Thus,  τ = µBB = F˫x = Eer0 where, F = tangential or perpendicular force, E = Electric field, e is the electron charge, and distance x = r0., the radius of each loop based on its Compton wavelength.

Giving,   µ_B B=Eer_(0 )

µ_B=E/B er_0=cer_0=ce ƛ_c/2

because c=|E ̃ |/|B ̃ | and r0 = ƛc/2.

☎ ➤ → ©

E = mc

Since then many of the greatest physicists, including Einstein, have expressed their desire to understand how this tiny object can possess its properties such as electric charge and magnetic moment. Even quantum mechanics, with all its success and accuracy, can offer no deeper insight into this fundamental particle, being concerned only with predicting experimental outcomes after giving it certain intrinsic properties. However, physics is still unable to say what it actually is or how these properties come about. It merely says they are intrinsic.

Currently, most particle physicists believe the electron has no structure, being an infinitely small point. However, SED disagrees and will explain why in this section. The electron is unique and theoretically the simplest of all particles. But until now there has been no model that successfully predicts its properties and structure.

SED proposes a model of the electron built from first principles, using simple classical physics. The size, mass, magnetic moment and even the alleged purely quantum concepts of spin state and half-integer spin, are quantitively and qualitatively derived from its model. Then an account of the mysterious Fine Structure Constant, along with the electron’s charge value are derived. The model we use is the roton or rotating photon as described above. We will see how well these predictions agree with experiment.

Firstly, we show that the electron is both a standing wave or soliton, as well as a particle. As a result it actually has a size due to its wavelength, but because it is a wave and not a solid particle with a hard surface, it appears to be a point in certain experiments. The wave is made from a single cycle of a pure E-M field, endlessly rotating over and over again, virtually infinitely. The path of this wave is a roton, the first three-dimensional standing wave that came into existence during the early Big Bang. It is also a soliton or special standing wave that occupies a tiny space or volume, giving it the attributes of a particle, such as mass and inertia. The remaining features of the electron such as half-integer spin, electric charge and magnetic moment can be readily derived from this model, a model made from a rapidly rotating E-M field moving in a special 3-D path consisting of two loops, that we call a roton or rotating photon.

Figure 16 - A model of the roton made with a marked up plastic strip (one E-M cycle). Note the constant direction of the electric (arrow) and magnetic (dot and cross) fields that give the electron its properties due to their endless cycles.

Figure 17 – For the electron, here we have shown the dimensions of the roton when it is drawn flat (left), and as viewed from the front when bent down at 90° (right). Note: these drawings are diagrammatic and the roton is really a continuous 3-D curved path with no edges (Fig 11 above). It forms a path lying on a hemisphere with a radius of ƛe√2.

The size and mass of the electron - ƛe and me

write E = mc2 for energy,

ƛe and me

The radius, r0√2, forms

just over 1/137th the spee

Earlier in the section on matter and energy, we discussed what mass is and now ask the vital question: How can an infinitely small point possess mass? According to SED this makes no sense. An infinitely small point is the same as nothing and no properties can be associated with it. Physics sensibly rejects the idea of a singularity in its other theories because of all the difficulties associated with this concept, as the inclusion of any type of infinity, either big or small, always leads to unbearable problems. So why does it hold on to such an illogical and impossible idea for elementary particles?

Therefore, we need to consider the question: Does the electron actually have a size?

SED suspects that because experiments are unable to measure any size for the electron, physicists dismiss the fact that it occupies any space at all. But this is precisely because it has no hard surface or edge and is not a solid, being purely a trapped wave of energy in the form of a soliton. If they were aware of this model, perhaps more physicists would change. Of course experiments are the ultimate proof of all scientific theories, but we need to keep an open mind into how we interpret experiments and what they are telling us. The electron does not have a ‘size’ in the sense of larger, harder particles, but it does occupy a particular space that it alone can fill, as confirmed so often by the well accepted Pauli exclusion principle.

Our model or roton as drawn in figure 12 above, shows us the key dimensions of an electron but remember it is actually a three-dimensional object, only photons are flat or 2-D. Also we know its size is based on the energy or mass held within it. This can vary according to the system the electron finds itself in and described mathematically by the Schoedinger equation.

For a free isolated electron, its size is directly related to its mass and currently its mass can only be determined by experiment. Once this is known we can calculate its Compton wavelength, then use that in our model to find the size of its structure plus the other properties of the electron.

Experiments show the electron has a mass of 9.10938371 x 10-31 kg, which has the symbol me. We need not explain the experimental procedures here, but it has been confirmed many times. Its Compton wavelength is calculated using the definition of Planck’s constant, h.

We have in general:        h = mcλ, so for the electron we write this as:      h = mecλe

After rearranging we get:              λe = h/mec              = 2.42631023867(73)×10−12m

As we have said, the Compton wavelength relates to a particle’s size and is the size or wavelength a photon would have if it had the same mass. For the electron it can be thought of as the circumference of its circular wavelength (λe), or as the radius of this circle, when it is then referred to as the reduced Compton wavelength (ƛe). So using Pythagoras’s equation, these are related by: ƛe = λe/2π. They have equivalent meanings, and it is simply a matter of which is more appropriate to the relevant situation. In the previous introduction on SED, we stated that when a roton or electron is produced from two gamma ray photons, the radius of each loop in the roton, ro is one quarter that of each constituent photon’s or, ƛ. Remember that it takes two flat photons to produce the 3-D roton which has twice the energy of each (half their size) and each loop comprises half the overall wavelength of the electron. Again, in that discussion, the radius was used because it is often easier to visualise a radius rather than the circumference (see figure 9 above).

