the connection of all things in the Universe. ... Reflect upon the multitude of bodily and mental events taking place in the same brief time, simultaneously in every one of us and so you will not be surprised that many more events, or rather all things that come to pass, exist simultaneously in the one and entire unity, which we call the Universe. ... We should not say ‘I am an Athenian’ or ‘I am a Roman’ but ‘I am a Citizen of the Universe'. (Marcus Aurelius, 170AD)

All things come out of the one, and the one out of all things. (Heraclitus, 500BC)
All phenomena, link together in a mutually conditioning network. (Buddha, 500BC)
Though One, Brahman is the cause of the many. (Rig Veda, 1200BC)
When the Ten Thousand things are viewed in their Oneness, we return to the Origin and remain where we have always been. (Sen T'sen)

Likewise, Western Philosophy and Physics has come to the same conclusion, as Leibniz, Bradley and Smolin write;

Leibniz (On Metaphysics / Cosmology) - Reality cannot be found except in One single source, because of the interconnection of all things with one another. (Leibniz, Monadology, 1670) cannot be found except in One single source, because of the interconnection of all things with one another. ... I maintain also that substances, whether material or immaterial, cannot be conceived in their bare essence without any activity, activity being of the essence of substance in general. (Leibniz, )

Bradley. On Metaphysics and Unity of Cosmology / Universe. (Bradley, 1846-1924) We may agree, perhaps, to understand by Metaphysics an attempt to know reality as against mere appearance, or the study of first principles or ultimate truths, or again the effort to comprehend the universe, not simply piecemeal or by fragments, but somehow as a whole.

Cosmology: Interconnection of all matter in finite spherical universe(Lee Smolin, 1997) It can no longer be maintained that the properties of any one thing in the universe are independent of the existence or non-existence of everything else. It is, at last, no longer sensible to speak of a universe with only one thing in it.

This is of course fundamentally important to our understanding of what Matter is, what the Universe is, and what Space is. It is the purpose of this article to explain the solution to the problem of understanding this interconnection between our Matter (the Many Finite Things), our Universe (the One Finite Thing), and Space (the One Infinite Thing).

Currently, Cosmology is obscured by an incorrect belief in the ‘Big Bang’ - that the universe is expanding, and thus had a beginning at some time in the past. As we shall explain, this is not correct, for the simple reason that the observed ‘Hubble’ redshift with distance is NOT caused by a Doppler shift due to receding Motion / expanding Universe, but rather, is caused by diminishing Wave Motion interactions with distance.
(This is explained in detail below, but quickly summarised, as reality must be founded on One thing existing (Space), there can be no expansion or creation of Space, Space simply exists, Infinite and Eternal. In fact the Wave Structure of Matter explains that Time is Caused by wave Motion, thus only Matter in Space, as the Spherical Wave Motion of Space, experiences Time. Space is Eternal (does not experience Time) thus it cannot be ‘created’.)

Again, both ancient Indian and Greek Philosophy correctly realised that something is never created from nothing ‘ex nihilo’, thus something has eternally existed;

Without beginning or end (through eternity) this world has continued to exist as such. There is nothing here to be questioned. In no place or time was this world ever observed otherwise by anybody in the past, nor will it be, in the future. (Madhva, 1250AD)

Alternatively, suppose we were to accept the mythical genesis of the world from night or the natural philosophers' claim that 'all things were originally together.' We are still left with the same impossible consequence. How is everything to be set in motion, unless there is actually to be some cause of movement? Matter is not going to set itself in motion - its movement depends on a motive cause. (Aristotle, 340BC)

Unfortunately, the 'Big Bang' theory for the creation of our Universe is now well established, and many careers are founded on this concept. Thus it is natural that the emerging school of ‘dissident’ scientists who disagree with this theory will cause conflicts within the academic world that, sadly, often have little to do with determining the truth. While I do not wish to become embroiled in this debate, nonetheless, as philosophers of science we are bound to follow the truth, as Tolstoy wrote;

Wrong does not cease to be wrong because the majority share in it. (Leo Tolstoy)

And from this most simple foundation of One thing, Space, existing as a Wave Medium it becomes obvious that the belief in a ‘Big Bang’ is founded upon a basic error, and that once the truth is realised then we find that all the problems and paradoxes of modern Cosmology are solved simply and sensibly. (See essays on the problems of the 'Big Bang' theory by 'dissident' scientists; Halton Arp, Bill Mitchell, and Eric Lerner.)

This Cosmology article has been written with the aid of quotes from two fine scientists;
i) Albert Einstein and his General Relativity, which founds modern Cosmology.
ii) Eric Lerner, who has a very good historical and philosophical understanding of Science, Cosmology, and their effects upon society. His work is important because it shows how Einstein's ideas have evolved and been interpreted by modern science over the past 80 years.

Brief Summary of The Wave Structure of Matter

Summary of Contents

I have started this page (below) with a brief summary of the Wave Structure of Matter Cosmology, and due to the errors of Big Bang Cosmology we find that it is also necessary to redefine the concept 'Universe'. This is followed by an explanation of how the Spherical Standing Wave Structure of Matter determines the size of our Finite Spherical Universe within an Infinite Space. From this foundation we then calculate the ‘Equation of the Cosmos’ and show how this correctly deduces the Hubble Redshift with distance (without assuming an expanding Universe). This is then followed by a very well written essay from Lerner which explains Einstein's profound influence on modern Cosmology and Society. We then return to Einstein’s ideas, and with some minor corrections, show how this new metaphysical foundation for Cosmology (an Infinite Eternal Cosmology) solves the major Problems of the current Big Bang Cosmology (that cause such conflict and confusion).

Geoff Haselhurst, Email


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Brief Summary of the History of Cosmology

I recently received a letter about this page which made the following interesting point;

I am a bit reluctant to include any of the anti big bang stuff you include here. This is not only because I have not had time to ponder it in detail. The thing that worries me most is that I thought that Einstein once described his cosmological constant as his biggest blunder. Is this true? Was he fooled by the arguments of others?

Here I shall make a brief reply to these comments, founded on the Wave Structure of Matter. The article which then follows provides a very comprehensive summary of Cosmology and a solution to most of the fundamental problems. (So you can skip this if you want.)

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 (and this will be explained in detail below, and thus will make more sense if you persevere!)

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.

I realise that some of this will not make much sense to you at first. I am sure though, that after reading on the Wave Structure of Matter, you will find it to be actually very simple and sensible in how it explains and solves many of the problems of Cosmology.

Defining 'Universe'

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!).


The following short section is taken from a letter I wrote to a (very nice) woman who has been studying the WSM Cosmology. Hopefully it helps clarify the above comments about the meaning of our Finite Spherical Universe within an Infinite Space.

When people first consider the Wave Structure of Matter there seems to be this common mistake of thinking of one wave-center / spherical standing wave on its own in infinite space (which is clearly not how reality is, as there is obviously matter all around us). That thought leads to imagining the spherical standing wave structure as infinite.

However, the correct way of thinking (since it matches reality of what we experience), is that the space around us has lots (and lots!) of other matter. And calculations show that wherever you are in an infinite space (as a wave-center) YOU ONLY INTERACT WITH A FINITE SPHERE OF THAT INFINITE SPACE AND OTHER MATTER (which we call universe). It is only this finite amount of other matter that directly contributes to your in-waves. i.e. Applying Huygens' principle - their out-waves combine to form our spherical in-waves. This is calculated in two different ways in the section on the Equation of the Cosmos: Deducing Finite Size of Matter and Universe and correctly deduces the observed size of our Universe.

This Equation of the Cosmos is very important, because it is basically solving the fundamental problem of the relationship between the Finite and the Infinite. i.e. How we can exist as part of Infinite Space, and yet only have a Finite Mass (mass-energy density). This then explains Mach's Principle - how all matter in our Finite Spherical Universe determines the mass (mass-energy density of space) of matter / space - and most importantly why that is finite (within an infinite space).

So we see that each wave-center 'particle' is really the center of its own universe. (We are each the centers of our own universe - what a nice thought). And this applies to any matter, wherever you are in an infinite space. So effectively finite matter and universe are the same thing. Thus if you imagine infinite space, there is an infinite amount of matter in it, and thus an infinite number of finite spherical universes.

