Solving Nature’s Mystery

On the Spherical Wave Structure of Matter and the Origin of the

Natural Laws. Explaining the Particle Wave Duality of Light and Matter

with the Wave Structure of Matter (WSM).

Technotran Press, 1124 Third Street, Manhattan Beach, CA 90266
(With editing and further comments from Geoff Haselhurst, Feb. 2003)

The structure of the electron is investigated and found closely entwined with the origin of the natural laws. The natural laws had been measured for hundreds of years but no one knew how Nature creates them. Richard Feynman wrote, speaking of the Conservation of Energy, Nature has a hidden accountant who keeps honest books of energy input and output but we don’t know how she does it. The origins had been proposed earlier by Clifford and Schrodinger, who pointed out that only a Wave Structure of Matter (WSM), can explain natural laws. Further, Einstein realised that matter was spherical and spatially extended and thus the Electron was not a point particle, but rather, a structure of space. He writes;

Physical objects are not in space, but these objects are spatially extended. In this way the concept empty space loses its meaning. … 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)

Einstein’s error was to represent matter as a continuous spherical field in space-time rather than as a Spherical Wave in continuous Space which causes the spherical force field effects.
Using the WSM a quantitative origin has been found based on the wave structure of the electron. It is shown that Space (the quantum wave medium) is a single entity underlying electron structure and the laws. Three Principles are found describing the wave medium, enabling calculation of particles and the laws. The predictive power of the WSM is shown by deriving the previously unknown physical origin of electron spin and making experimental predictions which solve the paradoxes of the famous EPR experiment. The WSM has important implications for research, industry, and our human role in the universe.

Part I – Introduction

1. Natural laws.
Our knowledge of science is based on the natural laws that describe the behaviour of particles. The laws are the rules for calculating electricity, gravity, relativity, quantum mechanics, and conservation of energy and momentum. The origins have been unknown. Now the origin of the natural laws is found to be a quantitative result of a Wave Structure of Matter (WSM). The basic method is very simple. The ancient Greek notion of a point particle, still in use today, is replaced with a spherical wave structure, thus confirming the beliefs of Clifford1 and Schroedinger2 that the Wave properties of both Light and Matter are in fact real.

Figure 1. The Electron. The electron is composed of spherical waves which converge to the center and then become outward waves. The two waves form a standing wave whose peaks and nodes are like the layers of an onion. The wave amplitude is a scalar number like a quantum wave, not an electromagnetic vector wave (a mathematical wave of force). The Wave-Center is the apparent location of the electron ‘particle’.

+  =  This (very rough!) diagram shows how the Spherical In and Out Waves form a Standing Wave around the Wave-Center ‘particle’.

The simplicity is illustrated by Figure 1. which shows the structure of an electron. It is just two waves: an inward wave converging to the Wave-Center, combined with an outward diverging wave, forming a Spherical Standing Wave about the Wave-Center (which we observe as the point ‘particle’). The properties of these simple waves are immense when combined with the equally simple waves of the proton. The myriad combinations are like the eight note musical scale which become the grand symphonies of Wagner and Beethoven.

The rules of wave combination are of great importance to science because the rules and quantum spin determine the structure of the Atomic Table, which dictates the varied forms of matter: metals, crystals, semi-conductors, and the molecules of life. The deep understanding of basic physics that is revealed opens a door to broad fields of applied technology such as integrated circuits, photonics, and commercial energy. It reveals a universe of real quantum wave structures in a space medium that we live in but seldom are aware of. The medium is the heart of wave structure because its properties underlie the wave properties.

2. Human senses and survival.

We don’t easily see the space wave medium because our survival as an animal species depended mostly on our ability to fight with other animals seeking food, and to compete for mates that produce children, not closely related to the quantum space medium. Our sensory mechanisms evolved to directly aid our survival not to be aware of quantum matter. In our self-focused human perspective few of us are even aware of the wave medium in which we exist. For survival, it doesn’t matter what space is, or whether we can observe it – it exists unseen. This situation is much like the life of a fish who cannot comprehend the existence of water because he is too deeply immersed in it. Like the fish, traditional scientists have tended to comprehend the universe in terms of their local experiences.

Our misconceptions are revealed by anthropology, which teaches that the quantum wave universe is not as helpful to survival of our personal genes as recognizing apples we can eat and avoiding tigers who want to eat us. We need to recognize those quickly. Thus it was not necessary that nature equip us to observe quantum waves, although as will be seen below we do observe their presence and effects. Lacking direct personal experience of simple quantum waves, people chose to imagine that the electron is a discrete ‘particle,’ like a bullet. Laboratory evidence does not support this human-oriented idea.

Accordingly, belief must change from discrete particles to quantum wave structure.
Human perspective has another bias. We tend to see space as three rectangular dimensions, one of which is the vertical gravity vector of Earth, plus two other vectors perpendicular to it, shaped like the houses we live in. But in the cosmos, the shape of the enormous universe isspherical whose important dimensions are inward and outward, the direction of waves in space. In fact it requires three coordinates to describe a sphere, and it is this spherical geometry of Matter that is the cause of the three rectangular dimensions (as formalised by Descartes). In the vast expanse of the real universe, gravity occurs so rarely, that its direction is inconsequential in the larger scheme of things, despite its local importance to us. Accordingly, we feel comfortable with rectangular coordinates but tend to ignore the spherical universe. This explains why Einstein used Spherical Geometry in his General Relativity, he writes;

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.

The proof of the WSM is that the physical structure of the electron, and the empirical natural laws can be obtained mathematically from three basic principles describing the wave space medium. In other words, all the experimental measurements of historical physics that described natural behaviour are now predicted by three fundamental principles. The laws and the principles agree with each other – each is the proof of the other.