In that section on SED, we saw how each loop of the roton lies on an imaginary sphere that has a diameter of ƛe√2. Using this reasoning we can say that the free electron occupies a hemispherical space with a diameter about 1.4 times its reduced Compton wavelength or approximately 4.85262046×10−12m. Again, we need to repeat that this is not a hard fixed volume because the electron is a roton and a wave that has no real surface, although we will see that it does have a kind of event horizon distinguishing internal and external field strengths, which will be examined later. For now, ƛe is one important aspect to the size of the free electron.

Next, we investigate: The classical size of the electron re

Another useful concept when discussing the electron’s size is what has been called the classical electron radius, re. This has been known since early last century and has a value of about 137th its Compton wavelength. In other words, tiny, but somehow larger than nothing. Modern physics always faces a dilemma when this topic arises because it insists the electron is a point particle of zero size. However it has been forced to acknowledge that re is a useful measurement of size in certain situations. How can this be? What an awkward situation this creates for physics! It is something that it, and especially the standard model, cannot continue to ignore.

SED has no problem with the idea of re. In fact it uses it openly in its investigation of the fine structure constant, α. Later in this book, SED devotes a whole section to α, but for now we will only say that α is a dimensionless or unitless number, with an absolute value like π, and it is intimately involved with elementary particles. Its value is accurately known but for convenience we say it is about 1/137. Being unitless implies it is related to the ratio of two similar things like length, or time, and energy etc. Why α has its exact value has always been a deep and unfathomable mystery for physics. SED maintains that it most likely comes about due to the ratio of re to ƛe being exactly α. In other words, if [1]re represents the path thickness, and ƛe the path length of the roton that forms the free electron, we find their ratio is α or ~ 1/137. This gives re a real physical significance. More will be said about this later. For now we just need to remember that the roton is not a solid ‘thing’, but only the path that light or E-M energy travels over, as it moves in space like a wave. However, surely it is reasonable to suppose this path has these dimensions of width and length and that they are the values that early experimenters discovered and used. Further, SED proposes that this path must have both a thickness and length in order to exist and create the properties we observe in the electron. This is how physics works, by giving measurements to things. Its thickness is what waves in each moment, creating the E-M fields, and its length is one wavelength. All entities that physics observes, and measures must be real and have a value.

Surprisingly, it turns out that the electron can have not only this one, but in fact two different sizes, depending on the system it finds itself in. It can be free as we have discussed, but it usually exists in an atom and most often in the universe the electron is found in the hydrogen atom. Many other types of atoms exist, giving the electron different properties when in these, as we will explore later in the section on the atom. For now though, we concentrate only on these two sizes; when it is free and when it is in a hydrogen atom, and we will see that again, α relates to both, but until now, physics has no idea why.

When the electron is trapped by a proton and forms hydrogen, it is the opposite electrical charges that cause this attraction. As the electron falls into the grip of the proton, it loses the electrical potential energy it possessed when free. As a result, its overall energy is less, and as we have said before, this causes it to become larger. Experiments show that in hydrogen, this new size has a constant particular value, and this is known as the Bohr radius, or a0 of hydrogen. Physics also refers to it as the size of the ground-state orbital. Interestingly, there is a simple direct relationship that exists between all these different sizes, and as we have said it always involves the fine structure constant. It can be written like this.

α = re/ƛe = ƛe/a0 = a04πR∞

In the last term, R∞ is the Rydberg Constant or largest wavenumber (reciprocal of wavelength) of any photon that can be emitted from a hydrogen atom. Physics has discovered this relationship, but not yet explained the reason why it has this value. The Rydberg constant is a measure of the size of the photon released by hydrogen when it loses its electron and becomes a proton. It is also a measure or value of the amount of energy required to ionize hydrogen, which happens to be about 13.6 electron volts. These are connected because the size of a photon is a direct measure of its energy. Again, larger photons have less. Now this photon’s size is related to the size of the Bohr radius (the larger size of the single electron’s soliton when in hydrogen) through the factor α/4π. This is because the last term can be written as a unitless ratio, just like the other two that contain the reduced Compton wavelength. To do this we convert the wavenumber to a wavelength by inverting it.

α = a04π/λRydberg

So far so good, but why 4π in addition to α? The reason is structure, and SED describes it this way - Both these structures (the large electron and the emitted photon) have inherent circular motion but the top term (a0 ) is a radius, while the bottom term (λRydberg) is a circumferential wavelength. Multiplying the Bohr radius by 2π converts it to a circumference, so they are both equal things, leaving only a factor of 2 to account for.

