Uniting Metaphysics and Physics
The Metaphysics of Space and Motion and the Wave Structure of Matter
Unites Albert Einstein's Relativity, Quantum Theory and Cosmology

Those whose hearts are fixed on Reality itself deserve the title of Philosophers. (Plato, 380BC)

The first philosophy (Metaphysics) is universal and is exclusively concerned with primary substance. ... And here we will have the science to study that which is just as that which is, both in its essence and in the properties which, just as a thing that is, it has. (Aristotle, 340BC)

Hi Everyone,
This page is very long and was written for publication in a book. The content is good so you are welcome to read it, but you will find the links on the side of the page present this knowledge in shorter, more concise articles.
All the best,
Geoff Haselhurst


Introduction - Properties of Space - General Laws (which explain the Necessary Connection between What Exists) - On the Evolution of Principles in Physics - The Metaphysics of Space and Motion (Aristotle and Leibniz solve Kant) - Leibniz's Monadology - The Solution to Hume's Problem of Causation and Popper's Problem of Induction - The Solution to the Problem of the One and the Many - 1. Einstein's Relativity - 1.1 Newton's Mechanics (1687) - 1.2 Faraday's Electromagnetic Force Field (1832) - 1.3 Maxwell's Equations and the Finite velocity of Light waves (1876) - 1.4 On Lorentz's Theory of the Electron (1900-1906) - 1.5 Einstein's Relativity (1905,1915) - 2. Quantum Theory - 2.1 Max Planck's Discovery of the Particle (Quantum) Properties of Light (1900) - 2.2 de Broglie's Discovery of the wave Properties of Electron Interactions (1927) - 2.3 The Schrodinger Wave Equations are founded on Standing Wave Interactions (1928) - 2.4 Explaining the Forces of Charge and Light - 2.5 Heisenberg's Uncertainty Principle & Born's 'Probability waves' (1928) - 2.6 Wolff's explanation of Feynman's Quantum Electrodynamics (QED, 1945) - 2.7 Wolff's Explanation of the Famous Einstein, Podolsky, Rosen (EPR) and Further Predictions that can be Confirmed by Modifying the EPR Experiment (1993-2003) - 3. Cosmology - 3.1 Our Finite Spherical Universe Perpetually Exists Within an Infinite Space - 3.2 The Equation of the Cosmos - 3.3 An Infinite Space - 3.4 Mach's Principle and How the Distant Stars Determine Our Inertial Mass - 3.5 Explaining Einstein's Famous Cosmological Constant & Further Prediction - 3.6 Explaining the 'Quantified' Hubble Redshift with Distance - 3.7 The Second Law of Thermodynamics only applies to Closed Systems - 3.8 On the Past Present and Future and the One Way Direction of Time - 3.9 How our Universe is Necessarily Connected but not Deterministic - Concluding Remarks on Cosmology, Religion and Morality - Philosophy as the 'discovery of the obvious'


For thousands of years philosophers have gazed at the stars and known that One thing must exist that is common to and connects the Many things within the Universe. As Leibniz profoundly says; Reality cannot be found except in One single source, because of the interconnection of all things with one another. (Leibniz, 1670)
Thus as matter interacts with all other matter in the universe, to ask 'What is matter?' is no different than asking, 'What is the universe?', or more completely 'What exists, what is Reality?'. The solution is found in One Principle which describes the One Substance which exists (Space) and its Properties (Wave-Medium) such that we can then explain the necessary connection between the many things which exist. From this One Principle we can deduce the following Properties of Space and General Laws. (This is further explained within this article)

Properties of Space

1. One Space must be Infinite, Eternal and Continuous. (As boundaries, creation, and particles require two things.)
2. Space is a nearly rigid wave-medium.
3. The wave velocity (velocity of light c) varies with both the wave-amplitude (causes charge/light) and mass-energy density of space (square of wave-amplitude, causes mass/gravity).

General Laws

(As Necessary Consequences of the Properties of Space, and which explain the Necessary Connection between What Exists)

1. The 'particle' effect of matter is caused by the wave-center of the spherical standing wave. (Fig:1)
2. Time (and matter) are caused by wave Motion. (As Aristotle realized, time is either identical to movement or is some affection of it.)
3. Newton's Law of Inertia, Force = Mass times Acceleration. A 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 the accelerated motion of the 'particle'. (Fig: 2)
4. Mach's Principle. The spherical In-waves are formed from the Huygens' Combination of Out-waves from All other matter in our finite spherical universe. (Fig: 3)
5. Minimum Amplitude Law. Wave-centers move to minimise total wave-amplitude (explains charge).
6. Maximum Density Law. Wave-centers move to maximise total mass-energy density of space (explains gravity. Fig: 2).In-Wave ----------Out-Wave---------In and Out-Waves

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:1.2 - Matter Exists as the Spherical Wave Motion of Space, the Wave-Center causes the observed 'particle' effect of Matter.

Fig: 2 Gravity is caused by a slowing of the In-waves (on the right) due to a higher mass-energy density of space where there is more matter. This changes the shape of the In-waves from being Spherical to Ellipsoidal and causes the wave-center to 'move' towards this other matter. (See Relativity section.)

Fig: 3 Our Spherical In-waves are formed from the Huygens' Combination of the Out-waves of all the other matter in the universe. This explains Mach's Principle and deduces the redshift with distance, by explaining how matter can be finite and yet perpetually exist within an infinite Space. (See Cosmology section)

Now I appreciate that this principle and laws which follow will not make much sense when first considered. To partly alleviate this problem I have included a brief summary of the Wave Structure of Matter below. What I would emphasise though, is that it simply takes time to understand new ideas, particularly if we have been brought up with the particle conception of matter (as I was). Given time, I can assure you that you will find the Wave Structure of Matter very simple and sensible.

On the Evolution of Principles in Physics

All logic depends upon Principles which gives rise to necessary consequences that are absolute and certain (rather than mere opinions). The aim of Science is to demonstrate that these logical deductions from (a priori) Principles exactly correspond with our sense of the real world from (a posteriori) observation and experiment. Einstein explains this scientific method very clearly;

Physics constitutes a logical system of thought which is in a state of evolution, whose basis (principles) cannot be distilled, as it were, from experience by an inductive method, but can only be arrived at by free invention. The justification (truth content) of the system rests in the verification of the derived propositions (a priori/logical truths) by sense experiences (a posteriori/empirical truths). ... Evolution is proceeding in the direction of increasing simplicity of the logical basis (principles). ... We must always be ready to change these notions, i.e. the axiomatic basis of physics, in order to do justice to perceived facts in the most perfect way logically. … For the time being we have to admit that we do not possess any general theoretical basis for physics which can be regarded as its logical foundation. … can we ever hope to find the right way? I answer without hesitation that there is, in my opinion, a right way, and that we are capable of finding it. I hold it true that pure thought can grasp reality, as the ancients dreamed. (Albert Einstein, 1954)

Ockham's razor (and Einstein) tell us that the better (simpler) theory explains more things with less assumptions, thus the extension of this principle is that the best theory (i.e. most simple description of Reality) must explain all things from One thing. This One thing should not only be 'firmly enough connected with sensory experiences', as Einstein argues, but it must cause our senses, and thus be a priori or necessary for us to experience the world. And as Kant (below) and common sense realize, it is Space which is a priori or necessary for us to be able to experience the world.

The Metaphysics of Space and Motion.
(Aristotle and Leibniz solve Kant)

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. (Bradley, from Urmson, 1991)

All Truth ultimately comes from Reality. Thus the past errors and ultimate failure to correctly describe Reality (which is now believed to be impossible) have left modern Metaphysics and Truth with an understandably bad reputation. With help from Aristotle, Leibniz, and Kant we can now correct these errors in the following simple way. As Aristotle confirms;

The first philosophy (Metaphysics) is universal and is exclusively concerned with primary substance. … It is the principles and causes of the things that are that we are seeking, and clearly it is their principles and causes just as things that are. … And here we will have the science to study that which is just as that which is, both in its essence and in the properties which, just as a thing that is, it has. (Aristotle, 340BC)

Thus at the heart of Metaphysics is Substance and its Properties, which exists and causes all things, and is therefore the necessary foundation for all human knowledge. Most importantly, Aristotle and Leibniz were correct to realize that One Substance must have Properties that account for matter's interconnected activity and Motion.

The entire preoccupation of the physicist is with things that contain within themselves a principle of movement and rest. And to seek for this is to seek for the second kind of principle, that from which comes the beginning of the change. … There must then be a principle of such a kind that its substance is activity. (Aristotle, 340BC)
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, 1670)

The solution is to realize that Space exists as a wave-medium and contains spherical wave-motions that cause matter and its interconnected activity/change. Let us now apply this knowledge to Kant, who clearly realized the unique importance of Space as being a priori (necessary) for us to be able to experience and sense the world around us, and that Metaphysics (and thus Physics) depend upon this a priori knowledge.

Natural science (physics) contains in itself synthetical judgments a priori, as principles. … Space then is a necessary representation a priori, which serves for the foundation of all external intuitions. (Kant, 1781)

Unfortunately for Human knowledge, Kant made a simple error when he assumed Time as the second a priori existent, rather than the PROPERTIES of Space as a wave-medium.

Time is not an empirical concept. For neither co-existence nor succession would be perceived by us, if the representation of time did not exist as a foundation a priori. (Kant, 1781)

And because Kant could not unite Space and Time back to One common connected thing he assumed that they must exist merely as ideas or representations of the world. His error can be clearly seen when he writes that motion is empirical / a posteriori and first depends upon the a priori existence of time.

Here I shall add that the concept of change, and with it the concept of motion, as change of place, is possible only through and in the representation of time. … Motion, for example, presupposes the perception of something movable. But space considered in itself contains nothing movable; consequently motion must be something which is found in space only through experience -in other words, is an empirical datum. (Kant, 1781)

The correct answer is that Space in itself must have Properties. i.e. That Space exists with the properties of a wave-medium and thus contains wave-motions which ultimately cause not only time, but also matter and its forces. (Kant made the common mistake of only considering Motion of matter 'particles' and not the (wave) Motion of Space itself!) Thus Space and Motion are a priori and first necessary for us to experience the world. This then explains the current confusion of modern physics due to the incorrect conception of the 'Motion of matter particles' in 'Space and Time', rather than the spherical wave-motion of Space causing both matter 'particles' and 'time'. Significantly, Kant realized the importance of this problem of synthetic a priori knowledge as the foundation of the Sciences and thus of certainty of knowledge.

Upon the solution of this problem, or upon sufficient proof of the impossibility of synthetical knowledge a priori, depends the existence or downfall of metaphysics. (Kant, 1781)

Leibniz Monadology Monad - On the Interconnection of All Things Leibniz’s Monadology, Monad

Monas is a Greek word which signifies unity or that which is one. As Leibniz writes;

I do not conceive of any reality at all as without genuine unity. (Gottfried Leibniz, 1670)

In his Monadology Leibniz describes Reality (the One thing which exists and connects the many things) as One Substance (which is active) and God;

.. the ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God. .. God alone is the primary Unity, or original simple substance, from which all monads, created and derived, are produced. (Leibniz, 1670)
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. (Gottfried Leibniz, 1670)

Gottfried Leibniz's Monadology is largely correct, matter and universe are One. But we can now better understand his Monad as a Spherical Wave Motion of Space that determines the size of our finite spherical universe within an infinite Space, and thus interacts with ALL other matter within our universe.

It follows from what we have just said, that the natural changes of monads come from an internal principle, and that change is continual in each one. … Now this connection of all created things with each, and of each with all the rest, means that each simple substance has relations which express all the others, each created monad represents the whole universe. (Leibniz, 1670)

Now this connection or adaption of all created things with each, and of each with all the rest, means that each simple substance has relations which express all the others, and that consequently it is a perpetual living mirror of the universe. (Leibniz, 1670)

1. The monad, of which we shall speak here, is nothing but a simple substance which enters into compounds; simple, that is to say, without parts.
2. And there must be simple substances, because there are compounds; for the compound is nothing but a collection or aggregatum of simples.
3. Now where there are no parts, there neither extension, nor shape, nor divisibility is possible. And these monads are the true atoms of nature and, in a word, the elements of things.
5. There is no way in which a simple substance could begin in the course of nature, since it cannot be formed by means of compounding.

9. Indeed every monad must be different from every other. For there are never in nature two beings, which are precisely alike, and in which it is not possible to find some difference which is internal, or based on some intrinsic quality.
10. I also take it as granted that every created thing, and consequently the created monad also, is subject to change, and indeed that this change is continual in each one.
11. It follows from what we have just said, that the natural changes of monads come from an internal principle, since an external cause would be unable to influence their inner being. (Leibniz, 1670)

22. And as every state of a simple substance is a natural consequence of its preceding state, so that the present state of it is big with the future (Leibniz, 1670)

Gottfried Leibniz, Philosophical Investigations, 1670

The Solution to Hume's Problem of Causation and Popper's Problem of Induction

Hume is famous for making us realize that until we know the Necessary Connection/Cause of things then all human knowledge is uncertain, merely a habit of thinking based upon repeated observation (induction), and which depends upon the future being like the past.

