Site Introduction (2012): This website is primarily on the subjects of truth and reality. We get about 600,000 page views each week and are one of the top philosophy / physics sites on the Internet. The central thesis is best stated in three parts;

i) We must know the truth to act wisely, and truth comes from physical reality.

ii) Our present and past societies are not founded on truth and act unwisely (overpopulation, destruction of nature, pollution, climate change, religious and economic wars, etc.).

iii) We now know the correct language for describing physical reality (all matter interactions are wave interactions in space), and this knowledge is critical for our future survival, being the source of truth & wisdom.

So how do we prove that this is true? Everyone will agree that

Thus by 1900 the central concepts of Physics were;

Continuous electromagnetic fields

Over the next 30 years

Most importantly, this Dynamic Unity of Reality provides simple solutions to all the 'strangeness' of quantum physics that has resulted from this discrete / disconnected 'particle' conception of matter.

i.e.

I realise this is a pretty abrupt / radical introduction to a new way of seeing things - that it will take some time to adjust. But the Wave Structure of Matter is simple sensible and obvious once known. Each Quantum Physics page has a short summary and important quotes, so it is easy to click around and confirm things for yourself. Enjoy! Think!

Geoff Haselhurst - Email - Nice Letters. - Share this Knowledge

In a time of universal deceit - telling the truth is a revolutionary act. (George Orwell)

You must be the change you wish to see in the world. (Mohandas Gandhi)

All that is necessary for evil to succeed is for good men to do nothing. (Edmund Burke)

Hell is Truth Seen Too Late. (Thomas Hobbes)

Explaining Light 'Photons' with the Wave Structure of Matter (WSM).

Standing Wave Interactions (Resonant Coupling) only occur at Discrete Frequencies which explains the Discrete Energy Exchanges of Light

On the one hand the **quantum theory** of light cannot be considered satisfactory since it defines the energy of a light particle (photon) by the equation E=hf containing the frequency f. Now a purely particle theory contains nothing that enables us to define a frequency; for this reason alone, therefore, we are compelled, in the case of light, to introduce the idea of a particle and that of frequency simultaneously. On the other hand, 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. (Louis de Broglie, Nobel Prize Speech, 1929)

** Light **and **matter** are both **single** entities, and the apparent **duality** arises in the **limitations** of our **language**.

(Werner Heisenberg)

The development during the present century is characterized by two theoretical systems essentially independent of each other: the **theory of relativity** and the **quantum theory**. The two systems do not directly contradict each other; but they seem little adapted to fusion into one unified theory.

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 do, really, correspond to the facts.

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, 1940)

We begin with a very good summary of Atomism, as their ultimate conclusion, that the 'particle' is a conceptual tool for the logical positivist / mathematical physicist, but does not physically exist, is correct. The Wave Structure of Matter explains the 'particle' effect is caused by the wave-center of a Spherical Standing Wave.

Atomism arose as an explanatory scheme with the ancient Greeks (around 400BC), Leucippus and Democritus, and Epicurus, and the Roman poet, Lucretius. At the most fundamental level atomism is the belief that all phenomena are explicable in terms of the properties and behaviour of ultimate, elementary, localized entities (or 'fundamental particles'). Thus it prescribes a strategy for the construction of scientific theories in which the behaviour of complex bodies is to be explained in terms of their component parts. That strategy has led to many of the successes of modern physical science, though these do not prove that there actually are 'ultimate entities' of the type postulated by atomism.

Their (the atomists) analysis goes 'behind' the appearance of minute, unchangeable and indestructible 'atoms' separated by the emptiness of 'the void'. It is the void which is said to make change and movement possible. All apparent change is simply the result of rearrangements of the atoms as a consequence of collisions between them. This seems to lead to mechanical determinism, though, in an attempt to leave room for freewill, Epicurus and Lucretius postulated that atoms might 'deviate' in their courses.

However if 'what exists' is 'atoms', what of the 'void'? In different ways both Aristotle and Descartes denied that there could be such a thing as literally 'empty space'. Physically therefore they saw the world as a plenum. Atomism was also associated with atheism, since as Lucretius put it, 'Nothing can ever be created out of nothing, even by divine power.' Conversely no thing can ever become nothing - so the atomists proposed a strict principle of conservation of matter.

