Christian,

I start with the fact that spacetime has impedance of Zs = c3/G which is obtained from gravitational wave equations.  Quantum mechanics allows waves in spacetime which produce a spatial displacement of ± Planck length and a temporal displacement of ± Planck time. These waves and this impedance are shown to have the correct properties to explain zero point energy and vacuum energy.  The "spacetime field" is modeled. Fundamental particles are units of angular momentum which are quantized by the properties of the spacetime field. This and other inputs allow the generation of a particle's "internal structure" which has specific values of wave amplitude, frequency, impedance, physical wave size, etc.  These specifics allow calculation of the particle's energy, angular momentum, inertia, forces, etc. Collision experiments are shown to produce the appearance of point particles. The spacetime particle model generates forces which are shown to be equivalent to the gravitational force and the electrostatic force. The magnitude of these forces can be calculated from the "internal properties" of the spacetime particles (field interactions).  This new approach predicted that there should be a previously unknown relationship between the gravitational force and the electrostatic force.  This and other predictions are analyzed and found to be correct. The paper will be published next month. For a preprint: http://onlyspacetime.com/QM-Foundation.pdf    

Fundamental particles, quarks and leptons, for instance, have been experimentally found, up to current LHC energies, not to have any ``internal structure'', i.e. to be bound states of other particles. Particles have mass and spin, as spacetime labels and carry other ``charges'', electric, weak and strong, that describe their non-gravitational interactions.That the muon has a mass about 200 times that of the electron can, in principle, be calculated from the equations of the Standard Model-it's just very difficult in practice (these are called the Schwinger-Dyson identities). The differences are determined by the interactions. 

In the same way that particles aren't made of anything-they ``make'' everything, (fundamental) strings aren't made of anything, they make everything, through their properties, kinematic and dynamic. They do provide a useful description of hadrons, particles that have strong interactions, at ``low energy'' and certain properties of quantum black holes; it's a research program to complete the picture. 

In the same way that, while mechanical waves can be described as collective motion of atoms, but electromagnetic waves can't, mechanical strings and membranes can be described as extended objects made of atoms, but fundamental strings and branes can't. The appropriate description turns out to be different, but can be consistently expressed. 

In physics the most difficult part of the process is learning what are the appropriate questions to frame. And this is learned step by step. 

From a strict classical point of view, elementary particles have a mechanical structure and an interacting (electromagnetic, weak, strong,...) structure. This defines two characteristic points, the center of mass (CM) and the center of charge (CC) either (electric, weak color,...). Only two things can happen: the two points are the same (point particle) or they are different (spinning particle). In the second case the CC moves around the CM in circles at the speed of light, and it is this relative motion which produces the dipole and spin structure. It is shown that the quatization of this last model leads to Dirac's equation. (See: Quantization of generalized spinning particles. New derivation of Dirac’s equation

(J. Math. Phys. 35,3380 (1994)) )

About the size or shape of an elementary particle, classical mechanics has not been able to say anything, only this separation between CM and CC which amounts half Compton's wavelength.

You can refer to attached papers. May they answer your question.

Article Journey of the Universe from Birth to Rebirth with Insight i...

Article A Spiral Structure for Elementary Particles

• About the general formalism, it is analyzed in detail in my book:

Kinematical theory of Spinning particles, (Kluwer Acad. Publ., 2001) or 

Springer 2002. Concerning the previous mentioned reference, it is attached here

Stam,     Thank you for your two answers. My question is designed to get physicists to admit that fundamental particles must have an internal structure which gives the different particles different properties. I agree that fundamental particles are not bound states of other particles. However, that is not the same as saying that particles have no internal structure. In probing the internal structure, I believe we are entering into the realm of fields and questions like: What is a field and how do they interact to make a fundamental particle?

For example, I have written a paper and a book describing how particles and forces can be made out of the quantum mechanical properties of 4 dimensional spacetime. For example, the description of an electron gives a physical description including: wave amplitude, frequency, impedance of spacetime, etc. This description then allows the calculation if its energy, inertia, angular momentum, gravitational curvature of spacetime, gravitational force, electrostatic force (assuming alpha), size in collision experiments, etc. I am now realizing that no other particle model is complete enough to be analyzed to this degree.