When matter is close to other matter, then its universes (in and out waves) overlap and you get matter interactions. For us, matter a 1,000 billion light years away is outside our Finite Spherical Universe and we can't interact with it / see it. It does not contribute its Out-Waves directly to our In-waves - it is hidden behind other matter.

So the Wave Structure of Matter Cosmology explains how we each exist as the center of our Finite Spherical Universe within an Infinite Space. I exist as the center of mine, you as the center of yours. But it just so happens that our centers are close together so we share 99.9999.........% of a common universe - which is why we can interact with one another, write to each other on the internet.

And if you think about it, you will realise that this must also cause a redshift with distance, because distant matter shares less of a common universe, thus less wave interactions, thus less energy exchange (which we see as a redshift with distance). Any smart mathematicians here can deduce this - just work out how the volume of two overlapping spheres changes as you move them apart - this should equate to redshift with distance (another meaningful deduction from the WSM - though i should add that there may be other factors affecting redshift, certainly the work of Halton Arp suggests there are).

This also explains another central and profound problem of Cosmology - why our Finite Spherical Universe does not gravitationally collapse. In an Infinite Space it is obvious that matter outside our Finite Spherical Universe, due to its gravitational forces, prevents our finite sphere of matter / universe from gravitationally collapsing. This then removes the need for both an expanding universe (which led to the idea of the Big Bang), or Einstein's antigravity / cosmological constant (which, is really just a gravity force from matter outside our Finite Spherical Universe within Infinite Space). So Einstein was close to the truth with his Cosmological Constant!


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

One Principle of the Wave Structure of Matter
On What Exists and its Properties

One Thing Space Exists with the Properties of a Wave-Medium

The Formation of Matter from Waves in Space

Matter Exists as Spherical Standing Waves in Space.
The ‘Particle’ Effect of Matter is Caused by the Wave-Center of the Spherical Standing Waves. (See Fig. 1)

Represents Spherical In-Wave (our future) flowing In to form the Wave-Center (our present) + Represents Spherical Out-Wave (our past) flowing Out of the Wave-Center (our present) = Combined In-Waves and Out-Waves form a Spherical Standing Wave about the Wave Center (our present). This explains the particle / wave duality of Matter. Matter is a Spherical Standing Wave - the Wave-Center causes the 'particle' effect of matter.

Fig 1. This (very rough) diagram shows how the Spherical In and Out Waves form a Standing Wave around the Wave-Center 'particle'.

The Properties of Space

i) Space, as One things existing, is necessarily Infinite, Eternal and Continuous (there are no 'particles').

ii) The velocity of Waves in Space is the Velocity of Light c.
This Wave Velocity is not constant and is determined by both the Wave Amplitude and mass-energy density of Space. i. e.
High Wave Amplitude Waves Propagate with a Faster Wave Velocity. (e.g. waves on water). This is the cause of Charge.
High mass-energy density Space causes a Slower Wave Velocity. (e.g. curvature of light near Sun). This is the cause of Gravitational Mass.

The Properties of Matter (Forces and Size of Matter)

i) Any Change in Velocity of the Spherical In-Waves from One Direction changes where these In-Waves meet at their respective Wave-Center which we see as a 'Force Accelerating a Particle'.
This is the Cause of Force = Mass * Acceleration. (See Fig. 2)

ii) The Spherical In-Waves are formed from the Huygens' Combination of Out-Waves from All other Matter in our Finite Spherical Universe. (See Fig. 3)
This is the Cause of Mach’s Principle: Matter's Mass (mass-energy density) is Determined by all other Matter in the Universe.

Fig. 2 Gravity is Caused by the Slowing of the In-Waves. In fact ALL forces are caused by a change in velocity of the In-Waves which changes the location of the Wave-Center, and which we observe as the accelerated motion of the 'particle'

Fig. 3 Huygens’ Principle explains how our In-Waves are created by other Matter’s Out-Waves

The remainder of this article is deduced from this One Principle (thus it is necessary and certain, not our opinion) and we are assuming that the reader understands these metaphysical principles and their importance to the Scientific Method (Physics, Philosophy, Metaphysics). We should also add that this central Principle of the Wave Structure of Matter not only explains and solves the problems of Cosmology, but also Einstein's Relativity and Quantum Theory, and thus unites these three famous subjects for the first time. (I know this is a big claim, but you can determine this for yourselves.)


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Space is Infinite Eternal and Continuous

The following two quotes describe an Infinite and Eternal Space very well. And to all scientists it must be both disturbing and sad to realise that it was only 400 years ago that Bruno was burnt to death for writing such things!

In his major work, paradoxically entitled On Learned Ignorance, Nicholas returned to the central idea of Anaxagoras - an infinite, unlimited universe. In contrast to Ptolemy's finite cosmos circumscribed by concentric spheres with earth at their center, Nicholas argued that the universe has no limits in space, no beginning or ending in time.
Nicholas's infinite universe is populated by an unlimited number of stars and planets, and, of course, has no center, no single immobile place of rest. The earth, he reasoned, must therefore move, like everything else in the universe. It appears at rest only because we're on it, moving with it. He cast aside the geocentric cosmos entirely. (Nicholas of Cusa, a German-born bishop, born 1401)
Giordano Bruno traveled to England and befriended its leading political and scientific figures; and when he returned, he popularised Copernican theory on the continent. Bruno took Digges's version of the infinite, Copernican universe and purged it of remaining Ptolemaic elements, such as the perfect spheres that carried the planets' orbits. He made this infinite universe, with its infinite inhabited worlds, the basis of his philosophy, integrating Nicholas of Cusa's thinking, even going beyond it. Bruno explicitly challenged the idea of creation ex nihilo, arguing that the universe must be unlimited in both space and time, without beginning or end. (Lerner, 1991)

Space is Infinite

As only One thing, Space, exists, there can be no boundary to Space (as a boundary is between two things) thus Space is unbounded and therefore Infinite. As Blake famously wrote;

If the doors of perception were cleansed, everything would be seen as it is, infinite. (William Blake, 1800)

Both Parmenides and Spinoza perfectly state the logic of One Infinite Substance;

No two or more substances can have the same attribute and it appertains to the nature of substance that it should exist. It must therefore exist finitely or infinitely. But not finitely. For it would then be limited by some other substance of the same nature which also of necessity must exist: and then two substances would be granted having the same attribute, which is absurd. It will exist, therefore, infinitely. (Spinoza, 1673)

'Existent’ is indivisible, for where is the second power, which should divide it? .. But there cannot exist several 'Existents,' for in order to separate them, something would have to exist which was not existing, an assumption which neutralizes itself. Thus there exists only the eternal Unity. (Parmenides, 450BC)

Space is Continuous

There can be no ‘Particles’ because ‘Particles’ require two things - the ‘Particle’ and the Space around the ‘Particle’, thus One Infinite Space must be a continuous medium. Or as Aristotle says;

This shows us two things: you cannot have parts of the infinite and the infinite is indivisible.
But indeed even if the One is more like a Principle, and the one is undivided, then the whole Universe will be undivided either in quantity or in form. (Aristotle, 340BC)

Lerner also importantly argues for the necessary existence of a continuous Space and Time (and continuous Time is simply caused by the continuous Wave-Motion in a continuous Space);

All of modern analysis, including most of the mathematics underlying modern technology, relies on the concept of continuity - that between any two points in space, there is an infinite number of other points. In the same way, between any two points in time there is an infinite number of other moments. Without these assumptions it's virtually impossible to use modern mathematics in a logically consistent way.
Indeed, the idea that space and time are infinitely divisible is vital to explaining the very existence of the irreversible time of the real world. Without such true infinities the world would be a vast digital computer, each instant predetermined by its initial state, without a past, present or future. So to argue that there is no true infinity, ... is tantamount to a rejection of modern mathematics, the technology based on the use of the mathematics, and the new discoveries in thermodynamics.
And once we accept the continuity of space and time it's hard to object on philosophical grounds to an infinite extent of space and time.
Thus while the idea of an infinite chain of cause and effect may appear mind-boggling, such an infinite chain exists even in the present, with each passing second- each an infinity of moments. To accept an infinite past is no more or less difficult philosophically than to accept the continuity of time - the infinity of moments in a single second.
While these conclusions are not commonsensical, they are logically consistent. … if an infinite universe is rejected philosophically, the infinity of space in a single inch or the infinity of instants in a single second must be rejected as well, along with all the science based on the hypothesis of continuity. (Lerner, 1991)