When we look about us towards external objects, and consider the operation of causes, we are never able, in a single instance, to discover any power or necessary connexion; any quality, which binds the effect to the cause, and renders the one an infallible consequence of the other. …There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert that it really exists, and is the origin of all our conclusions concerning matter of fact. This question I propose as much for the sake of information, as with an intention of raising difficulties. I cannot find, I cannot imagine any such reasoning. But I keep my mind still open to instruction, if any one will vouchsafe to bestow it upon me. (Hume, 1737)

We should respect Hume's open mind, which is necessary if we are to ever consider new ideas and thus advance Human knowledge. We can now simply explain this necessary connection of matter (cause and effect) due to the interconnection (and changing velocity) of the spherical In and Out-waves with all the other matter in the universe. (This will be explained when we discuss Physics.)

Popper's negative solution to the problem of induction (that all truth is evolving, we can never know the Absolute Truth, but only know what is false through scientific method) is correct while we do not know the necessary connection between things (e.g. cause and effect).

There could easily be a little quarrel about the question which is the deeper problem; Hume's Problem of Causation, or what I have called the Problem of Induction. One could argue that if the problem of causation were positively solved - if we could show the existence of a necessary link between cause and effect - the problem of induction would also be solved, and positively. Thus one might say, the problem of causation is the deeper problem. I argue the other way round: the problem of induction is negatively solved; we can never justify the truth of a belief in a regularity. But we constantly use regularities, as conjectures, as hypotheses; and we have good reasons sometimes for preferring certain conjectures to some of their competitors. It is through the falsification of our suppositions that we actually get in touch with 'reality'. It is the discovery and elimination of our errors which alone constitute that 'positive' experience which we gain from reality. (Popper, 1975)

It is important to explain and solve Popper because many scientists believe that Truth is always an approximation which is constantly evolving. In fact this is not the case, the solution to Metaphysics (to explain the One thing, Space, which must necessarily connect the Many things, matter) is a final solution, an Absolute and Eternal Truth, as there is nothing more simple than One, thus no further evolution of theories is possible. Thus Popper's negative solution to the Problem of Induction must now be discarded, as he writes;

If a theory corresponds to the facts but does not cohere with some earlier knowledge, then this earlier knowledge should be discarded. (Popper, 1975)

The Solution to the Problem of the One and the Many

Both Indian and Greek Philosophy originated from the correct realization that there must be One thing that is common to, and connects, the Many things, and further that Motion (activity, change) was also central to existence.

All things come out of the one, and the one out of all things. (Heraclitus, ~500BC)

In Indian philosophy, the main terms used by Hindus and Buddhists have dynamic connotations. The word Brahman is derived from the Sanskrit root brih – to grow- and thus suggests a reality which is dynamic and alive. The Upanishads refer to Brahman as 'this unformed, immortal, moving', thus associating it with motion even though it transcends all forms.' The Rig Veda uses another term to express the dynamic character of the universe, the term Rita. This word comes from the root ri- to move. In its phenomenal aspect, the cosmic One is thus intrinsically dynamic, and the apprehension of its dynamic nature is basic to all schools of Eastern mysticism.
They all emphasize that the universe has to be grasped dynamically, as it moves, vibrates and dances. (Fritjof Capra, 1972.)

The fundamental problem of the One and the Many (which is at the very heart of human conceptual knowledge of Reality) is the belief that One thing could never be understood with human reason, language and logic, as these require relationships between two or more things;

The problem of the one and the many in metaphysics and theology is insoluble: We have the universe of individuals which is not self-sufficient and in some sense rests on Brahman, but the exact nature of the relation between them is a mystery. … All ordinary human experience is conceptual in nature, i.e. is organized under the categories in which we ordinarily think. However, Brahman is said to be predicateless ( no concepts apply to it): concepts presuppose division, and Brahman is a unity. How, then, is any form of awareness of Brahman possible for human beings? (Collinson, 2000)

The solution to this problem is actually very simple. One thing, Space, exists (infinite and eternal), the second thing, Motion, as the wave Motion of Space, is the property of Space, and is necessarily connected to Space as it is Space which is moving! And once we have this connection between the One thing Space, and the many things, i.e. matter as the Spherical Wave Motion of Space, then we can in fact form concepts and logic (which require two necessarily connected things, i.e. the wave Motion of Space.)

Lama Govinda had an exceptional understanding of Indian Philosophy and he was very close to the truth, and thus the solution to this profound problem of the One and the Many;

The fundamental element of the cosmos is Space. Space is the all-embracing principle of higher unity. Nothing can exist without Space. Space is the precondition of all that exists, be it material or immaterial form, because we can neither imagine an object nor a being without space. … According to ancient Indian tradition the universe reveals itself in two fundamental properties: as Motion, and as that in which motion takes place, namely Space. This Space is called akasa, and is that through which things step into visible appearance, i.e., through which they possess extension or corporeality. 'Akasa is derived from the root kas, 'to radiate, to shine', and has therefore the meaning of 'ether', which is conceived as the medium of movement. The principle of movement, however, is prana, the breath of life, the all-powerful, all-pervading rhythm of the universe. (Lama Govinda, 1977)

In fact, as we shall explain, the Metaphysics of Space and Motion (Akasa Prana) not only unites and solves the Problem of the One and the Many, but also the Infinite and the Finite, the Eternal and the Temporal, the Absolute and the Relative, the Continuous and the Discrete, and the Simple and the Complex. i.e. One Space is Infinite, Eternal, Absolute, Continuous and Simple; Matter, as Many spherical standing wave Motions of Space is Finite, Temporal, Relative, Discrete and Complex (in its interconnected Motions).
Metaphysics: Problem of One and the Many - Brief History of Metaphysics and Solutions to the Fundamental Problems of Uniting the; One and the Many, Infinite and the Finite, Eternal and the Temporal, Absolute and Relative, Continuous and Discrete, Simple and Complex, Matter and Universe.

So let us now apply this new Metaphysical foundation to the problems of Physics. We begin with Einstein's Relativity, then Quantum Theory, and end with Cosmology.

1. Einstein's Relativity

The revolution which began with the creation of quantum theory and relativity theory can only be finished with their unification into a single theory that can give us a single, comprehensive picture of nature. (Smolin, 1997)


It is important to realize that Einstein's Relativity evolved largely from Newton's Mechanics (1687), Faraday's Electromagnetic Field Theory (1832), Maxwell's Equations (1876) and Lorentz's Theory of the Electron (1900-1906). By applying this new Metaphysical foundation to these earlier theories we can correct their errors, and this then leads to a simple solution to the problems of Einstein's Relativity.

1.1 Newton's Mechanics (1687)

Newton famously wrote;

Absolute Space, in its own nature, without regard to any thing external, remains always similar and immovable. (Newton, 1687)

While Absolute Space is correct, his first error was to assume that Space could not move (i.e. could not vibrate due to wave-motions - the same error as Kant). This of course leads to the second error of introducing an absolute Time, when this is actually caused by the wave Motion of Space. And Newton should have realized this close connection of Time with Motion, as he writes;

Common Time is some sensible and external (whether accurate or unequable) measure of duration by the means of motion. (Newton, 1687)

To Newton's great credit though, he realized that Metaphysics must be founded on Absolute Motion in Space rather than Relative Motion with other matter (which is empirical / a posteriori), as Metaphysics is founded on a priori causes, not on empirical / a posteriori effects. (And this becomes very important when we shortly consider Einstein's Relativity, which is founded on relative motion.)

And so instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in Philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them. (Newton, 1687)

Let us now briefly consider Einstein's analysis of Newton's Mechanics:

Physical events, in Newton's view, are to be regarded as the motions, governed by fixed laws, of material points in space. (Albert Einstein, 1954)

Thus the next error of Newton was to imagine matter as discrete 'particles' moving about in Space, rather than matter existing as the Spherical Wave Motion of Space, and that the wave-center causes the 'particle' effect. This leads to two insurmountable problems;

Firstly, how do these discrete particles gravitationally act-at-a-distance with other particles separate in Space? Newton himself was aware of this problem.

So far I have explained the phenomena ... by the force of gravity, but I have not yet ascertained the cause of gravity itself ... and I do not arbitrarily invent hypotheses. (Newton, 1687)

Secondly, how does matter exist as a discrete particle in Space and move through the Space around it? As Born explains;

One obvious objection to the hypothesis of an elastic Aether (Space) arises from the necessity of ascribing to it the great rigidity it must have to account for the high velocity of waves. Such a substance would necessarily offer resistance to the motion of heavenly bodies, particularly to that of planets. (Born, 1924)

While Born is correct that Space is very rigid and this explains the high wave-velocity, he (along with most physicists) mistakenly assumes that separate 'particles' exist in this Space, and thus it is inconceivable that Space itself can exist as it would resist the motion of these particles. The obvious solution to both these problems is to replace the concept of matter existing as discrete particles with matter existing as the Spherical Wave Motion of Space. We then realize that forces acting-at-a-distance can now be sensibly explained as simply the changing velocities of the spherical In-waves which cause the wave-center to change its location in Space, and which we observe as the accelerated motion of the 'particle'. This then leads to a simple explanation of Newton's Law of Inertia F = m.a.

An object at rest will remain at rest and an object in motion will continue in motion with a constant velocity unless it experiences a net external force. (Serway, 1992)

We can now translate the language of physics into the language of the Wave Structure of Matter (WSM). i.e. When we apply a Force to an object we are changing the velocity of the In-waves (from one direction), which changes the location of the wave-center, and which we see as the accelerated motion of the 'particle'. Conversely, if there is no change in the velocity of the spherical In-waves then there can be no change in the location of the wave-center, thus no change in the apparent motion of the 'particle'.

Finally, it is worth explaining here how 'solid bodies' can form from wave-motions as this relates to both the 'rigidity' of Space and the interconnection of the In and Out waves. The solution is simple as Wolff explains;

The solid crystal array is a matrix of atoms held rigidly in space. How are the atoms suspended in space? We must conclude that the crystal's rigidity derives from fixed standing waves propagating in a nearly rigid wave medium. Calculations for diamonds and nuclear structure yields an enormous rigidity. This is really a separate argument about the rigidity of space, which is one of its properties. (Wolff, 1994)

We also realize that because of this slight 'elasticity' of Space, there can be no absolutely rigid bodies in Space, as Einstein confirms;

The subtlety of the concept of space was enhanced by the discovery that there exist no completely rigid bodies. (Albert Einstein, 1954)

Wave Structure of Matter - Solid Bodies from Waves in a Rigid Space Fig. 1.1 Solid bodies form from fixed standing waves propagating in a nearly rigid wave medium.

1.2 Faraday's Electromagnetic Force Field (1832)

The greatest change in the axiomatic basis of physics - in other words, of our conception of the structure of reality - since Newton laid the foundation of theoretical physics was brought about by Faraday's and Maxwell's work on electromagnetic field phenomena. (Albert Einstein, 1954)

Faraday developed the mathematical concept of the 'electromagnetic force field' as a way of mathematically describing action-at-a-distance for charged particles (i.e. electrons and protons). This is a continuous mathematical 'plotting' of the effects (forces and thus accelerated motions) that matter has on other matter in the Space around it, thus it is a description of effects (inductive / a posteriori) rather than cause (deductive / a priori). And as we have explained, this is important because the ultimate Principles of Physics must be a priori, not a posteriori. It is also important to remember that the electromagnetic (e-m) field is a vector (directional) quantity that defines force and direction of acceleration of many charged particles upon one another. It is continuous in the sense that the distance and force between particles can vary by infinitely small amounts. As Einstein explains;

Faraday must have grasped with unerring instinct the artificial nature of all attempts to refer electromagnetic phenomena to actions-at-a-distance between electric particles reacting on each other. How was each single iron filing among a lot scattered on a piece of paper to know of the single electric particles running round in a nearby conductor? All these electric particles together seemed to create in the surrounding space a condition which in turn produced a certain order in the filings. These spatial states, today called fields, would, he was convinced, furnish the clue to the mysterious electromagnetic interactions. He conceived these fields as states of mechanical stress in an elastically distended body (ether). (Albert Einstein, 1954)

1.3 Maxwell's Equations and the Finite velocity of Light Waves (1876)

When Maxwell used this field theory to assume that light was an electromagnetic wave, and then correctly deduced the finite velocity of light, it was a powerful logical argument for the existence of the electromagnetic force field, and that light was a wave like change in the field (electromagnetic radiation) that propagated with the velocity of light c through the ether. In fact Maxwell was simply confirming that all wave-center to wave-center (particle) interactions are not instantaneous as Newton assumed, but are limited by the velocity of the In-waves which is the velocity of light c.
So while Maxwell misunderstood the true nature of the waves (which are real wave-motions of Space rather than mathematical vector e-m waves), he is largely correct. This new knowledge was significant as it established the importance of the finite velocity of light c and further enhanced the field theory, thus rejecting Newton's theory of particles and instant action-at-a-distance.