You will see that the wave structure of matter is simple. In contrast, old discrete particle-structured physics required dozens of assumptions plus many more arbitrary constants to explain the operation of the laws. Many properties and laws, like electron spin, were puzzling with no understanding or origin. The puzzles are now swept away. Particle-structured physics can be compared to the theory of epicycles of the planets around the Earth before Galileo found that the planets travelled around the Sun. It satisfies our human prejudices but does not explain the measured facts.

3. Philosophical Truth and Physical Reality

Many people, from the old Greek philosophers such as Democritus and Pythagoras, up to the colleagues of Albert Einstein, sought to understand the structure of the tiny atoms and molecules of the objects in our everyday world. Until recently, most answers have been speculation created in analogy to human scale objects around us; like baseballs and bullets, and grains of sand. Atoms were imagined to move like other familiar objects such as moons around planets and toy tops spinning on a table. These analogies make us feel comfortable. We prefer to ignore strange new ideas so as Churchill said,

We often stumble onto the truth but most of us brush ourselves off and pretend it did not happen! (Winston Churchill)

Serious thinkers, such as Einstein, Dirac, Schrodinger, and Ernst Mach, realized that the analogies were wrong. Instead, experimental measurements showed that the structure of matter was closely related to the properties of the apparently empty space around us, and that the elements of matter had to:
a)      have spherical symmetry.
b)      be extended in space. (As Einstein realised)
c)      possess a means of exchanging energy.
d)      possess wave properties (As Quantum Theory was founded on Wave Equations).

Their thinking produced conclusions which in hindsight were prophetic. For example, Einstein rejected the discrete point particle and stated, Matter must be spherical entities extended in space. Erwin Schroedinger8 understood the requirements of particle structure when he wrote in 1937:

What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen. (appearances)

He believed that quantum waves were real, not probability distributions with a particle hidden inside. He saw that abolishing the discrete point particle would remove the paradoxes of ‘wave-particle duality’ and the ‘collapse of the wave function’. They arrived at their valid conclusions by painstaking analysis and careful adherence to the rules of logic, and the philosophy of truth. But their thinking was ignored for sixty years. Truth is no match for belief. Machiavelli understood this human behaviour 500 years ago (1513):

here is nothing more difficult to plan, more doubtful of success, more dangerous to manage than the creation of a new system. The innovator has the enmity of all who profit by the preservation of the old system and only lukewarm defenders by those who would gain by the new system.

The predictions of these pioneers, verified and described here, is that matter is a wave structure embedded in space. This result not only satisfies the experimental work, but surprisingly displays an immense but simple tapestry of the physical universe. Awe-inspiring connections between matter, ourselves, and the cosmos are found. The application of the electron wave structure reaches out, on the one hand, to unsuspected fields of cosmology such as the big bang (there was no Big Bang, space has always existed, infinite and eternal), the red shift (is not caused by Doppler shift due to receding Motion, but rather due to decreasing Wave interactions with distance) and the structure of the universe (which is determined by the size of the electron / Spherical Standing Wave within an Infinite Space). On the practical side, a new tool is provided that will enable us to deeply understand and improve industrial devices such as computers, micro circuits, and the efficient transmission of electric energy.

The authors, and others who have contributed, recognize that wave structures truly describe physical reality for the first time. We are scientists who care greatly for truth and are aware of its power. Obviously we are aware that this is a major and remarkable claim; the discovery of physical reality has been a holy grail of intellectual thought earnestly sought for thousands of years. Our aim is to describe the Spherical Standing Wave Structure of Matter in the simplest possible way. Our hope is that readers will gain information and perspective so that they will be able to confirm for themselves that this is a sensible theory of reality which does indeed logically deduce the laws of Nature (reality) correctly as observed.

This does not mean that this is written only for the scientist and intellectual academic. On the contrary, one of the great powers of philosophy, the study of truth, is the awareness that truth simplifies and removes contradiction and paradox. Because the truth has remained hidden for so long and has deceived great minds, many people quite reasonably, could assume that this subject is too complex and difficult for them to understand. No! This is not the case. The structure of matter has an underlying simplicity that makes it easy to understand. The story of its discovery becomes an adventure for everyone. It is an exciting mystery of how centuries of effort, were thwarted not by scientific complexity, but by the frailties of human emotions, economic ambition, and the power of politics. Einstein, after developing the General Theory of Relativity, had an enormous knowledge of the foundation of nature. At that time his major uncompleted goals were to find connections between quantum theory and the role of space and matter in nature. Sadly, his ideas needed only slight alterations / additions to lead to the Wave Structure of Matter.

4. Finding Laws, space, and the structure of the electron

Obviously, finding the structure of the electron was also the key to finding the origin of the natural laws. As the Electron interacts with all other matter in the Universe it is necessary that the electron was entwined with the laws that describe the behaviour of all matter. Thus it should not be a surprise but merely, recognition that we had over-looked an important character of nature. Let us look at how the process of deduction might have proceeded to find the connections with the electron.

The origins of Natural Laws.
The business of physics is the abstract description and quantification of facts observed in nature.  The rules we form for reconstruction and expression of the observed facts are the laws and Principles of nature. Since past laws were obtained by measurement of nature rather than derived from other knowledge, they are by definition empirical and  of unknown origin.  Therefore if we seek to find the origins of laws we cannot use the existing laws themselves but must use other observed facts together with logical deduction and established mathematics to find the origins. The old empirical laws are only a guide and not the source.  We are on new ground. Kant first formalise this, and recognised that Physics must be founded on a prioriprinciples rather than a posteriori /empirical observations (which as Hume pointed out, were uncertain, merely habits of thinking that depended upon the assumption that the future would continue to be like the past). Kant writes;

‘Natural science (physics) contains in itself synthetical judgmentsa priori, as principles.’
Kant also realised that Space was a priori;
‘Space then is a necessary representation a priori, which serves for the foundation of all external intuitions. We never can imagine or make a representation to ourselves of the non-existence of space, though we may easily enough think that no objects are found in it. It must, therefore, be considered as the condition of the possibility of appearances, and by no means as a determination dependent on them, and is a representation a priori, which necessarily supplies the basis for external appearances.’

