Williamson Van Der Mark Electron Model Are Electrons Made Of Light

TITLE: Williamson & Van der Mark electron model | Are electrons made of light? CHANNEL: Huygens Optics DATE: 2025-11-15 ---TRANSCRIPT--- Hey everyone, this video is a bit different from the previous ones because today I want to discuss the structure of the electron. Since JJ Thompson demonstrated the electron’s existence in 1897, scientists have measured many of its properties like its charge, mass, dimensions, magnetic dipole moment, and spin. But despite all these properties, the electron is often still considered a pointlike entity. mainly because so far it has been impossible to measure its exact size or reveal its internal structure. In this video, we’ll look at the electron from a somewhat unconventional angle. I will discuss a model for the electron that was proposed by John Graeham Williamson and Martin Fondomar in 1997. In that year, they wrote a paper with the title, is the electron a photon with tooidal topology. As you can see, the title is formulated as a question rather than a firm statement, which I think represents the inquisitive nature of the paper. When it was published, it received the usual polite silence, which I think is quite common for papers that challenge the mainstream scientific perspective, but I think it’s still worthwhile to discuss it here because to me personally, it offered some interesting views on the properties of the electron. Let’s listen to what John Williamson said when asked about the origin of the theory that he developed with Fonder Mark

worked in Hi physics [music] CERN in Switzerland to see if we could analyze and learn about how stuff worked. Take electron apostron put them together and they anhilate to give pure energy in the form of light and what the inspiration was was maybe maybe these [music] particles are made of light. Okay, so this will be the main question that I’m going to discuss. What if particles are actually made of light? It’s an interesting thought, although using the word light when referring to gamma radiation will probably be stretching the imagination of many. But of course, gamma radiation is also electromagnetic field energy only with a much higher frequency than visible light. In the clip, Williamson referred to the anhilation process of an electron and posetron that results in gamma radiation with identical total energy content. Conversely, electron positron pairs can be created from very high energy gamma radiation. So, it’s not that weird to think that what’s on either side of these processes are basically two states of the same thing and that electrons and posetrons may be self-confined electromagnetic energy. Now, a moment ago I mentioned that the electron is generally considered a pointlike entity and this is based on experimental evidence. for example, high energy collision experiments. But if you assume that an electron is a point without any internal structure, you need to impose all those properties onto that point without any physical basis of how they arise. And the point-like view also creates some very fundamental questions. For example, how can we calculate the energy contained in a column field resulting from a point charge? As it turns out, we can calculate the energy of a field outside from a radius with respect to where charge resides in space. But for a point entity, this radius is by definition zero. Which means that the field of any pointlike charge would have to contain an infinite amount of energy. But we know that this is not the case. The total energy contained in an electron at rest is equal to its rest mass times the speed of light squared which we can calculate to be approximately half a mega electron volt. So without using some kind of renormalization of this infinity there must be a limit to the minimum dimensions of where charge as a property must live in space. Now by combining these two formulas we can arrive at the so-called classical electron radius which must be equal or larger than 2.8 * 10us 15 m. That’s a very small value but several orders of magnitude larger than the interaction radius derived from high energy collision experiments. But there are other properties of the electron that are rather incompatible with a pointlike entity. For example, magnetic dipole moment and spin. It’s impossible to imagine how properties with a spatial asymmetry can be physically present in a pointlike entity. And this is where the theory of Williamson and Fenomark is different. It deres the properties of the electron such as charge, magnetic moment and spin basically by assuming that internally the electron is just electromagnetic field energy. Unfortunately, the authors of this paper have both died in recent years, but I’ll try to do my best to explain what they came up with. And if the ideas presented in this video appeal to you, there is actually a website dedicated to this paper and the later work done by John Williamson. A link can be found in the description of this video. Now, the paper isn’t easy reading. So before we dive into it, there are two concepts that are key to understanding the paper which are Compton wavelength and circular polarization in electromagnetic fields. It might be that you are already familiar with these. So in that case you can skip ahead to either of these moments in the video. Let’s start with Compton wavelength. The Compton wavelength is named in honor of Arthur Compton who did a set of experiments involving X-ray scattering. And these experiments were vital for demonstrating the quantized nature of light especially in the high frequency domain. I’m not going to explain the experiments here. Instead, I’ll point you to a very good video on the subject. Here I’ll explain the meaning of content wavelength and give some context related to electromagnetic fields. Electromagnetic fields can be described classically by the Maxwell equations. Basically such a field consists of an electric and magnetic field component that are directly related and are orthogonal to each other. A field carries momentum and energy and has amplitude and wavelength or frequency. And of course this wavelength and frequency are related to each other by the propagation speed which is the speed of light C. Now if you look at the Maxwell equations that