The precise formulation of the time space laws of those fields was the work of Maxwell. Imagine his feelings when the differential equations he had formulated proved to him that the electromagnetic fields spread in the form of polarized waves and with the speed of light! To few men in the world has such an experience been vouchsafed. Only after Hertz (1888) had demonstrated experimentally the existence of Maxwell's electromagnetic waves did resistance to the new theory break down. And what was true for electrical action could not be denied for gravitation. Everywhere Newton's (instant) actions-at-a-distance gave way to fields spreading with finite velocity. At that thrilling moment he surely never guessed that the riddling nature of light, apparently so completely solved, would continue to baffle succeeding generations.' (Albert Einstein, 1954)

And this is true. Because they were using a mathematical construction of a continuous e-m wave, rather than the Spherical Standing Wave, they did not anticipate Planck's discovery of the discrete 'quantum' properties of light. For standing wave interactions only occur at discrete frequencies, like notes on the string of a guitar, thus while the Spherical Standing Wave Structure of Matter predicts that wave interactions will be discrete, the continuous e-m wave does not anticipate this. (This is explained shortly in the section on Quantum Theory)

1.4 On Lorentz's Theory of the Electron (1900-1906)

Hendrik Lorentz assumed the electron was a charged particle which 'generated' a spherical spatially extended electromagnetic field in the ether. Thus inadvertently he continued this error of assuming both the 'particle' and the 'field' to be real (rather than simply being mathematical constructions.) As Einstein explains; This field is generated by atomistic electric charges upon which the field in turn exerts ponderomotive forces. (Albert Einstein, 1954)

Lorentz imagined that the ether exists throughout Space and that fields existed as a 'state' of this ether.

Indeed one of the most important of our fundamental assumptions must be that the ether not only occupies all space between molecules, atoms, or electrons, but that it pervades all these particles. We shall add the hypothesis that, though the particles may move, the ether always remains at rest. (Lorentz, 1906)

As Max Born writes;

Lorentz proclaimed the ether at rest in absolute space. In principle this identifies the ether with absolute space. Absolute space is no vacuum, but something with definite properties whose state is described with the help of two directed quantities, the electrical field E and the magnetic field H. (Born, 1924)

Lorentz is correct that Space pervades the particles, and that space is at rest, (i.e. rigid, does not 'flow'), the error is to assume separate 'particles' generating a 'field' in this Space, which as Einstein explains, causes several problems;

The introduction of the field as an elementary concept gave rise to an inconsistency of the theory as a whole. Maxwell's theory, although adequately describing the behavior of electrically charged particles in their interaction with one another, does not explain the behavior of electrical densities, i.e., it does not provide a theory of the particles themselves. They must therefore be treated as mass points on the basis of the old Newtonian theory. The combination of the idea of a continuous field with that of material points discontinuous in space appears inconsistent. Hence the material particle has no place as a fundamental concept in a field theory. Thus even apart from the fact that gravitation is not included, Maxwell's electrodynamics cannot be considered a complete theory. (Albert Einstein, 1954)

History shows that this problem is insurmountable as 'forces' must have 'particles' to act upon, thus the particle was a necessary part of the evolution of the field theory.

1.4.1 The Lorentz Transformation - The Electron Changes Ellipsoidal Shape With Motion

The Spherical Wave Structure of Matter tells us that there is no discrete particle and instead we are considering the behavior of the wave-center. Thus we realize that the 'motion' of the 'particle' through Space is actually the apparent motion of successive wave-centers which are determined by where each successive spherical (in reality ellipsoidal) In-Wave meets at its respective Wave-Center. As the spherical In and Out waves combine and then cancel one another, the 'particle' effect of the wave-center appears in a discrete point in Space, then disappears, then re-appears again as the next In-waves meets at its wave-center (roughly 1020 times per second).
As Wertheim explains;

In the quantum world, subatomic particles lurch about, suddenly disappearing from their starting points and reappearing as if by magic somewhere else. (Wertheim, 1997)

Further, this apparent motion of the wave-center (particle) is caused by a difference in velocity of the In-waves from one direction, and this also necessarily changes the spherical shape of the In-waves (they become squashed or stretched spheres / ellipsoids)

Moving Waves

Fig:1.4.1 The Ellipsoidal Shape of a Moving wave-center: If the In-waves on the right are slowed down as they travel in through Space then they change ellipsoidal shape (rather than being exactly spherical) and have a shorter wavelength. It is this change in velocity, ellipsoidal shape and wavelength of the In-wave which causes the apparent motion of the wave-center and the Lorentz Transformations.

The Lorentz Transformations provide formulas for the change of ellipsoidal shape of matter (SSWs) with the apparent 'motion' of the 'particle' (wave-center) and how this affects Mass, Time and Length / Dimension. This explains the 'null result' of the Michelson-Morley experiment as Lorentz explains;

In order to explain this absence of any effect of the Earth's translation (in the Michelson/Morley experiment), I have ventured the hypothesis, that the dimensions of a solid body undergo slight change, of the order of v2/c2, when it moves through the ether. … From this point of view it is natural to suppose that, just like the electromagnetic forces, the molecular attractions and repulsions are somewhat modified by a translation imparted to the body, and this may very well result in a change of dimensions. … The electrons themselves become flattened ellipsoids. .. This would enable us to predict that no experiment made with a terrestrial source of light will ever show us an influence of the Earth's motion. (Lorentz, 1906)

Michelson Morley

Fig: 1.4.2 The Michelson-Morley experiment. Due to our dimension being determined by wavelength, we shall always measure arm 1 of an interferometer, to be the same length as that of arm 2, irrespective of which direction we rotate the interferometer. The arms are both 7 wavelengths long. Thus it takes the same time for the ellipsoidal In-waves to propagate in to the center along arm 1 as it does along arm 2. This must be true as this is where the ellipsoidal wave meets at the wave-center to determine the apparent 'motion' of the 'particle'. As there is no time difference for the two paths, no interference is observed. This explains the Null result of the Michelson/Morley experiment.

The Michelson Morley experiment confirms that light takes the same time to travel each path irrespective of the motion of the observer. This is a general principle, and is the foundation of Einstein's principle of special relativity and thus his postulate that the velocity of light is always measured to be the same.

The so called special or restricted relativity theory is based on the fact that Maxwell's equations (and thus the law of propagation of light in empty space) are converted into equations of the same form, when they undergo a Lorentz transformation. (Albert Einstein, 1954)

1.5 Einstein's Relativity (1905,1915)

The special theory, on which the general theory rests, applies to all physical phenomena with the exception of gravitation; the general theory provides the law of gravitation and its relation to the other forces of nature. … The theory of relativity may indeed be said to have put a sort of finishing touch to the mighty intellectual edifice of Maxwell and Lorentz, inasmuch as it seeks to extend field physics to all phenomena, gravitation included. (Albert Einstein, 1954)

Einstein's Special Relativity is founded on the Empirical (a posteriori) truth that the laws of Nature are always measured to be the same for all observers irrespective of their non-accelerated motion relative to one another. This Principle of Relativity has been known since the seventeenth century and applied to Newton's Mechanics. Einstein cleverly applied this Principle of Relativity to Maxwell's equations and Lorentz's Electromagnetic Theory of the Electron, and thus the velocity of Light, as one of the laws of Nature, must also be measured to be the same. In fact the Wave Structure of Matter tells us that the velocity of light actually varies dependent upon the wave-amplitude and density of Space. But the velocity is always measured to be the same because any relative difference in the velocity of the In-wave from one side of the wave-center to the other, causes a corresponding change in wavelength and location of the wave-center, such that the same In-wave always meets at its wave-center at the same time. As velocity is length / time then the velocity of the In-wave (velocity of light c) is always measured to be the same.

Pythagoras Theorem

Fig: 1.5.1: Matter is Spherically Spatially Extended: Pythagoras' Theorem is caused by the spherical shape and thus interaction of matter. Further, three dimensional space and spherical space are equivalent, as it requires three dimensions to define the surface of a sphere.

Einstein correctly realized that matter was spherically spatially extended, and thus interacted with other matter spherically (this being the cause of Pythagoras' Theorem).

From the latest results of the theory of relativity it is probable that our three dimensional space is also approximately spherical, that is, that the laws of disposition of rigid bodies in it are not given by Euclidean geometry, but approximately by spherical geometry. (Albert Einstein, 1954)

But Einstein did not actually know how matter existed in Space;

The theory of relativity leads to the same law of motion without requiring any special hypothesis whatsoever as to the structure and behavior of the electron. (Albert Einstein, 1954)

His theory is empirically (a posteriori) founded from observation of how matter 'pushes' other matter around, thus his 'representation' of matter as spherical force field.

Einstein's Metric equation is simply Pythagoras' Theorem applied to the three spatial co-ordinates, and equating them to the displacement of a ray of light (the hypotenuse).

Special relativity is still based directly on an empirical law, that of the constancy of the velocity of light. dx2 + dy2 + dz2 =(cdt)2 where cdt is the distance traveled by light c in time dt.The fact that such a metric is called Euclidean is connected with the following. The postulation of such a metric in a three dimensional continuum is fully equivalent to the postulation of the axioms of Euclidean Geometry. The defining equation of the metric is then nothing but the Pythagorean theorem applied to the differentials of the co-ordinates. … In the special theory of relativity those co-ordinate changes (by transformation) are permitted for which also in the new co-ordinate system the quantity (cdt)2 equals the sum of the squares of the co-ordinate differentials. Such transformations are called Lorentz transformations. (Albert Einstein, 1954)

The reason why Special Relativity works mathematically is twofold:

i) Special relativity assumes that the velocity of light is constant, and thus it is true that if there is no change in the velocity of the In-wave then there can be no acceleration of the wave-center. This explains why special relativity is limited to relative motion between matter that is non-accelerated. (Inertial reference frames)

ii) In Einstein's Metric Equations the displacement of the light beam is determined by cdt, thus it makes no difference, mathematically speaking, if the velocity of light is assumed constant, and thus time is changed to keep the metrical equation true (as Einstein did) or conversely, to assume a constant Time, and that the velocity of In-waves (Light) is different. As it turns out, it is this latter case which is true, and this different velocity of the In-waves (from one side of the wave-center relative to the other) is the cause of the apparent motion of wave-centers.
Significantly, Einstein confirms this view that the velocity of light is not always constant when he writes that;

Special Relativity is founded on the basis of the law of the constancy of the velocity of light. But the general theory of relativity cannot retain this law. On the contrary, we arrived at the result that according to this latter theory the velocity of light must always depend on the co-ordinates when a gravitational field is present. (Albert Einstein, 1954)

Now it is this relationship of the change in wavelength (and thus ellipsoidal dimension) with Motion that is at the heart of Relativity so it is important to hear what Lorentz has to say on the subject;

It is clear that, since the observer is unconscious of these changes, (the contraction of a measuring rod in the direction of motion), relying on his rod, he will not find the true shape of bodies. He will take for a sphere what really is an ellipsoid. …
Attention must now be drawn to a remarkable reciprocity that has been pointed out by Einstein. ...
Let us now imagine that each observer (one is moving with constant velocity relative to the other) is able to see the system to which the other belongs, ...
It will be clear by what has been said that the impressions received by the two observers would be alike in all respects. It would be impossible to tell which of them moves or stands still with respect to the ether. …
His results concerning electromagnetic and optical phenomena agree in the main with those which we have obtained in the preceding pages, the chief difference being that Einstein simply postulates what we have deduced from the fundamental equations of the electromagnetic field. By doing so, he may certainly take credit for making us see in the negative result of experiments like those of Michelson, Rayleigh and Brace, not a fortuitous compensation of opposing effects, but the manifestation of a general and fundamental principle. Yet, I think, something may also be claimed in the favor of the form in which I have presented the theory. I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter. (Lorentz, 1906)

Most profoundly, Lorentz first deduced the foundations of Einstein's Relativity from the assumption of a rigid Space (ether) that had the properties of a wave-medium (i.e. vibrations). Though Einstein related relative motions of matter only to other matter and not back to an Absolute Space like Lorentz did, (which is mathematically simpler I suppose) the important point is that the logic of Relativity is founded on, and completely consistent with, an Absolute Space. By only considering relative motion Einstein effectively renounced the concept of Absolute Space and Motion and instead tried to represented matter as a spherical (spatially extended) field;

Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning. (Einstein, 1961) Since the field exists even in a vacuum, should one conceive of the field as state of a 'carrier', or should it rather be endowed with an independent existence not reducible to anything else? In other words, is there an 'aether' which carries the field; the aether being considered in the undulatory state, for example, when it carries light waves? The question has a natural answer: Because one cannot dispense with the field concept, it is preferable not to introduce in addition a carrier with hypothetical properties. …
The field thus becomes an irreducible element of physical description, irreducible in the same sense as the concept of matter (particles) in the theory of Newton. (Albert Einstein, 1954)

These quote are worth close attention, for they highlight Einstein's error. We now realize that the continuous force field is an approximation of many discrete standing wave interactions (see Quantum Theory), and further, the field is an empirically founded (a posteriori) concept and thus cannot be fundamental. Hence we must reject the field, thus it is not only preferable, but necessary, to consider the 'carrier with hypothetical properties', i.e. Space existing with the properties of a wave-medium.

