1.2 Quantum Theory / Mechanics: de Broglie's Discovery of the Wave Properties of Electrons (1927)

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

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.

1.2.1 de Broglie's Interpretation of the Standing Waves as the Wave-Like Motion of a Particle in Orbit (1927)

In 1913, Niels Bohr had developed a simple (though only partly correct) model for the hydrogen atom that assumed; (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 =mc²) 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. (See Section 1.4)

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.

1.3 Quantum Theory: The Compton Wavelength 2.43*10^-12m of the Electron Y=h/mc (1923)

As stated, in hindsight there were many clues as to the Wave Structure of the Electron. Another obvious clue being that the electron itself has a 'Compton' wavelength (named after American experimental physicist Holly Compton who discovered this from experiments with electron beams). But unfortunately they had come to accept the particle / wave duality of matter and simply continued to assume that somehow this paradoxical conception of matter was true, and thus beyond human comprehension. (So they stopped looking for an obvious solution!)

So let us briefly explain the Compton Wavelength. Experiments show that Energy is directly related to both Frequency and Mass (this is true since we now realise that they are ALL caused by Wave-Motion). As we know from experiment the energy E and mass m of the electron, and the velocity of light c, we can calculate the Compton Wavelength Y of the Electron as follows; E=hf=mc² and f=c/Y, thus hc/Y= mc² resulting in Y=h/mc which for the Electron = 2.43*10^-12m.

Fig: 2.3 The Compton Wavelength (Y) of the Electron - While this wavelength is related to the actual Wavelength of the Spherical Standing Wave, it is more complex than this. As the Spherical In-Wave flows in towards the Wave-Center, both its Wave-Amplitude and mass-energy density of space increase, thus the velocity and wavelength will also change. (Thus there is still a substantial amount of mathematical analysis required on how the Wavelength of the Electron changes with distance from the Wave-Center.)

1.4 Quantum Wave Mechanics: The Schrodinger Wave Equations / Standing Wave Interactions (1928)

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=mc², 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.

1.4.1 Quantum Physics: On the Forces of Charge and Light

It is the nature of Principles that they are stated rather than deduced. Thus we must state the Properties of Space, as Principles, and then demonstrate that logical deductions from these Principles do in fact correspond to observation. What we have found is that if Space behaves in the following way, then it gives rise to deductions which correspond to observation and experiment.

The Wave Velocity (velocity of light c) varies with both the Wave-Amplitude and the mass-energy density of space (the square of the Wave-Amplitude).
i) The greater the Wave-Amplitude the greater the Wave-Velocity.
ii) The greater the mass-energy density of space the slower the Wave-Velocity.
We do not know why Space, as a Wave-Medium, behaves this way, other than to say that these are simply the properties of Space. What we do discover though, is that from these foundations we get a simple explanation of both Charge/Light and Mass/Gravity.

As gravity is explained in the article on Relativity, the general idea is only briefly summarised here. When In-Waves travel in through other Matter / Wave-Motions of Space, they slightly slow down due to the increased mass-energy density of space, and this causes the Wave-Centers to naturally move together, which we observe as Gravitational attraction. As mass-energy density of space is always positive (squares are always positive), thus the mass-energy density of space of Matter always causing a slowing of the In-Waves, and this then explains why gravity is always attractive.

On the other hand, Wave-Amplitude is both positive and negative, thus interacting Wave-Amplitudes can either increase or decrease (i.e. combine or cancel out), causing either an increase or decrease in the velocity of the In-Waves, and a consequent moving together, or moving apart of the Wave-Centers.
It is this property of Space that causes Charge / Electromagnetic Fields and in a slightly more complex manner, Light.

Thus when we place two electrons near one another in Space, then the Wave-Amplitude of Space between them increases because the Waves are in phase and the Wave-Amplitudes combine and increase, thus the Wave-Velocity increases (opposite to gravity's slowing of In-Waves) and this causes the Wave-Centers to move apart. This explains the electrical repulsion of like charges.