Accordingly the search for origins must probe deeper into the nature of Space than heretofore and we must be prepared to find new perspectives. The unexplained puzzles of nature, of particles and of cosmology are attractive sources of input data in the search for the origins of empirical laws. Finally, the proof of the origins of laws so deduced is a match between the observed empirical rules and the predictions of the new origins.

Circular reasoning. When seeking origins, it is important not to inadvertently use existing rules (laws) to deduce them.  Such circular reasoning can occur if, for example, a mechanical model from macro-physics is assumed to be the structure of an electron. Such common errors are the use of toy tops, sheets and rings of charge, masses in orbit around each other, , Although the quantum laws of quantum particles can be extrapolated to large macro-objects,  the inverse is not possible.  Logically, finding the origins of existing laws (rules) requires forming new concepts that nevertheless satisfy observed data.
As Einstein writes;

Physics constitutes a logical system of thought which is in a state of evolution, whose basis cannot be distilled, as it were, from experience by an inductive method, but can only be arrived at by free invention. … We must always be ready to change these notions – that is to say, the axiomatic basis of physics (Principles) – in order to do justice to perceived facts in the most perfect way logically. … It is the grand object of all theory to make these irreducible elements (Principles) as simple and as few in number as possible, without having to renounce the adequate representation of any empirical content whatever. … If, then, it is true that the axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented, 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. (Einstein, Ideas and Opinions, 1954)

The new perspective. The discovery of these origins creates a radical new perspective of the physical world: Quantum Mechanics and Einstein’s Relativity are united, a single origin of forces is found,  puzzles and paradoxes are explained and, most important, relationships between microphysics (electrons and particles) and the universe (cosmology) are seen to be a result of an all-pervading space (the vacuum, ether, wave medium) filled with oscillating quantum waves of the matter of the universe.

Part II
The Connections of the electron and the laws

This part is a discussion of the broad and universal relationships between electrons and the natural laws.
Let us examine the meaning of these words. Our concept of universe is a collection of particles and their distribution.  Thus without particles to populate a universe, the universe concept has no meaning. Accordingly, our concept of our universe depends on understanding the particles in it.  Especially we need to understand the connections with the electron and proton, because the charge fields of those two particles extend throughout the universe. The natural laws have no meaning without particles because laws demand the presence of particles, upon which the laws can operate.  Particles are meaningless without the laws to identify them. We conclude that an understanding of the connections between particles, laws, and the universe is essential to understand the whole and its parts. Each requires the existence of the others.  Therefore, we cannot expect to fully understand cosmology unless we also understand the relationships within the trilogy shown in Figure 2.

5. Measurement is a Property of an Ensemble of Matter.
A particle entirely alone in the universe cannot have dimensions of time, length or mass.  These measures are undefined without the existence of other matter because dimensions can only be defined in comparison with other matter.  For example, at least six separated particles are necessary to crudely define length in a 3D space: four to establish coordinates and two being measured.  Thus the measurement concept requires the existence of an ensemble of particles.  In our universe the required ensemble must include all observable matter, because there is no way to choose a special ensemble.  The importance of this fact becomes clear when we recall that time, length and mass are the basic unit set used to describe all scientific measurements.


Figure 2. Inter-dependence. Laws particles, and the cosmos are inter-connected by the quantum waves of particle structures in the ‘ether’ medium of space. These interconnections are described by three Principles that define the properties of the space medium.

6. Particle Properties Require Perception-communication Between Particles. 

  If there were no means for each particle to sense the presence of other matter in its universe, the required dimensional relationships above could not be established. How can a particle possess a property that is dependent on other particles, if there is no way for the particles to impart their presence to each other?  Without communication, each particle would be alone in its own separate universe. Therefore continual two-way perceptive communication between each particle and other matter in its universe is needed to establish the laws of Nature.  Spherical quantum waves forming the particles are the means of communication. The laws are then established in terms of the dimensions (units) established by waves of the entire ensemble of matter.

7. The Measurement of Time requires a cosmological clock.  

Using reasoning similar to the above but for the dimension of time, we can conclude that time measurement requires the existence of cyclic events among the particles of the universe; a kind of clock. Those properties of particles that involve the measurement of time, notably velocity, mass and frequency, cannot have a meaning if particles have no scale of time. That is, the particles must have a way to compare their own cyclic events with other particles.  Therefore, there must exist a standard cosmological clock. One proposal by de Broglie is an oscillator (clock) contained in every electron. By viewing his proposal in a wave medium, we see that electron oscillators can communicate with other electrons and particles. Because of the uniformity of space (the oscillator medium) the clock frequencies would be alike throughout the universe. We should note that a nearly uniform space medium is required in nature, otherwise each clock would tick independently of others; different clocks in different places would produce chaos of the laws. Natural laws involving time would be meaningless.
Thus we realise that Wave Motions are the underlying Cause of Time (and Matter), something both Aristotle and Spinoza suspected;

..about Matter’s coming into being and all its alterations we think that we have knowledge when we know the source of its movement.
… there is some other cause of the change. And to seek for this is to seek for the second kind of principle, as we would say, that from which comes the beginning of the change. … Unless the further factor is active, there will still be no movement.
Motion must always have been in existence, and the same can be said for Time itself, since it is not even possible for there to be an earlier and a later if time does not exist. Movement, then, is also continuous in the way in which time is – indeed time is either identical to movement or is some affection of it. … there being two causes of which we have defined in the Physics, they seem to have a glimpse of them, that of matter and that from which the motion comes, indistinctly though, and in no way clearly. (Aristotle, 350BC Metaphysics)

Moreover, no one doubts but that we imagine time from the very fact that we imagine other bodies to be moved slower or faster or equally fast. (Spinoza, Ethics)