It is now possible to show that Einstein's ideas need only a slight modification, from his foundation that matter is a spherical spatially extended 'field', to a foundation based upon Space rather than matter, and that matter is caused by Spherical Standing Wave Motions of Space. Thus Einstein is correct in rejecting the concept of the particle and to realize the connection between matter and Space;

According to general relativity, the concept of space detached from any physical content (matter, objects) does not exist. The physical reality of space is represented by a field whose components are continuous functions of four independent variables - the co-ordinates of space and time. Since the theory of general relativity implies the representation of physical reality by a continuous field, the concept of particles or material points cannot play a fundamental part, nor can the concept of motion. The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high. (Albert Einstein, 1954)

It is true that the particle can only appear as a limited region in Space in which the field strength/energy density is particularly high, for this is simply the high wave-amplitude & density of the wave-center of the Spherical Standing Wave.
This obviously also explains why matter can never exceed the velocity of light. As the 'particle' is the wave-center of the Spherical Standing Wave (SSW), it is impossible for this wave-center to ever move faster than the velocity of the incoming waves, which is the velocity of light. Unfortunately Einstein incorrectly assumed that a mathematical description of effects, the spherical, spatially extended continuous force field, was the best way of representing reality. In fact these force field effects are caused by the changing velocity of the In-waves which determine the future location of the wave-center (and thus the apparent force and accelerated motion of the particle). We now realize that the field theory is a continuous mathematical approximation of effects which are caused by many discrete (quantum) standing wave interactions. Hence the Wave Structure of Matter (WSM) explains the cause of both the 'field' and the 'particle effects'.

Though most of Einstein's discussion of Space is in terms of matter interactions described by fields (a purely mathematical analysis), it is important to realize that Einstein also had a reasonable understanding of metaphysics, thus he realized (particularly in his later life) that Space must somehow exist and have properties that caused these force fields, he just did not know how they existed and was not inclined to idle speculation. He writes;

Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of matter, as consisting of parts ('particles') which may be tracked through time. The idea of motion may not be applied to it. (Einstein, Leiden Lecture, 1920)

Thus, like Kant (and others), Einstein assumed that motion only applied to particles, and as he did not believe in particles he also did not believe in Motion, thus he never considered the wave Motion of Space itself!

1.5.2 General Relativity (On Accelerated Motion and Gravitation. 1915)

General Relativity extends Special Relativity to include accelerated Motion thus it is important to first ask what causes the acceleration of matter. The solution is quite simple. By understanding the spherical In and Out wave structure of matter we deduce that any change in velocity of the In-waves (from one direction) causes a change in where the In-waves meet at their wave-centers which we observe as the accelerated Motion of the particle. This is why acceleration exists and is defined as a change in velocity - because it is caused by a change in velocity of the In-waves! This change in the velocity of waves in Space is dependent upon the mass-energy density of space (for Gravitational Mass), and is the true physical cause of General Relativity and Einstein's gravitational fields, thus explaining Einstein's comment that; the velocity of light must always depend on the co-ordinates when a gravitational field is present. (Albert Einstein, 1954)

The Equivalence of Inertial Mass and Gravitational Mass

The empirical foundation of General Relativity is the equivalence of gravitational and inertial mass, as Einstein explains; Mass is defined by the resistance that a body opposes to its acceleration (inert mass). It is also measured by the weight of the body (gravity mass). That these two radically different definitions lead to the same value for the mass of a body is in itself an astonishing fact. (Albert Einstein, 1954)

The Properties of Space and the Wave Structure of Matter (WSM) explain the equivalence of these two forms of Mass.

i) Inertial Mass. Imagine the wave-center (electron) of a Spherical Standing Wave (SSW) in free Space away from massive bodies. As the mass-energy density of space is the same in all directions, therefore the velocity of the In-waves is the same from all directions and does not change, thus the In-waves will always meet at the same point in Space (the wave-center). This is the physical foundation of inertial mass, a body remains stationary (it does not accelerate) if there is no change in the velocity of the In-waves (no forces act upon it).

ii) Gravitational Mass. Consider the same stationary wave-center (electron) of a SSW but now imagine a massive body, such as the Earth, placed to one side of the electron. The Space that the Earth occupies has a higher mass-energy density of space, thus the velocity of In-waves and Out-waves (velocity of light) will be slower in this Space. This causes a change in ellipsoidal shape of the In-waves and results in the wave-center (electron) moving towards the Space of higher mass-energy density of space (the earth).

And so we see that it is the same property of Space that causes both gravitational mass and inertial mass, thus explaining their equivalence.

Let us now consider a simple example of this equivalence that will make it easier to understand. Imagine being in a spaceship away from any stars or other massive bodies. We would be weightless in the Space as there would be no gravitational effect. Now if we imagine the spaceship being accelerated upwards, (relative to the floor), at 9.8m/s, we would not be able to tell if we are being accelerated or if we are in the Earth's gravitational field. Further, if we were standing on scales, our weight could be due either to the inertia caused by accelerating the spaceship, or to our mass in a gravitational field. This is the empirical equivalence of gravitational and inertial mass.

Einstein cleverly used this equivalence to argue (mathematically) that gravity could be treated as an accelerated reference frame;

The principle of the equivalence of inertial and gravitational mass could now be formulated quite clearly as follows: in a homogenous gravitation field all motions take place in the same way as in the absence of a gravitational field in relation to uniformly accelerated co-ordinate system. … There is no reason to exclude the possibility of interpreting this behavior as the effect of a 'true' gravitational field (principle of equivalence of inertial/gravitational mass). (Albert Einstein, 1954)

Thus if we know the Lorentz transformation for moving with a constant velocity, (which require linear transformations of the co-ordinate system) then we can calculate how the Lorentz transformation would change (i.e. the changing ellipsoidal shape of matter) if the reference frame is now accelerated, and we can then use these transformations to describe not only an accelerated reference frame but also a gravitational field. Einstein is thus forced to use a curved (non-linear) co-ordinate system (rather than linear as per Special Relativity and the Lorentz Transformations), which he found from the work of Gauss and Riemann (on curved coordinate systems).

In order to account for the equality of inert and gravitational mass within the theory it is necessary to admit non-linear transformations of the four co-ordinates. Mathematics suggests an answer which is based of the fundamental investigations of Gauss and Riemann. (Albert Einstein, 1954)

To introduce this non-linear transformation, it was necessary for Einstein to adjust the velocity of light dependent upon the energy density (gravitational field) of Space. This is true, because it is this change in mass-energy density of space, due to the presence of matter (as Spherical/Ellipsoidal Wave-Motions of Space), that causes a slowing of the wave velocity and a change in its ellipsoidal shape, and this is the ultimate cause of gravitational forces and the resultant acceleration of the 'particle'.

Summary of Einstein's Relativity
(Explaining and Solving the Problems of Einstein's Relativity)

Einstein (from Faraday, Maxwell, Lorentz) represented matter as a continuous spherical electromagnetic force field in spacetime. Einstein is correct that there is no 'particle' and matter is spherically spatially extended. However, the spherical 'force field' can be sensibly explained with the Spherical Standing Wave Structure of Matter. We realize that forces are caused by a change in the velocity of the spherical In-wave (from one direction) as this changes where these In-waves meet at the wave-center, which we observe as a 'force accelerating a particle'. The change in ellipsoidal shape of the In-waves is the cause of Einstein's Metrics and the Riemannian geometry of General Relativity. With this new understanding let us then briefly summarize the problems of Einstein's Relativity, as their solutions become obvious once we understand the Spherical Standing Wave Structure of Matter.

i) Einstein's Relativity is a Theory of a posteriori Effects not a priori Causes, and is founded on Many things (Matter) rather than One thing (Space).

Einstein did not know how matter existed in Space and his electromagnetic field theory of matter is Inductive (empirical / a posteriori) and describes effects (of relative motion).

The theory of relativity leads to the same law of motion without requiring any special hypothesis whatsoever as to the structure and behavior of the electron. (Einstein, 1954)

His theory is empirically (a posteriori) founded from observation of how matter 'pushes' other matter around (thus his 'representation' of matter as spherical force fields).

As Ernst Mach insistently pointed out, the Newtonian theory is unsatisfactory in the following respect: if one considers motion from the purely descriptive, not from the causal, point of view, it only exists as relative motion of things with respect to one another.
It compelled Newton to invent a physical space in relation to which acceleration was supposed to exist. This introduction ad hoc of the concept of absolute space, while logically unacceptionable, nevertheless seems unsatisfactory.

Considered logically, concepts are free creations of the human intelligence, tools of thought, which are to serve the purpose of bringing experiences into relation with each other, so that in this way they can be better surveyed. The attempt to become conscious of the empirical sources of these fundamental concepts should show to what extent we are actually bound to these concepts. In this way we become aware of our freedom to create new concepts.

Descartes argued somewhat on these lines: space is identical with extension, but extension is connected with bodies; thus there is no space without bodies and hence no empty space.

It appears to me, therefore, that the formation of the concept of the material object must precede our concepts of time and space. (Albert Einstein, 1954)

Metaphysics, as a true description of Reality, must be based on a priori causes AND these must be united back to one common thing that causes and connects the many things (matter). The Metaphysics of Space and Motion is founded on the a priori existence of One thing, Space and its properties as a wave-medium, that One thing, Space, must first exist for Many things, matter to be able to exist and move about in an interconnected manner (as reality shows).

ii) Continuous Fields do Not Explain the Discrete Energy Levels of Matter and Light as Determined by Quantum Theory.

The Electric and Magnetic Force Fields were first founded on repeated observations (Induction / a posteriori) of how many trillions of charged 'particles' (electrons and protons) behaved. This explains why the fields were continuous, as many trillions of discrete standing wave interactions blend together into a continuous force. Thus the continuous field can never describe the real standing wave interactions of matter, as Einstein came to realize.

The great stumbling block for the field theory lies in the conception of the atomic structure of matter and energy. For the theory is fundamentally non-atomic in so far as it operates exclusively with continuous functions of space, in contrast to classical mechanics whose most important element, the material point, in itself does justice to the atomic structure of matter. (Einstein, 1954)

iii) Einstein's 'Fields' require 'Particles'.

As Einstein used the empirical/theoretical foundations developed by Faraday, Maxwell and Lorentz he required the existence of a 'Particle' to somehow generate the 'Field' which in turn acted on other 'Particles'.

The special and general theories of relativity, which, though based entirely on ideas connected with the field-theory, have so far been unable to avoid the independent introduction of material points, … the continuous field thus appeared side by side with the material point as the representative of physical reality. This dualism remains even today disturbing as it must be to every orderly mind. (Einstein, 1954)

iv) Einstein's Continuous Field Theory of Matter gives rise to Singularities and Infinite Fields.

The Maxwell equations in their original form do not, however, allow such a description of particles, because their corresponding solutions contain a singularity. Theoretical physicists have tried for a long time (1936), therefore, to reach the goal by a modification of Maxwell's equations. These attempts have, however, not been crowned with success. What appears certain to me, however, is that, in the foundations of any consistent field theory the particle concept must not appear in addition to the field concept. The whole theory must by based solely on partial differential equations and their singularity-free solutions. (Einstein, 1954)

As Wolff explains (see Quantum Theory), the equation for a scalar spherical wave give rise to a finite wave-amplitude at the wave-center (consistent with observation) whereas spherical vector electromagnetic fields tend to infinity as the radius tends to zero (and there are no vector e-m solutions in spherical coordinates!).

v) Einstein Rejects both 'Particles' and Motion.

While Einstein correctly rejected the point 'particle' concept of matter, he assumed that Motion only applied to 'particles' (a common error!) thus he also rejected the concept of Motion, and represented matter as spherical force fields. The error is twofold; firstly, he did not consider the (wave) Motion of Space itself, and secondly, he should have realized that to measure forces we must first measure the change in Motion of a particle, thus Motion is a priori to forces (i.e. Force = dE/dx).

Since the theory of general relativity implies the representation of physical reality by a continuous field, the concept of particles or material points cannot play a fundamental part, nor can the concept of motion. (Einstein, 1954)

We now realize that neither the 'Particle' nor the continuous electromagnetic force 'Field' is a complete description of Reality thus we must reject both the 'Particle' and the 'Field', and what remains is Motion. Hence we can now clearly see both Einstein's error and the true path left to explore - the study of Space as a wave medium for wave Motion - and that the Spherical Wave Motion of Space explains both the 'particle' (wave-center) and 'forces' (change in velocity of In-Waves, which changes the location of the Wave-Center).

vi) Einstein Assumed Matter Caused Space Rather than the Wave-Motion of Space Causing Matter.