Conversely, if we place an electron and a positron (anti-matter being the opposite phase Wave-Motion to Matter, thus a positron is the opposite phase to an electron) then the Wave-Amplitude between the two Wave-Centers tends to cancel out and become smaller, thus the Wave-Velocity between the two Wave-Centers decreases (like gravity) and thus causes the Wave-Centers to move together.
In fact this also explains the electron / positron (matter / antimatter) annihilation, as the Wave-Centers will eventually overlap one-another and the Wave-Amplitudes will completely cancel out (due to their equal and opposite phase) and thus disappear.
This explains Charge, but does not explain Light, which is slightly more complex, though it is still caused by the same fundamental properties of Space.

1.4.2 Quantum Physics: On Resonant Coupling as the Cause of Light

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 10⁸ to 10¹⁵ cycles to complete, depending on the degree of coupling and species of resonance.

For example, if one oscillator were an electron, its frequency mc²/h is about 10²³ hertz, and if the transition time were 10^-8 seconds, the frequency change requires about 10¹⁵ 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.

1.5.1 Quantum Theory: Heisenberg's Uncertainty Principle

On Chance and Probability in a Necessarily Interconnected finite spherical Universe within a Non-Determined Infinite Space

At the same time that the wave properties of matter were discovered, two further discoveries were made that also profoundly influenced (and confused) the future evolution of modern physics.

Firstly, Werner Heisenberg developed the uncertainty principle which tells us that we (the observer) can never exactly know both the position and momentum of a particle. As every observation requires an energy exchange (photon) to create the observed 'data', some energy (wave) state of the observed object has to be altered. Thus the observation has a discrete effect on what we measure. i.e. We change the experiment by observing it! (A large part of their problem though was to continue to assume the existence of discrete particles and thus to try to exactly locate both their position and motion, which is impossible as there is no discrete particle!)
Further, because both the observed position and momentum of the particle can never be exactly known, theorists were left trying to determine the probability of where, for example, the 'particle' would be observed.

1.5.2 Quantum Mechanics: Born's 'Probability Waves' Interpretation of QT (1928)

Born (1928) was the first to discover (by chance and with no theoretical foundation) that the square of the quantum wave equations (which is actually the mass-energy density of space) could be used to predict the probability of where the particle would be found. Since it was impossible for both the waves and the particles to be real entities, it became customary to regard the waves as unreal probability waves and to maintain the belief in the 'real' particle. Unfortunately (profoundly) this maintained the belief in the particle/wave duality, in a new form where the 'quantum' scalar standing waves had become 'probability waves' for the 'real' particle.
Albert Einstein unfortunately agreed with this probability wave interpretation, as he believed in continuous force fields (not in waves or particles) thus to him it was sensible that the waves were not real, and were mere descriptions of probabilities. He writes;

On the basis of quantum theory there was obtained a surprisingly good representation of an immense variety of facts which otherwise appeared entirely incomprehensible. But on one point, curiously enough, there was failure: it proved impossible to associate with these Schrodinger waves definite motions of the mass points - and that, after all, had been the original purpose of the whole construction. The difficulty appeared insurmountable until it was overcome by Born in a way as simple as it was unexpected. The de Broglie-Schrodinger wave fields were not to be interpreted as a mathematical description of how an event actually takes place in time and space, though, of course, they have reference to such an event. Rather they are a mathematical description of what we can actually know about the system. They serve only to make statistical statements and predictions of the results of all measurements which we can carry out upon the system. (Albert Einstein, 1940)

It seems to be clear, there and resultant probability inherent in Quantum Theory.

Thus the last and most successful creation of theoretical physics, namely quantum mechanics (QM), differs fundamentally from both Newton's mechanics, and Maxwell's e-m field. For the quantities which figure in QM's laws make no claim to describe physical reality itself, but only probabilities of the occurrence of a physical reality that we have in view. (Albert Einstein, 1931)
I cannot but confess that I attach only a transitory importance to this interpretation. I still believe in the possibility of a model of reality - that is to say, of a theory which represents things themselves and not merely the probability of their occurrence. On the other hand, it seems to me certain that we must give up the idea of complete localization of the particle in a theoretical model. This seems to me the permanent upshot of Heisenberg's principle of uncertainty. (Albert Einstein, 1934)

Albert Einsteiield structure of matter, instead, it is due to the interaction of the spherical spatially extended Standing Waves of matter with other matter's Wave-Centers distant in Space. Explaining this Standing Wave interaction of matter with other matter in the Space around it (action-at-a-distance) is largely the purpose of this Article and is one of the great powers of the Metaphysics of Space and Motion and the Spherical Wave Structure of Matter.