This arises because the electron, a roton, consists of one complete cycle of the E-M wave but has two loops, and each loop carries half the wave’s full cycle. However, a photon with its flat circular structure, contains only a single complete cycle of the E-M wave in its structure. When the hydrogen atom loses its electron and creates this photon, the photon’s energy comes from the externally supplied ionization energy. This energy or size is related by the above equation for α, which connects the Bohr radius with the Rydberg constant. In it we see that the top term concerns rotons or particles through a0, and the other concerns photons and their wavelength. The first two equations for α always had the same type of objects in both top and bottom lines. Referring to figure 11 above and remembering that when determining the size of rotons, we used their radius, ro which refers to the radius of each loop and we needed to convert this radius to a circumferential length the same as a photon, by multiplying it by 2π. But for a roton to produce a photon it takes both loops and so to make this an equivalent thing, with the same dimensions of a full wave cycle, the path length of each half-wave loop needs to be doubled when emitting a photon, hence the additional factor of 2. Only our model can explain these relationships this way.

SED further proposes that in hydrogen, the electron is not a point that forms a kind of probability cloud around the proton, but because it has a smaller total energy than when free, it actually is a new much larger soliton, that enfolds and surrounds the far smaller proton, giving the impression of a cloud, but it is actually a randomly orientated roton, with a hemispherical shape and no surface. Less energy means less mass and thus the captured electron expands as it relaxes to become the size of the Bohr radius in the hydrogen atom. This soliton is now about 137 times larger, but like the free electron it is also fixed and cannot be divided. According to the relationship shown above, the ratio of this new size in hydrogen, a0, to its original free reduced Compton wavelength, ƛe, is again α. This is just the ratio of its two total energies, before and after capture.

SED shows why this is so in the up-coming section on the fine structure constant. In brief, it is because when a stable atom of hydrogen is formed from a proton and an electron, the ratio of the electrical potential energy the electron loses, compared to what it originally had in total when free, is also α. This is another reason why α is so important to fundamental particles – It determines their behaviour and the value of all their interactions.

Returning now to the value of the mass of the electron, we noted that this is something that can only be revealed by experiment. There is no theory today that says why an electron has the mass it has. SED suspects that it may be due to the balancing of its internal fields with the inherent motion within the roton, but as yet has no definitive answer other than saying it will most likely be due to structure. For now we will concentrate on the idea of mass generally and how it arises in elementary particles. There is no need in this theory for such abstract and bizarre concepts like the Higgs boson with its associated Higgs field, that somehow miraculously imparts the quality of mass onto all fermions throughout the universe.

The Origin of Mass

We would like to answer the question: [2]What actually is mass and how does it arise?

To do this, we need Planck’s and Einstein's equations for photons and particles:

These are:              and    . . .   ①

Secondly, from the definition of Planck's quantum of action we have:      . . .   ②

where ƛ is the reduced wavelength or radius of motion in an object’s angular momentum. These are general equations and not concerned with an individual type of elementary particle.

If we multiply both sides by c and use equation 1 above, an equivalent equation is ћc = Eƛ.

Note: The left-hand side of this equation is always constant and therefore the right-hand side must also be. This shows that energy and wavelength always change inversely. If one is large, the other is small, if one increases, the other decreases etc.

Next, we will do a thought experiment: Consider a lighthouse with a rotating light sweeping out a beam once per second. How far do we have to go from this lighthouse until the sideways or tangential speed of the beam is c? The answer is about the distance from the earth to the moon or around 300,000 km away (temporally ignoring the factor of 2π), because light takes just over a second to travel this distance. Now, imagine a kind of a stationary photon with this wavelength and frequency, remembering that all photons have angular momentum of ћ. Then if we somehow reduce its size or radius to 1m, while keeping ћ and c (its circumferential speed) constant, what is its new frequency? Like an ice skater, its spin or angular frequency will increase, because its radius is reduced, so if ƛ = 1 meter, by using ωƛ = c, we get ω = 2.997925 x 108 radians/sec. From ① above, its energy has become 3.161527 x 10-26 joule. Finally, if we reduce this radius to ƛe = 3.861593 x 10-13 m (the reduced Compton wavelength of the electron), its angular frequency will increase further to an enormous value of ωe = 7.763440 x 1020 radians/sec, giving it an energy of 8.187105 x 10-14 joule. Using E = mc2, this is equivalent to a mass of 9.109383 x 10-31 kg - the mass of the electron me.

Unlike our soliton or roton, this was just an imaginary photon that remained fixed in space with zero rest-mass when infinitely large. We kept both angular momentum constant at ћ and its rotational speed constant at c. By reducing its wavelength or radius, we must increase its frequency in direct proportion. We did this by giving the imaginary photon energy that it stores and manifests as an increase in mass (rotational inertia). So, we find that mass is created where space is compacted. In the case of the real electron, this mass is a fixed constant formed inside the curl of the photon’s path from energy supplied by The Big Bang and trapped in a soliton. Remember though, that flat photons are unable to possess mass. Only the roton with its unique three-dimensional structure can do this when it is formed by the superposition of two highly energetic gamma rays colliding at 900, (see figure 8, in the section on SED above) The resultant structure is very stable and intimately connected with Planck’s constant. The basis of all things.

