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 at the top of the page present this knowledge in shorter, more concise articles.
All the best,
Geoff Haselhurst

Contents

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'

Introduction

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 wave-density (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 wave-density (explains gravity. Fig: 2).In-Wave ----------Out-Wave---------In and Out-Waves

+ =
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 wave-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’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).
See:
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)

Introduction

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)

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 10²¹ 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)

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)

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.

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 relatively 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 wave-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 wave-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 wave-density, 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 wave-density (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 wave-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 wave-density (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 wave-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 Wave-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)

Introduction

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)

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