Nonetheless, Albert Einstein was very close to the truth. He realised that because matter is spherically spatially extended we must give up the idea of complete localization and knowledge of the 'particle' in a theoretical model. For the particle is nothing but the Wave-Center of a Spherical Standing Wave, and thus can never be isolated as an entity in itself, but is dependent on its interactions with all the other Matter in the Universe. And it is this lack of knowledge of the system as a whole that is the ultimate cause of the uncertainty and resultant probability inherent in Quantum Theory.

Thus the last and most successful creation of theoretical physics, namely quantum mechanics (QM), differs fundamentally from both Newton's mechanics, and Maxwell's e-m field. For the quantities which figure in QM's laws make no claim to describe physical reality itself, but only probabilities of the occurrence of a physical reality that we have in view. (Albert Einstein, 1931)
I cannot but confess that I attach only a transitory importance to this interpretation. I still believe in the possibility of a model of reality - that is to say, of a theory which represents things themselves and not merely the probability of their occurrence. On the other hand, it seems to me certain that we must give up the idea of complete localization of the particle in a theoretical model. This seems to me the permanent upshot of Heisenberg's principle of uncertainty. (Albert Einstein, 1934)

Albert Einstein believed that Reality could be represented by spherical force fields, that reality was not founded on chance (as Bohr and Heisenberg argued) but on necessary connections between things (thus his comment 'God does not play dice'!). He was largely correct, Matter is necessarily connected due to the Spherical Standing Wave Structure of Matter, but due to lack of knowledge of the system as a whole (the Universe), and the fact that it is impossible to determine an Infinite system (of which our finite spherical universe is a part - see Article on Cosmology), then this gives rise to the chance and uncertainty found in Quantum Theory.

1.6 Quantum Physics: A Brief Analysis of Feynman's Quantum Electrodynamics (QED, 1945)

QED is founded on the assumption that charged 'particles' somehow generate spherical electromagnetic (vector) In and Out Waves (a dynamic version of Lorentz's Theory of the Electron, as Feynman uses spherical electromagnetic Waves, rather than static force fields). It is important to realise though, that like most post-modern physicists, Richard Feynman was a Logical Positivist. Thus he did not believe in the existence of either particles or waves, he simply used this conceptual language as a way of representing how matter behaves in a logical way. As he says;

.. some things that satisfy the rules of algebra can be interesting to mathematicians even though they don't always represent a real situation. (Feynman)

This explains why he had such success and such failure at the same time, as he had the correct spherical wave structure of Matter, but he continued with two further errors, the existence of the particle, and the use of vector 'electromagnetic' waves (mathematical waves of force), rather than using the correct scalar 'quantum' waves. It is this error of Feynman's that ultimately led Wolff to make his remarkable discoveries of the WSM.

The problem for QED is twofold;

Firstly, there is the Problem of 'Renormalisation' - Feynman must assume finite dimensions for the particle, else the spherical electromagnetic waves would reach infinite fields strengths when the radius of the spherical electromagnetic waves tends to zero. There must be some non-zero cut-off that is arbitrarily introduced by having a 'particle' of a certain finite size. Effectively, Feynman gets infinities in his equations, and then he subtract infinity from infinity and puts in the correct empirical answer (which is not good mathematics, but it does then work extraordinarily well!)

Secondly, it is a mathematical fact that there are no vector wave solutions of the Maxwell Equations (which found electromagnetic fields) in spherical co-ordinates!
These are profound problems that have caused contradiction and paradox within Quantum Theory to the present day, and have led to the self fulfilling belief that we can never correctly describe and understand Reality.

... the more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that. (Feynman)

In fact Nature behaves in a very sensible and logical way (which explains why mathematical physics exists as a subject and can describe so many phenomena, and also explains how we 'humans' have been able to evolve a logical aspect to our minds!). That it is not Nature which is strange, but our incorrect conceptions of Nature! Most importantly, the simple sensible solutions to these problems can be easily understood once we know the correct Wave Structure of Matter.