describe this type of field, the speed of light is nowhere to be found. And that is because field propagation speed is the result of two constants in these differential equations called electric permitivity and magnetic permeability. These are two very fundamental properties of the vacuum that together describe the elastic behavior of the field as a result of charge being accelerated in space. Now the energy and momentum contained in radiation can also be transferred to matter and this is where photons enter the picture. There are different ways that you can look at photons in the high energy regime. I guess it’s okay to think as photons in terms of particles of light because the field actually starts to behave very particle-like. But in my opinion, the best way to understand photons is to state that they’re not the field, but the energy transactions or interactions with the field. The reason why I personally prefer this view is that it allows for interference to be understood intuitively. So a field might for example transfer an amount of energy to an atom leading to an excited state. And this means that energy previously contained in the field is now stored locally in the atom. for example, as electrostatic energy in the electron configuration around the nucleus or as kinetic energy transferred to an electron being expelled. And so this exchange is in fact the absorption of a photon of energy by the atom. Now the remarkable thing about this energy exchange is that it occurs in well-defined discrete amounts or quanta. Additionally, the energy in a quantum is not related to field strength but merely to the frequency of the radiation. And this relationship between energy and frequency is actually a linear one. And this is described by this factor which is plank’s constant. And we can experimentally demonstrate that field frequency is a key parameter regarding the amount of energy transferred in a photon. For example, in the photoelectric effect. Now, as a side note, the probability of an energy transfer actually happening is related to the intensity of the radiation. In other words, to field amplitude squared. Okay. Now, we get to the definition of Compton wavelength. The Compton wavelength is not some given number or constant. It’s actually unique to a specific particle. We can for example talk about the Compton wavelength of the electron. As I’ve just discussed, the energy exchange in a quantum between field and matter is related to wavelength. Now, at very short wavelengths, we can get to a point where the energy exchange in a quantum is so high that it allows for the creation of matter in the form of particles with mass. And that is because there’s also a relationship between energy and mass, which is Einstein’s famous ESMC squ relation. Now in this case you see that the creation of matter involves two particles at the same time an electron and a posetron and that is because the creation of matter is bound to certain symmetry conditions like conservation of charge which for this case means that you cannot create a single electron from a photon. But the creation of two particles would actually require double the amount of energy and so double the radiative frequency. Just for reference, the energy required to create these two particles is a little over 1 mega electron volt, which is approximately half a million times higher than the energy contained in a photon of visible light. But the Compton wavelength of a particle merely relates the wavelength of radiation to the energy required to create it. And with the electron containing 0.511 mega electron volt of energy, its Compton wavelength is equal to 2.4 4 * 10 -12 m. So that is the Compton wavelength of a particle. The wavelength of the radiation required to make a photon with sufficient energy to create that particle. In the previous schematics, I illustrated an electromagnetic field like this, which schematically shows the electric and magnetic field values along a specific line of points in space. In the real world, fields are way more complex and propagate in 3D space. This animation was made by Grant Sanderson of Three Blue, One Brown. It shows the electric field factors around a linearly accelerated charge. In 3D, it looks a bit busy and it’s easier to understand by just considering the values in a single plane or even just what it looks like along a single line. Here you observe that in every single point along the line the electric field alternates between positive and negative values. But there are also electromagnetic fields that look somewhat different. For example, circularly polarized fields associated with circularly accelerated charge. What you notice in this case is that the electric field value is never zero but has a constant magnitude while its direction rotates. I wanted to show you this because circular polarization also plays a role in the model presented. And since it’s so different from how most people imagine the propagation of electromagnetic field energy, I wanted to show you this animation, if only to emphasize how limited and simplified the schematics are that I’ve used so far to visualize fields. The way that Williamson and Fondmark imagined an electron is as follows. And I must warn you that the visualizations they use are highly schematic and conceptual. Visualize a Compton wavelength of circularly polarized electromagnetic field as sort of a twisted strip. The electric and magnetic field components are indicated by E and B. The magnetic component is oriented in the plane of the strip and E is perpendicular to the plane either directed towards or away from us. The direction of linear momentum and the propagation speed are indicated as L and C which are both pointing to the right. Now imagine that you are able to bend this strip into a closed loop that forms a double helix and this then results in a continuously curved field. So the total length contained in this double helix is still one Compton wavelength. But if you now look at the model, it’s clear that the linear momentum that was originally contained in the field has now been converted to angular momentum. And due to the internal orientation of the magnetic field, the helical shape also results in a net magnetic dipole moment. Also, due to the bend shape, the electric field on