Regardless of which theory of the atom we examine, the concept of the electron as a particle seems to prevail. Yet the exact size of the electron seems to evade scientific investigation. In this article, we explore a new possibility, which suggests the electron cloud does not exhibit a particle nature, and is instead constituted by an energy field that exhibits the property of 4th dimensional geometry.
Overview
KEy Points

a wave solution to the ultraviolet catastrophe and photoelectric effect enable the electron cloud to be consider from purly a wavelike perspective

The 1/2 spin of the electron is expalined in terms of 4d geometry

The wave modle of the electron explains probabilty, and superposition is simple terms without any quantum wierdness
What is an electron?
Electrons are often considered as elementary particles, which means they cannot be divided into any smaller constituent parts, unlike the proton that is formed of quarks. The idea that electrons are a tiny particle that circle the nucleus is the predominating view held by most people. Even today, this model is used to explain the functioning of the atom.
Yet, this model was disproven as far back as the 1920s, when the wave nature of the electron was first discovered. When shone through a double slit, they produce an interference pattern, indicative of a wavelike phenomenon. The same experiment was conducted by Thomas Young in 1801, which initially proved that light was a wave. It was only when Albert Einstein suggested the idea of a photon, 100 years later, that the particle model of light resurface. This led to the assumption the light exhibits a waveparticle nature. Therefore, when the wavelike nature of the electron was established, is also adopted the wave particle duality concept.
However, more often than not, this nature is ignored. The main reason for the popularity of the particle model of the electron is due to the simplicity of the explanation. The wave equations proposed by Erwin Schrödinger are so complex that even highpowered computers are unable to solve them. As each electron has the same amount of charge, the particle model, although incorrect, does allow for a certain level of prediction, which is enough to calculate simple molecular bonds. However, the problem still remains, that the electron can be considered as both a cloud, based on vague notions of probability, or an over simplified particle model.
The reintroduction of the particle nature of light is derived from the results of just two experiments, the Ultraviolet Catastrophe, and the Photoelectric effect. Through our reexamination of these key experiments, we have identified a wave only solution, which no longer requires the concept of a particle. This discovery fundamental changes the entire concept of quantum physics, erasing the idea of wave particle duality. The result is a return to a logical science, that does not require probability theory in order to establish itself. This new interpretation finds a distinct mathematical and geometric relationship between the various frequencies of light, and the energy of the vacuum. This in turn unifies the quantum physics concept of a Quantum Foam, with the astrophysical discovery of the Cosmic Microwave Background (CMB) that permeates the whole universe. The result is a new theoretical framework that reunites the laws of classical electromagnetism with the nature of 4D geometry.
Find out more about the 4D Aether
If you are unfamiliar with the concept of the 4D Aether, then these posts explain the concept in great detail.
These new discoveries have deep implications for our perception of the atom. Instead of existing in isolation, each atom is intimately connected to the vacuum of space into which it is emersed. This means that the electron cloud can for the first time be considered from the perspective of a wave only phenomena.
Electron Waves
The wave model of the electron cloud is described by the Schrödinger Equation. These complicated mathematical expression are an expression of a harmonic oscillator. In its most simple explanation, this can be seen as a particle that moves back and forth, creating a wave. Without going to deep into the mathematics of the equations themselves, the result is a series of standing wave models, which produce sets of geometric waveforms.
Harmonic Oscillators can be depicted as a particle moving back and forth on a spring. The example A and B represent a normal oscillator found in classical mechanics. Notice that whenever B reaches its maximum or minimum, then A will be found in the midpoint. C shows the most simple quantum oscillator composed of 2 waves. Similar to the first example, the waves are offset, so that whenever one reaches its maximum peak, the other will be at zero. The same be said of C, D, E and F. These form standing wave oscillations called stationary states, which are found in the electron cloud. The last 2 examples, G and H, are called superposition states, and are created when two atoms react, or when an atom is charged by a certain frequency of light. These arise from the addition of more than one wave. The red wave is generated on the complex number plain, whereas the blue is derived from the real numbers. Whilst the mathematics that generates these waveforms are quite complicated, the visual solution is much easier to grasp.