8. We live in an inter-connected universe.

The above discussions of the requirements of the laws of science make it clear that inter-connections must exist between matter, the laws, and the universe. Independence of objects is not possible, for example, no planet, no star, no galaxy, can exist without the rest. We know this because astronomical measurements show that the same laws apply in the farthest galaxy, as here on Earth. And we also know because ‘time’ has the same meaning from one moment to the next. These requirements are not the fantasy of a supreme law-maker who declares that the Standard Model applies everywhere. The only logical conclusion is that matter and laws are inter-connected throughout the universe by a physical mechanism – waves. As Smolin correctly writes;

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)

The details of inter-connection will be discussed in later sections and it will be seen that the natural laws originate from the properties of the quantum waves of the particles (electron, proton, etc) , and the properties of space.  It will also become clear that the classic point-particle model of charge and mass substance cannot satisfy either the logic of science or the many puzzles of physics. The model is only a historical relic and its presence in the ‘Standard Model’ of physics is an obstacle to progress. This is evident in the comments from Davies, which highlights the problems of modern physics which is founded on the particle concept;

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 visualise a wave-particle, so don’t try. … The notion of a particle being everywhere at once is impossible to imagine.’ (Davies, Superforce)

New physics and old physics

Study of the wave structure of the electron and other matter is a rewarding adventure in which you find the origin of the natural laws, a new powerful tool of technology, and a revealing window on science, cosmology, and ourselves. But some old mainstream attitudes must be discarded. For instance, a quantum physicist may expect that all quantum phenomena must derive from Schrodinger’s Equation. No. It is the other way around; Schrodinger’s Wave Equation is derived from the quantum wave structure of matter.

Some concepts must be changed such as the meaning of charge and mass. They are not inherent properties of each independent ‘particle’. Instead Nature exists, as Schrodinger suspected, such that location, charge and mass are properties of the wave structure. Some new concepts are added, for example, as Ernst Mach deduced, natural laws and matter here on Earth are dependent on the matter of the rest of the universe. The building blocks of the universe are not the high-energy transient states (hadrons) of the proton, but waves of the electron and positron. Accordingly, the most fruitful arenas of research in the future will be learning the properties of the wave medium (not building accelerators!).

Part III – A short history of the Wave Structure of Matter

9. The pioneers.
A wave structure of matter was proposed 130 years ago by the famous English geometer, William Clifford1, who spoke before the Cambridge Philosophical Society in 1870, All matter is simply undulations in the fabric of space. He developed this concept as three-dimensional dynamics that reduces to four-dimensional kinematics describing matter, electromagnetism and kinetic energy as curvature of a dynamic Riemannian space. His work, the progenitor of the WSM and General Relativity was neglected. In Clifford’s thoughts, the mass and charge substances that we assume, do not exist but are properties of a wave structure in space. In short, space waves were real, while mass and charge points are mere appearances of the wave structure;Schaumkommen in the words of Schroedinger3. Their proposals were consistent with present day quantum theory, since quantum mathematics does not depend on a belief in particle or charge substance.

Ernst Mach4 proposed about 1890, that the law of inertia depended on all the matter of the universe. This is known as Mach’s Principle. It was the first recognition that a natural law depends on cosmology. Albert Einstein was greatly influenced by it when he deduced the General Theory of Relativity (GTR). Now, Mach’s Principle, in a more exacting form, has become Principle II (below) of the Wave Structure of Matter from which all the laws derive.

Paul Dirac5 was never satisfied with the discrete point particle because the infinity of the Coulomb force law had to be corrected by ‘renormalization’. He wrote,

This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity because it turns out to be small, not neglecting it because it is infinitely large and you do not want it!

Of course the inference is that the basic equations are wrong and radical changes need to be made. Dirac seemed to foresee the WSM.

In 1945 Wheeler and Feynman5 (W&F) sought the cause of the radiation from an accelerated charge. Their calculation assumed that the charge generated equal amplitudes of advanced (inward) and retarded (outward) spherical electromagnetic waves. The outward waves evoked aresponse of the universe; that is, the production of inward waves from absorbing charges elsewhere in the universe. However, the absorber waves began before the moment of acceleration and before arrival of the source waves. The calculated forces due to combined local and absorber waves agreed with empirical formula and appeared to be the cause of energy transfer. Their remarkable result attracted much attention.
However, W&F pointed out that the derivation had not been rigorous. Especially, there are no electromagnetic wave solutions in spherical coordinates. In hindsight, the success of the W&F calculation was in part due to suppression of the vector character of the electromagnetic waves so that in effect they were calculating scalar (quantum) waves. A scalar wave equation can rigorously produce two solutions; namely inward and outward spherical waves. Below it will be shown that two scalar waves combined have all the properties of positrons and electrons. The combined waves themselves are the electron and no point mass or charge is needed.

10. The Calculation by Wheeler and Feynman (W&F) wished to verify the empirical formula for the force of radiation used by DiracForce = [da/dt]2e2/3c3
where e is the electron charge, c is the velocity of light and a is the acceleration. The mechanism of the force was unknown. They discussed this problem with Einstein who suggested a proposal by Tetrodethat light (energy) transmission was not a one-way process, but two-way communication between a source molecule or atom and a receiver molecule utilizing inward and outward waves. This proposal was not popular since it appeared to violate the causality concept: Actions should appear before their causes, and because the inward waves appear to be travelling backward in time.

Electromagnetic waves were assumed generated by the acceleration of the ‘particle’, using special solutions of the wave equation.
Half the difference between inward and outward waves was prescribed. Outward travelling spherical waves encountered absorber charges in the universe that produced spherical inward waves that returned to the initial charge – a response of the Universe. The inward waves from the universe were assumed to begin before the acceleration occurs.
Dirac’s empirical formula for the force of acceleration was verified and found to be independent of the properties of the absorber provided that absorption was complete. Remarkably, no inward waves appeared to violate causality because the inward waves from the absorber were cancelled upon arrival by interference with waves from the source charge. The remaining wave fields gave the disturbance demanded by experience in agreement with the prescription of Dirac.
W&F summarized the behaviour of the inward waves:

Absorber charges at a large distance produce spherical waves headed towards the source. . . . At the moment the source is accelerated, these waves, just touch the source. . . . Thus all the waves from the absorber charges form an array of approximately plane waves marching towards the source. The (Huygens) envelope of these plane waves is a spherical in-going (advanced) wave. The sphere collapses on the source, and then pours out again as a divergent outward wave.