The attempt of the ancient atomists to solve a metaphysical problem about the nature of change resulted in a brilliantly fruitful strategy for the construction of theories in the physical sciences. However there are unanswered philosophical objections to atomism and the very successes it has stimulated suggest that 'the stuff of the world' cannot ultimately be understood in terms of atomism. A thoroughgoing positivism will continue to hold that 'atomic theories' are simply devices for talking about observable phenomena.

(The Concise Encyclopedia of Western Philosophy and Philosophers, 1991)

The Wave Structure of fundamental Particles evolved over five years. It began with a simple speculation that waves in Space could explain the de Broglie wavelength. It continued to agree with more laws and observations than I first expected and I was amazed. The 'Particle' is two identical spherical waves travelling radially in opposite directions so that together they form a spherical standing wave. The wave which travels inward towards the center is called an In-Wave, and the wave travelling outward is an Out-Wave. The nominal location of the ‘Particle’ is the Wave-Center, but as must be true for any charged Particle, it has presence everywhere in Space because the charge forces extend throughout the Universe.

What is a Light 'Photon'?

Two Spherical Standing Waves (SSW) oscillators exchange energy much like classical coupled oscillators, such as electric circuits or joined pendulums. The coupling provided by the non-linear centers of the resonances (high mass-energy density of space Wave-Centers) allows them to shift frequency patterned by the modulation of each other's In and Out-Waves. Since significant coupling can only occur between two oscillators which possess the same resonant elements, the frequency (energy) changes are equal and opposite. This we observe as the law of conservation of energy. When opposite changes of frequency (energy ) take 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 can sample part of it and see a beam of light (which causes the continuous electromagnetic waves of Modern Physics). When single exchanges occur we see 'photons' as discrete Standing Wave interactions. Thus the transitory modulated waves travelling between two resonances create the illusion of the 'photon particle'.

How do Solid Bodies form from Waves?

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 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. (Milo Wolff, 1990)

For more on the Wave Structure of Matter see Dr Milo Wolff on the Wave Structure of Matter. (Also includes Digital Video Interview between Maths Physicist Milo Wolff and Philosopher Geoff Haselhurst.)

With this understanding of the Wave Structure of the 'particle' in mind (and with Albert Einstein as our guide) it is useful to now consider Newton's Mechanics, and thus also appreciate how his 'particle' theory profoundly (though incorrectly) shaped the face of modern physics.

We begin with two very famous quotes from Newton on Absolute Space and Time. Newton's comments on Absolute Space being the foundations of the Relative Motions of Matter in Space is correct and very astute as Newton effectively predicts the evolution of relativity (that it is easier to measure the motion of matter relative to other matter, rather than to Space itself!)

Absolute Space, in its own nature, without regard to any thing external, remains always similar and immovable. Relative Space is some moveable dimension or measure of the absolute spaces; which our senses determine, by its position to bodies; and which is vulgarly taken for immovable space. ...

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. For it may be that there is no body really at rest, to which the places and motions of others may be referred. ...

Absolute, True, and Mathematical Time, of itself, and from its own nature flows equably without regard to any thing external, and by another name is called Duration: Relative, Apparent, and Common Time is some sensible and external (whether accurate or unequable) measure of Duration by the means of motion, which is commonly used instead of True time; such as an Hour, a Day, a Month, a Year. ...

For the natural days are truly unequable, though they are commonly consider'd as equal, and used for a measure of time: Astronomers correct this inequality for their more accurate deducing of the celestial motions. It may be, that there is no such thing as an equable motion, whereby time may be accurately measured. All motions may be accelerated and retarded, but the True, or equable progress, of Absolute time is liable to no change. The duration or perseverance of the existence of things remains the same, whether the motions are swift or slow, or none at all. (Newton, 1687)

Newton is also largely correct that Time is intimately connected to Motion, for Time is ultimately caused by the Wave-Motions of Space. It is also correct to assume an absolute Time (like QT rather than Relativity) such that we have a constant reference to measure the changing velocity of wave-motion. (But Time does not exist as a 'thing in itself' like Newton thought!)

Let us now consider Albert Einstein's analysis of Newton's Mechanics (which is lucid and logical as reflects the greatness of Albert Einstein).