When we consider these waveforms, we cannot help by notice a similarity to the traditional notion of electromagnetic waves, which are also formed of two types of waveform offset at 90° to each other. This is defined as the E and B field, which are in in phase with each other. This means that both waves start at the same point, zero, and rise and fall in unity with each other. The electron waves are offset by a quarter of a waveform, which means there is always an equal distance between the two points. Note that it is possible to create circular polarisation of light, which offsets the wave E and B field in the same way as presented in the Schrödinger Equations.
The simplicity of this observation is never considered. Often we find that the expression of the Schrödinger waves are superimposed over each other, which obscures this curious fact. Whereas previous models of the atom suggested the electron particle orbited the nucleus, the Schrödinger wave model expresses the electron as a standing wave. These were subsequently shown to be correct, by charging a hydrogen atom, from which an image is then recorded. The one addition required was the notion of electron spin, which explained why electrons always come in pairs.
The Electron Charge
Electrons are supposed to exhibit a negative charge, whereas the proton in the nucleus exhibits a positive charge. The traditional view suggest that this is the mechanism by which both particles attract each other. You might think that this would cause the electron to plummet towards the nucleus. However, as both particles exhibit exactly the same amount of charge, then electron can only fall into is the lowest shell, call its ground state. This is the point where the positive proton and negative electron charges come into balance to produce an overall charge value of zero.
The charge value of the proton and electron is determined by the elementary charge constant (e). In Dimensionless Science, this has a value of ½π. When we consider the offset nature of the electron compared to the EM wave, we can begin to see a direct relationship to the unit of elementary charge.
In the image above, the A and B portions of the electromagnetic wave travel a distance of 1 before recombining at zero. The A and B portions of the Electron wave are offset by ½ so the wave never combine. However, the distance between the zero point of the A and B wave is instead equal to ½. This notion begins to alter the reasons for the lowest energy level of the electron, and begins to reveal the root nature of charge. Presently, there exists no explanation as to why the universe should exhibit charge. The wave solution suggests that the reason for charge is due to an offset of the waveforms of electromagnetic waves, and the wave function of the electron. This also explains why electrons are always found in pairs. When we multiply the unit of elementary charge by two, then the result is π. The combination of the two wave now falls into the same phase as the electromagnetic wave.
In the above image, we can see that the combination of the electron pairs produces a wave pattern, whereby the A and B waves of the now come into phase with each other. However, unlike the EM wave, this new electron wave produce two sets which are still offset by ½.
electron spin
The concept of electron pairs is expressed by the notion of quantum spin. Each electron exhibits an up or a down spin orientation. This concept is rather confusing when viewed from the particle model. However, from the perspective of a wave, this simply means that the wave form inverts. We have just seen how this can bring the two waves into phase, which brings the electron cloud into alignment with the EM wave. However, we also notice that the combined electron wave produces two overlapping circles, as opposed to the EM wave that comprised of a single circular wave.
According to quantum field theory, the electron must perform 2 rotations in order to complete a single rotation in 3D space. At first, this seems like an illogical possibility. Yet, once we adopt as 4th dimension view of the electron cloud, the notion begins to make perfect sense.
A torus is a 4D sphere, which in 3D appears as two spheres superimposed over each other. When it rotates 360° through is timespace axis, the first sphere swaps places with the second. Upon the next 360° rotation, the spheres swap places again to complete a full rotation. In total, the 4D sphere has rotated 720° to arrive back at it original starting point.
If you are relatively new to the nature of the 4th dimension, this might seem slightly confusing. The concept of 4D space are still relatively new. However, the concept becomes much clearer with the example of a hypercube. Unlike the sphere, the rotation of a cube produces a shadow projection that changes as it moves. This makes it far easier to congisied the concept of 4D rotation.
Like the 4D sphere, the Hypercube comprises two cubes superimposed in 3D space. This projection reduces the size of one of the cubes, to that it can be perceived as a shadow projection. As the form rotates, the two cubes swap places. In terms of the electron, one rotation in 3D swaps the cubes over, which on the second rotation returns the original cube to its starting point. This is the correct view of quantum spin.