11. Philosophical Importance.
W&F’s work has implications beyond an explanation of radiation forces because the transfer of energy and the implied motion of matter are the most fundamental processes of science. Further, the concept that spherical waves from all matter of the universe perform the roles of charged particles suggests that the whole universe of particles is involved, i.e. Every charged particle is a structural part of the universe and the whole universe contributes to each charged particle. Their work pioneered the concept that every particle sends quantum waves outward, and receives an inward response from the universe. In hindsight, if they had used scalarquantum waves entirely, this paper would have appeared 55 years ago. A hair’s breadth separates the false and true.

Research of wave structure. After 1945, particle physicists chose to work on post WWII weapons. Research on wave structure stopped until 1985 when Milo Wolff 8,9, using a scalarwave equation with spherical quantum wave solutions, found the Wave Structure of Matter described here. It successfully predicted the natural laws and the properties of the electron, except its spin. Below, this article describes the WSM, derives a physical origin of spin that accords with quantum theory and the Dirac Equation, and adds new results.

Part IV – The Wave Structure of Matter

The wave-structured electron, Figure 1, is termed a space resonance (SR) or Spherical Standing Wave (SSW). Space, that supposed void of which we formerly knew little, is the medium of the waves and the leading player in this new physics of the universe. The properties of electrons, other matter, and the laws they obey are derived from properties of the medium – space. Thus, space described by three principles, underlies our knowledge of the sciences.

12. Principle I. The Wave Equation (Space is a Wave-Medium and Propagates Wave-Motions)
This Principle describes how quantum waves are formed and travel in the space medium. The wave amplitudes are scalar numbers. If the medium is uniform, typical nearly everywhere, onlyspherical waves occur. If observed in relative motion, Doppler modulation and elliptical waves appear. If the medium is locally dense, as in the central region of a proton, waves circulate like sound waves in a drum or a crystalline sphere.

Principle I is: Quantum matter waves exist in space and are solutions of a scalar wave equation:


Where F is a scalar amplitude, c is the velocity of light, and t is the time. Its solutions in Figure 1, are a pair of spherical in/out waves that form the simple structure of the electron or positron. Being superimposed, they form a resonance in the space medium.

Outward wave = Fout = (1/r) F0 exp(iwt – kr)

Inward wave = Fin = (1/r) F0 exp(iwt + kr) (2)

These two waves can be combined in only two ways to form continuous spherical wave structures (See Figure 1) that form charged ‘particles’:

electron = Fin– Fout + CW spin

positron = Fout – Fin + CCW spin(3)

There are only two combinations of the two in/out waves which have opposite phase and spin rotation to form electrons and positrons. Thus matter is constituted of binary elements – like computer hardware. Although the variety of molecules and materials populating the universe is enormous, the building bricks are just two, a spherical In-Wave and a Spherical Out-Wave.

13. Properties of electron and positrons.
The two wave combinations contain all experimental electron-positron properties. Briefly, charge polarity depends on whether there is a + or – amplitude of the in-wave at the wave-center. If a resonance is superimposed upon an anti-resonance, they annihilate. The amplitude at the center is finite as observed, not infinite as in the Coulomb rule. Figure 3 shows a radial plot of the electron. Note that the maximum amplitude Ao is finite, not infinite as in the Coulomb 1/r rule. The properties of quantum mechanics (QM) and special relativity (SRT) are the result of the motion of one space resonance relative to another, which produces a Doppler shift in both the in- and out-waves. The Doppler shifted terms contain the parameters of QM and SRT for a moving particle; that is, the de Broglie wavelength of QM and the relativistic mass and momentum changes, appearing exactly as experimentally measured. More details are in the Math Appendix.
Figure 3.

14. Energy Transfer and the Action-at-a-Distance Paradox

An important property not previously known is the mechanism of energy exchange. Experience tells us that communication or acquisition of knowledge of any kind occurs only with an energy transfer. Storage of information, whether in a computer disk or in our brain, always requires an energy transfer. Energy is required to move a needle, to magnetize a tape, to stimulate a neuron. There are no exceptions. This rule of nature is embedded in biology and our instruments. Finding the energy transfer mechanism between particles is essential to understanding the natural laws.

The first hint of the mechanism of cosmological energy transfer was Ernst Mach’s observation3in 1883. He noticed that the inertia of a body depended on the presence of the visible stars. He asserted: ‘Every local inertial frame is determined by the composite matter of the universe’ and jokingly, ‘When the subway jerks, it is the fixed stars that throw us down.’ His deduction arose from two different methods of measuring rotation. First, without looking at the sky one can measure the centrifugal force on a rotating mass m and use the inertia law F = ma = mv2/r to find circumferential speed v and position, as in a gyroscope. The second method is to compare the object’s angular position with the fixed (distant) stars. Both methods give exactly the same result. The inertia law appears to depend on the fixed stars!

Mach’s Principle was criticized because it appeared to predict instantaneous action-at-a-distance across empty space. How can information travel from here to the stars and back again in an instant?
As Einstein observed; Forces acting directly and instantaneously at a distance, as introduced to represent the effects of gravity, are not in character with most of the processes familiar to us from everyday life.
The answer had to await the WSM where Nature’s energy exchange mechanism, formerly unknown, is now seen as the interaction of waves in an ever-present universal medium ofspace. Space is not empty because, although we do not observe it easily, it is the quantum wave medium produced (See Principle II below) by waves from every particle in the universe as predicted by Mach’s Principle long ago. The energy exchange of inertia, charge, and other forces are mediated by the presence of the space medium. There is no need to travel across the universe.