1.6.1 The Solution to the Problem of 'Renormalisation'.

Richard Feynman's PhD thesis (with J. A. Wheeler, 1945) used Spherical IN (Advanced) and OUT (Retarded) e-m waves to investigate this spherical e-m field effect around the electron and how accelerated electrons could emit light (e-m radiation) to be absorbed by other electrons at-a-distant in space.
One vexing problem of this e-m field theory was that it led to infinitely high fields (singularities) at the center of the point particle electron. This was avoided with a mathematical process called renormalisation whereby infinity was subtracted from infinity and the correct experimental result was substituted into the equation. It was Dirac who pointed out that this is not good mathematics - and Feynman was well aware of this!
In 1937 Paul Dirac wrote;

I must say that I am very dissatisfied with the situation, because this so called good theory does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it turns out to be small - not neglecting it just because it is infinitely great and you do not want it! (Dirac, 1937)

Richard Feynman was obviously also aware of this problem, and had this to say about renormalisation.

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

Albert Einstein was also aware of this problem as he explains in his critique of Lorentz's electromagnetic field theory for electrons (as it is still the same fundamental problem of the particle / electromagnetic field duality).

The inadequacy of this point of view manifested itself in the necessity of assuming finite dimensions for the particles in order to prevent the electromagnetic field existing at their surfaces from becoming infinitely large. (Albert Einstein, 1936)

Feynman's Spherical IN OUT wave theory is largely correct (and of course explains his success) but his error of using vector e-m waves resulted in infinities at the point particle as the radius tended to zero, and this led to the errors of renormalisation. In reality, Matter, as a structure of scalar spherical quantum waves, has a finite wave amplitude at the Wave-Center (as observed) and thus eliminates the infinities and the problems of renormalisation found in Feynman's Quantum Electrodynamics (QED).(See the Work of Wolff at QuantumMatter.com for a complete explanation.)

1.6.2 The Solution to the Problem of there being NO Vector Wave Solutions of Maxwell's Equations in Spherical Co-ordinates

James Maxwell (1876) used the experimental (empirical) results of Faraday, Coulomb, etc. to develop four equations, now famous, whose solutions described an electromagnetic (e-m) wave which correctly deduced the velocity of light c. Maxwell was correct that light is a wave traveling with velocity c - but it is a wave developed from the interaction of the IN and OUT waves of two spherical standing waves whose Wave-Centers are bound in resonant standing wave patterns. (Thus it is the interaction of four waves which probably explains why there are four Maxwell Equations.)

The Maxwell's Equations (M.E.), which describe the formation of electric fields E by a charge distribution q and changing magnetic fields H, as well as the formation of the H field by a changing E and electric currents i, cannot describe a spherical electromagnetic wave! It is a mathematical fact that there are no wave solutions of the M.E.s in spherical co-ordinates! Only the scalar 'quantum' wave equation has spherical wave solutions. Similarly, there are no imaginable M.E. solutions for a 'photon particle'. It is clear that the M.E.s are not fundamental and the photon is only a mathematical construction.

The failure of the M.E. in spherical co-ordinates can be imagined by saying, You cannot comb the hair on a tennis ball. This means that if you attempt to comb down an E field (the hair representing the electric vector) everywhere flat onto a tennis ball (a spherical surface), you must create a 'cowlick' somewhere on the ball which frustrates your attempt to comb it.

The questions arise, Why did theorists continue to favour the e-m field, the photon, and M.E. for 70 years in spite of the well-known flagrant failure of the mathematical description to agree with observation? Why were alternative descriptions of nature not sought? We suspect the answer is because it worked once the errors were removed with a bit of 'hocus pocus' mathematics and the aid of empirical data.
Unfortunately, this logical positivist view to retain the point particle and vector force fields has been the root cause of the many paradoxes and mysteries surrounding quantum theory. The resulting confusion has been increasingly exploited in the popular press. Instead of searching for the simple behaviour of nature, the physics community found that 'wave-particle duality' was an exciting launching pad for more complex proposals that found support from government funding agencies. The search for truth was put into limbo and wave-particle duality reigned.