Space is Eternal

There are two separate arguments for an Eternal Space which support one another;
i) As only one thing, Space, exists, there can be no creation of Space as creation requires two things (Space, and that which is not Space but created Space) thus Space is Eternal. As Spinoza writes;

A substance cannot be produced from anything else: it will therefore be its own cause, that is, its essence necessarily involves existence, or existence appertains to the nature of it. (Spinoza, 1673)

ii) As we explained earlier, Time is a consequence of the Wave Motions of Space, and that it takes ‘Time’ for Wave Motions to flow from place to place in Space. Time does not exist as a thing in itself, it is, like the ‘Particle’, an effect of the Wave Motion of Space, not a cause! Thus Time only applies to Matter, as the Spherical Wave Motion of Space and not to Space itself. Therefore Space was not created for this requires the concept of time (that the Space that now exists was created at some time in the past) thus Space is Eternal. (Space simply exists.) As Aristotle correctly writes;

It need hardly be pointed out that with things that do not change there is no illusion with respect to time, given the assumption of their unchangeability. (Aristotle, 340BC)

Motion is Eternal

Aristotle also realised that Motion cannot come from no Motion, thus Motion must always exist. He also realised the close connection between Time and Motion!

Motion must always have been in existence, and the same can be said for time itself, since it is not even possible for there to be an earlier and a later if time does not exist. Movement, then, is also continuous in the way in which time is - indeed time is either identical to movement or is some affection of it. (Aristotle, 340BC)


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

How Our Finite Spherical Universe Perpetually Exists Within an Infinite Space

Can we visualize a three-dimensional universe which is finite yet unbounded? (Einstein, 1921)

In fact it is possible for a finite spherical Universe to form within an Infinite Space. Unfortunately for Einstein, he incorrectly imagined a 'curved space' such that if you traveled far enough you would return to your starting point (a very abstract and confusing concept). The solution is in fact far more simple, and is found instead from Huygens' Principle, and to realise that other Matter's Out Waves create our Matter's In-Waves (as we shall now explain in more detail).
Three hundred years ago Christiaan Huygens, a Dutch mathematician, found that if a surface containing many separate wave sources was examined at a distance, the combined separate waves of the sources appeared as a single wave front with the shape of the surface. This wave front is termed a 'Huygens Combination' of the separate waves.
As stated by the central Principle of the Wave Structure of Matter, this explains how the In-Waves are formed.
Begin with the Spherical Out-Wave which travels outward from an initial Wave-Center. When the Out-Wave encounters other Wave-Centers in the universe then its Out-Wave effectively becomes part of the In-Waves of these other Wave-Centers. Conversely, when the Out-Waves of these other Wave-Centers in Space flow into the initial Wave-Center they effectively become part of its In-Waves. Effectively the Out-Waves of other SSWs (spherically distributed in the Space around us) have combined to form a Huygens’ combination wave front which forms the Spherical In-Wave of our Wave-Centers. (See Fig: 3.2.1 below)

Although we can imagine each SSW separately as a pair of In-Waves and Out-Waves, that SSW cannot exist without the presence of other SSWs in the Space around it. It cannot exist alone because each SSW depends on other SSWs in the Space around it to create its In-Waves. Thus Smolin is correct;

It can no longer be maintained that the properties of any one thing in the universe are independent of the existence or non-existence of everything else. It is, at last, no longer sensible to speak of a universe with only one thing in it. (Smolin, 1997)

Fig. 4 Huygens Combination and the Formation of the In-Wave of a Spherical Standing Wave (SSW). This diagram was constructed by drawing twelve circles whose centers are themselves located on a circle, such that their circles have begun to form the circle you can see at the center. Likewise with Spherical Standing Waves, if many SSWs are spherically distributed in Space around us then their Out-Waves form the Spherical In-Waves of our Matter.

This Huygens' sharing of waves means that once you go out past a certain distance in Space (the size of our finite spherical universe) then you can no longer count the Out-Waves of this farther distant matter as direct contributors to our In-Waves, because these waves have already become part of closer Wave-Center's In and Out-Waves and thus have already been counted as contributing to our In-Waves. This sharing of waves is a profound discovery (Wolff, 1994) as it leads to the solution of the connection between the Infinite and the Finite, and correctly explains the cause of the redshift with distance. Briefly stated (as this is discussed a little later) this explains how we can have a finite Wave-Amplitude/Density (and thus a finite mass and energy for matter) within a finite spherical universe, and yet also be part of an infinite perpetual system of Waves in Space. As stated in the above Principle of the Wave Structure of Matter, this unites Huygens' Theory with Mach's Principle.

Cosmology - Finite Spherical Universe
Fig: 1.2.2 A Finite Spherical Standing Wave within an Infinite Space. The Out-Waves of the Spherical Standing Wave on the right (in red) must travel through (and have become part of) a closer Wave-Center and thus their Out-Waves have already been counted once and cannot be counted again as directly contributing to the In-Waves of the central SSW.

We see that this Finite Spherical Universe agrees with Einstein's logic on the Structure of the Universe as deduced from General Relativity. The quote is broken up into three parts;

i) Suppose we draw lines or stretch strings in all directions from a point, and mark off each of these the distance r with a measuring rod. All the free end-points of these lengths lie on a spherical surface. With increasing values of r, (the spherical surface) increases from zero up to a maximum value which is determined by the 'radius of the universe'
ii) but for still further increasing values of r, the area gradually diminishes to zero.
iii) At first, the straight lines which radiate from the starting point diverge farther and farther from one another, but later they approach each other, and finally they run together again at a 'counter-point' to the starting point. Under such conditions they have traversed the whole spherical space (of our finite spherical universe). (Einstein, 1916)

It is important to realize that Einstein does not explain what happens at the 'radius of the universe' that causes an expanding spherical surface to begin to contract. (Because he did not know!) The solution is now solved using Huygens' Wave Combinations as we have previously described. Thus;
i) Describes the Out Waves from the Wave-Center, these carry on going Out and become the In-Waves of distant Matter.
ii) Describes the In-Waves - but rather than still going Out these Waves are coming back In and have been formed by the Out Waves of all the other matter in our finite spherical Universe.
iii) Thus the point and the counter-point are united as the Wave-Center of Spherical Standing Waves the size of the Universe.
The 'Radius of the Universe' is the Sphere where the In-Waves (from distant Matter's Out-Waves) first form into a coherent Spherical In Waves, and this determines both the size of our Spherical Standing Waves, and thus the size of our Finite Spherical Universe within an Infinite Space.

Thus we realise that the Metaphysics of Space and Motion and the Wave Structure of Matter describes a perpetual finite system within an Infinite Eternal Space. Space has always existed, as have the Wave-Motions which flow through this Space. ‘Creation’, like ‘Particles’, ‘Time’ and ‘Forces’, are human constructions, concepts that in Reality do not exist.
Now it is necessary to explain, with a little basic mathematics, how we can now deduce the redshift with distance without assuming a Doppler shift due to receding Motion / an expanding Universe.