the outside always points in the same direction. And finally, because of the confinement of field energy and momentum in space, this structure would automatically represent its energy worth of inertial mass. So, let me show you how this works using a bit of tinkering. Here you see me drawing the electric and magnetic field orientations and the energy propagation direction on a strip of paper. And I’ll do the same on the other side. So if I take this strip and bend it into a configuration that represents circular polarization, I can connect the beginning and end such that the field is continuous and arrive at this double helix. And if we now examine the outside of this helix, we indeed observe the indicated electric and magnetic field directions of the schematic. Okay, this model is kind of crude. So let’s now refine it a bit. What the authors propose is that the field and its internal momentum is distributed through space in what looks like a donut or tooid. In this image, a chunk of the donut is cut out to reveal its internal structure, showing several nested toid shapes. This representation might suggest that the electron is a little donut, but that’s not what this figure tries to express. It’s actually a schematic of how energy flows and how the momentum is distributed in this model for the electron. On the surface of the donut, the authors have drawn curved lines which are called geodessics. Each geodessic curves over the surface of the donut in a closed loop and is one Compton wavelength long. One of the geodessics is accentuated and shows the direction of momentum and the flow of energy. And if you follow along its path, you see that it indeed describes a double loop. The nested toids are drawn here to indicate that the internal momentum is not located in a single surface, but is contained in a continuous structure that expands both inward as well as outward. Because a single Compton wavelength is contained in a double helix, the radius R is equal to the Compton wavelength divided by 4 pi, which would suggest that the core of the structure is somewhat smaller than the Compton wavelength. From a physics perspective, it would actually be impossible to contain all the energy inside a space that is smaller than approximately half a wavelength. So the characteristic size of this object would be in the order of between half and one content wavelength. But as we’ll see later, the exact size is not really that relevant. Let’s now dive a bit deeper into the electromagnetic configuration as described in the model. So what the authors propose is that the magnetic field is always parallel to the surfaces indicated in the toid. So the magnetic field lines shown here in blue form closed loops. Given the direction of the internal momentum, the electric field must therefore be perpendicular to the surface. This results in the electric field component shown in red to be orthogonal everywhere to the surface. Since the electron is negatively charged, the field is pointing inwards according to the conventions of how to describe field direction. But of course, a situation where the magnetic field lines run in the opposite direction is equally feasible and would represent positive charge. Because we’re considering the electron, let’s stick with the negative charge representation for now. So if you look at how the field itself rotates along the surface of a tooid, it’s very similar to circularly polarized light. It actually rotates over two pi along the toid surface and over 4 pi inside the toid shape in a double loop. Now I guess the most difficult aspect in this field description is how can you bend light such that it follows a curved path in space and I will get back to this near the end of the video. Let me first elaborate a bit on the current model. The magnetic field lines are now oriented such that this structure has a net magnetic moment as indicated by the large blue arrow through the center. But there’s something else that I want to point out about this structure that is much less obvious. If you take the mirror image of this object, the momentum is flowing in the opposite direction. This results in the magnetic moment pointing downwards instead of upwards. But if you now try rotating this structure back on itself, you’re actually not going to get the exact same thing back. And that is because the geodessics will be following a different rotational path along the toid surface. So these particles come in two different flavors that have different kyality and internally have two unique spin states for a part of the internally contained momentum. But both of these lead to an identical charge distribution and value for the magnetic dipole moment. If we analyze the internal momentum along one specific geodessic, we can distinguish two types of angular momentum. One due to the momentum rotating around the toidal axis over 4 pi and the other due to a rotation of 2 pi along the toidal surface. And as a consequence, the entity as a whole will not be some static momentum distribution in space, but one that is constantly reorienting itself due to precession with the energy racing around at the speed of light inside a volume that is the size of a Compton wavelength or smaller. The internal oscillation frequency will occur at two times the Compton frequency, which results in a rather large value for the internal oscillation frequency. What this effectively means is that the electron and its resulting external field will appear as fully spherosymmetric at any measurable time scale. Of course, everything I stated so far is also valid for the situation that the electric field lines are pointing outwards and the magnetic field is rotating in the other direction. And this state represents the positron which we know has an identical charge but of opposite sign and has an identical value for the magnetic moment. And the posetron like the electron can also have two unique internal spin states. So let me quickly summarize what just happened. By assuming a toidally shaped electromagnetic field distribution in the electron, charge and magnetic moment are emergent properties. The resulting electric field is sphere or symmetric and allows for two opposing field directions indicative of positive and negative charge. And each of these two differently