The torus field acts in exactly the same way, to produce the ½ spin of the electron cloud. when we compare this to the nature of light, we can see that the torus acts as a ‘container’ for the electron energy, whereas the light wave is an expanding sphere. This is the fundamental difference between electromagnetic energy, and the energy of the electron. This fact is also verified by the nature of the transmission of a signal. When an antenna is charged, it forms a near field that is shaped like a torus. Once the electromagnetic signal passes beyond the near filed, does it start to expand to infinity. This is called the far filed. In fact, all matter exhibits a near field as its surface boundary. These are called evanescent waves, which are generated by the electron cloud. For this reason, we do not actually touch anything. We only experience the effect of the repulsion of the electron field.
Quantum foam
Uncertainty Principle
One of the key features of quantum mechanics is the concept that a particle can be in multiple places at the same time, yet when it is observed, i.e. measured, it will collapse into a single state. The key to unravelling the quantum mystery is quite simple, from the perspective of the wave model of the electron. When an electron beam shines through a double slit, is forms an interference pattern. The two interfering waves creates overlapping nodes which increase the amplitude of the wave. Inversely, where a peak of one wave meet the trough of another, the two waves cancel out. This is call constructive and destructive interference, indicative of all wavelike phenomena. When waves collide, the new resultant wave is formed from the combination of all other waves. Some peaks will amplify, whilst others will cancel out.
The difficulty arises once we try to describe this nature from the perspective of a particle. This requires a measurement at a particular location of the wave. If a point is chosen where the wave peaks, the suggestion is that the electron has been found. Conversely, wherever the wave is flat, caused by destructive interference, the electron cannot be found. The problem with the particle model of the electron is the assumption that once the electron has been located, it ceases to exist in any other location. This is simply not true. The electron wave continues to ‘exist’ in all the places where the wave peaks. It does not magically collapse into a single location, as quantum mechanics suggests.
In Quantum Mechanics, this is termed the Uncertainty Principle, which suggests that it is impossible to ascertain both the momentum and position of an electron at the same time. It was first suggested by Werner Heisenberg in 1927 shortly after the wavelike nature of the electron, suggested by Louise DeBogie in 1924, was verified by the Davisson–Germer experiment. In order to salvage the failing Bohr Model of the particle electron, the concept of uncertainty and probability needed to be introduced. This theory is called the Copenhagen interpretation of the atom, which is the prevailing model of particle physics. At around the same time, the Schrödinger equations were also formulated, which offer a far more accurate prediction of the behaviour of the electron cloud based on the constructive and destructive interference of waves. The idea of probability was venomously opposed by many scientists of the time, including Albert Einstein.
The Cat in the Box thought experiment was originally proposed by Erwin Shrodigner to exemplify how ridiculous the notion of probability is in the realm of science. Ironically, this was subsequently used to promote the ‘weirdness’ of quantum physics. The Observer Effect was an extension of the Heisenberg Uncertainty principle, which suggested that the whole of reality only exists once it is observed. This concept was further compounded into the popular science framework, through the alternative spiritualist movement. Selfhelp books and course, have sought to convince people that ‘we create reality‘, often generating large incomes in the process. This helped to establish the Copenhagen Interpretation within popular science culture, whereby a quantum wave now becomes a strange unquantifiable phenomenon, governed by probability theory.
You may have seen video animations that seem to demonstrate the strange behaviour of the waveparticle duality of electrons and EM wave. These often depict the notion idea that the wave pattern is produced on a photographic plate, until someone places a detector at the slit to determine which one the particle passed through. At which point the pattern on the plate magically changes to produce two straight lines, indicative of a particle. Unfortunately, this has never been observed, and was only a thought experiment performed by John Wheeler. The detection of a single particle is actually produced by dimming or filtering the light or electron source, until only a single point is detected by the plate. In other words, only by tuning the threshold of detection are socalled individual particles detected. If the plate is constructed of multiple sensors that trigger the detection of the particle, then it is possible to create the effect of the particle appearing at different points on the screen. However, over time the interference pattern will again emerge. This video show the actual experiment. Notice that the light source is filtered to such a degree that only a single point appears visible. When this happens, the interference pattern does not ‘disappear’. It only becomes harder to detect. The only thing that prevents the obvious conclusion that this is purely a wave phenomenon, is the conviction that the particle must exist.