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

The Equation of the Cosmos
Deducing the Finite Size of Matter & Universe within an Infinite Space

So let us now explain, with a little basic mathematics, how we can now deduce the finite size of matter (which determines the size of our spherical universe) within an infinite Space. Imagine a clear balloon, and you had a 'marker pen' that could make black dots on the surface of the balloon. If you were patient you could cover the balloon in black dots until the balloon was completely black and no light could get inside the balloon. Thus if we know the size of our dots, and how many dots we are allowed to use, then we could calculate the surface area and size of the balloon such that all the dots would just cover the balloon and block out the light. This analogy is valid with our finite spherical universe within an infinite Space. The 'size of the balloon' is the size of our universe we wish to calculate. The size of our black dots is the size of the wave-centers ('particles'), the number of our black dots is the number of 'particles' in the universe. (We assume a 'particle radius Re = 10-14 and number of particles N = 1080 as consistent with current observations of matter in the universe.) Thus if we assumed that all matter in the universe was distributed on the surface of a sphere, such that the wave-centers completely filled this surface, then this means that the Out-waves of any more distant matter would not directly contribute to our In-waves as they must flow through (and become part of) one of these 'shielding' wave-centers, thus we have already counted their wave contributions. (While the real universe obviously has some matter closer and some farther out, this approximation is adequate for calculations.) Our equations are; Area of wave-center = pi Re2; area of N wave-centers = N pi Re2; the radius of a spherical universe that has this surface area is 4 pi R2 = N pi Re2; which reduces to the Equation for the Radius of our universe R;

The Equation of the Cosmos: 4 R2 = N Re2

Substituting in our values for N and Re we get a Radius of the universe R = 1026 m
Currently the classical calculation for the Hubble radius of the universe is 1026 m so the Metaphysics of Space and Motion and the Spherical Wave Structure of Matter has deduced the same value using the above simple assumption!
These simple calculations suggest that the redshift with distance is actually due to the decreased sharing of waves with distance (as we share less of a common spherical universe) and thus distant matter contributes less to our wave-amplitude and mass-energy density of space (the cause of our mass/energy) which we see as a redshift (energy decrease) with distance. This seems to be a most profound solution, for it explains and solves many of the current problems of Cosmology (as explained below) by finally solving the Problem of the Finite and the Infinite, how matter, with finite mass and spherical size, can perpetually exist in a finite spherical universe within an infinite Space.

Thus we see that logic from the Metaphysics of Space and Motion and the Spherical Wave Structure of Matter, demonstrate a different cause of the redshift with distance, based on diminishing Huygens' wave combinations with distance. Further, it confirms Mach's Principle, that our mass-energy density of space and Mass are determined by all the other matter in our finite spherical universe, as only their Out-Waves directly contribute to our In-Waves.

Let us then briefly examine the classical assumptions of an expanding Universe. The calculation of the Hubble Radius is fairly simple. Edwin Hubble observed that spectral lines in the light from different stars shift towards longer wavelengths (towards the infra-red) in proportion to the distance of the star from us, the observers. If the cause is assumed to be a Doppler shift due to the receding motion of the stars, then a receding velocity v can be calculated. A 'Hubble constant' H is then obtained from D = vH where D is the measured distance of the star.
The constant can be written as a distance R such that the expansion velocity has reached c, the velocity of light. If light travels the distance R, it will require time T, where R = cT, thus T is often assumed to be the age of the universe, after the imagined 'Big Bang'. R is called the 'Hubble Radius', and represents the largest distance from which we can receive information by light transmission if our cosmological age is T. Thus T = 1/H. Using current values for you get an age of the universe of about 10 billion years, and thus a radius of 10 billion light years = 1026 m.

Most Cosmologists would now be painfully aware of the many problems associated with this assumption of an expanding universe. As Einstein explains, one of the fundamental problems for the Big Bang relates to this ‘apparent age’ of our Universe;

There does arise, however, a strange difficulty. The interpretation of the galactic line-shift discovered by Hubble as an expansion leads to an origin of this expansion which lies 'only' about a billion years ago, while physical astronomy makes it appear likely that the development of individual stars and systems of stars takes considerably longer. It is in no way known how this incongruity is to be overcome. (Einstein)

While modern cosmologists have been able to stretch this time from the Big Bang out to about 10-15 billion years (with the help of a dubious ‘inflation theory’), at the same time they now theorize that large super galaxy clusters likely take 80 billion years to form. A fundamental problem, as Lerner writes;

Present evidence shows that the Big Bang, initially introduced to explain the Hubble expansion, does not make predictions that correspond to observation. It is clearly contradicted by Tully's observations of supercluster complexes and by the more recent confirmations of large-scale structures. This returns us to the problem: What caused the Hubble expansion? The cosmological debate will not be resolved until this basic question is answered.
The question of the Hubble relation remains unanswered, and other fundamental questions about the cosmos must also remain unanswered until an adequate theory is found. Far more theoretical and observational work is needed. (Lerner, 1991)

As we have explained though, the solution is quite simple - the Hubble Redshift is not caused by a Doppler shift due to the receding Motion of Matter in an expanding Universe, but rather, is due to this Huygens' sharing of waves, and thus a decreasing Wave Motion interaction with distance (there is less sharing of waves with distance as we share less of a common Spherical Universe) and thus distant matter contributes less to our Wave-Amplitude/Density (the cause of our mass and energy) which we see as a redshift (energy decrease) with distance.
This is a most profound solution, for it solves the remaining major problems of Cosmology (as explained below) by finally solving the Problem of the Finite and the Infinite, how our Matter, with finite mass and spherical size can perpetually exist in our Finite Spherical Universe within an Infinite Space.


Let us now show how Dr Milo Wolff (Mathematical Physicist who first formalised the Wave Structure of Matter) comes to the same conclusion as to the Equation of the Cosmos, but using a method more suitable to Mathematical Physics.
From: http://quantummatter.com/articles_html/body_point.html

Note: Milo Wolf uses the term Space Resonance (SR) to describe the Spherical Standing Waves (SSW) that form matter.

Mach's Principle

The unknown origin of Newton's law of inertia, F=dp/dt, has attracted frequent attention. Ernst Mach in 1883 boldly suggested that inertia depends upon the existence of the distant stars. His concept arises from two fundamentally different methods of measuring the speed of rotation.
First, without looking at the sky, one can measure the centrifugal force on a mass m and use Newton's Law in the form, F=mv2 /r, to find circumferential speed v. The second method compares the object's angular positions with the fixed (distant) stars. Mysteriously, both methods give exactly the same result. Mach reasoned that there must be a causal connection between the distant matter in the universe and inertia. He asserted: Every local inertial frame is determined by the composite matter of the universe. (This wave structure of the electron now proves that Mach was right.)

Assumption II - Establishing the Density of Space

The wave equation provided a structure which possesses some of the electron's characteristics but a means for the SRs to interact and exchange energy is also needed. Unfortunately, since waves in a homogeneous medium pass through each other, the medium has no means for interaction. To find the means of interaction, we recognize that space is not homogeneous everywhere. For example, it has been observed that a star will bend the path of light which goes near it. A similar behavior occurs at the center of a charged particle.

To examine this requirement we first make a quantitative assumption, similar to Mach's Principle, which establishes the density of space (ether or vacuum). Then we will examine the density formula seeking a means of interaction. The mass-energy density of space assumption is:

Assume that the mass (wave frequency) and propagation speed of an SR wave in space depends on the sum of all SR wave intensities in that space; a superposition of the intensities of waves from all particles inside the Hubble (H) Sphere of radius R = c/H, including the intensity of a particle's own waves.

mc2= hw= k' SUM OF:{(AMPn)2 x (1/rn2)}          (4)

In other words, the frequency w or mass m of a particle depends on the sum of amplitudes squared of all waves AMPn, from the N particles in the universe, whose intensities decrease inversely with range squared. That is, waves from all particles in the universe combine their intensities to form the total density of 'space'. This density determines the electron's wave frequency. This space corresponds to Einstein's 'aether' or quantum theory's 'vacuum.'

Now examine the homogeneity of the space. The universe contains so many particles that the density of space is nearly constant everywhere. But close to the center of an electron, the amplitude of an electron's own waves following the 1/r2 rule, is larger, producing a 'lump' in mass-energy density of space. This lump at the center of the electron causes wave interactions. It is the way energy is transferred and what we call 'charge'. Its correctness is tested below.

Energy Transfer Mechanism of the Space Resonance

How does the charge mechanism operate? It is well-known that a-c signals flowing through a non-linear element in a circuit will mix. That is, if there is a two-signal input:

INPUT = Acos(w1t ) + Bcos(w2t)

then the output will be:

OUTPUT = AB[ cos(w1t + w2t) + cos(w1t - w2 t ) ] /2 + other components

The non-linear element produces sum and difference frequencies of the original w1 and w2.

Similarly in space, different waves passing through the dense, non-linear region at the particle center will mix. If an input frequency and a particle frequency are similar, resonance can occur. An example of this is a tuned radio receiver. An energy (frequency) exchange between resonances behaves like two coupled oscillators in a circuit, or like two pendulums joined with a spring.