Einstein was profoundly influenced by Mach;

Mach, in the nineteenth century, was the only one who thought seriously of the elimination of the concept of space, in that he sought to replace it by the notion of the totality of the instantaneous distances between all material points. (He made this attempt in order to arrive at a satisfactory understanding of inertia.) (Einstein, 1954)

Because we only observe the motion of matter relative to all the other matter in the universe, thus Einstein thought that matter, rather than Space, must be the central perspective for representing Reality. Thus Einstein's Relativity is empirically (a posteriori) founded from observing the motion of matter relative to other matter. The Metaphysics of Space and Motion is founded on the a priori fact that Space is first necessary for matter to be able to exist and move about. Einstein is empirically correct, and at the same time this was his error because Metaphysics (and thus Reality) is not founded on empirical observations. In reality there is no motion of matter, there is only the spherical wave-motion of Space, and the changing location of the wave-center gives the 'illusion' of the motion of matter 'particles'. (Thus Einstein's Relativity is founded on an illusion that matter moves, when it is Space which is moving / vibrating.)
Thus Newton was ultimately correct;

And so instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in Philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them. (Newton, 1687)

Further, Lorentz's assumption of an Absolute Space is the foundation for the Lorentz transformations and thus for Einstein's Relativity.

I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter. (Lorentz, The Theory of the Electron, 1906)

Einstein choose to ignore Space / Aether and work with relative motions of matter to other matter, with matter being represented by spherical fields.

The electromagnetic fields are not states of a medium, and are not bound down to any bearer, but they are independent realities which are not reducible to anything else. (Albert Einstein, Leiden Lecture, 1920)

In other words, is there an ether which carries the field; the ether being considered in the undulatory state, for example, when it carries light waves? The question has a natural answer: Because one cannot dispense with the field concept, it is preferable not to introduce in addition a carrier with hypothetical properties. (Albert Einstein, 1950)

Once we realise that the particle and the continuous electromagnetic field it generates are both merely ideas, human approximations to reality, then we solve these problems. We return to Lorentz's foundation of One thing Space, and its properties as a wave medium (vibrations) and replace the spherical particle & field with the spherical wave Motion of Space. The idea of the field theory of matter misled Einstein, and yet Einstein also realised that there must somehow be a Space that interconnects matter.

Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it. (Albert Einstein, Leiden Lecture, 1920)

vii) Einstein Never United the Electromagnetic & Gravitational Fields into a Unified Field Theory for Matter

Einstein's Relativity requires both an Electromagnetic Force Field to explain Charge, and a Gravitational Field to explain Mass. He tried and failed throughout his life to unite these two fields into one (and to remove the 'particle' concept from them).

But the idea that there exist two structures of space independent of each other, the metric-gravitational and the electromagnetic, was intolerable to the theoretical spirit. We are prompted to the belief that both sorts of field must correspond to a unified structure of space. (Einstein, 1954)

We can now unite these two fields by demonstrating how they are both caused by the properties of Space, i.e. that the wave velocity varies with both wave-amplitude (charge) and mass-energy density of space (mass).

viii) Einstein's 'Curvature of the 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 (for gravitational forces) 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 which changes the ellipsoidal shape of matter and causes the curved path of matter and light in Space. And this caused Einstein considerable problems (it took him ten years to work out the ellipsoidal geometry for gravity/general relativity!)

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. (Albert Einstein, 1954)

Further, the four dimensional space-time continuum 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 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. (Albert Einstein, 1954)

The inseparability of time and space emerged in connection with electrodynamics, or the law of propagation of light.
With the discovery of the relativity of simultaneity, space and time were merged in a single continuum in a way similar to that in which the three dimensions of space had previously merged into a single continuum. Physical space was thus extended to a four dimensional space which also included the dimension of time. The four dimensional space of the special theory of relativity is just as rigid and absolute as Newton's space. (Albert Einstein, 1954)

In fact the spherical wave Motion of Space requires three spatial dimensions and a (wave) motion dimension (rather than a time dimension, as motion causes time). Now this is very important, for it is this 'curvature' that largely led to Einstein's early fame. 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. 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. (Einstein, 1954)

Concluding Remarks

Towards the end of his life Einstein was acutely aware that he had failed to realize his dream of a unified field theory for matter and that the continuous spherical spatially extended force field may not truly represent the reality of matter. In 1954 Einstein wrote to his friend Michael Besso expressing his frustration;

All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. … I consider it quite possible that physics cannot be based on the field concept, i.e., on continuous structures. In that case, nothing remains of my entire castle in the air, gravitation theory included, [and of] the rest of modern physics.

Albert Einstein's General Theory of Relativity (GTR) has been summarized as, 'The matter of the universe determines the properties of Space, and the properties of Space determine the behaviour of matter.'
The GTR is an experimentally correct description of the universe but how or why it occurs was mysterious. With the Wave Structure of Matter (WSM) we now see the existence of a universal symmetry and interdependence of all matter in the universe. The Wave Structure of Matter is the cause of this profound symmetry.
Principle Two of the WSM can be rephrased as, All waves from matter of the universe determine the mass-energy density of space which determines the velocity of the waves c which then determines the behaviour of matter in Space.
We can further shorten this to Matter affects Space affects Matter.
Thus the Wave Structure of Matter (WSM) explains the fundamental origins of Albert Einstein's General Theory of Relativity (GTR) and its application to the cosmic scale gravitational motion of the matter of planets, stars, galaxies, etc.

Significantly though, the WSM also explains the Quantum realm, and how Wave-Centers (particles) interact with other particles in the Space around them, thus explaining Quantum Theory and the cause of the discrete 'quanta' (photon) properties of light. Hence the Spherical Standing Wave Structure of Matter explains both the large scale (Cosmic realm) geometry of General Relativity (gravity) as well as the small scale (Quantum realm) particle interactions of Quantum Theory (light). (As a true description of reality must.)
All that needs to be done now (though this is no easy task I imagine!) is for some clever and curious Mathematician to apply the Two Principles of the WSM to Albert Einstein's Relativity and show that the two are mathematically equivalent. This mathematics will be simpler, contain no infinities/singularities, and will also be consistent with Quantum Theory and Cosmology. Thus there now exists the opportunity for mathematical physicists to explore a profound new logical language which should provide many solutions to their current problems and in time lead to a revolution of their subject.

2. Quantum Theory

A careful analysis of the process of observation in atomic physics has shown that the subatomic particles have no meaning as isolated entities, but can only be understood as interconnections between the preparation of an experiment and the subsequent measurement. Quantum theory thus reveals a basic oneness of the universe. The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena. The verbal interpretation, on the other hand, i.e. the metaphysics of quantum theory, is on far less solid ground. In fact, in more than forty years physicists have not been able to provide a clear metaphysical model. (Fritjof Capra, 1975)


The One Principle of the Metaphysics of Space and Motion and the Spherical Wave Structure of Matter provide this 'clear metaphysical model'. The problem, as we shall explain, has been the conception of the 'particle' and thus the resulting paradox of the 'particle / wave' duality. These problems have caused great confusion within modern physics over the past seventy years, as both Heisenberg and Davies explain;

Both matter and radiation possess a remarkable duality of character, as they sometimes exhibit the properties of waves, at other times those of particles. Now it is obvious that a thing cannot be a form of wave motion and composed of particles at the same time - the two concepts are too different. (Heisenberg, 1930)

The idea that something can be both a wave and a particle defies imagination, but the existence of this wave-particle 'duality' is not in doubt. .. It is impossible to visualize a wave-particle, so don't try. ... The notion of a particle being 'everywhere at once' is impossible to imagine. (Davies, 1985)

The solution to this apparent paradox is to simply explain how the discrete 'particle' properties of matter and light (quanta) are in fact caused by the Spherical Standing Wave Structure of Matter.

2.1 Max Planck's Discovery of the Particle (Quantum) Properties of Light (1900)

In the year nineteen hundred, in the course of purely theoretical (mathematical) investigation, Max Planck made a very remarkable discovery: the law of radiation of bodies as a function of temperature could not be derived solely from the Laws of Maxwellian electrodynamics. To arrive at results consistent with the relevant experiments, radiation of a given frequency f had to be treated as though it consisted of energy atoms (photons) of the individual energy hf, where h is Planck's universal constant. This discovery became the basis of all twentieth-century research in physics and has almost entirely conditioned its development ever since. Without this discovery it would not have been possible to establish a workable theory of molecules and atoms and the energy processes that govern their transformations. Moreover, it has shattered the whole framework of classical mechanics and electrodynamics and set science a fresh task: that of finding a new conceptual basis for all physics. Despite remarkable partial gains, the problem is still far from a satisfactory solution. (Albert Einstein, 1954)

Albert Einstein (1905) used Planck's relationship to explain the results of the photoelectric effect which showed that the energy E of ejected electrons was dependent upon the frequency f of incident light as described in the equation E=hf. It is ironic that in 1921 Einstein was awarded the Nobel Prize for this discovery, though he never believed in particles and acknowledged that he did not know the cause of the discrete energy transfers (photons) which were contradictory to his continuous field theory of matter. However, his work on the photoelectric effect confirmed that light energy was only emitted and absorbed by electrons in discrete amounts or quanta. This quanta of light energy soon became known as the 'photon' (i.e. discrete like a particle) and led to the paradox that light behaved both as a continuous e-m wave (Maxwell, Einstein) as well as a discrete particle/photon (Planck, Einstein). We can now understand the cause of this discrete energy 'quanta' because Standing waves only exist and interact at discrete frequencies, like notes on the string of a guitar. This then leads us to the work of de Broglie and Schrodinger.

2.2 de Broglie's Discovery of the wave Properties of Electron Interactions (1927)

The next step was taken by de Broglie. He asked himself how the discrete states could be understood by the aid of current concepts, and hit on a parallel with stationary (standing) waves, as for instance in the case of proper frequencies of organ pipes and strings in acoustics. (Albert Einstein, 1954)

de Broglie's realization that standing waves exist at discrete frequencies and thus energies is obviously true and important, yet he continued with the error of the particle concept and thus imagined particles moving in a wavelike manner! Nonetheless, as he was close to the truth he had considerable success with his theory as Einstein confirms;

Experiments on interference made with particle rays have given brilliant proof that the wave character of the phenomena of motion as assumed by the theory does, really, correspond to the facts. (Albert Einstein, 1954)

So by 1927 the wave properties of matter had been predicted theoretically by de Broglie, and then confirmed by experiment. But unfortunately these scientists continued to believe in the existence of discrete particles, and thus they misinterpreted this most important discovery of the standing wave properties of matter.

2.2.1 de Broglie's Incorrect Interpretation of the Standing waves as the wave-Like Motion of a Particle in Orbit (1927)

In 1913, Niels Bohr had developed a simple (though only partly correct) model for the hydrogen atom that assumed;
i) That the electron particle moves in circular orbits about the proton particle. (This is nearly correct, they are not 'orbits' but complex standing wave patterns.)
ii) Only certain orbits are stable. (This is nearly correct, only certain standing wave patterns are resonantly stable.)
iii) Light is emitted and absorbed by the atom when the electron 'jumps' from one allowed orbital state to a another. (This is nearly correct, the electrons move from one stable standing wave pattern to another.)
de Broglie was aware of Bohr's model for the atom and he cleverly found a way of explaining why only certain orbits were 'allowed' for the electron, as Einstein explains;

de Broglie conceived an electron revolving about the atomic nucleus as being connected with a hypothetical wave train, and made intelligible to some extent the discrete character of Bohr's 'permitted' paths by the stationary (standing) character of the corresponding waves. (Albert Einstein, 1954)

de Broglie Electron Wave Orbits

Fig: 2.2.1 Electron Orbits. de Broglie imagined the standing waves to be related to discrete wavelengths and standing waves for certain orbits of the electron 'particle' about the proton. (Rather than considering the actual standing wave structure of the electron itself.)

de Broglie further explains his reasoning for the particle/wave duality of matter in his 1929 Nobel Prize acceptance speech;

Determination of the stable motion of electrons in the atom introduces integers, and up to this point the only phenomena involving integers in physics were those of interference and of normal modes of vibration. This fact suggested to me the idea that electrons too could not be considered simply as particles, but that frequency (wave properties) must be assigned to them also.

2.3 The Schrodinger Wave Equations are founded on Standing Wave Interactions (1928)

Erwin Schrodinger discovered that when frequency f and de Broglie wavelength y were substituted into general wave equations it becomes possible to express energy E and momentum mv as wave functions - thus a confined particle (e.g. an electron in an atom/molecule) with known energy and momentum functions could be described with a certain wave function.
From this it was further found that only certain frequency wave functions, like frequencies on musical strings, were allowed to exist. These allowed functions and their frequencies depended on the confining structure (atom or molecule) that the electron was bound to (analogous to how strings are bound to a violin, and only then can they resonate at certain frequencies). Significantly, these allowed frequencies corresponded to the observed discrete frequencies of light emitted and absorbed by electrons bound in atoms/molecules. This further confirmed the standing wave properties of matter, and that only certain standing wave frequencies could exist which corresponded to certain energy states.