This reasoning shows that perhaps we don't need a separate entity called mass - only energy in the form of angular inertia confined in a 3-D soliton. Inertia directly related to frequency. The universe becomes simpler. The soliton localises this energy and because mƛ = ћ/c = constant, increasing the mass of a soliton means reducing its size and increasing its curvature. Mass (or energy) and wavelength are inversely proportional. This is why an electron is much smaller than a photon involved with light. Its wavelength is about one millionth the size, so it is twisted into a very tight curl. It is also why all protons and neutrons are smaller than electrons and portray more mass. The entire electromagnetic spectrum bears this out.

So what are the other measured values in the electron that SED predicts using first principles and the structure of its roton? Two basics are the value of its magnetism and charge.

Bohr Magneton - µB

Definition:                                        Value = 9. 27400999083 x 10-24 JT-1

This is the dipole moment of the electron. Generally, the dipole (or magnetic) moment, µ is the quantity that determines the torque τ a magnet experiences in a magnetic field B, where τ = µB. This equation is the magnetic equivalent of the electric equation, F = eE. In our larger world, the dipole moment of a solenoid is µ = nIA, where n = number of turns, I = current and A = area of each loop. Inside the tiny electron things behave differently due to its structure and yet we will discover how classical physics can be used to derive the correct value of the Bohr magneton. See the upcoming section on SED and Maxwell's equations for more details on the concept of torque, or what physics also refers to as ‘curl’.

For now we will use the equation: torque τ = µB and also the fact that torque equals the product of an applied force a distance x from the centre of circular turn. In the electron it is this torque that turns or twists the two loops and creates a soliton.

Figure 18 - Electric Torque inside the electron

Thus,  τ = µBB = F˫x = Eer0 where, F = tangential or perpendicular force, E = Electric field, e is the electron charge, and distance x = r0., the radius of each loop based on its Compton wavelength.

Giving,  

or,         ,                 because     and   r0 = ƛc/2.

So we have finally,        ,                using   cƛc = ћ/me.

This shows our model can be used to derive the Bohr Magneton of the electron, with nothing but standard elementary physics.

The spin of the electron: s = ћ/2

Until now, electron spin has always been something that apparently only quantum mechanics could account for. After all, if the quantum of angular momentum is ћ, how can anything have half this amount? Further, why do photons and bosons have a spin of ћ but fermions with their mass have a spin of ћ/2? It seemed nonsensical and non-classical - and what would be spinning anyway? This model provides an answer.

The key lies in the twist or curl the roton acquired from high energy photons supplied by the extreme temperatures after The Big Bang. When two gamma ray photons collided and superposed, the fundamental laws of conservation of angular momentum and energy were never broken. A neutrino carried the extra ћ away. The frequency of the electron was exactly that amount which kept it stable and gave it mass and charge. The electron is a design that stores energy, while creating charge plus magnetism, and its spin is real angular momentum of the rotating photon.

In our larger world, angular momentum, L, manifests through circular motion and is calculated from the product of a spinning object's mass, tangential velocity and radius. Thus L = mvr, in units of ћ. (Following convention, we will in future write s rather than L for the electron's spin angular momentum).

Our soliton is no different as it moves in two twisted circular paths at the speed of light, as energy flows and jumps from loop to loop at the speed of light. First in one loop then the other, not both simultaneously, as the next diagram shows.

In each loop we have a spin value of s = mecr0  = ћ/2

The twist causing this roton to form is created by energy in the form of a magnetic field, but it does not change total angular momentum. Like all photons this remains constant at ћ. However, the path of each loop now has a radius half the photon's radius we would expect for a particle with this mass or energy. That is, a wavelength of ƛe. Moving sequentially from loop to loop, the photon's angular momentum at any one time is therefore half this amount. Thus spin, s = mecr0  = mecƛe/2 = ћ/2. When we measure or calculate its instantaneous spin value the answer is ћ/2. Total angular momentum is shared between two loops. This structure explains spin value and its physical reality in fermions.

Spin, measurement and quantum uncertainty

We know that total spin for elementary particles is always ћ, a tiny but absolute amount. For fermions with their mass due to compressed space and structure in the roton, we measure spin as ћ/2 at any instant, because it exists in either one or the other of the two loops that have half the radius of the original photon. Taken as a system however, the overall spin of the roton is still ћ.

Further, angular momentum is a 2-dimensiopnal property and can be aligned in any direction, either clockwise or anticlockwise. A free electron has no preference. The act of measurement is an external influence and causes the electron to align or anti-align with the measuring device’s magnetic field. It forces one direction, either positive or negative, to be chosen and retained if there is no further external interaction. This is why it has spin in only one axis, either x, y or z, and knowledge of one means zero knowledge of the other two – they don’t exist. Again, spin is 2-dimensional, and according to this model its axis is real and can be visualised even if its direction and sense are unknown before measurement. There is no mystery or paradox due to quantum uncertainty of spin about more than one axis at a time.

SED and the two quantum spin states

Experiments like those of Stern and Gerlach tell us the bound electron has two and only two responses to the presence of a non-uniform external magnetic field. Quantum mechanics calls these two states spin-up and spin-down but insists that we must not try to visualize any actual spin. It insists they are purely a quantum phenomenon. Their energy levels can be accurately determined but their origin cannot.