A Test of Assumption II

If an electron's own waves can create a denser region near its center, then the intensity I of those waves at some radius of non-linearity ro, must be comparable to the intensity of waves from all other N particles in the Universe. This requirement is written:

Intensity I = AMPo2/ro2 = SUM { AMPn2/rn2 } = N/V x INTEGRAL OF:{ AMPo/ro}2 4 pi r 2dr

where V is the volume inside the Hubble Sphere and R its radius. The integral, from r = 0 to R = cT = c/H, extends over a sphere whose expanding radius R depends on the age T of the particle. Thus T is the maximum range of the particle's spherical waves. This reduces to

ro2 = R 2/3N      (5)

Inserting values from astronomy measures, R = 1026 meters and N = 1080 particles, the critical radius ro equals 6 x 10-15 meter. If the assumption is right, this should approximate the classical radius rc = e2 /mc2of an electron, which is 2.8 x 10-15 meters. The two values almost match, so the prediction is verified. Apparently dense wave centers do exist, and

e2 / mc2 = R / SQUARE ROOT OF: {3N}         (6)

Equation (5) is a relation between the size ro of an electron and the size R of the Hubble Universe.
It is termed the

 


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Newton, Mach and Einstein's Infinite Mass Paradox

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.

The Birth Of The Big Bang

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 - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Mach's Principle
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=mv2/r to find circumferential speed v.
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.


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Einstein's Curvature of Four Dimensional Space-Time Continuum

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 3H2 / 8piG, (See Wolff references) that is, of a 'flat' universe in general relativity.


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Explaining Einstein's Famous Cosmological (Antigravity) Constant

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.


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

WSM Cosmology Predicts Motion of Distant Galaxies

Now this leads the Metaphysics of Space and Motion and the WSM to make a very important prediction:

That the motion of distant Galaxies behaves as if there is anti-gravity due to the gravitational influence of Matter outside our finite spherical universe.

With our increasing powers of observation of the distant universe perhaps it is already possible to confirm this! (Please feel free to Email us if you have any knowledge on this!)


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Solution of the 'Quantified' Hubble Redshift with Distance

It is useful to begin with some comments by Halton Arp, which clearly point out the problems of a quantised redshift with distance being caused by receding motion/expanding universe;

The fact that measured values of redshift do not vary continuously but come in steps - certain preferred values - is so unexpected that conventional astronomy has never been able to accept it, in spite of the overwhelming observational evidence. Their problem is simply that if redshifts measure radial components of velocities, then galaxy velocities can be pointed at any angle to us, hence their redshifts must be continuously distributed. For supposed recession velocities of quasars, to measure equal steps in all directions in the sky means we are at the center of a series of explosions. This is an anti-Copernican embarrassment. So a simple glance at the evidence discussed in this Chapter shows that extragalactic astronomy and Big Bang theory is swept away. (Arp, 1998)

Arp is very close to the truth when he writes;

In addition it appears increasingly useful to view particle masses to be communicated by wave like carriers in a Machian universe. Therefore the possibility of beat frequencies, harmonics, interference and evolution through resonant states is opened up. ... My attitude toward this result is that in a Machian universe there must be some signal carrier for inertial mass coming from distant galaxies.
In the phenomena of quantization, we have a connection from the redshifts of the quasars, to the redshifts of the galaxies, to the properties of the solar system and finally to the properties of fundamental particles like the electrons. The quantization of physical parameters would seem to be governed by the laws of non-local physics. .. It is clear that we are not running out of problems to solve. In fact, contrary to some rumours that we are reaching an end to physics, the more we learn the more primitive our previous understanding appears, and the more challenging the problems become. (Arp, 1998)

We can now at last solve these problems from the foundations of the Metaphysics of Space and Motion and the Wave Structure of Matter. It is both obvious and necessary that the Spherical Standing Wave Structure of Matter will exhibit 'quantum' or discrete standing wave interactions that explain why so many phenomena occur in discrete states. (See article on Quantum Theory)


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Why our Finite Spherical Universe does not Become 'Impoverished'

Einstein explains a further problem with the concept of the 'island' universe as required by Newton's Law;

According to the theory of Newton ... The stellar universe ought to be a finite island in an infinite ocean of space.
... This conception in itself is not very satisfactory. It is still less satisfactory because it leads to the result that the light emitted by the stars and also individual stars of the stellar system are perpetually passing out into an infinite space, never to return, and without ever again coming into interaction with other objects of nature. Such a finite material universe would be destined to become gradually but systematically impoverished. (Einstein, 1954)

This problem is also solved by realizing that matter is distributed uniformly (on the very large scale) throughout an infinite Space (but that only a part of this matter, a finite sphere, contributes to our In-Waves and thus our finite size/universe and mass).
For every SSW, the Spherical In-Wave (made up from contributions of many trillions of distant SSWs Out-Waves) flows in through the Wave-Center and becomes an Out-Wave. Thus the total mass-energy density for the In-Wave must equal that of the Out-Wave as it is the same wave at a later time.
This must also be true for the many trillions of SSWs that make up our visible universe, thus there are as many waves flowing into our finite spherical universe as there are flowing out. Again, this describes a perpetual Finite Spherical Universe within an Infinite Space. So we see that the WSM gives rise to a perpetual system that would not become impoverished over time, exactly as Einstein (and sensible logic) required.


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Explaining Olbers’ Paradox
Why the Stars of the Night Sky do not Appear Infinitely Bright

Olbers pointed out that if the number of stars were infinite, we should observe the entire sky with the light intensity of the surface of a star like the Sun. Obviously we do not observe this! As Lerner explains;

Newton was undecided on whether his laws of gravitation preclude an infinite collection of matter. He thought that only a divinely precise positioning of all the stars could prevent such an infinite collection of matter from collapsing into a series of heaps. Much later, in 1832, the astronomer Heinrich Olbers pointed out that an infinite universe seemed to imply a paradox. If there were an infinite number of stars, if one went far enough in any direction from earth, one would hit a star. This implied that the sky should be uniformly bright, as bright as the surface of the sun, which it obviously is not. (Lerner, 1991)

The solution to this paradox is the same as for the other paradoxes discussed above. Huygens' Sharing of Waves (which explains our finite Mass within an infinite Space) also explains why we only 'see' the Finite number of Wave-Centers (of matter in distant stars) within our Finite Spherical Universe. Thus the number of observable stars and the resultant brightness of the night sky are finite rather than infinite.
We should further add that the 'divine' positioning of matter in an infinite Space needed to prevent 'matter from collapsing into a series of heaps' is simply due to the fact that Matter is a Wave Structure that depends upon the Out Waves of other matter around it. This limits how the Wave-Centers can be distributed within an infinite Space (thus also explaining the quantised redshift with distance).


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

The Second Law of Thermodynamics
Why Our Finite Universe is Ordered & Complex

Eric Lerner has obviously been strongly influenced by Prigogine and therefore he writes well on Time and Thermodynamics. Thus it is useful to use his knowledge as a simple way of demonstrating the solution to this interesting problem of the Second Law of Thermodynamics, which suggests that over time our Finite Spherical Universe should become more disordered.
The reason why our universe remains Ordered is simply because it is part of an infinite perpetual system, and the Second Law of Thermodynamics only applies to Closed systems (not infinite systems), as Lerner clearly explains;