In your second answer you say “(fundamental) strings aren't made of anything, they make everything”. This answer apparently satisfies those physicists devoted to string theory. However, to someone outside the string theory community this sounds distinctly unsatisfactory. The properties of strings and branes are adjusted as needed to give the desired answers. My fundamental building block is 4 dimensional spacetime which has quantifiable properties completely separate from particles. Therefore, if it is found that these same properties can explain particles and forces between particles, this has a lot of appeal.

Wonderful question and some wonderful answers too!

Typical answers like those from dear Stam are really impressive for beginners but I like with the approach of John Macken, the original questioner on a deeper analysis of things.

The way we explain science often stifles the very spirit of inquiry inherent in us.

As long as we have a finite dimensional structure it must have substructure for the simple reason that it is finite and real numbers are continuously distributed in any finite segment. This being the truth, we propose and postulate principle after principle to uphold a certain intermediate structure as a fundamental particle/string and try to build models to describe phenomena. But there is nothing sacrosanct about it all, no matter how compelling the experimental evidences at a particular energy scale are, as rightly mentioned by Stam.

Regards,

Rajat

we do not know all the characteristics of each particle, only a few (charge, flavour, snd so on). We term each particle just for a few peculiarities, but we do not know the possible others. To make the picture more complicated, we need to take into account the possible presence of unknown gauge fields, in which still unknown Lagrangians are preserved. This is probably the key to get deeper into supersymmetries and the constituents of the "simple" particles.

Dear John,

This is a wonderful question that we all should have in our minds. From my quick look at your  published work available on internet, I understand that you base your fundamental description essentially on the quantum mechanical properties of 4 D spacetime. From this platform you arrive at a physical description of the established properties of the most known elementary particles.

This model appears to give an almost complete description (ToE) of the entire universe. Nevertheless my personal feeling is that we might miss out of something important, unless we do not also address the conjugate properties (energy-momentum) of spacetime.

A proper characterization of these two "entangled" quantities leads to equations, like the Schrödinger-, Klein Gordon or the Dirac equations, from which the fundamental characteristics of the entities, being, EM-, matter- or other types of waves, can be determined.

Since the present question enters uncultivated soil one needs to be open to many practices and methodologies, but in the end, results must be compared and reformulations analysed with respect to the deductive properties of physical theories, in order to fully understand the far reaching consequences of any new proposition.

I wrote a book about a new framework for physics based on the unit particle idea which my colleague and I dubbed 'the microbit' - that was in 2001. The book is called "From Microbits to Everything". So all so called matter and energy is simply a grouping  of "microbits". The book is available free of charge on Scribd and another article written a decade later on academia.edu. According to this model, which is based on absolute space and the motion of microbits (that do not have an internal structure) and were the first particles to split from the Big Bang, all elementary particles are not really elementary - they are all composites of microbits. This in a natural way unifies physics. So it dispenses with the geometrization of Physics with General Relativity  and sides with Quantum Mechanics to certain extent - but is wholly deterministic; underlying our observations are hidden variables (particles affecting behaviour at 'larger levels'). Couder's experiment (https://www.youtube.com/watch?v=W9yWv5dqSKk) is indirectly (analogously) pointing to this now. Patti and Abdus Salam etc. had sub-quark models, but my colleague and I took it to first principles. A second volume also touches on the question of how and why the universe was created, thus trying to discuss so called issues of 'theology'. Once we find out that quarks etc. are comprised of smaller particles, I think 'all hell will break loose' and we will be forced to look into a simpler yet at the same time profounder unified way of describing reality.

A supplementary article to my book was written about 10 years later and it is now on Researchgate: "THE ULTIMATE REALITY SUSTAINING THE COSMOS: A NEW EMERGING SYNTHESIS"

The book itself (that is based on internal structures, where fields themselves are particles at sub-levels up to the final (microbit level)) is available here, freely downloadable:

http://www.scribd.com/doc/47770990/Microbits-Vol1-v-2

I think that the way we have been looking at matter in the past needs to be redefined as well as mass and mass-less!