As Einstein explains;

How can one assign a discrete succession of energy values E to a system specified in the sense of classical mechanics (the energy function is a given function of the co-ordinates x and the corresponding momenta mv)? Planck's constant h relates the frequency f =E/h to the energy values E. It is therefore sufficient to assign to the system a succession of discrete frequency f values. This reminds us of the fact that in acoustics a series of discrete frequency values is coordinated to a linear partial differential equation (for given boundary conditions) namely the sinusoidal periodic solutions. In corresponding manner, Schrodinger set himself the task of coordinating a partial differential equation for a scalar wave function to the given energy function E (x, mv), where the position x and time t are independent variables. (Albert Einstein, 1954)

And here we have a final piece of the puzzle in a sense, for it was Schrodinger who discovered that the standing waves are scalar waves rather than vector electromagnetic waves. This is an important difference, vector e-m waves are mathematical waves which describe a direction (vector) of force, whereas the wave Motions of Space are scalar waves which are simply described by their wave-amplitude. With de Broglie's introduction of the concept of standing waves to explain the discrete energy states of atoms and molecules, and the introduction of scalar waves by Schrodinger, they had intuitively grasped important truths of nature as Einstein confirms;

The de Broglie-Schrodinger method, which has in a certain sense the character of a field theory, does indeed deduce the existence of only discrete states, in surprising agreement with empirical facts. It does so on the basis of differential equations applying a kind of resonance argument. (Albert Einstein, 1954)

So let us now explain in more detail this phenomena of light energy being emitted and absorbed in discrete amounts (photons) due to standing wave interactions and resonant coupling.

2.4 Explaining the Forces of Charge and Light

It is a property of Space that the greater the wave-amplitude the greater the wave-velocity (and vice versa) and this then provides a sensible explanation of both charge and light. Because wave-amplitude is both positive and negative, thus interacting wave-amplitudes can either increase or decrease (i.e. combine or cancel out), causing either an increase or decrease in the velocity of the In-waves, and a consequent moving together, or moving apart of the wave-centers. Thus when we place two electrons near one another in Space, then the wave-amplitude of Space between them increases because the waves are in phase and the wave-amplitudes combine and increase, thus the wave-velocity increases (opposite to gravity's slowing of In-waves) and this causes the wave-centers to move apart. Conversely, if we place an electron and a positron (anti-matter being the opposite phase wave-motion to matter, thus a positron is the opposite phase to an electron) then the wave-amplitude between the two wave-centers tends to cancel out and become smaller, thus the wave-velocity between the two wave-centers decreases (like gravity) and thus causes the wave-centers to move together.(This explains the Minimum Amplitude Law and the electrical repulsion of like charges, and attraction of opposite charges.)
In fact this also explains the electron / positron (matter / antimatter) annihilation, as the wave-centers will eventually overlap one-another and the wave-amplitudes will completely cancel out (due to their equal and opposite phase) and thus disappear. This explains Charge, but does not explain Light, which is slightly more complex.

2.4.1 On Resonant Coupling as the Cause of Light

We must further realize that light is only emitted and absorbed by electrons bound in atoms or molecules, and these electrons have some complex repeating standing wave-motion about the nucleus. Thus the electrons behave as 'oscillating resonators' and it is common knowledge to electrical engineers and physicists that two interconnected resonators can undergo resonant coupling, where one resonator decreases in frequency and the other one increases a corresponding amount. (Like two connected pendulums.) The coupling provided by the non-linear centers of the resonances (high wave-amplitude wave-centers where the wave-velocities change ) causes them to change velocity, frequency, and wavelength, due to the interaction (modulation) of each other's waves. When opposite changes of frequency (energy ) takes place between two resonances, energy seems to be transported from the center of one resonance to another. We observe a loss of energy where frequency decreases and added energy where it increases. The exchange appears to travel with the speed of the In-waves of the receiving resonance which is c, the velocity of light. When large numbers of changes occur together we see a continuous beam of light (i.e. electromagnetic radiation). When single exchanges occur we see 'photons' as discrete energy exchanges. The transitory modulated waves traveling between two resonances (as the electrons/wave-centers move from one standing wave pattern to another) create the illusion of the 'photon'. An exchange may require 108 to 1015 cycles to complete, depending on the degree of coupling and species of resonance.

Fig: 2.4.1 Light is Caused by the Resonant Coupling of two bound wave-centers of Spherical Standing Waves (electrons) with oscillating wave functions. This diagram is only an approximation, but it gives you some idea of the 'secondary' wavelength (the 'electromagnetic' wavelength of light) caused by the interactions of the In and Out-waves of the two oscillating electrons/wave-centers.

These standing wave patterns cause a cyclical oscillation in the ellipsoidal shape of the In and Out-waves which describes a wave function that is ultimately the cause of the 'electromagnetic' wavelength and frequency of light. As only certain discrete 'orbits' (standing wave functions described by Schrodinger's wave equations) exist for the wave-center of the Spherical Standing Wave, then it can only exchange frequencies in discrete levels which correspond to discrete energy exchanges of light 'photons'.

2.5 Heisenberg's Uncertainty Principle & Born's 'Probability waves' (1928)

At the same time that the wave properties of matter were discovered, two further discoveries were made that also profoundly influenced (and confused) the future evolution of modern physics.
Firstly, Werner Heisenberg developed the uncertainty principle which tells us that we (the observer) can never exactly know both the position and momentum of a particle. As every observation requires an energy exchange (photon) to create the observed 'data', some energy (wave) state of the observed object has to be altered. Thus the observation has a discrete effect on what we measure, limiting how precisely we can determine both the position and momentum of the particle.
Max Born (1928) was the first to discover (by chance and with no theoretical foundation) that the square of the quantum wave equations (which is actually the mass-energy density of space) could be used to predict the probability of where the particle would be found. Since it was impossible for both the waves and the particles to be real entities, it became customary to regard the waves as unreal 'probability waves' and to maintain the belief in the 'real' particle. Unfortunately this maintained the belief in the particle/wave duality, in a new form where the 'quantum' scalar waves had become 'probability waves' for the 'real' particle.

Einstein agreed with this probability wave interpretation, as he believed in continuous force fields (not in waves or particles) thus to him it was sensible that the waves were not real, and were mere descriptions of probabilities.

It seems to be clear, therefore, that Born's statistical interpretation of quantum theory is the only possible one. The wave function does not in any way describe a state which could be that of a single system; it relates rather to many systems, to an 'ensemble of systems' in the sense of statistical mechanics. (Albert Einstein, 1954)

Einstein is correct that matter is spherically spatially extended (but as a Spherical Standing Wave, not as continuous spherical force fields) thus it is true that matter is intimately interconnected to all the other matter in the universe (by the spherical In and Out-Waves). It is this lack of knowledge of the system as a whole that is the ultimate cause of the uncertainty and resultant probability inherent in Quantum Theory.

Thus the last and most successful creation of theoretical physics, namely quantum mechanics (QM), differs fundamentally from both Newton's mechanics, and Maxwell's e-m field. For the quantities which figure in QM's laws make no claim to describe physical reality itself, but only probabilities of the occurrence of a physical reality that we have in view. … I cannot but confess that I attach only a transitory importance to this interpretation. I still believe in the possibility of a model of reality - that is to say, of a theory which represents things themselves and not merely the probability of their occurrence. On the other hand, it seems to me certain that we must give up the idea of complete localization of the particle in a theoretical model. This seems to me the permanent upshot of Heisenberg's principle of uncertainty. (Albert Einstein, 1954)

Einstein believed that Reality was not founded on chance (as Bohr and Heisenberg argued) but on necessary connections between things (thus his comment 'God does not play dice.'). He was largely correct, matter is necessarily connected due to the Spherical Standing Wave Structure of Matter, but due to lack of knowledge of the system as a whole (the universe), then this gives rise to the chance and uncertainty found in Quantum Theory. It is also true that we must give up the idea of complete localization and knowledge of the 'particle', which is merely a mathematical concept and is caused by the wave-center of the Spherical Standing Wave.
Remarkably, Stephen Hawking was very close to the truth when he wrote;

But maybe that is our mistake: maybe there are no particle positions and velocities, but only waves. It is just that we try to fit the waves to our preconceived ideas of positions and velocities. The resulting mismatch is the cause of the apparent unpredictability. (Hawking, 1988)

2.6 Wolff's explanation of Feynman's Quantum Electrodynamics (QED, 1945)

QED is founded on the assumption that charged 'particles' somehow generate spherical electromagnetic (vector) In and Out waves. This explains why Feynman had such success and such failure at the same time, as he had the correct spherical wave structure of matter, but he continued with two further errors, the existence of the particle, and the use of vector 'electromagnetic' waves (mathematical waves of force), rather than using the correct scalar 'quantum' waves. The solution to these problems was first found by Wolff (1986).
Wolff realized that there are no solutions for spherical vector electromagnetic waves, and he had the foresight to try using real 'quantum' waves, which are scalar. He then discovered that when one spherical standing wave was moving relative to another the Doppler shifts gave rise to BOTH the de Broglie wavelength AND the Mass increase of Einstein's Special Relativity. Thus in the one equation he had deduced the two observed phenomena due to relative motion, which respectively found central parts of both Quantum Theory and Einstein's Special Relativity. This then led to his further work on the Spherical Wave Structure of Matter and explanations for the following problems;

2.6.1 The problem of 'Renormalization'

The electromagnetic field theory of matter gives rise to infinitely high fields (singularities) at the center of the point particle electron. This was avoided with 'renormalization' whereby infinity is subtracted from infinity and the correct experimental result was substituted into the equation. Paul Dirac wrote;

Sensible mathematics involves neglecting a quantity when it turns out to be small - not neglecting it just because it is infinitely great and you do not want it! (Paul Dirac)

Richard Feynman also knew this;

But no matter how clever the word, it is what I call a dippy process! Having to resort to such hocus pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self consistent. ... I suspect that renormalization is not mathematically legitimate. (Richard Feynman, 1985)

The solution is to realize that scalar spherical 'quantum' waves have a finite wave amplitude at the wave-center and thus eliminate the infinities.

2.6.2 Maxwell's Equations Cannot describe a Spherical e-m wave.

The failure of the M.E. in spherical co-ordinates can be imagined by saying, 'You cannot comb the hair on a tennis ball.' This means that if you attempt to comb down an E field (the hair representing the electric vector) everywhere flat onto a tennis ball (a spherical surface), you must create a 'cowlick' somewhere on the ball which frustrates your attempt to comb it. The solution is to replace the vector e-m waves with scalar 'quantum' waves which do in fact have spherical wave solutions. (See work of Milo Wolff)

2.6.3 The puzzle of the 'photon'

Despite Feynman using spherical electromagnetic waves to explain light, he also paradoxically argued that light must be a particle (thus maintaining the particle/wave duality of light).

When experiments were made with very weak light hitting photomultipliers, the wave theory collapsed: as the light got dimmer and dimmer, the photomultipliers kept making full sized clicks - there were just fewer of them. Light behaves as particles. This state of confusion was called the 'wave/particle duality' of light. (Feynman, 1985)

In fact the Spherical Standing Wave Structure of Matter actually demands that all energy exchanges for light be of discrete amounts due to 'Resonant Coupling' (and for standing wave interactions in general).

2.6.4 The Puzzle of Antimatter and the Positron moving 'backwards in time'.

The backwards-moving electron when viewed with time moving forwards appears the same as an ordinary electron, except that it is attracted to normal electrons - we say it has a positive charge. For this reason it's called a positron. This phenomena is general. Every particle in Nature has an amplitude to move backwards in time, and therefore has an anti-particle. (Feynman, 1985)

As Wolff explains this is simply a mathematical truth caused by the fact that if you substitute a negative time into the spherical wave equations, then this changes the phase of the standing waves to be equal and opposite, which corresponds to antimatter. Further, notice what Feynman says about photons, which are treated as particles in QED, and thus by Feynman's logic there should also be anti-photons, whereas the WSM is clear on this point - there are anti-electrons (positrons) which are opposite phase Spherical Standing Waves, but there are no separate photon particles, thus no anti-photons!

And what about photons? Photons look exactly the same in all respects when they travel backwards in time, so they are their own anti-particles. You see how clever we are at making an exception part of the rule! (Feynman, 1985)

While it may be clever, it is not good philosophy, and it has led to a very confused and absurd modern physics, and has led to the self fulfilling belief that we can never correctly describe and understand Reality, as Feynman and Heisenberg argued;

The more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that. (Feynman, 1985)
Light and matter are both single entities, and the apparent duality arises in the limitations of our language. (Heisenberg, 1930)

In fact Nature (Reality) must be logical (Necessarily Connected) to explain how we have evolved a logical aspect to our minds that allows us to create mathematical physics which correctly describes so many phenomena.

2.7 Wolff's Explanation of the Famous Einstein, Podolsky, Rosen (EPR) and Further Predictions

In l935, Einstein, Podolsky, and Rosen (EPR) put forward a gedanken (thought) experiment whose outcome they thought was certain to show that there existed natural phenomena that quantum theory could not account for. The experiment was based on the concept that two events cannot influence each other if the distance between them is greater than the distance light could travel in the time available. In other words, only local events inside the light sphere can influence one another.
Their experimental concept was later used by John Bell (1964) to frame a theorem which showed that either the statistical predictions of quantum theory or Einstein's Principle of Local Events is incorrect. It did not say which one was false but only that both cannot be true, although it was clear that Einstein expected the Principle of Local Events to be confirmed.