Conversely, if one asserts that the universe had no origin in time, then one must explain how it is that the universe has not completely decayed into uniform equilibrium in the infinite time that it has already existed. How is order maintained? How is progress possible?
... Pope Pius XII wrote; ‘Through the law of entropy, it was recognized that the spontaneous processes of nature are always accompanied by a diminution of free and utilisable energy. In a closed material system, this conclusion must lead eventually to the cessation of processes on a macroscopic scale. This unavoidable fate, which ... stands out clearly from positive scientific experience, postulates eloquently the existence of a Necessary Being.’
... Pope Pius XII concluded that a flagging universe necessarily must come to an end, but more significantly, requires something outside itself to imbue it with order at the beginning - a direct link between the idea of ever-increasing disorder and Christian theology.
From this proof, Boltzmann propounded a new concept with profound cosmological implications. The universe as a whole, must, like any closed system tend toward an equilibrious state of entropy: it will be completely homogeneous, the same temperature everywhere, the stars will cool, their life-giving energy flow will cease. The universe will suffer a 'heat death'. Any closed system must thus go from an ordered to a less ordered state- the opposite of progress.
... Boltzmann was aware that his ideas contradicted the notion, then widely accepted, of a universe without beginning or end. The present-day universe is far from a state of equilibrium, comprising as it does hot stars and cold space. If all natural systems 'run down' to disorder, the present state of order must have been created by some process that violates the second law at a finite time in the past. Conversely, at a finite time in the future, the world will cease to exist, becoming a lifeless homogeneous mass: human progress is but an ephemeral and inconsequential episode in a universal decay.
... Boltzmann found his results disturbing. Since he rejected a supernatural origin of the universe, he tried to argue that, in an infinite amount of time, extremely improbable events do occur, such as the spontaneous organisation of a universe, or a large section of it, from a prior state of equilibrium. The second law is, after all, a statistical one stating what is likely to happen, not what must happen.
..some thermodynamicists pointed out that Boltzmann had proved far less than he claimed. He assumed that gas began in a high degree of disorder, close to equilibrium, and never got far from it. Moreover, he only allowed for atomic collisions, but took no long-range forces, such as electromagnetism or gravity, into account. In most real physical situations, though, these restrictions aren't valid, so Boltzmann's proof is not applicable. A century later scientists were to demonstrate that, in the general case, Boltzmann's law of increasing disorder simply isn't true.
... Poggio goes on to point out that it is a gross over extrapolation of the second law to assume that because it works in certain simple situations on earth, it would work everywhere in the universe. He too points out that fusion is an example of building up, not a decay, of the universe. 'Let us not be too sure that the universe is like a watch that is always running down,' he warns, 'there may be a rewinding. The process of creation may not yet be finished.
... To be sure, the tendency toward equilibrium is supposed to hold only in 'closed systems' and because the earth is heated by the sun, it is not a closed system.
... The universe we observe is simply not decaying; the generalization of 'the law of increasing disorder' to the entire cosmos is unsupported by observation. (Lerner, 1991)


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Past Present and Future and the One Way Direction of Time

Lerner also perfectly explains this important problem of why Time must be directional, contrary to the laws of modern particle physics;

This is one of the deepest paradoxes of conventional physics today. According to all the laws of physics there should be no distinction between past and future, no direction to time. Since the second law says that entropy necessarily increases with time, and thus the past and future differ, the second law, too, is contradicted.
In relativity theory, for example, time is simply the fourth dimension - there is no more difference between past and future than between left and right. There is no flow of time: all the equations would look the same if time were reversed. Nor is this true of relativity alone. Newton's laws and the laws of quantum mechanics also are what physicists call 'time reversible'; they define no unique direction for time. If one were to make a movie of two billiard balls colliding, for example, it would look just as credible if it were run in reverse.
But in the real world, there is a difference. If it is two raw eggs that collide and break in the movie, it would look absurd in reverse. The two eggs would assemble themselves out of a puddle and roll off. In the real world babies are born, never unborn, they grow up, never down, and eggs are scrambled, never unscrambled. These processes are all irreversible: time moves forward, toward growth or decay.
Hence the fundamental question: If 'the laws of the universe' have no direction in time, why does the real world? Why do laws like the second law, which have a direction for time, work?
The conventional answer to this question is, strangely, the Big Bang. The Big Bang started the universe off in a highly orderly and regular state- a 'perfect' state of very low entropy. Since the universe must run down through states of increasing disorder, closer to equilibrium (the state in which there is no flow of energy), the direction of time is defined. Time is just the direction 'away' from the Big Bang. If there was no Big Bang, there would supposedly be no difference between past and future. The universe would be at equilibrium, and no event would diminish past from future. But the unique event of the Big Bang, so symmetric in space, creates an asymmetry in time.
Thus, if there was no Big Bang - as seems to be the case - we have further questions: Why does time move forward? Is there a difference between past and future, or is it, as Einstein believed, merely a persistent illusion?
The importance of the answers extends far beyond their role at the center of a consistent cosmology. They strike at the heart of some of the greatest mysteries faced by science, philosophy and religion - the questions of the nature of human consciousness, the relation of mind and body, and free will. The distinction between past, present, and future is basic to our experience of consciousness - we are conscious in the now, we remember the past, but we cannot know the future. It also is central to our idea of free will, for it implies that our actions in the present affect the future, that the past is fixed but the future can be changed. How can these ideas be reconciled with a concept of physical laws in which past, present and future all exist equally and cannot be distinguished?
The problem of 'reversible time,' then, arises because scientists improperly abstract reality and believe their highly accurate equations to be absolutely, infinitely precise. It is reversible time that is subjective, an illusion, not irreversible time. The real world is continually coming into existence, created by an infinitely complex web of instabilities and interactions. As Prigogine puts it, 'Time is creation. The future is just not there.'
Time's irreversibility is based on the continuity of space, on its infinite divisibility. (Lerner, 1991)

Once we realize that it is not Time but wave Motion which is fundamental, then it becomes obvious why Time is directional. If we apply this understanding of Time to Matter as Spherical Standing Waves in Space, this then leads to the following explanation of Past, Present, and Future. As it takes Time for the In-Wave to flow into its Wave-Center, thus the In-Waves are the Future, and in time will meet at their Wave-Center (the Present) and after flowing through the Wave-Center become Out-Waves (the past). This is important for it explains why Time is directional because the Wave Motion of Space is Directional, i.e. In and Out Waves travel in Opposite Directions relative to the Wave-Center (Present).


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

How our Universe is Necessarily Connected but not Deterministic

It is very important to appreciate the difference between a Necessarily Connected Universe, which ours is, (as explained by the central Principle of the Wave Structure of Matter) and a Deterministic Universe which requires knowledge of the 'initial conditions' from which things, being necessarily connected, can then be determined.
Again the solution is obvious, for we live in a finite and 'Necessarily Connected' Universe, but because it is within an Infinite Space, and continually has waves flowing into it that have come from Infinity, they can never be pre-determined. This explains the uncertainty of Quantum Theory and that we can never exactly know where each successive In-Wave will meet at its Wave-center, thus we can never exactly know both the future motion (momentum) and position of the ‘Particle’ (i.e. Heisenberg’s Uncertainty Principle). Thus Spinoza is correct when he writes;

A body in motion or at rest must be determined for motion or rest by some other body, which, likewise, was determined for motion or rest by some other body, and this by a third and so on to infinity. (Spinoza, 1673)

This also explains why even the Motion of planets is not determinable if we consider long periods of time, as Lerner explains;

The Cartesian idea of a set of universal laws which control natural occurrences exercised a powerful appeal in the succeeding centuries. Laplace, even as he developed his theory of a naturally evolving cosmos, endorsed the idea that, given the laws of gravitation, Newtonian mechanics, and the 'initial conditions' of the universe, every subsequent event not only can be accurately predicted, but is predetermined. The whole history of the universe, and of earth, is the inevitable operation of a set of eternal laws. In modern terms, Laplace believed that mathematical physics constitutes a Theory of Everything.
With absolute, infinite knowledge of the comet's velocity and infinite precision in calculation, its orbit is simply unpredictable. Yet this is not an effect of 'chance'. At all points the orbit was under precise control of the laws of gravitation as programmed into the simulation. The unpredictability came from the instability of the three-body interaction.
This doesn't mean we can't make useful predictions about the future. We can if the amount of time we try to predict is short enough. For unstable systems this time limit is the amount of time that passes between collisions of the particles that make up the system. For the comet this is a single orbit, but for a gas a tiny fraction of a second. We can, however, make useful statistical predictions; on average the comet will probably last about 150 orbits. And of course many systems are sufficiently close to stable that we can ignore their instability because the rate at which their instabilities grow is far longer than we need to worry about. For example, the orbits of the planets in our actual solar system appear to be unpredictable in excess of twenty million years from now. For all intents and purposes, in plotting a space mission the system is absolutely stable, predictable and reversible. (Lerner, 1991)


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Limited Free Will in a Necessarily Connected Universe

The Problem of Free Will & Determinism

The problem of Free Will vs. Determinism has puzzled philosophers for thousands of years. It is a profound problem for without Free Will there can be no morality, no right and wrong, no good and evil. All our behaviours would be pre-determined and we would have no creativity or choice. Common sense (and most importantly, Darwinian Evolution) suggests that we do in fact have Free Will, that we can decide and determine our futures within the limits of physical reality. However, the only absolute way to solve this problem of Philosophy is to know what exists and how it is interconnected, i.e. True Knowledge of Reality.
Recent discoveries on the Properties of Space and the Wave Structure of Matter (WSM) can now explain this reality of the world which we experience, and thus explain how we can have limited free will in a necessarily connected universe.