The reason that I asked the question about internal structure of fundamental particles is that I believe that this is going to be the next big area to theoretical research.  To analyze this we have to switch from thinking of particles and forces to thinking about the nature of fields and their interactions.  I have proposed a model of fundamental particles by starting with a quantifiable description of zero point energy and vacuum fluctuations.  This has led to some exciting insights into gravity and the electrostatic force.  For example, the proposed internal structure of electrons and muons implies that forces should scale with their reduced Compton wavelength.  Testing this insight has led to numerous equations which relate the electrostatic force and the gravitational force in a way not previously recognized.  For example, suppose that we have two electrons and they are separated by a distance equal to N reduced Compton wavelengths.  Then the forces between these two electrons is given by the equation  FgFp = (FeN/α)2 .  In this equation Fg is the gravitational force, Fe is the electrostatic force, Fp is Planck force, α is the fine structure constant and N has been defined.  The gravitational force can be shown to scale with the square of the electrostatic force.  Internal structure analysis also yields insights into electric fields, spin, internal energy, etc.

Christian,

I start with the fact that spacetime has impedance of Zs = c3/G which is obtained from gravitational wave equations.  Quantum mechanics allows waves in spacetime which produce a spatial displacement of ± Planck length and a temporal displacement of ± Planck time. These waves and this impedance are shown to have the correct properties to explain zero point energy and vacuum energy.  The "spacetime field" is modeled. Fundamental particles are units of angular momentum which are quantized by the properties of the spacetime field. This and other inputs allow the generation of a particle's "internal structure" which has specific values of wave amplitude, frequency, impedance, physical wave size, etc.  These specifics allow calculation of the particle's energy, angular momentum, inertia, forces, etc. Collision experiments are shown to produce the appearance of point particles. The spacetime particle model generates forces which are shown to be equivalent to the gravitational force and the electrostatic force. The magnitude of these forces can be calculated from the "internal properties" of the spacetime particles (field interactions).  This new approach predicted that there should be a previously unknown relationship between the gravitational force and the electrostatic force.  This and other predictions are analyzed and found to be correct. The paper will be published next month. For a preprint: http://onlyspacetime.com/QM-Foundation.pdf    

The latest Unified Field Theory considered that the subatomic particles are composed of fundamental waves with the unit charge (electron) mass as their unit. The paper can be dowload via the following URL:

http://pubs.sciepub.com/ijp/1/6/4/index.html

Additional papers can be found as follow:

https://www.researchgate.net/profile/Zhiliang_Cao/contributions?sorting=recentlyAdded

For my part, I think that to consider particles such as electrons like pointlike entities without internal structure and indivisible is a mistake. Or the quarks. At first, the mass is a manifestation of internal movement, too the spin. For example, a fraction of the mass of proton is kinetic energy of quarks, other fraction is potential energy of internal fields. Obviously, the six masses of quarks reflect its internal properties. In other hand, I think that the theories such as the string theories and derivatives are models of the reality that can to reflect, at a restricted mode, the internal dynamical of the particles, but like all our theories, they aren't the reality itself. I seem wrong to think that the matter is an excitation of the fields or of the space-time. The void space is the absent of matter. The material particles or bodies are the sources of fields, There aren't fields without material particles or bodies that generates it.

This concepts has caused many theoretical mistakes, such as to attribute to the void phenomena like the Lamb displacement or the Cassimir effect

Dear John,

As you are, I too think it is important to further understand the physical nature of matter. This will supplement the current mathematical understanding of it. Both are needed in order to advance the field.

Based on our studies, we are finding that the electron is a tiny cylindical field unto itself. The tiny field displays both particle and wave characteristics, as well as all other electron properties. We too found, in our derivation of the electron's gravitational field and force, that such is closely related to its electrostatic force by way of the Lorentz magnetic force equation. 

Although our models and derivations are based on a different platform than yours, we thought our studies might be of interest to you and maybe even provide some support.

An introduction and pictorial view of the electron is attached; it is excerpted from "New Physics Framework". If you are so inclined, Chapter 10 of the book explains why particles, such as those in the lepton group, have different masses.

Regards,

Dan S. Correnti

Article UNVEILING of the ELECTRON (Post #1) [A Proposed Electron Structure]

In UFT, space-time-energy-force are inseparable. There are no true void, as universes is in the "Torque Grid", commonly "void" in the higher hierarchy universe. It is hard to imaging first, but the researchers who understand it get answers they're looking for and love the theory. The theory is a model,  as no one can locate the boarder via experiments, as boarder and inside are the same. Noticeably,  UFT made many predictions. I am old man who have been studying these things for fourteen years and happy to see you get benefits from my discoveries. You can follow my previous post to get URL that leads to papers. I hope that you can understand the papers after reading papers many times.