Once we understand though, that the particle theory of matter is a mathematical (logical positivist) description of nature, then it becomes less confusing. Essentially the particle is a mathematical construction to describe energy exchange. It says nothing about the energy exchange mechanism and thus makes no comment about how the particle exists, how it moves through Space, what the Space around the particle is made of, and how matter particles 'emit' and 'absorb' photon particles with other matter particles distant in Space.

Let us then consider one fundamentally important argument of Feynman's that light must be a particle.

For many years after Newton, partial reflection by two surfaces was happily explained by a theory of waves,* but when experiments were made with very weak light hitting photomultipliers, the wave theory collapsed: as the light got dimmer and dimmer, the photomultipliers kept making full sized clicks - there were just fewer of them. Light behaves as particles.
* This idea made use of the fact that waves can combine or cancel out, and the calculations based on this model matched the results of Newton's experiments, as well as those done for hundreds of years afterwards. But when experiments were developed that were sensitive enough to detect a single photon, the wave theory predicted that the clicks of a photomultiplier would get softer and softer, whereas they stayed at full strength - they just occurred less and less often. No reasonable model could explain this fact.
This state of confusion waso the electron, and is an example of an anti-particle. ..This phenomena is general. Every particle in Nature has an amplitude to move backwards in time, and therefore has an anti-particle. (Feynman, 1985)

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

And what about photons? Photons look exactly the same in all respects when they travel backwards in time, so they are their own anti-partics a photon.

This can now be simplified to two actions with the WSM;
Action #1: An Electron, as the Wave-Center of a Spherical Standing Wave, goes from place to place in Space (as determined by the spherical In-Waves.)
Action #2: An Electron resonantly couples with another Electron (emits or absorbs a photon)

Once we realise that there are no separate electron or photon particles, thus we remove the problem as to how an electron particle can interact with a separate photon particle! Thus this solution is actually more consistent (and simpler) than Feynman's QED, particularly when we consider Feynman's further explanation of a positron being an electron which goes backwards in Time.

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

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

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

While it may be clever, it is not good philosophy, and it has led to a very confused and absurd modern physics. Surely it is time for physicists to start considering the fundamental theoretical problems of the existing theories and to appreciate that the Metaphysics of Space and Motion and the Spherical Wave Structure of Matter is a simple, sensible, and obvious way to solve these problems!
Finally, let us explain how we can experimentally confirm the Spherical Wave Structure of Matter (which would obviously be very convincing to the skeptics!)

1.7 Quantum Theory: Wolff's Explanation of the Einstein, Podolsky, Rosen (EPR) Experiment & Further Predictions

'The Ultimate Paradox - Bell's Theorem' by Milo Wolff, Exploring the Physics of the Unknown Universe, 1994

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

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

Figure 1.7.1 Experiment to test Bell's theorem Polarized photons are emitted at the center, pass through the adjustable polarization filters on the left and right, and enter detectors on each side. Coincidences (simultaneous detection) are recorded and plotted as a function of the angular difference between the two settings of the polarization filters.

The Essence of Bell's Theorem

His theorem relates to the results of an experiment like the one shown in Figure 1.7.1 (see above): A source of two paired photons, obtained from the simultaneous decay of two excited atomic states, is at the center. At opposite sides, are located two detectors of polarized photons. The polarization filters of each detector can be set parallel to each other, or at some other angle, freely chosen. It is known that polarizations of paired photons are always parallel to each other, but random with respect to their surroundings. So, if the detector filters are set parallel, both photons will be detected simultaneously. If the filters are at right angles, the two photons will never be detected together. The detection pattern for settings at intermediate angles is the subject of the theorem.

Bell (and Albert Einstein, Podolsky, and Rosen) assumed that the photons arriving at each detector could have no knowledge of the setting of the other detector. This is because they assumed that such information would have to travel faster than the speed of light - prohibited by Albert Einstein's Special Relativity. Their assumption reflects the Principle of Local Causes, that is, only events local to each detector can affect its behaviour.
Based on this assumption, Bell deduced that the relationship between the angular difference between detector settings and the detected coincidences of photon pairs was linear, like line L in Figure 1.7.2. His deduction comes from the symmetry and independence of the two detectors, as follows: A setting difference of X, at one detector has the same effect as a difference X, at the other detector. Hence if both are moved X, the total angular difference is 2X and the total effect is twice as much, which is a linear relationship.