Again, SED and this model explain spin states in the electron both qualitatively through its structure and quantitatively through its calculation of the two values. How do the two spin states arise? The answer lies in a fundamental premise of the theory. If we imagine the path of the photon being temporally flat like the infinity symbol ∞, field energy flow is always clockwise in one loop and anticlockwise in the other, thus having opposite poles in each loop. There would naturally be a magnetic attraction from loop to loop because opposite poles attract and so the path would curve either up or down forming our roton’s hemispherical shape. Due to symmetry, either possibility has a 50% chance. One is termed spin-up, the other spin-down. Once set, external energy is required to swap or flip from state to state - a little bit like turning an umbrella inside-out. The path is always bent over a hemisphere in one of these two states and never flat.

Figure 20 - The two states of the electron shown here on two horizontal hemispheres

Analysis of this swap-over reveals that while charge is unaffected, the magnetic poles reverse. Further, the path not only turns itself inside-out but the direction of field energy flow in each loop is also reversed. That is, the loop that had clockwise flow is now anticlockwise and vice versa. (This is best understood by examination of an actual strip model of the roton). Spin angular momentum in each loop is given by s = mecr0  and what reverses is the direction of c (not absolutely but relative to its shape). Therefore, for s = +ћ/2 we get s = -ћ/2, and s = -ћ/2 becomes s = +ћ/2. These are the only two values of electron spin in accordance with quantum mechanics. This is why they are quantised.

When the two poles reverse, so does the direction of magnetic moment. The electron exhibits one of the two possible responses to the external magnetic field and must take energy from this field to reverse c and flip states. If no external field exists, its orientation is random and therefore its spin value is unknown until we measure it. Once measured, it remains in that state if no further interaction occurs. This is how the electron can be in a superposition of both spin states simultaneously. They are absolutely identical, having the same probability, without an observation or external magnetic field to distinguish them.

Flipping from state to state requires energy which can only come in the form of an external photon. Now, photons carry energy (value ћω) and angular momentum (value ћ). This causes a change in both energy and angular momentum to the electron and either creates or destroys the photon. Due to conservation of total angular momentum, when the spin state of the electron flips from -ћ/2 to +ћ/2, its angular momentum change is +ћ provided by absorbing the photon. When changing from +ћ/2 to -ћ/2 this change is -ћ, which is given to a new photon. This is how c reverses as mentioned above. Likewise, energy is also conserved but here the photon's energy is very much less than the electrons. Angular momentum always changes by a fixed amount (ћ) but for bound electrons energy change, (ΔE), can vary depending on the time taken for the interaction (i.e. from frequency or time rate of change and E = ћω, where a short time means a high frequency or large energy change). This is also expressed through ΔEΔt ≥ ћ/2. Energy is only quantised when there are boundary conditions, as we shall discuss later when considering the state change in a non-bound or free electron.

Following on from this reasoning, after a free electron absorbs a photon, it must emit another before it can absorb a photon again. Otherwise, its angular momentum would become greater than +ћ/2 and this is forbidden. Similarly, after emitting a photon, it must absorb another before emitting again.

These two states with their slightly different energies, (ΔE), give rise to the splitting or double lines of energy transitions (i.e. fine structure) as observed for bound electrons in spectroscopy, where the gap or energy difference is a fixed proportion of time taken for energy transfer. The transition always begins or ends in a spin-up or spin-down state and their energy difference is based on the time rate of energy change or frequency of the interacting photon multiplied by a fixed proportion, α - the fine-structure constant.

Fine Structure Constant - α

Discovered through early experiments in spectroscopy, the Fine Structure Constant is a unit-less number like π with a value of 0.00729735257 (or approximately 1/137) which some say gives us the probability that an electron and photon will interact. In other words, for about every 137 electrons, one photon will be absorbed or emitted at any one time. Like radioactivity, we can only predict probabilities, and not which electron will do this. Science has asked where does this exact number come from? It can be measured but not yet explained. Its value is related to the charge of the electron and can be accurately calculated in a number of ways.

In addition to its standard definition, empirically we also find α is the ratio of these four things:

1.     The angular momentum inside the electron () to ћ, i.e.  (Note: This angular momentum, Le is not the same as its spin, s which is mecr0).

2.     The classical size of the electron (re) to its reduced Compton wavelength (ƛe) i.e.

3.     The sideways spin velocity of the electron’s path (ve = reωe). to the speed of light c           i.e.

4.     The time light takes to cross the electron's classical radius re, compared to its Compton period T i.e.

It is important to note that these are all examples of α in the electron and are all based on its classical size, re. We will discuss this further in the next sections. However, it does raise two important questions: Why does α equal these ratios and are they physically real? How can the classical size of the electron be so small?

Considering its intrinsic momentum, we find the classical size normally assigned to an electron is much less than that available to it according to the Uncertainty Principle because it is about 137 times smaller than ƛe. We will find later though that re does have a surprising yet important mathematical significance, combining the fundamental behaviour of the soliton that is the electron, to the value and meaning of the fine-structure constant, plus the size and shape of the roton that is this model. To do this, we first need to examine some more properties of the electron.