This is very important as it also explains why we can have limited free will, and thus live as moral creatures creating better futures for ourselves and our society (a very important thing). We should also emphasize that our free will is limited by this necessary connection of matter. We do not have the freedom to defy gravity and make ourselves float upwards, but within the constraints of necessary connection there are still many possible futures. We can choose to read this, or we can decide to stop reading it. Both are possible futures that obey the laws of physics and the necessary connections between things.

Our Finite Spherical Universe within Infinite Space is Necessarily Connected but not Deterministic

It is very important to appreciate the difference between a Necessarily Connected Universe, which ours is, (as explained by the central Principle of the Wave Structure of Matter) and a Deterministic Universe which requires knowledge of the 'initial conditions' from which things, being necessarily connected, can then be determined.
As this WSM Cosmology explains, we exist in a finite and 'Necessarily Connected' Universe (due to the Properties of Space as a continuously connected wave medium), whereas Space itself must be Infinite (One thing existing is necessarily Infinite and Eternal). Thus our finite spherical universe continually has waves flowing into it that have come from Infinity, and can never be pre-determined (an infinite system cannot be predetermined). Thus Spinoza is correct when he writes;

A body in motion or at rest must be determined for motion or rest by some other body, which, likewise, was determined for motion or rest by some other body, and this by a third and so on to infinity. (Spinoza, 1673)

This also explains why even the Motion of planets is not determinable if we consider long periods of time, as Lerner explains;

The Cartesian idea of a set of universal laws which control natural occurrences exercised a powerful appeal in the succeeding centuries. Laplace, even as he developed his theory of a naturally evolving cosmos, endorsed the idea that, given the laws of gravitation, Newtonian mechanics, and the 'initial conditions' of the universe, every subsequent event not only can be accurately predicted, but is predetermined. The whole history of the universe, and of earth, is the inevitable operation of a set of eternal laws. In modern terms, Laplace believed that mathematical physics constitutes a Theory of Everything.
With absolute, infinite knowledge of the comet's velocity and infinite precision in calculation, its orbit is simply unpredictable. Yet this is not an effect of 'chance'. At all points the orbit was under precise control of the laws of gravitation as programmed into the simulation. The unpredictability came from the instability of the three-body interaction.
This doesn't mean we can't make useful predictions about the future. We can if the amount of time we try to predict is short enough. For unstable systems this time limit is the amount of time that passes between collisions of the particles that make up the system. For the comet this is a single orbit, but for a gas a tiny fraction of a second. We can, however, make useful statistical predictions; on average the comet will probably last about 150 orbits. And of course many systems are sufficiently close to stable that we can ignore their instability because the rate at which their instabilities grow is far longer than we need to worry about. For example, the orbits of the planets in our actual solar system appear to be unpredictable in excess of twenty million years from now. For all intents and purposes, in plotting a space mission the system is absolutely stable, predictable and reversible. (Lerner, 1991)

Determinism Vs. Free Will

The problem of whether Humans have free will or whether all our actions are pre-determined and our apparent free will is simply an illusion is profoundly important to Humanity, for the answer to this question will tell us whether we can determine our own future, and whether the concept of Morality actually exists (for if we had no free will, then there could be no such thing as morality!).
The solution is quite simple though and can be easily understood with the aid of the following example;

Let us take a normal pack of playing cards (52 cards - 13 Hearts, Diamonds, Spades, and Clubs) and I shall place the Ace of Hearts face down on the top of the pack.
Thus I am both necessarily connected to the Ace of Hearts (as I am to all matter in the universe) and I have pre-determined knowledge of the exact card, thus I can be certain that if I turn the card over it will be the Ace of Hearts. So we see that while I have complete knowledge of the system then there is no chance involved - the system is both necessarily connected and pre-determined.
Now let us further imagine that I place this pack of cards in front of someone else who has no knowledge of the fact that the Ace of Hearts is the top card. So while they are still necessarily connected to the top card (Ace of Hearts) they do not have pre-determined knowledge of this card, thus if I ask them to tell me which card is on top of the pack they only have a one in fifty two chance of guessing correctly. Thus we see how chance exists when we do not have pre-determined knowledge (even though we are still necessarily connected).

Further, in a necessarily connected but non determined universe, there are many possible futures (within the constraints of the properties of Space and the waves structure of matter - we can't flap our arms and fly!).
If we now apply this knowledge to the matter of brain and body (which is the cause of our human mind) we realise that while we are necessarily connected to the other matter in the universe, we can never have pre-determined knowledge of the motions of this other matter (as explained above due to the system being infinite) thus explaining how chance (due to lack of pre-determined knowledge) exists in the universe. Hence evolution of our brain and mind can use this chance to allow us to creatively think of new and novel ideas and relationships that we can then remember, and then we can use chance again to select from these various chance relationships to determine actions. Now while this is a very simplified explanation of how our mind works, and there may be millions of ‘layers’ to these chance selections, each with various degrees of probabilities for selecting different outcomes, nonetheless the principles are true and do explain how lack of pre-determined knowledge in a necessarily connected Universe within an Infinite Space allows chance and limited ‘free will’.

A simple example of this process can be found when considering a game commonly found in fairgrounds, where there is a clown's head with open mouth that is rotating backwards and forwards, and you must drop a ball and try and get it to land in a certain slot. Depending on the time that you drop the ball ultimately determines where it will land. But all options are possible, and if we use this chance (due to lack of knowledge, as explained above) to determine when the ball is dropped, then we realise that we are using chance to decide on the future of the universe.

Thus Spinoza is both right and wrong when he writes;

There is no mind absolute or free will, but the mind is determined for willing this or that by a cause which is determined in its turn by another cause, and this one again by another, and so on to infinity. (Spinoza, 1673)

His error was to not understand how lack of pre-determined knowledge in an infinite though necessarily connected system causes chance and limited free will.

Karl Popper also intuitively understood that there had to be some 'balance' between complete determinism (clocks) and complete disorder and chance (clouds) when he wrote;

What we need for understanding rational human behaviour - and indeed, animal behaviour - is something intermediate in character between perfect chance and perfect determinism - something intermediate between perfect clouds and perfects clocks. (Popper, 1975)

He was absolutely right, for a 'Necessarily Connected', but infinite and ‘Non-Determined’ universe allows us to have limited free will (based upon this lack of pre-determined knowledge which gives rise to chance).