When later experiments (Clauser & Freedman 1972; Aspect, Dalibard, and Roger, 1982; and others) confirmed that quantum theory was correct, the conclusion was startling. The Principle of Local Events failed, forcing us to recognize that the world is not the way it appears. What then is the real nature of our world?
The important impact of Bell's Theorem and the experiments is that they clearly thrust, a formerly only philosophical dilemma of quantum theory, into the real world. They show that post-modern physics' ideas about the world are somehow profoundly deficient. No one understood these results and only scant scientific attention has been paid to them.

Einstein Podolski Rosen Experiment

Figure 2.7.1 Experiment to test Bell's theorem. Polarized photons are emitted at the center, pass through the adjustable polarization filters on the left and right, and enter detectors on each side. Coincidences (simultaneous detection) are recorded and plotted as a function of the angular difference between the two settings of the polarization filters.

The Essence of Bell's Theorem

His theorem relates to the results of an experiment like the one shown in Figure 2.7.1. A source of two paired photons, obtained from the simultaneous decay of two excited atomic states, is at the center. At opposite sides, are located two detectors of polarized photons. The polarization filters of each detector can be set parallel to each other, or at some other angle, freely chosen. It is known that polarizations of paired photons are always parallel to each other, but random with respect to their surroundings. So, if the detector filters are set parallel, both photons will be detected simultaneously. If the filters are at right angles, the two photons will never be detected together. The detection pattern for settings at intermediate angles is the subject of the theorem.

Bell (and Einstein, Podolsky, and Rosen) assumed that the photons arriving at each detector could have no knowledge of the setting of the other detector. This is because they assumed that such information would have to travel faster than the speed of light - prohibited by Einstein's Special Relativity. Their assumption reflects the Principle of Local Causes, that is, only events local to each detector can affect its behaviour.
Based on this assumption, Bell deduced that the relationship between the angular difference between detector settings and the detected coincidences of photon pairs was linear, like line L in Figure 2.7.2. His deduction comes from the symmetry and independence of the two detectors, as follows: A setting difference of X, at one detector has the same effect as a difference X, at the other detector. Hence if both are moved X, the total angular difference is 2X and the total effect is twice as much, which is a linear relationship.

Einstein Podolsky Rosen Results

Figure 2.7.2 The result of an experiment to test Bell's theorem. Data points R of the experiments are shown with black dots. They agree with the curved line QM, predicted by the quantum mechanics, and do not agree with the straight line L, predicted by Einstein's concept of causality. This was a big surprise, because the failure of causality suggests that the communication is taking place at speeds greater than the velocity of light.

The curved line is the calculation obtained from standard quantum theory. Einstein, Podolsky, and Rosen, or anyone who does not believe in superluminal speeds, would expect to find straight line L. In fact, the experiments yielded points R, which agreed with the curved line statistically predicted by Quantum Theory. The predictions of quantum theory had destroyed the assumptions of Einstein, Podolsky and Rosen!

The results of these experiments were so disbelieved that they were repeated by other persons, using different photon sources, as well as particles with paired spins. The most recent experiment by Aspect, Dalibard, and Roger, used acousto-optical switches at a frequency of 50MHz which shifted the settings of the polarizers during the flight of the photons, to completely eliminate any possibility of local effects of one detector on the other. Nevertheless, they reported that the EPR assumption was violated by five standard deviations, whereas quantum theory was verified within experimental error (about 2%).

Do Non-local Influences Exist?
Bell's Theorem and the experimental results imply that parts of the universe are connected in an intimate way (i.e. not obvious to us) and these connections are fundamental (quantum theory is fundamental). How can we understand them? The problem has been analysed in depth (Wheeler & Zurek 1983, d'Espagnat 1983, Herbert 1985, Stapp 1982, Bohm & Hiley 1984, Pagels 1982, and others) without resolution. Those authors tend to agree on the following description of the non-local connections:
1. They link events at separate locations without known fields or matter.
2. They do not diminish with distance; a million miles is the same as an inch.
3. They appear to act with speed greater than light.
Clearly, within the framework of science, this is a perplexing phenomenon. In some mysterious quantum way, communication does appear to take place faster than light between the two detectors of the apparatus. These results showed that modern physics understanding of the physical world is profoundly deficient.

Explaining the EPR-Bell 'Instant' Communication
The Spherical Wave Structure of Matter, particularly the behaviour of the In and Out Waves, is able to resolve this puzzle so that the appearance of instant communication is understood and yet neither Einstein nor Quantum Theory need be wrong. In order to show this, it is necessary to carefully look at the detailed process of exchanging energy between two atoms, by the action of the In and Out waves of both atoms. Remember that for resonant coupling it is necessary for the In and Out Waves of both electrons to interact with one another. The passage of both In-Waves through both wave-centers precedes the actual frequency shifts of the source and detector. A means to detect this first passage event is not a capability of the usual photo-detector apparatus and remains totally unnoticed. But the In-Waves are symmetrical counterparts of the Out-Waves and carry the information of their polarization state between parts of the experimental apparatus before the Out-Waves cause a 'departing photon' event. The In-waves travel with the speed of light so there is no violation of relativity.
Thus effectively the electrons in the experiment are already interconnected with one another, and hence are already 'aware' of one another's resonant state and polarization, before the paired photons are emitted. It is this subtle interconnection of matter that explains the apparent conflict of the EPR experiment.

Experimental Proof of the Spherical Standing Wave Structure of Matter
For someone to really believe a new theory, an experiment to show the existence of new phenomena not previously known is most persuasive. To prove the existence of the In and Out-waves (and thus the pre-existing interconnection of the electrons with the rest of the apparatus) would be just such a critical experiment. This can likely be accomplished with an apparatus of the type used by Aspect, Dalibard, and Rogers (1982) except that instead of making a random filter setting during a 'photon's' passage time, the filter setting should occur during the time period preceding photon departure. The purpose is to frustrate communication by the In-Waves. As the In-Waves are necessary to the energy exchange process, then the result of the experiment would be a linear relation between the angular difference of the two filters. This would be the result originally expected by Einstein for the EPR experiment.

The Spherical Standing Wave Structure of Matter is a profound new way of looking at how matter exists and interacts with other matter in Space. Wolff has explained a very simple change to a very famous experiment that currently causes Quantum Theory, and Human intellectual knowledge in general, profound problems and paradoxes. Thus it seems to us absolutely essential that this experiment be re-done as suggested above. We sincerely hope that this work on the Metaphysics of Space and Motion and the Spherical Standing Wave Structure of Matter will ultimately lead to this new 'Paradigm' being taken seriously, and that this experiment will be performed sooner rather than later!
Unfortunately, it is simply human nature to stubbornly stick to our existing beliefs, as Planck well realized; 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. (Planck, Scientific Autobiography, from Kuhn, 1962)
Science is founded on experimental verification of theoretical predictions, which help to break down this natural resistance to new ideas. Thus one central purpose of this article is to provide enough information to justify scientists re-doing this experiment as proposed. I sincerely ask for their help in getting this important experiment re-done as soon as possible!

3. Cosmology

Suppose we were to accept 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. Matter is not going to set itself in motion. (Aristotle, 340BC)
The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. (Albert Einstein, 1954)
As people's views of the universe are bound up with their views of themselves and 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. (Lerner, 1992)


To begin we briefly explain how matter, as a Spherical Standing Wave, determines the size of our finite spherical universe within an infinite Space. From this foundation we calculate the 'Equation of the Cosmos' and show how this correctly deduces both Mach's Principle and the Hubble redshift with distance (without assuming a Doppler shift due to receding motion and thus an expanding universe). We then consider Einstein's ideas, and with some minor corrections, show how this new foundation solves many of the current Problems of Cosmology.

3.1 Our Finite Spherical Universe Perpetually Exists Within an Infinite Space

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

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 rather abstract and confusing idea!) The solution is far more simple and sensible, and is found instead from Huygens' Principle.
Christiaan Huygens found that a surface containing many separate wave sources appeared, from a distance, as a single wave front with the shape of the surface. This wave front is termed a 'Huygens combination' of the separate waves. This explains how matter's spherical In-waves are formed. The Out-waves of other SSWs (spherically distributed in the Space around us) combine to form a Huygens' combination wave front which forms the spherical In-wave of our wave-centers.

Fig: 3.1 Huygens Combination and the formation of the In-wave of a Spherical Standing Wave (SSW). This diagram was constructed by drawing twelve sets of 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.

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)

Most importantly, this Huygens' sharing of waves means that once you go out past a certain distance in Space (the size of our finite spherical universe) you can no longer count the Out-waves of farther distant matter as direct contributors to our In-waves, as 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. As we shall explain, 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, explains Mach's Principle, and explains the redshift with distance without assuming an expanding universe.

3.2 The Equation of the Cosmos

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 further 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.

3.3 An Infinite Space

Throughout history there has been common agreement amongst many philosophers that Space (and time) are most likely infinite, as Einstein explains;

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. However far we might travel through space, we should find everywhere an attenuated swarm of fixed stars of approximately the same kind and density. (Albert Einstein, 1954)

Unfortunately for Einstein an infinite Space led to many problems.

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. (Albert Einstein, 1954)

Clearly Einstein thinks this 'island' universe unreasonable, nonetheless, it is a logical consequence of Newton's force laws 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.

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. (Albert Einstein, 1954)

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 due to the Huygens' sharing of waves it contributes less and less to our In-waves, and thus our mass, with increasing distance (and once we reach the size of our Spherical Standing Waves {size of our universe} then farther distant matter does not directly contribute to our In-waves nor to our gravitational forces). Thus the force laws with distance do decrease more rapidly than would result with the inverse square law.
This not only prevents our mass from becoming infinite, but also solves a number of previously puzzling problems.

i) This infinite space and matter prevents our finite spherical universe from collapsing upon itself due to gravitational forces. (Thus there is no need for an expanding universe - this is explained when we shortly consider Einstein's famous antigravity cosmological constant.)

ii) Our universe is perpetual and does not become 'impoverished' over time (as it necessarily would if it was an 'island' universe as required by Newton's Law). As Einstein explains;

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. (Albert Einstein, 1954)

This problem is now easily solved by realizing that due to this matter outside our finite spherical universe there are as many waves flowing into our universe (forming our In-waves) as there are flowing out (our Out-waves).

iii) Olbers' Paradox.

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, which it obviously is not. (Lerner, 1991)

The solution to this paradox is the same as for the other problems discussed above. Huygens' Sharing of waves 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.

3.4 Mach's Principle and How the Distant Stars Determine Our Inertial Mass

Mach (1883) 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 behavior of each body with all other matter (the stars) of our universe.

The obvious problem of the 'particle' conception of matter is to explain how all the distant matter of the universe could instantaneously act upon a moving body here on earth. 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. Nothing is instantaneous and the waves only travel at speed c. Further, the Equation of the Cosmos confirms that the mass of an object is determined by all the other matter in the universe (as it is their Out-waves that form our In-waves, and thus our mass-energy density of space and Mass) as required by Mach's Principle. Thus the universe is finite (within an infinite Space), spherical and Machian, as required by Einstein's general relativity;

I must not fail to mention that a theoretical argument can be adduced in favor 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. … The results of calculation indicate that the universe would necessarily be spherical. (Albert Einstein, 1954)

3.5 Explaining Einstein's Famous Cosmological Constant & Further Prediction

We begin with a good summary from Halton Arp on Einstein's famous 'Cosmological Constant (which is really just an assumed anti-gravity force to prevent a finite spherical Universe from gravitationally collapsing).

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 (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, 1954)

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.
As we have explained, our finite spherical universe is 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. Now this leads the Metaphysics of Space and Motion and the WSM to make a very important prediction:

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

(Due to our increased powers of observing the distant universe perhaps it is now possible to confirm this prediction. Please email me if you have any information.)

NOTE - This was confirmed by observation in 2008. See;

But as chance would have it Einstein found another explanation and thus famously renounced his cosmological constant as 'my greatest mistake'.

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, 1961)

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. 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, 1961)

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 it is how a careful scientist like Einstein expresses it), 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 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 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 I quote a few scientists who have made this error, simply because I wish to strongly make the point about how we begin to assume things to be true, above and beyond what the observation tells us. (Scientist have a responsibility to be careful, and should clearly recognise the distinction between empirical facts and their further interpretations!)

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. (Born, 1964)
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)

It is also important to realize that the modern conception of the 'Big Bang' is that Space itself is expanding, and as the Doppler shift only applies to the motion of matter in Space thus it is unscientific to apply this empirical observation to the expansion of Space. Thus the 'Big Bang' is without both empirical or theoretical foundations, it is, quite simply, not a scientific theory.
In conclusion of this argument we should emphasize two things;
i) That Einstein's Cosmological Constant is largely correct, but is caused by the gravitational forces of matter outside our finite spherical universe (within an infinite Space) which prevents our universe from gravitationally collapsing.
ii) Thus there is no need for an expanding universe, and then they would have realized, from the Spherical Wave Structure of Matter, that the redshift can be correctly calculated from Huygens' Principle and the decreasing wave interactions with distance.