The Fine Structure Constant - α, and the Electron Energy Equation

The standard definition for α is:              . . .   ③

However, empirically we also find:         . . .   ④                Value = 0.00729735257

Combining ③ and ④ we have:                    , which upon rearranging gives:

Electron Energy:            . .   ⑤            Value = 8.18710564965 x 10-14 J

The first term is the electron's potential energy (via charge: e) and the equation tells us for a free electron, this is equal to its total energy of mec2 or hfe. This is a huge amount for such a small object. Remember that re is the classical radius of the electron and not the radius of its path in the roton, which we write as r0. (Qui-Hong Hu in his article [1], swapped these terms and possibly he is right to do so. However, for the sake of clarity and to avoid confusion with the current literature we will not do this at present).

It shows how much energy is stored inside the electron and the relation between its different types. The important point to note here is that re is simply the value we need in order to make this equation correct. It is too minute to be a physically realizable distance for an object with this momentum. For a given charge, e, which we will derive later, there is only one value of re that satisfies this. It is the size the electron would be if all its energy were electrical potential energy. In addition to being energy derived from its frequency or mass, this potential energy is equal to the work that would be required to bring two identical point charges, e initially separated by infinity, to the tiny distance, re from each other. This length is much less than the radius of each of its loops because the energy stored in the electron is a combination of types and so large. If it were purely electrical, it would be this size, but as stated before, the Uncertainty Principle precludes such a small dimension having any objective reality. The space occupied by re can be thought of as a kind of path thickness in the electron while the energy repeatedly moves over its much larger Compton path length.

Said another way, the energy equation (⑤ above) gives the electron's theoretical maximum electrical potential energy it could achieve at radius re and equal to mec2. It defines the distance re. However, its actual electrical PE is much less or α times this, due to the ratio re/ƛe = α.

Using our model, we can now form a new understanding of the fine structure constant. It was noted that α is the ratio of various properties in the electron. Is this also true for the standard definition? We may rewrite it as follows:

. . .   ⑥

Here the first term on the right is also one of electrical potential energy and the second is the reciprocal of mec2. So, expressed this way, α is the ratio of energies - electrical potential energy at a distance ƛe, as a fraction of its total or intrinsic energy. Both of these terms are real physical properties of the electron, and this is why α can be thought of as a measure of charge - α is that fraction (i.e. ~ 1/137th) of the electron’s total energy (i.e. mec2) due to its electrical energy. Thus, e is called the elementary charge.

Further predictions on the origin and meaning of the Fine Structure Constant

The fine-structure constant or α, is always a ratio of magnitudes of two similar properties in the electron (e.g. size, energy, speed, time etc.). We have also seen that it is the ratio of electrical potential energy compared to the electron’s total or inherent energy (i.e. mec2). But is this the true origin of α, a number that Richard Feynman said is one of the greatest mysteries in physics? [3]

Is there a structural property in this model that may help clarify the meaning and value of α?

The two spin states (i.e. up and down) arise naturally when the path of an electron may or may not invert like an umbrella after an interaction with a photon. For a free electron with its fixed total energy and thus boundary conditions, only two energy values for these two states are allowed. These occur due to its polarization or alignment when responding to an external magnetic field, and by the exchange of a photon of one particular frequency with this field.

It is proposed that for this state change we can write:

ΔE = αE,

where ΔE, the energy of the interacting photon (i.e. ћωphoton), is also the difference in magnetic energy levels of these two states of the free electron when in a field, and E is the electron’s total or intrinsic energy (i.e. mec2). This equation has two critical aspects. The first being that this energy difference has only one specific value, αE. It is an absolute property of the free electron. The second is that α is now defined by the ratio of ΔE to E. In other words, two fundamental energy values create α in the electron. The intrinsic energy, E, is accurately known, but work will need to be done to confirm that the correct experimental value of ΔE agrees with that predicted by this model, which is 5.97441964239 x 10-16 J. The photon providing this energy would have a frequency of 9.016535560303 x 1017 Hz. These values are ~108 times larger than those normally used in Electron Spin Resonance (ESR) research because the free electron is so much smaller (i.e. higher energy) than the path of a bound electron in an atom.

The difference in magnetic potential energy between the aligned and anti-aligned states is also ΔE = 2µBB, where µB is the Bohr magneton and B is the value of the external magnetic field. Of course, a magnetic field can have a range of values but there will be only one minimum for which enough energy will be supplied to allow this interaction or state change to occur in the free electron – a threshold value (Bmin). This minimum B-field is predicted to be Bmin = 3.22105520947 x 107 Tesla

Soon we will derive the value of the internal B-field in the electron, (Bint). Using this value, it can be easily shown that the ratio of Bmin to Bint is α/2, creating a new meaning for the fine-structure constant based on the free electron’s interaction with an external magnetic field.

A suitable experiment confirming the existence of Bmin and thus the two states of a free electron in a magnetic field needs to be conceived because so far, this has not been observed.

The electron, being essentially a trapped photon or standing wave, is intimately connected to α and c. All photons have rapidly rotating electric and magnetic fields and inside our soliton they determine its charge and magnetic moment. So our task now is to determine these values of E and B. To do this, however, we first need to again make use of the little-known constant - The Magnetic Flux Quantum which has the symbol Ø0 . This enables us to evaluate the electron’s internal magnetic field B, and thereby calculate its associated electric field E. We will see that the strength of these fields make α and the electron the special things that they are.