The first attempt to lay a uniform theoretical foundation was the work of Newton. In his system everything is reduced to the following concepts:

i) Mass points with invariable mass

ii) Instant action-at-a-distance between any pair of mass points

iii) Law of motion for the mass point.

Physical events, in Newton's view, are to be regarded as the motions, governed by fixed laws, of material points in space. This theoretical scheme is in essence an atomistic and mechanistic one. There was not, strictly speaking, any all-embracing foundation, because an explicit law was only formulated for the actions-at-a-distance of gravitation; while for other actions-at-a-distance nothing was established *a priori* except the law of equality of actio and reactio. Moreover, Newton himself fully realized that time and space were essential elements, as physically effective factors, of his system. (Albert Einstein, 1940)

We now realise his obvious error was to introduce discrete 'particles' with Motion, rather than the (wave) Motion of Space itself, i.e. Spherical Standing Wave Motion, which creates the 'particle effect' at its Wave-Center.

Newton's endeavours to represent his system as necessarily conditioned by experience and to introduce the smallest possible number of concepts not directly referable to empirical objects is everywhere evident; in spite of this he set up the concept of absolute space and absolute time. For this he has often been criticized in recent years. Therefore, in addition to masses and temporally variable distances, there must be something else that determines motion. That something he takes to be relation to absolute space. He is aware that space must possess a kind of physical reality if his laws of motion are to have any meaning, a reality of the same sort as material points and their distances. (Albert Einstein, 1954)

Albert Einstein considered matter to be spatially extended (and represented by Spherical Force Fields) thus he did not believe in the existence of a fundamental Space or Time that was separate from Matter. As with Leibniz and Mach, Albert Einstein believed that all motion of matter in Space could instead be understood as motion of matter relative to other matter, thus the concept of an absolute Space became unnecessary.

In Newtonian physics the elementary theoretical concept on which the theoretical description of material bodies is based is the material point, or particle. Thus matter is considered *a priori* to be discontinuous. This makes it necessary to consider the action of material points on one another as action-at-a-distance. Since the latter concept seems quite contrary to everyday experience, it is only natural that the contemporaries of Newton - and indeed Newton himself - found it difficult to accept. Owing to the almost miraculous success of the Newtonian system, however, the succeeding generations of physicists became used to the idea of action-at-a-distance. Any doubt was buried for a long time to come. (Albert Einstein, 1950)

The solution though is obvious once known - to discard the discrete particle in Space and replace it with the Spherical Standing Wave (SSW) in Space. Then instant action-at-a-distance between discrete particles becomes action-at-a-distance between the In and Out-Waves of the Wave-Centers 'particles' in Space. This leads to a clear understanding of how matter interacts with other matter at-a-distance in Space, as it is the interaction of the In-Waves and Out-Waves with other SSWs (and particularly their Wave-Centers) that explains all matter to matter interactions in Space. These interactions are limited by the velocity of the In-Waves and Out-Waves which is the velocity of light c. Thus actions-at-a-distance are not instantaneous as Newton had assumed, but are limited by the velocity of the In-Waves (velocity of light c, as Albert Einstein realised).

On the other hand, with respect to an absolute Space, it is one purpose of this article to show that in fact Newton was correct, there does exist a fundamental physical Space which exists as a wave medium and necessarily connects all things. Newton's error was to further assume the existence of the motion of material particles in this Space, rather than the (Spherical) Wave-Motion of Space itself.

Newton's error, of assuming too many existents, leads to two insurmountable problems;

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. Astronomy has never detected departures from Newton's Laws of Motion that would point to such a resistance. (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 is to replace the concept of matter existing as discrete particles with matter existing as Spherical Standing Waves in this Space, thus the motion of the particle becomes the apparent motion of successive Wave-Centers.

Newton simply assumed that discrete particles could act instantly on other particles at-a-distance in Space (Newton's instantaneous action-at-a-distance) though he was well aware of this problem as he explains in his famous letter to Bentley;

It is inconceivable that inanimate brute matter should, without mediation of something else which is not matter, operate on and affect other matter without mutual contact. ... That gravity should be innate, inherent and essential to matter, so that one body may act upon another at-a-distance, through a vacuum, without the mediation of anything else by and through which their action may be conveyed from one to another, is to me so great an absurdity that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it.