15. Principle II – Mass-energy density of space Principle
This principle defines the quantum wave medium – space. It is fundamentally important because the properties of waves depend on properties of their medium. But, since the natural laws depend on the waves we deduce that the natural laws in turn depend on the medium. Thus, space – the medium – is the wellspring of everything.

Principle II is: At each point in space, waves from all wave center ‘particles’ in the universe combine their intensities to form the mass-energy density of space.

Mass-energy density of space ~ mc2 = hf = k [SUM(Fn) 2/rn2)]

In other words, at every point in space, the frequency f or the mass m of a particle depends on the sum of squares of all wave amplitudes Fn from the N particles inside the ‘Hubble universe’. Amplitude decreases inversely with their range rn squared. The ‘Hubble Universe’ has a radius R = c/H, where H is the Hubble constant.

This principle is a quantitative version of Mach’s Principle because the space medium is the inertial frame of the law F=ma. When mass or charge is accelerated, energy exchange takes place between their waves and the surrounding space wave-medium. In hindsight, this is the mechanism of charge radiation, sought by Wheeler and Feynman5 in 1945, (though they incorrectly used vector e-m waves instead of scalar ‘quantum’ waves).

Because the number of particles, N ~ 1080, is large in the Hubble universe, the medium is nearly constant everywhere and we observe a nearly constant speed of light. But close to a large astronomical body like the Sun, the larger mass-energy density of space produces a measurable curvature of the paths of the inward and outward waves and thus of light and the motion of matter. We observe the curved paths as the effect of gravity described by Newton and the space curvature of Einstein’s general relativity.

Unfortunately, due to Einstein’s Special Relativity (where the velocity of light c is assumed to be constant) most scientists incorrectly assume c is always constant. In fact Einstein confirms that the constant velocity of Light is only true in non-accelerating systems (i.e. Special Relativity) – General Relativity (the real world of accelerating systems and thus Gravity) is founded on a changing velocity of Light in a Gravitational Field, which is in turn created by Matter. e.g. The curvature of the Light past the Sun. Thus he writes;

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 coordinates when a gravitational field is present.

16. The appearance and origin of Charge
Schrodinger predicted that charge was a shape in the structure of space. In the WSM this happens because the In-waves of an electron resonance are very large at their wave center due to the 1/rdependence. Thus space has a high mass-energy density of space near the resonance centers due to the large wave amplitude. The dense space at the central region propagates waves non-linearly (engineering jargon – in fact the wave-velocity changes!), which promotes energy transfer or coupling between two resonances. We observe this process and call it ‘charge.’ But as Schrodinger and Clifford wrote, there is no charge substance involved. It is a property of the wave structure at the center.
The high mass-energy density of space wave centers appear to us as the location of point charges because electric force interactions occur there. The center wave amplitude is finite, as shown in Fig. 3 and not infinite as in the puzzling Coulomb law; otherwise the law is the same.

Origin of motion. The in-waves, on arrival at the wave-center, determine this location which we observe as the particle location. Thus any matter nearby, which changes the medium mass-energy density of space, also changes the in-wave velocity, thus changing the location of the wave-center which we observe as the motion of the ‘particle’. This motion is observed as the force of gravity. (See Fig: 4) The acceleration of matter also changes the wavelengths (Doppler effect) and moves their center producing energy exchange (inertia) to the wave medium similar to the W&F response of the universe. This also produces Mach’s Principle because the mass-energy density of Space is a result of ALL the matter of the Universe.
Figure 4. Gravity is caused by a slowing of the In-Waves (on the right) due to more matter and thus a greater mass-energy density of space.

17. Equation of the Cosmos. Can this mechanism be tested? Yes. If a resonance’s In-waves can be dominant in its local space, then at some local radius, ro from the center, self-mass-energy density must equal the total density of waves from the other N particles in the Universe. Evaluating this equality8 yields

ro 2 = R2/3N

The best astronomical measurements, R = 1026 meters, N = 1080 particles, yield ro = 6 x 10-15meters. To satisfy the test, ro should be near the classical radius, e2/mc2 of an electron, which is 2.8 x 10-15 meters. It is. The test is satisfied verifying Mach’s Principle. This is called theEquation of the Cosmos a relation between the ‘size’ ro of the electron and the size R of the Hubble Universe. Astonishingly, it describes how all the N particles of the Hubble Universe create the mass-energy density of space of the space medium and the ‘charge’ and ‘mass’ of each electron as a property of space.

Figure 5. Energy exchange / Light. The spherical IN and OUT waves of the source and receiver oscillate in two-way communication until a minimum amplitude condition is obtained (i.e. Resonant Coupling). The decrease of energy (frequency) of the source will equal the increase of energy of the receiver. Thus energy is conserved. We observe ‘e-m waves’ as a large number of such quantum changes.

18. Principle III – Minimum Amplitude Principle (MAP)
This third principle can be obtained from Principle II, but because it is a very useful law of the universe, which determines how interactions take place and how wave structures will move, I write it out separately:

The total amplitude of all ‘particle’ waves in space always seeks a minimum.

This principle is the disciplinarian of the universe. That is, energy transfers take place and wave-centers move in order to minimize total wave amplitude. Amplitudes are additive, so if two opposite resonances move together, the motion will minimize total amplitude. This explains empirical rules such as, ‘Like charges repel and unlike charges attract’ because those rules minimize total amplitude. The origins of some other rules are also now understood. For example, MAP produces the Pauli Exclusion Principle, which prevents two identical resonances (two fermions) from occupying the same state. Two identical states are not allowed because total amplitude would be a maximum, not a minimum. The operation of MAP is seen in ordinary situations like the water of a lake, which levels itself, and in the flow of heat that always moves from a hot source to a cold sink, which are example of the increase of entropy principle.