The probabilistic nature of the electron, and all the bizarre theories that emanate out of it, such as the Observer Effect, Many Worlds Theory, and Bells inequality, can be simply resolved once the electron is viewed as a wave. The reason the wave only view of the electron has never been considered might be due to the fact that the waveparticle duality of light is generally already excepted. However, the wave solutions to the Ultraviolet Catastrophe, and Photoelectric effect, from which this belief emerged, lift this limiting view. This establishes the wave only view of light and matter, and returns the world of scientific enquiry to logical coherence, rather than thought experiments that have no foundation in physical reality.
Probability Waves
When the wavelike nature of the electron became apparent, the new theory of probability was introduced to explain the electron. By taking multiple point measurements, a probability curvature is generated, which represents the likelihood of finding the electron at that particular point.
The space inside the curvature is termed the electron density. Where the curvature touches the bottom of the graph, no electron will be found. The most likely place where an electron can be found is at the peak of the curve. The problem of the location of the electron is quite simply resolved with the wave model, which distributes the electron cloud over an area surrounding the nucleus. We no long need to even use the probabilistic nature as an excuse as to why the electron can appear distributed over an area surrounding the atomic nucleus. Once we disposed of the assumption that the electron is a particle, all quantum ambiguity evaporates.
One of the most disturbing facts about modern quantum theory, is that it claims to predict the behaviour of the atom to an incredibly high degree. At the same time, it fails to come even close to the experimentally observed radius of even the most simple atom, hydrogen. According to the Bohr radius, the radius of the hydrogen atom is around 53 picometres. Yet when experimentally measured the result suggest a radius of only 25 picometres. The Quantum mechanical model is out by over 100%. How does it overcome this problem? It appears, by repeatedly informing people, that the radius of the hydrogen atom is 53pm. The situation get worse for the second element Helium, which has been experimentally determined to exhibit a radius of 120pm, whereas the Bohr model suggest it should only be 31pm. That is a disparity of 400%!
To overcome these shortcomings, a second set of measurements were derived, termed the Van Dar Waal Radius, which considers the atom as an ‘hard shell’, where the electron is considered from its furthest possible point from the nucleus. This offers a radius of 140pm for Helium, only 20pm out. As the radius of each atom varies widely as we progress through the periodic table, we find that it is necessary to swap between the two types of system in order to preserve the mathematical integrity of chemical calculations.
The mathematics of electron density therefore employs various different systems in order to try to produce accurate predictions. This serious problem persists even today, and has been noted by Chemists, who often struggle to find a quantum mathematical model that actually fits the description of the behaviour of observed phenomena. Since the 1920s, numerous mathematical theories have been developed to try to create a system that will work for all predictions. Yet, as time has progressed each of these models has been shown to produce even greater inaccuracies in many cases.
The maximal deviation of the density produced by every DFT method from the exact one (lower is better!). The line shows the average deviation per year, with the light gray area denoting its 95 percent confidence interval. Credit: Ivan S. Bushmarinov
As science advances its exploration of the atom, the need for accurate predictions becomes more important. Yet, with a lack of a predictive mathematical system, advances are severely hindered. So is there an alternative that might be able to resolve this problem? Thus far, the notion of probability has dominated quantum thinking. Yet once we begin to adopt the view of the electron cloud from the perspective of geometry, something quite remarkable happens. We suddenly find we are able to produce a single model that is able to predict the atomic radii of all the stable atoms, within a 3 picometre margin of error. The theory of Geoquantum Mechanics is the first model of the atom that considers both the nucleus and electron cloud from the perspective of 4D geometry. It is able to accurately explain the reason for lanthanide contraction, and the instability of elements 43 and 61 on the periodic table. Whilst still in its infancy, could it be that the key to producing a stable mathematical theory lies in the nature of geometric ratio? Only once the scientific community begin to test the theory will we know for sure.