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. Letter to Richard Bentley 25 Feb. 1693)

Action-at-a-distance has puzzled philosophers and physicists since Newton first assumed instantaneous action-at-a-distance for gravitational Mass. For if matter is assumed to be a tiny particle, how could it interact (instantly!) with other matter at a distance in Space (across the entire universe)? For example, how do we, here on earth, sense the heat and light from the sun so distant in Space. We now realize that matter is not small, it is large. Indeed Albert Einstein was very close to the truth - matter is spherically spatially extended, thus as we have said, Newton's instant action-at-a-distance from a particle becomes action-at-a-distance from the Wave-Center of Spherical Standing Waves in Space, due to the interaction and change in velocity of their In and Out-Waves. (i.e. As a consequence of Principle Two, the In-Waves of the Spherical Standing Wave in Space interact with other SSWs in Space (particularly their high Wave-Amplitude/Density Wave-Centers) as they flow in through them and change their velocity accordingly. This determines where each successive In-Wave will ultimately meet at their respective Wave-Center (i.e. the future position of the Wave-Center / 'particle') which causes the apparent motion (acceleration) of the 'particle'. This then explains action-at-a-distance (from the Wave-Center) and why it is not instantaneous, but rather, is limited by the velocity of the In-Waves / Velocity of light c.)

It is true that Newton tried to reduced light to the motion of material points in his corpuscular theory of light. Later on, however, as the phenomena of finite velocity, polarization, diffraction, and interference of light forced upon this theory more and more unnatural modifications, Huygens' undulatory wave theory of light prevailed. (Albert Einstein, 1936)

Albert Einstein clearly realized, as did physicists of the time, that the particle concept of light is unable to explain experimental phenomena like polarization, diffraction, and interference, which are obviously explained by wave phenomena. This divide between Newton's particle conception of light and Huygens' wave theory of light was decided by Thomas Young's (1801) famous double slit experiment which showed interference patterns that could only be explained by a wave theory. For how could a single particle travel through two slits and interfere with itself?

Further, as Albert Einstein argues, it is impossible to explain how particles of matter emit and absorb particles of light.

What in that case becomes of the material points of which light is composed when the light is absorbed? (Albert Einstein, 1931)

So while Newton's particle theory for light and matter had substantial logical (mathematical) success at explaining certain phenomena, particularly the orbits of planets, it clearly produced many paradoxes due to its fundamental error of assuming the existence of discrete particles.

Yet no serious doubt of the mechanical (particle) foundation of physics arose, in the first place because nobody knew where to find a foundation of another sort. Only slowly, under the irresistible pressure of facts, there developed a new foundation of physics, 'Field' physics. (Albert Einstein, 1954)

It is obvious that Waves are central to Quantum Theory and thus to understanding the structure of Matter. The problem, as we shall explain, has been the further introduction of the 'particle' concept, and thus the resulting paradox of the 'Particle/Wave' duality.

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 Standing Wave interactions.

In fact the Metaphysics of Space and Motion and the Spherical Standing Wave Structure of Matter not only explains and solves the problems of Quantum Theory, but also Albert Einstein's Relativity and Cosmology.

So let us now explain and solve the many problems and paradoxes of Quantum Theory from the foundations of a pure Wave Structure of Matter.

During the years 1900-1930, many experiments were done on the interactions of light beams, particle beams, and metal targets. Analysis of these experiments showed that Light and Matter had both Particle and Wave properties. As we have said, the solution to this apparent paradox of the Particle/Wave duality is to simply explain how the discrete 'particle' properties (quanta) are in fact caused by standing Wave interactions.

To do this we must begin by explaining the experimental foundations of Quantum Theory;

1. Max Planck's Discovery of the Particle (Quantum) Properties of Light, E=hf. (1900)

2. de Broglie's Discovery of the Wave Properties of Electron Interactions, y=h/mv. (1927)

3. The Equivalence of Energy, Mass and Frequency and the Compton Wavelength Y of the Electron Y=h/mc = 2.43*10-12m.

In 1900 Max Planck made a profound discovery. He showed (from purely formal/mathematical foundations) that light must be emitted and absorbed in discrete amounts if it was to correctly describe observed phenomena (i.e. Blackbody radiation).