19. The Conservation of Energy
The energy transfer mechanism between atoms and molecules is a result of the high wave amplitude and density of space at resonance centers, which permits coupling or changes of their wave frequency. When the waves of a potential source and a potential receiver, pass through each other’s centers, and an allowed transition exists between them, MAP minimizes the total of both amplitudes by choosing the transition. In the source, the frequency (energy) of a wave state shifts downward. In the receiver, there is an equal shift upward, as in Fig. 5. Only wave states (oscillators) with equal frequencies ‘tuned’ to each other can couple and shift frequency. Accordingly, the frequency (energy) changes must be equal and opposite. This is exactly the content of the Conservation of Energy law, not too different from tuning up an orchestra matched to the ‘A’ played by the first violin! Instruments which cannot resonate are not allowed.

This mechanism also describes the phenomenon noted by Einstein in the writing of Tetrode5,10,When I see a star 100 light-years away, the star knew that its light would enter my eye, 100 year ago – before I was born! Tetrode was predicting that energy exchange is a two-way symmetrical process between source and receiver – not a one-way photon. This energy transfer mechanism lies at the heart of cosmology. If you use the traditional assumption that matter consists of points of mass and charge substance where energy exchange is a one-way e-m photon travelling between particles, you are doomed to the paradoxes of causality violation, wave-particle duality, Heisenberg uncertainty, redshift, and others. Only the two-way exchange of the WSM matches observation. Even though Einstein had originally proposed the ‘photon’ he never understood the cause of these discrete energy exchanges of light. 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.

Einstein also came to realise that Matter could not be described by a continuous field – and it cannot simply because Spherical Standing Wave interactions (which cause the ‘field effect’) are discrete rather than continuous;

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. (Einstein, 1954)

20. The Origin of the IN Waves and the Response of the universe.
At first thought, it is puzzling where the in-waves come from. This puzzle is our own fault – a result of looking at the waves of only one particle, and ignoring the waves of all other particles in space – over simplification! To find reality, we must deal with the real wave-filled universe. When we study this question5,10 we find a rational origin of the inward waves.———-
Figure 6. Our In-Waves are formed from a Huygens’ Combination of the Out-Waves of all the other Matter in the Universe.

Three hundred years ago Christiaan Huygens, a Dutch mathematician, found that if a surface containing many separate wave sources was examined at a distance, the combined wavelets appeared as a single wave front having the shape of the surface as shown in Fig. 6.
This wave front is termed a ‘Huygens Combination’ of the separate wavelets. This mechanism is the origin the in-waves whereby our In-Waves are formed from a Huygens’ Combination of the Out-Waves of all the other Matter in the Universe. This occurs throughout the universe so that every particle depends on all others to create its in-wave. We have to think of each particle as inextricably joined with other matter of the universe. Although particle centers are widely separated, all particles are one unified structure. Thus, we are part of a unified universe and the universe is part of us.

21. Connecting Quantum Theory and Relativity
Before the WSM, there had been no known physical reason for the theoretical mass increase of relativity. Likewise there were no physical explanations for quantum theory. Were these apparently separate laws connected or not? Indeed, many theorists proclaimed that these phenomena were irreconcilable! Few had thought about a connection because most physicists using a point particle, were satisfied with the traditional concepts despite a few puzzles. After all, they had been in the textbooks for decades. Dirac’s work was a clue that they are connected because relativity, and QM were joined in Dirac’s work, albeit theoretically. The WSM now reveals their simple physical connection – Doppler effects.
The Appendix shows that the Doppler increase of frequency causes increase of mass (energy or frequency) so that m = mo[1 – v2/c2]-1/2 as seen by a moving observer. Rearranged, this equation gives the energy equation used by Dirac:

E2 = p2c2 + mo2c4

This energy equation is also shown by the wave perspective because E and p are super-imposed waves, and the total intensity of two waves is given by the sum of their squares. Likewise, the de Broglie wavelength L = h/p is also a Doppler change of wavelength seen by a moving observer (See Appendix) and it leads to the Schrodinger Equation.

Part V – Discussion
We can have confidence that the Wave Structure of Matter is the true physical reality of the universe. The logical requirement is that the experimental measurements of the empirical natural laws, must agree with the laws predicted by the WSM. It does. In fact, the experimental evidence agrees better with the WSM predictions than with conventional rules. For example, an infinity of charge potential at r=0 is expected from Coulomb’s law. It is not found. Instead, the finite experimental value agrees with the WSM. Conventional physics has no explanation for energy exchange, or the Pauli Principle, or charge attraction and repulsion. All of these are in the WSM.

The philosophical conclusions from the connectedness of laws and matter in the universe are thought provoking: Everything we observe here on Earth: mind, life and matter, depend on the existence of the matter elsewhere in the universe. Thus if the stars and galaxies were not in the heavens, we could not exist! Thus, we are part of the universe, and the universe is part of us. Einstein was close to the truth when he wrote (most profoundly);

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… We shall require a substantially new manner of thinking if humanity is to survive.

But the practical value of the WSM theory is the insight it provides. It allows scientists to deeply analyze quantum wave structures. In the R&D laboratory, the new insight should advance electronic applications, especially IC and memory devices because their tiny transistor elements use quantum effects to control the flow of currents. The new knowledge should improve communication and the efficiency of energy transmission.

Part VI. Mathematical Appendix

1. Solutions of the Wave Equation (Principle I)

The wave equation must be written (Wolff12) in spherical coordinates because cosmological space has spherical symmetry. Uniform density of the medium (space) is assumed which yields a constant speed of the waves (and ‘light’). Then the only two solutions describe the charge waves of common charged particles including the electron, positron, proton, and anti-proton. They are:

IN-wave amplitude = (1/r){ Fmax} exp (iwt + ikr) (a)

OUT-wave amplitude = (1/r){ F max } exp (iwt – ikr) (b)

F= wave amplitude, k = mc/h = wave number, w = 2πf, r = radius from wave center, and energy = E = hf = mc2.