3.6 Explaining the 'Quantified' Hubble Redshift with Distance

Another problem with the expanding universe concept is that the redshift with distance is quantized, as Arp clearly explains; 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. (Arp, 1998)
Arp is also 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. (Arp, 1998)

The Spherical Standing Wave Structure of Matter sensibly explains these 'quantum' or discrete standing wave interactions.

3.7 The Second Law of Thermodynamics only applies to Closed Systems

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'.
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)

The reason why our universe remains ordered / complex 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).

3.8 On the Past Present and Future and the One Way Direction of Time

Lerner also 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. Hence the fundamental question: If 'the laws of the universe' have no direction in time, why does the real world? 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 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.
Time's irreversibility is based on the continuity of space, on its infinite divisibility.' (Lerner, 1991)

Lerner is correct, time is related to the continuity of Space, or more precisely, to the finite velocity of the wave-Motions of Space. i.e. It is not Time but Motion which is fundamental (a priori). And then it becomes obvious why time is directional. As it takes time for the spherical 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 explains why time is directional because the In and Out waves travel in opposite directions relative to the wave-center (present). Thus the direction of time is simply unrelated to the second Law of Thermodynamics (which does not apply to an infinite Space) nor is it related to the 'Big Bang' (which is simply incorrect).

3.9 How our Universe is Necessarily Connected but not Deterministic

It is important to appreciate the difference between a Necessarily Connected universe, which ours is, (due to Space and its interconnected wave-motions) 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, an infinite system can never be pre-determined. 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. Certainly our free will is limited by the 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. Karl Popper intuitively understood this 'balance' between complete determinism (clocks) and complete disorder and chance (clouds) when he wrote;

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

Concluding Remarks on Cosmology and Morality

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 our view of nature, to religion, philosophy and society as a whole. (Lerner, 1991)

A correct understanding of the Cosmos is a correct understanding of ourselves. Though we see matter as discrete 'particles', this is an illusion due to the Darwinian evolution of our minds (reason tells us that there must be a connection between things). We must simply gaze at the stars and consider how we can see them to realize that we must be connected to them – that we are a part of those stars, just as those stars are a part of us! This is the true 'mystical/religious' experience, to see beyond the daily illusion of life here on Earth and realize our true existence as structures of the cosmos. Thus the foundations for Human Morality, 'To do unto others as you would have done unto yourself' is true, for the 'other' is in fact a part of the 'self'. This morality is at the heart of all world Religions (the word religion comes from Latin 'Religare' which means 'to bind', i.e. how we are bound/connected to the cosmos).

Currently the world suffers great conflicts, not only between people, but also with the destruction of Nature. (It was my love of Nature, and despair at its destruction, that first led me to study Philosophy and Physics as a way of understanding what Nature actually is.) And after many years of study, I now write this believing it to be a true account of how matter and thus ourselves (as a part of Nature) exist in the Universe. I believe that this is important, simply because I am now convinced that it is true because it explains so many things so simply and sensibly. (And I well realise how unfashionable is my belief in Truth in our 'enlightened' age of No Absolute Truths!).
All philosophers though, have realized that Humanity must know the truth to be wise, as this necessarily limits how we may behave.
I know that my opinion on this is irrelevant, I simply agree with Schrodinger;

The scientist only imposes two things, namely truth and sincerity, imposes them upon himself and upon other scientists. (Schrodinger, 1967)

So I sincerely ask that this Metaphysics of Space and Motion be fairly judged with an open mind to determine its truth.
Perhaps I am a romantic, but it is my hope that in the future Humanity will live by the truth, with greater harmony between different people, their religions and cultures, and to life in all its complex beauty. As Einstein profoundly writes;

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 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)

Summary - Philosophy as the 'Discovery of the Obvious'

That Matter exists as the Spherical Standing Wave-Motion of Space now seems obvious to me. It obviously explains the problem of the Particle/Wave duality of Matter - Matter is a Spherical Wave Structure whose Wave-Center creates the point 'particle' effect. It also obviously explains how matter is interconnected across the Universe by the In and Out-Waves. So why has this fairly obvious solution of the Wave Structure of Matter (WSM) only recently been considered? (Wolff first discovered the WSM in 1986, Haselhurst in 1997) I have listed ten reasons below, though I suspect that there are many more due to past errors of Human knowledge that have confused and deceived us.

i)The error of imagining matter as a tiny 'particles' and thus assuming 'forces' to connect the 'particles'. In fact Matter is Spherically Spatially extended. (Matter and Universe are one and the same thing.)

ii) The fact that our mind 'represents' the world that we sense, founded on evolutionary principles of survival (Naive Realism), thus we see matter as discrete objects/particles (like sand on the beach) yet reason tells us that there must be some connection between these objects. (i.e. There must be One thing that connects the Many things, this being the foundation of ancient Indian and Greek philosophy.)

iii) The philosophical problems of connecting/uniting the One and the Many and the Infinite and the Finite were believed to be impossible to solve.

iv) The error of assuming Space and Time as a priori, (i.e. necessary for us to experience the world) rather than Space and its Properties as a Wave-Medium (i.e. Space and Motion), and that the Spherical Wave Motion of Space is the Cause of Time (and Matter/Forces).

v) No Absolute Space - Leibniz's Monadology and Einstein's Relativity were founded on the Motion of matter relative to other matter, thus they did not require the Existence of an Absolute Space. Further, Newton's Mechanics, which did correctly assume an Absolute Space, included the errors of an Absolute Time, and discrete 'particles' acting instantly at a distance. (i.e. Forces, without explanation) and these obvious errors then gave his Absolute Space a 'bad name'.

vi) Wrong Waves. Einstein's Relativity and Feynman's QED used 'electromagnetic' waves (mathematical vector waves described by both the size and direction of force) rather than the real waves discovered by Quantum Theory (scalar 'quantum' waves described by wave amplitude only). Further, Quantum Theorists (Born) used the 'quantum' waves as 'probability' waves for determining the location of the 'particle' (thus maintaining the confusion of the particle/wave duality). In fact the scalar quantum waves are real Wave-Motions of Space.

vii) In Cosmology, the redshift with distance was assumed to be caused by a Doppler shift due to an expanding universe, thus it must have expanded from a 'pointlike beginning', i.e. the 'Big Bang'). Our calculations show that the redshift with distance is actually caused by decreasing Wave Motion interactions with distance, thus the Universe is not expanding and consequently there was no 'Big Bang'.

viii) Religious beliefs and our Human emotions. We sometimes do not want to know the Truth as it prevents us from believing in things that makes us feel good. As the Bhagavad-Gita says; Man is made by his belief. As he believes, so he is.

ix) Humans have evolved as social/tribal creatures and are inclined to believe famous people of the past without careful critical analysis of their ideas. As Kuhn writes; Almost always the men who achieve these fundamental inventions of a new paradigm have been either very young or very new to the field whose paradigm they change. (Kuhn, 1962)

x) And due to these past errors, we came to believe that it was impossible to describe/understand Reality, which was simply beyond the limitations of our language and mind. (Post-modern Relativism).

In fact these errors have arisen due to an incorrect understanding of the Wave Structure of Matter, and once this is realised then we find that we can perfectly understand and describe how matter (and thus ourselves) exist in this Space of the Universe.
Plato, Leibniz, Wittgenstein, and Saul (and many other philosophers) understood how things so simple and obvious (like Space and Motion) could be ignored, it is simply human nature to ignore that which is normal and obvious (and to abstract to more complex 'specialised' ideas).

We are like people looking for something they have in their hands all the time; we're looking in all directions except at the thing we want, which is probably why we haven't found it. (Plato, 380BC)

The fact is, I think, that my objection is so simple that its very simplicity operated to deceive him, since he could not believe that a comment which was so easy could have escaped the notice of so many able people. (Leibniz, 1670)

The aspects of things that are most important for us are hidden because of their simplicity and familiarity. (Wittgenstein, 1958)

One of the specialist's most successful discoveries was that he could easily defend his territory by the simple development of a specialized language incomprehensible to the nonexperts. ..The example of philosophy actually verges on comedy. Socrates, Descartes, Bacon, Locke and Voltaire did not write in specialized dialect. They wrote in basic Greek, French and English and they wrote for the general reader of their day. Their language is clear, eloquent and often both moving and amusing. The contemporary philosopher does not write in the basic language of our day. He is not accessible to the public. Stranger still, even the contemporary interpreter of earlier philosophy writes in inaccessible dialect. ..Why, then, would anyone bother to read these modern obscurings of the original clarity? The answer is that contemporary universities use these interpretations as the expert's road into the original. The dead philosophers are thus treated as if they were amateurs, in need of expert explanation and protection.
The new specialized terminology amounts to a serious attack on language as a tool of common understanding. Certainly today, the walls between the boxes of expertise continue to grow thicker.
The purpose of language is communication. It has no other reason for existence. A great civilization is one in which there is a rich texture and breadth and ease to that communication. When language begins to prevent communication, the civilization has entered into serious degeneracy. (Saul, 1992)

I completely agree with Saul, specialisation leads to complex language that is ultimately unfounded and serves more to confuse than enlighten. This is simply human nature, as we like to create things (and is in fact an ancient problem that has become more acute over the past century), as Aristotle explains;

..as they were not sufficient to generate the nature of entities, once again, by the truth itself, as we have said, they were obliged to seek out the next principle.

And thus we tend to keep creating new concepts and entities/existents to explain things we don't understand.

The shortcoming of current examinations of these topics is not their failure to be philosophy, but the priority of substance. (Aristotle, 340BC)

The language of the Metaphysics of Space and Motion is very simple, founded on the basic concept of the Wave Motion of Space (i.e. One Substance and its Properties). And as Reality is ultimately simple (founded on One thing) it is correct that our language to describe Reality must also be simple.

Acknowledgements: My sincere thanks to Milo Wolff and Karene Howie. Milo has been a guiding light for me over the past five years. My own knowledge would be poor indeed without his pioneering work on the Wave Structure of Matter. Karene is a fine student of Philosophy and her many hundreds of hours of reading philosophy and physics and selecting ideas for quoting (and typing out the quotes) has been invaluable. Thank you!

References: Dates in ( ) cite when the work was written if different to the date of publishing.
Aristotle 'The Metaphysics' (~340BC) Penguin 1998
Arp, Halton 'Seeing Red' Apeiron 1998
Born, Max 'Einstein's Theory of Relativity' Methuen Company 1924
Capra, Fritjof 'The Tao of Physics' Wildwood House 1975
Collinson, Plant and Wilkinson 'Fifty Eastern Thinkers' Routledge 2000
Davies, Paul, 'Superforce', London, Unwin Paperbacks, 1985
Einstein, Albert 'Ideas and Opinions' (1919-1954) Crown Trade Paperbacks 1954
Einstein, Albert 'Relativity' (1916-1952) Crown Trade Paperbacks 15th Ed.1961
Feynman, Richard and Wheeler, John 'Interactions with the Absorber as the Mechanism of Radiation' PhD Thesis- Palmer Physical Laboratory, Princeton University, Princeton, New Jersey 1945
Feynman, Richard P. 'The Strange Theory of Light and Matter' Penguin 1985
Haselhurst, Geoff 'The Metaphysics of Space and Motion and the Spherical Standing Wave Structure of Matter' http://www.spaceandmotion.com (2000)
Hawking, Stephen W. 'A Brief History in Time' Bantam Books 1988
Heisenberg. 'Quantum Theory' University of Chicago, 1930
Hume, David 'Enquiries Concerning The Human Understanding and Concerning The Principles of Morals' (1737) Oxford University Press 2nd Ed. 1957
Kant, Immanuel 'Critique of Pure Reason' (1781) Everyman 1935
Kuhn, Thomas S. 'The Structure of Scientific Revolutions' University of Chicago 1962
Lama Anagarika Govinda 'Foundations of Tibetan Mysticism' Red Wheel / Weiser 1969
Leibniz 'Philosophical Writings' (1670) Everyman 1934
Lerner, Eric J. 'The Big Bang Never Happened' Vintage Books 1992
Lorentz, Hendrik 'The Theory of the Electron' 1906
Newton, Isaac 'The Principia' (1687) Prometheus Books 1995
Plato 'The Republic' (~380BC) Penguin 1955
Popper, Karl 'Objective Knowledge' Oxford University Press 1975
Saul, John Ralston 'Voltaire's Bastards' Penguin 1992
Smolin, Lee 'The Life of the Cosmos' Phoenix 1998
Urmson, J.O. and Ree, J 'The Concise Encyclopedia of Western Philosophy and Philosophers' Routledge 1991
Wertheim, Margaret 'Pythagoras' Trousers' Fourth Estate Limited 1997
Serway, R. A. 'Physics for Scientists and Engineers' 3rd Ed. Saunders College Publ. 1992
Wolff, M. 'Exploring the Physics of the Unknown Universe, Technotran Press, CA 1994
Wolff, M 'Fundamental Laws, Microphysics and Cosmology,' Physics Essays, 6, 1993

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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.

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