Prior to then light had been considered as a continuous electromagnetic wave, thus the discrete nature of light was completely unexpected, as Albert Einstein explains;

About fifteen years ago [1899] nobody had yet doubted that a correct account of the electrical, optical, and thermal properties of matter was possible on the basis of Galileo-Newtonian mechanics applied to molecular motion and of Maxwell's theory of the electromagnetic field. (**Albert Einstein**, 1915)

Then Planck showed that in order to establish a law of heat radiation (Infra red light waves) consonant with experience, it was necessary to employ a method of calculation whose incompatibility with the principles of classical physics became clearer and clearer. For with this method of calculation, Planck introduced into physics the quantum hypothesis, which has since received brilliant confirmation. (**Albert Einstein**, 1914)

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.

During the years following, it was shown that light was everywhere produced and absorbed in such energy quanta. In particular, Niels Bohr was able to largely understand the structure of the atom, on the assumption that the atoms can only have discrete energy values, and that the discontinuous transitions between them are connected with the emission or absorption of energy quantum. This threw some light on the fact that in their gaseous state elements and their compounds radiate and absorb only light of certain sharply defined frequencies. (**Albert Einstein**, 1940)

Even the Greeks had already conceived the atomistic nature of matter and the concept was raised to a high degree of probability by the scientists of the nineteenth century. But it was Planck's law of radiation that yielded the first exact determination - independent of other assumptions - of the absolute magnitudes of atoms. More than that, he showed convincingly that in addition to the atomistic structure of matter there is a kind of atomistic structure to energy, governed by the universal constant h, which was introduced by Planck.

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**, 1950)

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 wholly dependent upon the frequency f of incident light as described in the equation E=hf. It is ironic that in 1921 Albert 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!

In 1954 Albert 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. (**Albert Einstein**, 1954)

Most importantly, Albert Einstein also suspected that Matter could not be described by a continuous spherical force field;

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**, 1954)

Albert Einstein's suspicions were well justified, for he had spent a lifetime trying (and failing) to create a unified field theory of matter that explained both Quantum Theory / Light and Relativity / Gravity.

In fact Matter, as a Spherical Standing Wave which causes the 'Field' effect, interacts with other matter in discrete standing wave patterns, not with continuous force fields as he had imagined, thus his task was ultimately impossible, as he sadly came to realise towards the end of his life.

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, Albert Einstein) as well as a discrete particle/photon (Planck, Albert Einstein). So we see that Albert Einstein was partly responsible for the discovery of the particle/photon concept of light, though he completely rejected the notion of discrete particles. He writes;

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. (**Albert Einstein**)

Albert Einstein is correct that there are no discrete particles, and that The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high. But it is the high Wave-Amplitude of the Wave-Center of a Spherical Standing Wave in Space (not of a continuous spherical force field) that causes the particle effect. Thus of three concepts, **particles**, **force fields**, and **motion**, it finally turns out that Motion, as the spherical wave motion of space, is the correct concept, as it then explains both particles and fields.

It is most important to realise though that Albert Einstein was correct in imagining matter as being spatially extended, as he explains;

I wished to show that space time is not necessarily something to which one can ascribe to a separate existence, independently of the actual objects of physical reality. **Physical objects are not in space, but these objects are spatially extended**. In this way the concept empty space loses its meaning. (**Albert Einstein**)

It is certainly true that the particle and its forces are very useful mathematical concepts, unfortunately, they also cause many problems and paradoxes because they are approximations to reality and do not physically exist.

We can now finally solve these problems by understanding the reason for these discrete energy states, which are due to the fact that standing waves only exist at discrete frequencies, like notes on the string of a guitar, thus while the correct Spherical Standing Wave Structure of Matter predicts that energy exchanges will be discrete, as observed, the continuous e-m wave does not anticipate this.

Thus the Spherical Standing Wave Structure of Matter explains Max Planck's (1900) discovery that there are only certain allowed discrete energy states for electrons in molecules and atoms, and further, that light is only ever emitted and absorbed by electrons in discrete or 'quantum' amounts, as the electrons move from one stable standing wave pattern to another.