The red and yellow lines show the Bohr and Van dar Waal radius predictions, whereas the blue line are the experimentally measured values. The green line is the Geoquantum mechanical model, which follows the experimentally observed values so closely, it is hard to tell them apart.
Superposition
The quantum mechanic concept of superposition spans a variety of different phenomena. For this reason, it is one of the most misunderstood concepts of modern science. In essence, it suggests that a particle can exist in multiple places at the same time. As with the Uncertainty principle, much of this notion can be easily described once we adopt a wave view of the electron cloud, or EM wave. The wave spreads out over an area. We can take a reading from different points in space to find the supposed particle. It is a simple as that. However, developments of the waveparticle theory have evolved to create more elaborate definitions.
One such example is derived from the Stern–Gerlach experiment, first conducted in 1922. In the original experiment, silver was evaporated at high temperatures, and the atoms passed through a magnetic field which deflects its trajectory. If the electron were a small particle circulating the atom, we would expect the distribution to vary dependent on the position of the electron as the atom passed through the magnet. Instead, the atom is deflected up or down, forming two distinct lines on the photographic plate. This experiment was one of the first that clearly demonstrated the concept of ‘electron spin’. It is not that the electron particle is spinning, it is that the electron field has a north and south, or up and down, polar opposite, just like a torus field. The atom becomes deflected up or down dependent on its orientation.
When the concept of electron spin is viewed from the perspective of a 4D torus, the up and down state become simplified as an expression of a flipping of the north and south poles, as the 4D object rotates through time. Just like the in the example of the hypercube, that exhibits only two possible states, where each cube falls into alignment with the second. The north and south poles swap places, alternating between two states. As the torus passes through the magnetic field, each atom becomes orientated, either pole up or pole down. This causes the deflection of the wave in two discrete directions. This simple solution explains the nature of the Stern–Gerlach experiment, and the reason for the quantisation of the electron spin.
Variations of the Stern–Gerlach experiment involve placing more than one magnetic field in series. One of the pathways is blocked, and the other is allowed to pass through. When both fields are orientated in the same direction, the beam continues to be defected in the same orientation. If the second magnetic filed is rotated at 90°, then the bean again gets divided into two parts. This is the expected outcome of a 4D wave with a ½ spin property. If only the electrons with an up spin are sent through a second magnetic field of the same orientation, the outcome is not affected by the second magnetic in the same orientation. If the second magnetic field is offset at 90°, then some will be deflected left, and some right. Once again, we find that the electron field can only exhibit two possible states. This tells us that even the electrons with an up spin can also be equally divided into a +x and x direction, indicating that the property of spin in not confined to a single electron type. Moreover, each still contains and up and down spin quality. Again, this is easily explained from the perspective of a 4D torus field.
This simple notion of quantum superposition has been misrepresented by certain quantum physics teachers, such as Allan Adams. In his MIT lecture on quantum superposition, he implies that the x and z orientations of the magnets are two distinct qualities of the electron, termed colour and hardness. It is unfortunate that this inaccurate translation of the SternGerlach experiments have been used by numerous video presentations as an ‘easy to understand’ perspective of quantum spin. The consequence is that the notion of superposition begins to lose this simple wavelike expression, as he addresses the issue from a particle only perspective. The result is an irrational and illogical approach to quantum theory.