The particles have internal structures of course, even the photon. The "point particle" is an inexcusable nonsense. However, to understand it, we need use totally different principles and language, and some other physics in whole. You can try!

http://vixra.org/author/george_kirakosyan

With Regards!

Electron plays an important role in physics. The attached link provides my latest paper. A charged energy is associated with an arbiter 3D movement. 

http://pubs.sciepub.com/faac/1/1/4/index.html

George 's paper is interesting.  I agree that physics constants have deep meanings. Explaining them is a necessary step for the new theories. Similarly, UFT tries to explain 137 from different angles. 

Yes, from my exploration, we have both forms and transforms, the latter being the change in energy states or informational states. forms and transforms allow us to have a logical framework for particle theory. Something Feynman dreamed of and was inspirational and a genius at describing. He opened the door for discovering a comprehensive system of mapping the quantum mechanical framework. A string is a way of representing waves and topology, at the Planck length and even smaller in scale. It allows us to describe a logical spacial charge function smaller than the photon, which is best described as optical magnetic fields, or partial wave functions of the photon. These sub Planck functions are/can be theorized and tested using string theory. Complex arrangements of these same functions can demonstrate transforms and forms, which can become all of the known and unknown particle types. It also can provide us with the branch points of synthesis for matter and dark matter and all of the branch point predictions for charge based informational packets (radiation). This includes neutral charge as well.

BTW John, it is interesting to note that I ran into a colleague who was doing the same analysis of the two electrons , just a few months ago. We discussed it over a coffee. If one changes the problem to one of space-time reference, instead of viewing this as an inertial problem, you will find that gravity is an operator at a much lower scale of gauge, and operates in a more complex manner , setting the framework for how space operates in these conditions and to what operations can and which cannot be obtained. It is not an energy (inertial) limit, but when we do the math it seems to be the case, because of what we are limited to in terms of information from classical models. I remember reading Nassim H's paper, where he went to great lengths to defend how all physical constants support all other physical constants. He found this magical ratio, which ironically is how the very best physicists, rationalized these through math in the first place (he discovered nothing new LOL) He was simply going in logical circles and discovering that you cannot gain more than you already know, because all of these constants depend on each other for validity. I find that one has to work at the next lower logical layer , of informational theory and charge, to gain new information and have a quantum mechanical operation set to dig into the actual foundation of the properties of space. It is here you can develop operators that can show more than simple cases and predictions for two electrons. It is there you will get the exotic interactions we need to extend our technology beyond the present. I do apologize if I have not been clear enough. I have been out of the loop, with no correspondences, for a few months. Best wishes, Mark

I think the internal structure of the fundamental particles would be in the form of various combinations and configurations of individual waves of which the particle wave packet is made up. It will be similar to visible light spectrum which consists of combination seven monochromatic waves.

In general relativity, there is a discontinuity between electromagnetic spectrum and massive particle spectrum of the standard model. I have proposed a theory that generalizes special relativity and removes this discontinuity. So particles like neutrino can fall at the borderline between these two spectrum. Therefore neutrino oscillation can be seen as something like red shifting or blue shifting of light. Same can be said about Muon and electron. These individual waves of the wave packet can decide the charge, spin or whether it is matter or anti-matter, and it may also dictate the collapse of the wave function.

Regarding neutrino oscillations, current belief is that neutrino acquire their mass by interacting with the higgs field, but I differ from this view. I think the kinetic energy of the particle can change into mass and vice versa.

If a particle does not have internal structure in my humble opinion it can not be a particle of any kind.

What an excellent question!

There are too many views to comment individually, but I see some that are close to what I imagine. There are too many to follow each one, but many or going on my list.

I agree with whoever said that they thought this will bring on the next huge step forward in Physics. But it has a huge heap of embedded thinking based on some wrong assumptions and in which many notable Physicists have staked their careers.   As someone said in another 'topic', we may have to wait for them to die off before these new approaches become mainstream.

And pray that they dont 'breed'.