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)

It is with some frustration that I now read these quotes, as it is obvious in hindsight as to their errors, and how simply they can now be solved! de Broglie's realisation 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, and these predicted wave properties of matter were shortly thereafter confirmed from experiments (Davisson and Germer, 1927) on the scattering of electrons through crystals (which act as diffraction slits). As Albert 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.

In 1913, Niels Bohr had developed a simple (though only partly correct) model for the hydrogen atom that assumed; (Our further comments in brackets)

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. This is known as 'Resonant Coupling' and is explained in Section 1.4.)

This early atomic model had some limited success because it was obviously created to explain the discrete energy states of light emitted and absorbed by bound electrons in atoms or molecules, as discovered by Planck in 1900.

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 Albert 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**, 1940)

**Fig: 1.2.1 The allowed discrete orbits of the electron as imagined by de Broglie.**

de Broglie assumed that because light had both particle and wave properties, that this may also be true for matter. Thus he was not actually looking for the wave structure of matter. Instead, as matter was already assumed to be a particle, he was looking for wave properties of matter to complement the known particle properties. As a consequence of this particle/wave duality, 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.)

From de Broglie's perspective, and from modern physics at that time, this solution had a certain charm. It maintained the particle - wave duality for BOTH light and matter, and at the same time explained why only certain orbits of the electron (which relate to whole numbers of standing waves) were allowed, which fitted beautifully with Niels Bohr model of the atom. de Broglie further explains his reasoning for the particle/wave duality of matter in his 1929 Nobel Prize acceptance speech;

On the one hand the quantum theory of light cannot be considered satisfactory since it defines the energy of a light particle (photon) by the equation E=hf containing the frequency f. Now a purely particle theory contains nothing that enables us to define a frequency; for this reason alone, therefore, we are compelled, in the case of light, to introduce the idea of a particle and that of frequency simultaneously. On the other hand, 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. (**de Broglie**, 1929)

The solution to their problems was first found by Wolff (1986). He discovered two things (both of which deserve a Nobel prize in their own right);

Firstly, from reading Feynman's PhD thesis (see reference, Feynman and Wheeler, 1945) he was aware of Feynman's conception of charged particles which 'somehow' generated Spherical Electromagnetic In and Out Waves (Feynman called them advanced and retarded waves), but Wolff realised that there are no solutions for spherical vector electromagnetic waves (which are mathematical waves which require both a quantity of force and a direction of force, i.e. vector). Wolff had the foresight to try using real waves, which are Scalar (defined by their Wave-Amplitude only).

And this then led to a series of remarkable discoveries.

He realised that spherical In and Out-Waves removed the need for a separate particle, as the Wave-Center of the Spherical Waves created the particle effect.

He then discovered that when one spherical standing wave was moving relative to another the Doppler shifts gave rise to BOTH the **de Broglie Wavelength** AND the **Mass increase of Albert Einstein's Relativity**. (i.e. Wolff demonstrated that when two charged particles (Wave-Centers of two SSWs) are moving relative to one another they gives rise to beats of interference (caused by the Doppler shifting of the In and Out Waves due to relative Motion) which were identified in experiments as the de Broglie wavelength y=h/mv, and also gave rise to the frequency increases and thus energy/mass increases (as E=hf =mc^{2}) of Special Relativity.

Thus in the one equation he had deduced, with mathematical certainty, the two observed phenomena due to relative motion, which respectively found central parts of both Quantum Theory and Albert Einstein's Special Relativity. (Thus for the first time uniting these two theories from one common theoretical foundation!)

This then led to his further work on resonant coupling which finally solved the puzzle of the 'photon' and explained why light energy is only ever emitted and absorbed in discrete amounts.

Unfortunately for modern physics, and ultimately for human knowledge, this obvious solution was never considered by de Broglie, Albert Einstein, Bohr, Schrodinger, Heisenberg, Dirac, Born, Feynman, etc. etc. Thus the now obvious solution of realising that matter was a Spherical Standing Wave that causes the point particle effect at the Wave-Center remained unknown and ignored, and instead, the confusing and paradoxical concept of the particle/wave duality was retained.

Quantum theory was thus essentially founded on the experimental observations of frequency and wavelength for both light and matter. These empirical facts are obviously consistent with the Spherical Standing Wave structure of matter.