Magnetic Flux Quantum - Ø0

Definition:                         . . .   ⑦                                 Value = 2.067833831 x 10-15 Wb

This is the minimum quantum of magnetic flux, and flux refers to the product of field and area (i.e. BA, where B = magnetic field strength and A = area the field penetrates). This is a very important constant in the universe but largely ignored in the study of particle physics today, where, flipping from loop to loop, it is the tick that beats time in the electron. Using simple physics and our model, we can derive the above definition.

Consider a circulating charge in a magnetic field. From circular motion we know its path is defined by the magnetic force:      , using the equation from circular motion.

so for the electron this is:                                                , as r =  in the roton

Therefore,                                      , after rearranging

and                   , after multiplying both sides by  then using r0 = ƛe/2 and ћ

So we can write,                                     , after multiplying both sides by

Thus,                            , as h = 2πћ  and  Aloop =

becomes,                              , as total area, A = 2Aloop because there are 2 loops

Finally giving,                      , as the definition because  

Conductance Quantum G0

There is another constant related to Ø0 ,called Conductance Quantum or G0. It is measured in Siemens and is the inverse of resistance, so, we have G = I/V, where, in our larger world, I is current (Amps) and V is voltage (Volts).

Definition:                        . . .   ⑧                                Value = 7.748091731 x 10-5 S

This is the minimum quantum of conductance, and interestingly, these two constants are connected through the relationship: G0 Ø0 = e, the charge of the electron. We will discuss this further in the section on Maxwell's equations.

Analysis of E and B fields in the electron and Zitterbewegung

Examination of the orthogonal E and B fields’ behaviour while traversing the roton shows that the resultant B-field manifests as two stationary but opposite poles in the centre of each loop. According to our model these vary rapidly and sinusoidally in time, whereas the location of the point of charge due to its E-field varies in space and moves at the speed of light over the two adjacent circular rings or loops inside the electron.

This rapid oscillatory motion of the position of charge is known as Zitterbewegung (German: for trembling motion) and was first proposed by Schrodinger when looking at free electrons and their behaviour according to the Dirac Equation.

This model provides a structural reason why he found the frequency of oscillation to be 2mc2/ћ and a wavelength of ƛe. Geometry shows Zitterbewegung arises in our roton due to the sinusoidal projection of the E-field from its path around the soliton.

An actual model, such as the plastic strip twisted into the roton, clarifies this. If the two loops are arranged side by side, with the crossover point at the top, then the E-field projects horizontally into two parallel circles directly below this crossover, where both fields are momentarily zero. In the electron the E-field always points inward to form these circles (outward for the positron). The point of charge, or projection of a loop’s E-field, moves around each circle in turn, with the centre of mass of the system at the centre of these circles. In contrast, the B-field, being orthogonal to E, projects as two fixed poles, pulsating sinusoidally, one at a time, at the centre of each loop, giving an overall magnetic moment to the electron. Each field creates the other in accordance with Maxwell’s laws, as this field energy flows around the roton at speed c creating one magnetic flux quantum per cycle.

We can now calculate the values of these fields. Since magnetic flux is a quantum constant, i.e. Ø0 = BA, we can use our model to first calculate the total area or A within the electron, then in turn the value, summed over each complete cycle, of its B and E fields (written here as |Ee| and |Be|). Now, this area, A = 2Aloop (as there are always 2 loops in one cycle) = , where r0 = ƛe/2 and ƛe = 3.86159267633 x 10-13 m, (its reduced Compton wavelength). Again, refer to figure 10 above for clarification.

Using this radius of each loop:     . . .   ⑨

We get:                  |B| = Ø0/A =

And so we have    . . .   ⑩

From which    . . .   ⑪   using, E = Bc

Note: Both these fields are of fixed integrand magnitude for a number of reasons, one of which is obviously because the Magnetic Flux Quantum is also a fixed constant and so is area, A. Also, because of the uncertainty principle, it is meaningless to consider times and positions less than one half cycle. Only integrands have a real value here, producing constant fields. They appear sinusoidal only from our external perspective.

Using the equation for the Bohr Magneton, we are now able to see why these numbers make the electron so special. From it we have:     

which can be written as:      so we get,      . . .   ⑫  

And because c = E/B, the ratio of the two fields, we can go further:       . . .   ⑬  

This equation states that the ratio of the magnetic torque compared to the electric force inside the electron is equal to the radius of each loop. This torque can only occur at one frequency, the frequency of the electron. If we rewrite Equation ⑬ as: µBBe = Eeer0  it means that the electron's magnetic torque and the torque due to its electric field are only equal if this radius is r0. This is also a type of energy equation, and the same radius comes about from its energy and frequency. They are balanced and stable. Only an electron having this size, shape and field values can sustain such vibrations and maintain these properties.

Value of electric charge e for the electron

Now that we know the value of the electric field |Ee| inside the electron, we can use it to calculate its electric charge, e. Since the internal electric, magnetic and mechanical forces must all balance, we can use our model and some basic formulae for force and circular motion to do this.

Following a previous procedure where we had: F = Eq = mv2/r = Bqv, giving the relationship between electric and magnetic forces in order to maintain circular motion, we can use our derived values to write that the force necessary to keep the energy stable and flowing in each circular loop is:

Rotational Force:      . . .   ⑭

This also equals the force due to the electric field or,  Frot = Fe = Eee.