Figure 1.7.2 The result of an experiment to test Bell's theorem Data points R of the experiments are shown with black dots. They agree with the line QM, predicted by the quantum mechanics, and do not agree with the line L, predicted by Albert Einstein's concept of causality.

This was a big surprise, because the failure of causality suggests that the communication is taking place at speeds greater than the velocity of light.
The curved line is the calculation obtained from standard quantum theory.
Bell, Albert Einstein, Podolsky, and Rosen, or anyone who does not believe in superluminal speeds, would expect to find line L.
In fact, the experiments yielded points R, which agreed with line QM. The predictions of quantum theory had destroyed the assumptions of Albert Einstein, Podolsky and Rosen!
The results of these experiments were so disbelieved that they were repeated by other persons, using different photon sources, as well as particles with paired spins. The most recent experiment by Aspect, Dalibard, and Roger, used acousto-optical switches at a frequency of 50MHz which shifted the settings of the polarizers during the flight of the photons, to completely eliminate any possibility of local effects of one detector on the other. Nevertheless, they reported that the EPR assumption was violated by five standard deviations, whereas quantum theory was verified within experimental error (about 2%).

Do Non-local Influences Exist?

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

Explaining the EPR-Bell 'Instant' Communication

The Spherical Wave Structure of Matter, particularly the behaviour of the In and Out Waves, is able to resolve this puzzle so that the appearance of instant communication is understood and yet neither Albert Einstein nor QM need be wrong. In order to show this, it is necessary to carefully look at the detailed process of exchanging energy between two atoms, by the action of the IN/OUT waves of both atoms. Remember that for resonant coupling it is necessary for the In and Out Waves of both electrons to interact with one another. The passage of both In-Waves through both Wave-Centers precedes the actual frequency shifts of the source and detector. A means to detect this first passage event is not a capability of the usual photo-detector apparatus and remains totally unnoticed. But the In-Waves are symmetrical counterparts of the Out-Waves and carry the information of their polarization state between parts of the experimental apparatus before the Out-Waves cause a departing photon event. The IN-waves travel with the speed of light so there is no violation of relativity.
At this point you may be inclined to disbelieve the reality of the In-Wave. But there is other evidence for it. Remember, it explains the de Broglie wavelength and thereby QM. It is necessary to explain the relativistic mass increase of a moving object or the symmetry in its direction of motion. It is responsible for the finite force of the SR electron at its center. Are all of these merely coincidence? Especially, it is the combination of In and Out Waves which explains these laws, not just the In-Waves. If you believe in one you are forced to believe in the other.
(Note added by Haselhurst - In fact without In-Waves there can be no Out-Waves, as the Out-Waves are simply the In-Waves after they have propagated In and Out through the Wave-Center. Thus effectively Wolff is saying that the electrons in the experiment are already interconnected with one another, and hence are already 'aware' of one another's resonant state and polarization, before the paired photons are emitted. It is this subtle interconnection of Matter that explains the apparent conflict of the EPR experiment.)

Can Proof of the In-Waves be Found?

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

The Wave Structure of Matter is a profound new way of looking at how Matter exists and interacts with other matter in Space. Wolff has explained a very simple change to a very famous experiment that currently causes Quantum Theory, and Human intellectual knowledge in general, profound problems and paradoxes. Thus it seems to us absolutely essential that this experiment be re-done as suggested above. We sincerely hope that this work on the Metaphysics of Space and Motion and the Spherical Wave Structure of Matter will ultimately lead to this new 'Paradigm' being taken seriously, and that this experiment will be performed sooner rather than later!