Dear Vikram Zaveri,

I liked your remark above, yet a one point I found slightly Regarding neutrino oscillations, current belief is that neutrino acquire their mass by interacting with the higgs field, but I differ from this view. I think the kinetic energy of the particle can change into mass and vice versa.wildering:

"Regarding neutrino oscillations, current belief is that neutrino acquire their mass by interacting with the higgs field, but I differ from this view. I think the kinetic energy of the particle can change into mass and vice versa."

I guess that you thought of some thing else writing this sentence, as you, I believe, know well that so called velocity dependent mass of a particle in movtion is strongly a reference system effect and the "mass" notion in this case is exlusively related  to a particle intrinsic inertia property, uncerstanding well enough that with respect to another reference frame this particle will be in rest, and its internal, mainly I guess the one of electromagnetic origin, will persist to be unchangable.

Regards, sincerely,

A.

Dear Anatolij K. Prykarpatski:

As you must know, there is no satisfactory explanation to the origin of neutrino mass. There are several proposals covering Higgs field, Majorana masses, R-parity, supersymmetry. You are also correct in writing that the velocity dependent mass is the relativistic mass and not the rest mass. And there is no reason for the rest mass to oscillate in the universe we know.

In my article given below, I have shown that it is possible to convert the kinetic energy of the particle into rest energy in the very early universe. It is like plasma at high energy condensing into mass. The equation governing this process is given by eq.38, which combines Lorentz invariant equation, Hubble parameter and Planck freqency. The output shown in tables describe how all particles acquire their mass when their velocity drop from c to v. Three neutrinos are shown at Record Nos. 11, 15 and 16. This conversion for neutrino takes place at temperatures of order 10^28 to 10^21 K. Whether this process can occur at low temperatures at present epoch or not, is not very clear.

Article Periodic quantum gravity and cosmology

I ask : if  you assume that  the Lorentzian invariance present at the very initial evolution epoches,  youtr model will fail in "condensing" particles masses from any kind of energy. Even more, the neutrino oscillations can be in part explained by means of their strong interaction with vacuo... Such works are also present in the literature.

Regards!

I did not say that the unmodified Lorentzian invariance equation is present at early epochs. I said the three combinations mentioned earlier and given by eqn.38 is operating in the early epochs. If you see this equation you will notice that there are only four variables there. Energy, radial distance between particle anti-particle pair, frequency roll down number k, and the particle rest mass. I have nothing against other models if they explain the phenomenon in full.

It should also be noted that the neutrino oscillation problem came to notice while developing the solar model. And the estimated temperature at the solar core is 10^6 K.

Manuel,     You ask, "How have you experimentally found your predictions to be correct?" Some predictions can be verified theoretically if the predictions indicate there should be a previously unknown relationship between two known facts.  For example, Maxwell "predicted" that the speed of light could be derived from εo and µo and gave the equation c = (εoµo)-1/2.  This was a previously unknown relationship that theoretically proved that Maxwell’s equations were correct. No experiment was necessary.  Similarly, my model of particles have internal structure which affects the forces generated by these particles.  One prediction is that both gravity and the electric field produced by a particle should have a static component which strains spacetime and a component oscillating at the particle’s Compton frequency. This oscillating component causes fields to scale with the particle’s reduced Compton wavelength.  Furthermore, gravity should be a nonlinear effect which scales with wave amplitude squared while electric field should be a linear effect which scales with wave amplitude (not squared). 

 These predictions were proven correct because equations given in the preprint paper (linked below) show that starting with the Coulomb law equation and Newton’s gravitational law equation there is indeed the previously unknown square relationship between gravity and the electrostatic force when the separation distance between particles is stated using the number of reduced Compton wavelengths rather than using meters.  The vast difference between an electron’s gravitational force and its electrostatic force can be expressed as a simple square of wave amplitude and α, the fine structure constant.  The paper also proposes a new constant of nature which converts charge and electric field into a distortion of spacetime. Application of this constant predicts that photons and electric fields should have limiting conditions.  These predictions are also shown to be correct because they correspond to conditions which would produce black holes.

http://onlyspacetime.com/QM-Foundation.pdf

The real answer, I think, is that we don't know. We know as deep as we can measure

(d~hbar/p~10^-19m --> if you take p to be ~1 TeV/c). 

So far we have seen no contact interactions, no internal structure, preons and so on.