At the center, the in/out waves are joined by rotating the in-wave to transform it to the out-wave. Superposition of the two amplitudes to produce a standing wave can occur in two ways depending on rotation, CW or CCW. One is the electron, the other the positron, with opposite spins. Write the rotation operators as Rccw or Rcw . Then the two resonance amplitudes are:

The electron = E(-) = {- InWave + OutWave} Rccw (c)

The positron = E(+) = {+ InWave – OutWave} Rcw (d)

You can experiment with particle inversions by changing the (+ or -) signs in the amplitude equations. To perform a Time inversion, change t to -t, which converts the positron into an electron. To perform a mirror inversion (Parity), imagine that the waves are viewed in a mirror. You will see that a positron is a mirror image of the electron. To change a particle to an anti-particle (Charge inversion), switch the in-waves and the out-waves, and the spin direction. Thus, successive CP, and T inversions returns to the initial state which is a proof of the empirical-theoretical CPT rule, now seen to be a property of the wave structure.
If you add the electron amplitude to the positron amplitude, the resulting amplitude is zero orannihilation.

16. Origin of Special Relativity (SRT) Mass Increase and the De Broglie Wavelength of QM Theory

Write the equation of a SR, as seen by an observer with relative velocity b = v/c, as shown in Wolff8. Then, insert relativistic Doppler factors, g = [1-v2/c2] -1/2. The amplitudes received by the observer are

Received amplitude = 1/r {(2Fmax) exp [ikg (ct + br)]sin [kg (bct + r)]}.

This is an exponential oscillator modulated by a sine factor. The origin of the de Broglie wavelength (Quantum Mechanics) and the relativistic energy and momentum ( mass increase of Einstein’s Special Relativity) is as follows:

In the exponential factor:

Wavelength = h/mvg = de Broglie wavelength with relativistic momentum.

Frequency = kgc/2π = gmc/h = mass frequency with relativistic energy.

And in the sine factor:

Wavelength = h/mcg = Compton wavelength with relativistic momentum.

Frequency = b gmc2/h = b x (mass frequency) = relativistic momentum frequency.

You see that the Doppler factor g causes the correct de Broglie wavelength and SRT mass to appear in the observed waves, as a function of the relative velocity. It is important to note that the effect is symmetrical; it does not depend on whether the relative velocity is +v or -v. This symmetry is exactly as observed. Examination of the algebra shows that this is due to the symmetrical presence of both the inward and outward waves. Thus the space resonance (Spherical Standing Wave) physically displays all properties of an electron, viz: Quantum Mechanics, SRT, forces, annihilation, conversion to a positron, and CPT relations betweenCharge, Parity (mirror image) and Time; all of which were formerly empirical or theoreticalproperties. These properties depend on the spherical wave structure and ultimately on the wave medium – space.

17. References

1. Clifford, William (1870), ‘On the Space Theory of Matter‘, Cambridge Philosophical Society, 2, pp.157-158.
2. Clifford, William (1882), Mathematical Papers, Editor: Robert Tucker, Chelsea Publishing, N.Y. 1968.
3. Moore, Walter (1989), Schrodinger – Life and Thought, Cambridge U. Press, England, p. 327.
4. Dirac, Paul (1937), Quantum Electrodynamics Nature, London, 174, p. 321.
5. Wheeler, J. A. and Feynman, R. (1945), ‘Interaction with the Absorber….’ Rev. Mod. Phys.,17, p.157.
6. Wolff, Milo (1991), Microphysics, Fundamental Laws and Cosmology, Invited paper at 1stSakharov Conf. Phys, Moscow, pp. 1131-1150
7. Wolff, Milo (1993), ‘Fundamental Laws, Microphysics and Cosmology,’ Physics Essays, 6, pp. 181-203.
8. Wolff, Milo (1990), Exploring the Physics of the Unknown Universe, ISBN 0-9627787-0-2, Technotran Press, CA.
9. Mach, Ernst (1883 – in German), English edition: The Science of Mechanics, Open Court, London (1960).
10. Eisele, John A. (1960), Modern Quantum Mechanics with Elementary Particle Physics, John Wiley, NY.
11. Battey-Pratt, E. and Racey, T. (1980), Geometric Model of Fundamental Particles, Intl. J. Theor. Phys., 19, pp. 437-475.
12. Misner, C. W., Thorne, K. and Wheeler, J.A. (1973), Gravitation, W.H. Freeman Co. San Francisco, p. 1149.
13. Wolff, Milo (1997), ‘Exploring the Universe‘, Temple University Frontier Perspectives, 6, No 2, pp. 44-56.
14. Wolff, Milo (1995), ‘Beyond the Point Particle – A Wave Structure for the Electron‘, Galilean Electrodynamics, Sept-Oct, pp. 83-91.
15. Wolff, Milo (1999), ‘Matter Waves and Human Consciousness‘, The Noetic Journal, 4, No 2, pp. 67-75.

Further References (from Geoff Haselhurst’s editing and comments, February, 2003)

Aristotle The Metaphysics (340BC) Penguin 1998
Davies, Paul, ‘Superforce’, London, Unwin Paperbacks, 1985
Einstein, Albert Ideas and Opinions Crown Trade Paperbacks 1954
Einstein, Albert Relativity Crown Trade Paperbacks 1961
Haselhurst, Geoff, ‘The Metaphysics of Space and Motion and the Wave Structure of Matter’ 2000
Hume, David Enquiries Concerning The Human Understanding and Concerning The Principles of Morals 1737
Kant, Immanuel Critique of Pure Reason (1781) Everyman 1935
Smolin, Lee  The Life of the Cosmos Phoenix 1998
Spinoza Ethics (1673) J.M. Dent & Sons LTD 1910

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