Introduction - Summary of WSM Cosmology: Defining Universe - One Principle: Space Exists as Wave Medium - Space is Infinite Eternal Continuous - Finite Spherical Universe in Infinite Eternal Space - Equation of the Cosmos: Deducing Finite Size of Matter and Universe - Newton, Mach, Einstein Infinite Mass Paradox - Cosmology: Mach's Principle - Einstein's 'Curvature of 4D Space-Time Continuum' - Einstein's Famous Cosmological (Antigravity) Constant - WSM Cosmology Predicts Motion of Distant Galaxies - Solution to Quantified Hubble Redshift - Why Finite Spherical Universe not 'Impoverished' - Solving Olbers' Paradox - 2nd Law of Thermodynamics - Past Present Future / One Way Direction of Time - Matter in Universe is Necessarily Connected but not Deterministic - Determinism Vs Free Will - Concluding Remarks - Top of Page

Concluding Remarks

Eric Lerner demonstrates an intelligent understanding of the important interconnection between Society and Scientific/Cosmological Theories. Though his knowledge of the true cause of the redshift with distance was incomplete, nonetheless he knew that ultimately Space and Time (Motion) must be Infinite, that the Big Bang theory was itself collapsing under the weight of its own inconsistencies, and that we are at the beginning of a new cosmological revolution. He writes;

Today, another scientific revolution is beginning, one that may change our view of the cosmos as radically as the last. And today it again seems likely that the effects of this revolution, both social and scientific, will be profound.
If the universe is truly infinite in time and space, then the implications go well beyond cosmology to the whole of our view of nature, to religion, philosophy and society as a whole.
Teilhard de Chardin anticipated many of Prigogine's more concrete ideas. But equally important, he argues that only this prospect of an unlimited future can be the basis for human morality, even for human activity - the only prospect that can prevent humanity from despairing. If mankind came to believe that progress would halt, then ‘mankind would soon stop inventing and constructing for a work it knew to be doomed in advance. And stricken at the very source of impetus that sustains it, it would disintegrate from nausea or revolt and crumble into dust. If progress is a myth ... our efforts will flag. With that the whole of evolution will come to a halt - because we are evolution.’ (Lerner, 1991)

If as a result of some interior revolution, I were to lose in succession my faith in Christ, my faith in a personal God, and my faith in spirit, I feel that I should continue to believe invincibly in the world. The world (its value, its infallibility and its goodness) - that , when all is said and done is the first, the last and the only thing in which I believe. It is by this faith that I live. (Teilhard de Chardin, 'How I Believe')

But the new ideas of the emerging scientific revolution bring an entirely different outlook. If the universe is evolving from an infinite past to an infinite future, if human development is only the latest stage of continual progress stretching through the unlimited reaches of time, then the very idea of an 'end to history' is ludicrous, an unfunny joke. History can no more have an end than time itself. If human development pauses or retreats, then it is only because some specific form of society has reached its limits. If there is something wrong, then it must be fixed.
Such an outlook offers a hope of renewed progress. It asserts that scientific advance and technological development are not at an end, but could be starting a new period of explosive growth. It provides the motivation human beings need to join together in collective efforts rather than to fragment into self-cantered anarchy. It shows that the technology exists to eradicate want on earth and open the path outward into an infinite universe.
In every system, be it physical or social, there are times when small events determine the course of ensuing events - either forwards to new and higher plains or backward, cut off by the barriers of the old. Society stands at such a crossroads now, at the end of the second millennium. If it falls backward then the present embryonic scientific revolution will be swept away in the general retreat, becoming, like Aristarchus' heliocentric theory, a mere footnote to a debacle. (Lerner, 1991)

Though there is much still to explain, and a great deal of mathematical analysis to be done, nonetheless the Metaphysics of Space and Motion and the Wave Structure of Matter provides a powerful new theoretical method for analysing our Cosmos. As we have demonstrated, this Metaphysic explains and solves the major problems and paradoxes that currently do such damage to modern Cosmology (and Physics, Philosophy, and Society as well).
The WSM unites Relativity with Quantum Theory, and even more impressive, then unites these famous theories with Cosmology and provides us with a very simple Equation of the Cosmos. (On the other hand, Einstein's Relativity never explained Quantum Theory, and invariably led to paradoxes in Cosmology.) Thus to us it has become obvious that the reality of our world and our universe is found by understanding the Spherical Standing Wave Structure of Matter in Space.

It is fitting to end with a quote from Thomas Kuhn, famous for his work on ‘The Structure of Scientific Revolutions’;

All crises begin with the blurring of a paradigm and the consequent loosening of the rules for normal research. .. Or finally, the case that will most concern us here, a crisis may end with the emergence of a new candidate for paradigm and with the ensuing battle over its acceptance.
It is, I think, particularly in periods of acknowledged crisis that scientists have turned to philosophical analysis as a device for unlocking the riddles of their field. Scientists have not generally needed or wanted to be philosophers.
Copernicanism made few converts for almost a century after Copernicus' death. Newton's work was not generally accepted, particularly on the Continent, for more than half a century after the Principia appeared. The difficulties of conversion have often been noted by the scientists themselves. Darwin, in a particularly perceptive passage at the end of his Origin Of Species, wrote: 'Although I am fully convinced of the truth of the views given in this volume .. I, by no means expect to convince experienced naturalists whose minds are stocked with a multitude of facts all viewed, during a long course of years, from a point of view directly opposite to mine. .. But I look with confidence to the future - to young and rising naturalists, who will be able to view both sides of the question with impartiality. And Max Planck, surveying his own career in his Scientific Autobiography, sadly remarked that a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. (Kuhn, 1962)


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Smolin, Lee 'The Life of the Cosmos' Phoenix 1998
Spinoza 'Ethics' (1673) J.M. Dent & Sons LTD 1910
Wertheim, Margaret 'Pythagoras' Trousers' Fourth Estate Limited 1997


Cosmology
The Wave Structure of Matter (WSM) Cosmology explains how our Finite Spherical Universe Exists within an Infinite Space

Giordano Bruno's universe was infinite ... he integrated Nicholas of Cusa's thinking, but purged it of remaining Ptolemaic elements, such as the perfect spheres that carried the planets' orbits. (Lerner)
Can we visualize a universe which is finite yet unbounded? ... The supreme task of the physicist is to arrive at those universal laws from which the cosmos can be built up by pure deduction. (Albert Einstein)
The Big Bang is a wonderful myth that deserves a place of honor in the columbarium which already contains the Biblical myth of creation, the Ptolemaic cosmological myth, and many others. (Hans Alfven)
Time is either identical to Motion or is some affection of it. ... about Matter's coming into being and its alterations, we think we have knowledge when we know the source of its Motion. (Aristotle, 340BC)
Wolff Haselhurst Cosmology: The Wave Structure of Matter (WSM) solves many problems of Cosmology by explaining how a Finite Spherical Universe exists within an Infinite Eternal Space.
The Equation of the Cosmos is a relation between the 'size' r of the electron and the size R of the Hubble Universe. It describes how all the N wave centers 'particles' of the Hubble Universe determine the wave density of Space. (Milo Wolff, 2005)
It should be pointed out that Edwin Hubble 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)
The only thing which is 'certain' of CMBR, is that we detect 'some radiation' at 3K in the night Sky. ... I conclude that since hydrogen is well known in space, the Planck spectrum observed (erroneously attributed to the Big Bang) is due to Hydrogen at 3K in the universe. (Paul Marmet)
The universe we observe is simply not decaying; the generalization of 'the law of increasing disorder' to the entire cosmos is unsupported by observation. (Lerner)
What we need for understanding rational human behaviour - and indeed, animal behaviour - is something intermediate in character between perfect chance and perfect determinism - something intermediate between perfect clouds and perfects clocks. (Karl Popper, 1975)
Our Solar System consists of the nine planets and all other celestial bodies that orbit the Sun. The sun is by far the most massive part of the solar system, containing almost 99.9% of the system's total mass. (answers.com)
The Milky Way is the galaxy of which the sun and our solar system are a part, seen as a broad band of light arching across the night sky from horizon to horizon ... comprising of an estimated 200 billion stars. (answers.com)
The Hubble Space Telescope (HST) is a telescope orbiting the Earth 370 miles above the atmosphere. It is a space observatory ... named after Edwin Hubble, it was launched into orbit in 1990 as a project of NASA. (Wikipedia)
A human being is part of the whole called by us universe ... the true value of a human being is determined by the measure in which they have obtained liberation from the self. ... We shall require a substantially new manner of thinking if humanity is to survive. (Albert Einstein, 1954)



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Albert Einstein"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. ...
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Biography: Geoffrey Haselhurst, Philosopher of Science, Theoretical Physics, Metaphysics, Evolution. Our world is in great trouble due to human behaviour founded on myths and customs that are causing the destruction of Nature and climate change. We can now deduce the most simple science theory of reality - the wave structure of matter in space. By understanding how we and everything around us are interconnected in Space we can then deduce solutions to the fundamental problems of human knowledge in physics, philosophy, metaphysics, theology, education, health, evolution and ecology, politics and society.

This is the profound new way of thinking that Einstein realised, that we exist as spatially extended structures of the universe - the discrete and separate body an illusion. This simply confirms the intuitions of the ancient philosophers and mystics.

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