Using ⑪ above for |Ee| we get:     . . .   ⑮

The electron’s charge is quantized with this value because of the dynamic nature of this structure. Thus our model is self-consistent.

The Origin of the Fine Structure Constant using Coulomb's Law

The value ⑪ derived for the constant E-field inside the electron is remarkable. It turns out that we can write exactly equivalent expressions of it in terms of Coulomb’s law and its corresponding electric force.

The equations are:        and    . . .   ⑯

The first equation yields the identical number as that obtained independently using Ø0.  Moving just outside the electron, we know from classical physics that the magnitude of the E-field decreases with the square of distance. Significantly, Coulomb's law, at the specific radius r0√2, gives a field value that is exactly α or ~137 times smaller than that inside (see Figure 12 below where Er0√2 = αEint). This is due to the soliton projecting and compacting the field within by virtue of its shape. As mentioned earlier in the section on mass and the electron, it is this compression of field energy and space that is the origin of mass. Now we find it is the origin of α.

The radius, r0√2, forms a kind of event horizon, being the size of the sphere on which the roton rests (see Figure 10, above). It defines the location of the vacuum state where the electron’s energy is minimised and forms a mathematical transition surface, separating internal and external fields. So we find that α is the ratio of fields inside and outside the electron and this is why it is a measure of charge.

This structure holds more energy below r0√2 than above by compacting or having a tight curl or twist and that is why it is a soliton. Its internal energy though is fixed - a constant as defined by the electron energy equation ⑤ above, and one that is independent of radius, r once we are inside the electron (i.e. for r < r0√2).

Figure 21 - Electric Force for the electron. (Vertical axis not drawn to scale)

The reason why this field must be constant below r0√2 is that if it were to follow Coulomb's law we would find Eint approaching infinity as r approached zero. Somewhere inside there would have to be an infinite field - a singularity. But this is impossible. As we said before, the electron cannot be a structureless, infinitely small point.

SED and String Theory

String theory proposes that elementary particles are not points but can be either one, two or more (up to 11) dimensional vibrating objects called strings and branes (from membranes). These strings may be open or closed in that they form a single open-ended thread or a closed loop. It is their vibratory states that contain energy and hence mass and other properties.

The model of the roton in SED can be thought of as a type of string that is based on similar, but more structural, ideas. The trapped photon of this soliton moves in a closed path forming two loops. The path length of this closed string is fixed at 2πƛe (or λe), so, due to boundary conditions, its vibratory states must be quantised in integral multiples of this length.

Each loop in the roton is one half of the cycle of ћ and is called a brane in string theory. We saw that over one complete cycle, their total area, A, multiplied by the fixed magnetic field, B, inside the electron, gives rise to another quantised property, known as the Magnetic Flux Quantum, Ø0. This ceaseless magnetic field oscillation also has an associated electric field which, from outside the electron, never changes direction or sense, and thus maintains the charge, e, of the electron. This process is similar to that of the straight-line photon that Maxwell so elegantly describes. However, Maxwell’s photons do not create charge due to the sense of the two E and B-fields constantly reversing.

Concluding remarks

Our task here has been to consider the question - What is an electron?

Like most things, ideas do not occur in isolation. Little of this would have been possible without the articles and books by others, a few of whom may have been thinking along similar lines. These ideas plus a strong belief in the simplification and unification of nature have been used to construct this theory.

Two further candidates for similar study are obviously the proton and the neutron where consideration of its half-life when isolated, together with its mass and charge, suggest the neutron is some combination of a proton and electron. The mass difference is about two and a half electrons. Although the standard model does not consider these nucleons fundamental, they are both stable when locked together in the nucleus. If they could be understood and unified by using a similar structural approach, this may help illuminate subatomic or particle physics. Possibly all matter could be viewed in this light.

As stated earlier, we have only been concerned with a free electron in isolation from all other systems. However, most electrons are found in atoms, and it is in this environment where the vast majority of interactions with light and photons occur. The allowed, but much smaller energy changes, due to variations in orbital motion make this possible. Quantum mechanics has theories concerning this. Perhaps, following some ideas presented here, we may discover new insights into these interactions and their probabilities.

Scientists explain chemical behaviour and molecules by reference to their structure. We also use structure to understand electron orbitals, valency and energy levels within the atom. Is it then so different to try to comprehend subatomic physics by means of structure?

It is interesting to compare the model proposed here with that of the S-orbitals in the lightest atoms. In the electron, the energy path is a lemniscate bent over a hemisphere forming the roton. In hydrogen, this spins with a rotational precession speed of αc or just over 1/137th the speed of light, thus giving it the shape of a hollow hemispherical surface with a larger size equal to the Bohr radius (also its de Broglie wavelength where speed is αc). In helium, the second electron with its different spin state forms the opposite hemisphere making a complete sphere. This structure causes helium to be very stable and unreactive. So both the free electron and single S orbitals are hemispherical shells of similar structure, but with a size difference of α. Nature often likes to reuse her designs.

We will pursue these ideas in the next section on the atom.

[1] It is important to distinguish the radius of the path’s thickness, re from the radius of either of the roton’s loops ro as shown in Figure11 above.

[2] SED does not subscribe to the Higgs theory as proposed by the standard model.

sdfsdf sdfsd