Summary

Quantum Theory (1900-1930) discovered four main things;
a) Both matter and light sometimes behave as particles and sometimes behave as waves. (Planck, de Broglie)
b) Schrodinger's Standing Wave equations can be used to describe the allowed discrete energy states for electrons (Wave-Centers) in atoms or molecules.
c) It is impossible to know both the location and momentum of a particle and this inherent uncertainty can be calculated using the square of the Wave equation to determine the probability of where the particle will be found. (Heisenberg, Born)
d) Matter seems to be subtly interconnected with other matter in the Universe. (EPR Experiment)

With the Metaphysics of Space and Motion and the Wave Structure of Matter we can now sensibly explain these phenomena;
a) The solution of the particle/wave duality of matter is obvious - Matter is a Spherical Standing Wave which creates a 'particle effect' at the Wave-Center'. The solution to the particle/wave duality of light is more complex (though it is still obvious once known) and is a consequence of the standing wave structure of matter and that only discrete standing wave interactions can occur during 'Resonant Coupling' of two bound electrons.
b) Schrodinger's Wave equations confirm this discrete standing wave interaction, that only certain discrete standing wave frequencies between matter are resonantly stable which causes frequency (and thus energy) exchanges to be in discrete 'quanta' which can be mathematically explained as 'particle/photon' interactions.
c) Because Spherical Standing Waves are the size of the Universe, their In-Waves are interacting with all the other matter in the Universe. As we exist as complex arrangements of Wave-Centers here on earth, we do not have immediate knowledge of how these In-Waves are interacting with this other matter in the universe, and must simply wait until the In-Waves arrive at the Wave-Center where we observe these changes in motion and position of the Wave-Center. This lack of knowledge causes the uncertainty as to how a Wave-Center will move about over time and thus qualitatively explains why probability based upon wave equations can describe this uncertainty.
d) The Albert Einstein, Podolsky, Rosen (EPR) experiment performed by Aspect in 1972 famously and controversially confirmed the apparent instant interconnection of particles and contradicted Albert Einstein's Relativity which requires that all matter to matter interactions be limited by the velocity of light. Albert Einstein is in fact correct, the error of the experiment was to assume matter was a particle rather than the Wave-Center of a Spherical Standing Wave. Once this is understood then it explains how matter is subtly interconnected with other matter in the Space around it (by the In and Out-Waves) and leads to a minor change in the experiment which will confirm the Metaphysics of Space and Motion and the Spherical Wave Structure of Matter as a sensible and obvious solution to the problems and paradoxes of not only Quantum Theory, but also of Albert Einstein's Relativity and Cosmology.

Thank you for reading our work. Please feel free to write to us if you wish to discuss any of this article, or if you are able to help in getting this experiment performed.

Geoff Haselhurst, Milo Wolff

References

Einstein, Albert Ideas and Opinions, Crown Trade Paperbacks, 1954
Einstein, Albert Relativity, Crown Trade Paperbacks, 1961
Feynman, Richard and Wheeler, John Interactions with the Absorber as the Mechanism of Radiation PhD Thesis- Palmer Physical Laboratory, Princeton University, Princeton, New Jersey, 1945
Feynman, Richard P. The Strange Theory of Light and Matter, Penguin, 1985
Haselhurst, Geoff The Metaphysics of Space and Motion and the Wave Structure of Matter, 2000
Serway, R. A. Physics for Scientists and Engineers Third Edition, Saunders College Publishing, 1992
Wolff, Milo Exploring the Physics of the Unknown Universe, Technotran Press, CA. 1990
Wolff, Milo Fundamental Laws, Microphysics and Cosmology, Physics Essays, 6, 1993 http://www.quantummatter.com/

Quantum Physics Quantum Theory / Wave Mechanics 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, EPR, Non Locality & Quantum Entanglement.
Max Planck Quantum Physics Discrete Light Quanta	Albert Einstein 'Photon' Quantum Theory Photoelectric Effect	Niels Bohr Quantum Physics Copenhagen Interpretation	Louis de Broglie Physics Matter Waves Particle Wave Duality	Erwin Schrodinger Quantum Physics Wave Equations	Max Born Quantum Physics Probability Waves
Werner Heisenberg Quantum Mechanics Uncertainty Principle	Paul Dirac Quantum Physics Dirac Equation	Richard Feynman Quantum Physics Electrodynamics QED	John Bell's Inequality Quantum Mechanics EPR Paradox	David Bohm Quantum Physics Bohmian Mechanics	Milo Wolff Quantum Mechanics Wave Structure Matter

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