charged entities can have two distinct internal spin states. Now the paper describes these ideas in much more detail. For example, it demonstrates how this configuration leads to half integral spin values or how to calculate a magnetic dipole moment that matches experiments. I will not replicate these derivations here. But what I will do is quickly show you the calculation for the value of the charge. The derivation of charge from photon energy works as follows. We assume that there is some dimension R that represents its size and has a direct relationship with Compton wavelength. This allows us to estimate the electron’s volume. We’re also assuming that the energy density in the electron is stored in equal amounts in the electric and magnetic field density. This results in the electric field energy density to be half of the total energy density. We actually know the total internal energy based on the constant wavelength of the electron. And this allows us to relate field value at dimension r to the total energy contained in the electron. So by combining all these relationships we can calculate the average resulting field value. And what we’ll do next is relate this field value to the field of a classical kum charge at radius r. Here are the two equations together. To the left our particle and to the right the field at radius r for a classical colum charge with a charge value q. And what we can do is combine these two formulas and extract the charge value Q that satisfies the equality. Now in the paper this elaborate equation is simplified a bit first. But by using this final result we can now fill in the values and arrive at 1.47 * 10us 19 k for the charge generated by the model. If you compare this value to the value experimentally measured for the electron, you see that it’s quite close but not exactly the same. It’s about 9% lower. However, it illustrates how with relatively simple reasoning, we can calculate a value for charge that is remarkably close to the experimental value. Now, you might not have noticed at this point, but this formula for charge does not contain a radius or a Compton wavelength. And that is because we’ve made a specific assumption about the relationship between radius R and Compton wavelength. And the charge value that emerges under these assumptions is a consequence of the tooidal configuration and the internally stored energy. So the model would allow for tweaking of the theoretical value of the charge using some smudge factor in the relation between radius and quantum wavelength. However, the authors decided not to go down this path in the current paper. Okay, so that’s in a nutshell how a fairly realistic value for charge emerges from the tooidal model. What I want to do next is discuss two questions that I’m pretty sure a lot of viewers might have now. And those are how can you justify that a particle with the size of a content wavelength interacts pointlike in high energy collision experiments? And second, what could be behind the apparent curvature of space that leads to this type of field confinement? Let’s start with the first question. From the model, a typical dimension for the electron in the order of a Compton wavelength emerges. But in high energy collision experiments where electrons are accelerated very close to the speed of light, neither their size nor their internal structure is revealed. So why would electrons interact point-like when they aren’t? To explain this discrepancy, the authors refer to the theory of Louis de Bruy called harmony of faces. And this theory states that the phase associated with the internal oscillation should remain synchronized between different inertial reference frames. So this theory tries to reconcile the relativistic effects of time dilation with the internal phase or clock of the energy oscillating within a moving particle. And the conclusion of the Bruy was that every moving particle must have an accompanying wave with a wavelength that is dependent on its momentum. In other words, dependent on its internal mass and velocity. And under relativistic conditions, you’d have to add the Laurens factor in the momentum calculation. So where does this wave behavior in particles come from? Well, basically it’s the result of interference between the Doppler shifted parts that make up the total internal momentum. Let me try to explain this using some simplified schematics. Here we have a particle that is static with respect to the reference frame we’re currently in. And for illustrative purposes, we assume that the internal energy is running in circles with the speed of light like a little clock. Now because this particle is static its velocity and therefore its momentum is zero. So according to the formula a particle at rest would have an infinitively long debris wavelength. But this statement is actually meaningless because defining a debris wavelength only makes sense for particles that are actually moving through space as hopefully will become clear. Consider the same particle moving with velocity V in our reference frame. To maintain internal phase synchronization, part of the internal oscillation must be redshifted to a lower frequency and another part blue shifted to a higher frequency. And the red and blue shifts are of course intended as an analogy to visible light to indicate this change in frequency. So for a moving particle, internal momentum and energy is distributed over a range of frequencies. And these frequency components are not spatially separated as this schematic illustration implies. They’re actually superimposed and produce a net phase interference in the internal momentum distribution. And it’s this interference that results in a beat frequency. Now the de bruy wavelength corresponds to the wavelength of this beat pattern as a particle moves through space. So the fact that every moving particle has a de wavelength does not mean that a particle is actually a wave. It means that the internal oscillation of energy and momentum manifests itself as a wavelike distribution within a specific inertial reference frame. So with this in mind we can understand why a faster moving particle has a shorter debris wavelength. It’s because the red and blue shifts are larger in this case and the interference results in a higher beat frequency. And