Ideas such the particle acting in multiple states at the same time whilst being unobserved, are inaccurate and misleading descriptions of experimental results. The reasons why the particle’s location cannot be ascertained is due to the fact that the act of measurement destroys the atom in question. Therefore, it appears from the particle view as if the electron ceases to exist in other states once observed. Once we identify the wave nature of the electron, or other socalled particles, the superposition concept returns to the logical notions of waves that are in certain phase orientations.
quantisation of the Electron Cloud
Another form of quantum superposition is derived from the nature of the electron cloud that surrounds the atom. When a light wave of a certain frequency is projected at an atom, the electron cloud becomes excited. This increases the size of the electron cloud, which is traditionally seen as the electron ‘jumping’ to a higher energy shell. In fact, when excited, the atom starts to fluctuate between states. Often it is suggested that the electron occupies two states at once, until it is observed. If you think about this logically, there is no way that anyone can prove the unobserved state of the atom. The act of observation therefore does not ‘collapse’ the wave into a single particle. Moreover, the atom flips from being excited to being nonexcited in an alternating series. When we take a measurement, we are only examining the atom in that particular state at that particular time. Just as the idea of quantum superposition in terms of electron beams is very simply resolves with the wave model, so the same can be said of the electron cloud itself. This idea lies at the heart of the theory of quantum computing.
However, there is a slight difference. The electron cloud does not gradually expand. It suddenly jumps, and no kind of measurement will ever detect it in an in between state. This is why the concept of quantised reality is so widely accepted. However, we can just as easily suggest that the electron can only exist where the shells fall into a specific resonance. This explains why only light at a specific frequency can excite the electron cloud. From the perspective of a 4D electron cloud, this quantisation can be quite easily solved. A 4D object does not exist completely within our 3D realm. When it moves through a rotation on it time (W) axis, so the form moves between the two states. The absorption of the EM wave triggers the rotation, which expands in 4D space to magically appear in the higher shell in 3D space.
In the particle view, we see a single electron absorbs a photon, which makes the electron jump to a higher shell. When the electron falls back into a lower shell, so a single photon is emitted. In the 4d view a similar process occurs, however, the light is emitted in all directions. This maintains the spherical nature of the light wave. Additionally, it can explain the quantised nature of the electron cloud. What appears as a single sphere in 3D comprises two spheres in 4D. These are in constant rotation. When the energy field is struck by a light wave of a specific frequency, it causes the expansion of the 4D sphere as it rotates through its Waxis. Therefore, the electron appears to jump, without appearing in between. More details about the geometric structure of the electron cloud can be found in our new theory of Atomic Geometry, which accurately maps the different orbital shapes.
THE
Conclusion
What is the 4D Electron Cloud?
The 4D electron cloud model suggests that the electron exists as a wave, which is quantised by the 4D mature of space. This explains the reason when there are only two possible state, spin up or spin down. The rotation of the 4D sphere swaps the up and down magnetic pole, which when aligned within a magnetic files produces two lines on the imaging plate. This theory disregards the notion of probability, as we no long need to determine the exact position of the electron particle. Instead, the wave is distributed over an area, which explains why the electron radius has never been established. The nature of 4D also explains why the electron is quantised into discrete bands, and why only certain frequencies of light are able to move the electron into a higher energy level.
What does this mean for Qauntum theory?
The traditional view of particle interaction seems to dominate the literature of quantum science. However, problems have arisen when theoretical models have failed to predict more complex systems, such as those found in quantum chemistry. The 4D view is able to reproduce the experimental measure radii for all stable elements, whereas the other models such and the Van Dar Wall and Bohr radius which show an inaccuracy of up to 400%.
Carry On Learning
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YOUR QUESTIONS ANSWERED
Got a Question? Then leave a comment below.
Question?
Surely if the electron was a wave, someone would have suggested this before?
ANSWER?
You might have thought so, however, as the particle nature of light was already established, the assumption has always been that the electron is a particle. When the search for the Aether was abandoned, the particle nature was required to explain how light and electrons could travel through the vacuum of space. Ironically, the idea of the quantum filed had to be reintroduced, but the particle model still prevailed as the idea of probability became adopted.
Question?
I thought the electron has a mass, so it must be a particle, right?
ANSWER?
In the standard model, there are also massless particles, such as the photon. However, the mass of an electron was first calculated by J.J Thompson by firing an electron beam through an electromagnetic field and calculating from the amount that the bean was deflected. The second measurement comes from oil drop experiments performed by Millikan. However, the mass also changes dependent on velocity. Thus, the electron mass is calculated, when not at rest. No one has weighed an electron on a set of scales.