1. Planck's discovery that energy is related to frequency in the equation E=hf

2. The Equivalence of Energy, Frequency and Mass E=hf=mc^{2}, which deduces the Compton Wavelength Y=h/mc

3. The de Broglie wavelength y=h/mv

It was Erwin Schrodinger who 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 (from the above equations) 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 thus that only certain standing wave frequencies could exist which corresponded to certain energy states. The agreement of observed frequencies and Schrodinger's Wave Equations further established the fundamental importance of Quantum Theory and thus the Wave properties of both light and matter.

As Albert 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**, 1936)

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 a most important difference. Electromagnetic waves are vector waves - at each point in Space the wave equations yield a vector quantity which describes both a direction and an amplitude (size of force) of the wave, and this relates to the original construction of the e-m field by Faraday which described both a force and a direction of how this force acted on other matter.

Spherical Wave Motions of Space are Scalar waves - at each point in Space the wave equations yield a single quantity which simply describes the wave amplitude (there is no directional component). For example, sound waves are scalar waves where the wave amplitude describes the Motion (or compression) of the wave medium (air). Likewise Space is a nearly rigid Wave-Medium which propagates Wave-Motions.

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 Albert 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.

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**, 1927)

So let us now explain in more detail this phenomena of Light energy being emitted and absorbed in discrete amounts (photons) due to Resonant Standing Wave interactions. Firstly, we must understand Principle Two and realise that the velocity of wave Motions in Space is not constant, and in fact depends upon both the Wave-Amplitude and the mass-energy density of space (square of Wave-Amplitude). These are simply the properties of Space as a Wave-medium.

What we must further realise is 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.

Thus two bound resonating electrons (oscillators) exchange energy much like classical coupled oscillators, such as electric circuits or joined 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. Since significant coupling can only occur between two oscillators which possess the same resonant elements, the frequency (energy) changes are equal and opposite. This we observe as the law of conservation of energy.

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, so we can sample part of it, we see a beam of light. When single exchanges occur we see photons as discrete energy exchanges. The transitory modulated waves traveling between two resonances (as the Electrons/Wave-Centers move from one standing wave pattern to another) create the illusion of the photon. An exchange may require 10^{8} to 10^{15} cycles to complete, depending on the degree of coupling and species of resonance.

For example, if one oscillator were an electron, its frequency mc^{2}/h is about 10^{23} hertz, and if the transition time were 10^{-8} seconds, the frequency change requires about 10^{15} cycles to complete. Such a large number of cycles implies, in engineering slang, a large Q value, which indicates great precision of the equal and opposite changes in oscillator frequency, and the conservation of energy.

**Fig: 1.4.2 Light is Caused by the Resonant Coupling of two bound Wave-Centers of Spherical Standing Waves (Electrons) with oscillating wave functions**. This diagram is only an approximation, but it gives you some idea of the 'secondary' wavelength (the 'electromagnetic' wavelength of light) caused by the interactions of the In and Out-Waves of the two Electrons/Wave-Centers.

Thus we realise that these different standing Wave patterns cause a cyclical oscillation in the Shape of the In and Out-Waves which describes a wave function that is ultimately the cause of the 'electromagnetic' wavelength and frequency of light. As only certain discrete 'orbits' (standing wave functions) exist for the Wave-Center of the Spherical Standing Wave, then it can only exchange frequencies in discrete levels which correspond to discrete energy exchanges of light 'photons'. i.e. E=hf where only discrete frequencies (f) area resonantly stable and thus 'allowed'. (There are no separate light 'particles / photons' or collapsing wave functions, both being mathematical existents only!)

Most importantly, these standing wave interactions and resonant coupling are the reason for Schrodinger's Standing Wave Equations and their obvious success at explaining the allowed energy states for electrons in atoms, and thus the discrete photon effect of light as these electrons move from one resonant standing wave pattern (quantum state) to another.

The Wave Structure of Matter (WSM) and Spherical Standing Wave Interactions explains Discrete Energy States of Quantum Physics (Quantum Theory / Quantum Wave Mechanics).

A Simple Solution to the Particle / Wave Duality of Light and Matter & Quantum Entanglement

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