if we now consider a particle with larger mass in other words a particle with a shorter content wavelength and a higher internal frequency the resulting de wavelength will be shorter than that of a lighter particle at the same velocity. The characteristic wavelength revealed in this way is inversely proportional to the momentum of the particle. And yes, it’s real. It can be experimentally observed in basically every particle that has momentum. And this made the equation of the bri to one of the pillars of modern physics. What I just described is actually very closely related to the Heisenberg uncertainty principle. If you compare the distribution of momentum circulating in a particle that is moving to that of a stationary one, it must be wider due to a shift to higher and lower frequencies within the total momentum distribution. And so the uncertainty in momentum widens as a particle moves faster, which allows for the uncertainty of a particle’s position to shrink in measurements because of the uncertainty relationship between the two. Determining the size of a particle in experiments is all about observing its interaction with other particles. And the authors determined that the resolving power of one particle with respect to another one is equal to the de wavelength divided by two. But in the paper they also show that the characteristic dimension of the electron due to relativistic effects must be smaller than this value. And this effectively means that you cannot resolve the internal structure of an electron using an electron. The last question that I want to discuss here is the mechanism behind the energy self-confinement. So how can an electromagnetic field curve such that it becomes a local oscillation in space? Now in search of an explanation, the authors consider several mechanisms. Can the curvature leading to the confinement, for example, be gravitational? Light is known to bend around heavy objects and cause gravitational lensing. And of course, an electron is not a heavy object, but the effects of gravity are not related to mass per se, but to the energy density in space. And the electron might locally contain a high energy density. However, we can rule out gravitation as a cause because the effects expected based on the local energy density would be way too small to offer any kind of explanation. Okay, so what about some kind of magnetic confinement? In the model, we observe that the magnetic field lines are neatly aligned in closed loops. So maybe this creates some kind of energy minimum which keeps the field in the current state. Williamson and Fenomark don’t rule out this option, but they argue that it cannot be the only mechanism responsible and that is because this type of confinement should be scalable and allow for different values of the internal energy. In other words, it would not by itself have to lead to a single unique internal energy of half a mega electron volt. So the distinct energy value indicates that there must be some additional mechanisms at play which brings us to whether the confinement involves nonlinear phenomena. It’s known that intense electromagnetic fields can also curve space time and the field value where this is expected to happen is known as the swinger limit. It refers to a critical field value of approximately 1.3 * 10 18 volt per meter which is extremely high. At this field value, the polarization of space becomes so strong that the vacuum cannot support the field anymore. And it’s at these field values that matter can emerge from an electromagnetic field. However, if we estimate the average field value inside the electron based on the current configuration, it’s quite a bit smaller than the swinger limit value. So I guess the curvature of space cannot be explained from the field value being at the swinger limit here. However, the shrinking limit could of course serve as a barrier between two different types of electromagnetic field behavior. One where the field can frolic around freely and one where it got trapped locally in space. And in that sense, it’s interesting to think about how the energy confined in an electron could escape spontaneously. Electrons are considered to be stable because they do not decay in isolation unlike for example much heavier elementary particles like the muon or composite particles like the neutron which both have relatively short lifetimes. But electrons and posetrons are stable and they also have the lowest mass of all charged elementary particles. There are actually two other fundamental particles that contain less internal energy, but these are nutrinos. So they do not have charge, which means that an isolated electron cannot annihilate to form a bunch of nutrinos, nor can it convert back to photon energy because such a conversion would also violate the conservation of charge. In fact, the conservation of charge is a super powerful principle that applies to every creation and annihilation process. Now in this model, charge arises from how energy is contained in a very peculiar magnetic field configuration. And this configuration appears to be a topologically continuous and self-closed entity. This seems to be the main difference between these two electromagnetic field configurations, which would mean that going from one state to the other is all about closing and opening this magnetic self-ontinuity. something that can apparently only happen when the vacuum itself breaks down temporarily under extreme field conditions. So, is an electron a photon with tooidal topology? I would be very interested to know what you think. Is this indeed a model to be politely ignored or does it resonate with you? Please let me know in the comments. What I personally like is how it turns an abstract and pointlike entity into something that is truly physical. How charge, magnetic moment and spin emerge by confinement of a field in a tooidal shape and the fact that we cannot measure its size or structure is a consequence of relativistic physics. In fact, in this theory, there’s just one building block for everything, the vacuum. Okay, vacuum spiced up with a bit of energy. But all you need for a theory of everything is how this vacuum behaves, especially under high frequency strain. So my suggestion would be let’s just keep questioning the universe.