 Emmanuel,   Your answer does not apply if the "internal structure" is a rotating distortion of spacetime possessing quantized angular momentum.  This probably sounds like pseudo-science, but there is a great deal of analysis and support for this model.  This model can be quantitatively analyzed and it gives the correct energy, inertia, gravity, electric field etc.  At the instant of collision, the kinetic energy is temporarily converted to internal energy of the electrons which reduces the radius and maintains the quantized angular momentum.  An analysis shows that a collision experiment will always indicate a point particle because the rotational radius is always less than the theoretical detectable size of the experiment.  The details are explained further in the technical article referenced in one of my earlier answers.  

Manuel,    You say, "Physics can only know 'as deep as we can measure". In my previous post I claim, "This model can be quantitatively analyzed and it gives the correct energy, inertia, gravity, electric field etc." The point is that the human intellect can analyze information and find connections so that many disjointed pieces of information can be organized into a conceptually understandable model (theory). Presently we have many mysteries of quantum mechanics which have been experimentally observed but not yet organized into a conceptually understandable theory. For example, entanglement of photons was theoretically predicted and experimentally observed. If there is a theory which explains entanglement, gives equations and connects entanglement to other physical effects, this will be an example of going "deeper than we can measure." I claim that an analysis of spacetime has found a previously unknown connection between electric fields and gravity. This can be expressed as equations and a conceptually understandable model of particles, fields and forces.  

John,

You say: The gravitational force can be shown to scale with the square of the electrostatic force.

How do you administer scaling in the Schwarzschild metric?

Erkki,    In the short post I did not state my position precisely. A more accurate statement would be that the referenced article takes the first step in unifying gravity and the electromagnetic force. This is not complete unification of all aspects of general relativity with all aspects of the electromagnetic force. This first step shows that the gravitational force between two fundamental particles as described by Newton's gravitational equation can be stated as the square of the electrostatic force as described by the Coulomb law equation. The wave-based analysis predicted that the gravity and electric field produced by fundamental particles includes a component that is oscillating at the particle's Compton frequency. This means that the relationship between these two forces is revealed when the separation distance is expressed as the number of reduced Compton wavelengths. So far the gravitational force analysis has only included the first term which yielded the Newtonian equation.

So the scaling relation is far-sighted not near-sighted.

Yes. Elementary particles like the electron, muon, neutrino, and proton must have an internal structure. They cannot simply be "point masses." If they were "point particles" there would be nothing to generate the electric fields, mass, and spin angular momentum, not to mention the magnetic dipole moment.   

I published a paper regarding this. Please review the paper and let me know your thoughts.

Article Unified Field Theory and the Configuration of Particles

The unification of major forces was proposed in a simple paper as attached:

Article Unified Field Theory

Dear John

You mention the option of "point particles" with the assumed restriction that it could involve only the mathematical dimensionless definition of the concept, which obviously involves no internal structure.

Wouldn't the concept of "point-like particle" be more appropriate for exploration purposes? After all, aren't the trajectories of Earth, Moon, Sun etc calculated using the very same idea (assuming that the whole mass of the body is concentrated at its point center, that is, its center of mass)?

Point-like behavior does not imply total absence of internal structure, why not some sort of local electromagnetic oscillation, even if a definite volume cannot be measured, the latter possibly due to the oscillatory nature of the energy making up the mass of the particle?

To me a greater mystery than mass, spin, charge, dipole moment etc, which all play some role in the dynamics of interactions between particles, are the "static" properties of so called elementary particles. For example "lepton number", "flavor" etc. These are just conserved quantities that do not play any role in the dynamics. If there is no underlying structure where do these properties come from. Did *** in *** wisdom create three intrinsically different types of matter ?

Ion,

I think you are correct. The science behind making things up is interesting to say the least. Why is it that a scientist only looks at things that have scientific prove of them yet they can turn around and make up some attribute that has no place or true meaning in the science and that is okay?

We should realize that just because we do not understand something or can not explain it mathematically does not mean that by adding in layers of complex math and theory does not make it correct just because we can show it works with the math.

Magnetic moments do suggest a geometry and structure.

There are many strong suggestions that electron is not a perfect point, e.g.:

- the problem of infinite energy of electric field if assuming perfect point,

- ultraviolet divergence: some minimal distance/size we can consider,

- divergence of perturbative QFT series - there is no place for too large scenarios (Feynman diagrams).

Electron is a stable configuration of fields - technically is a soliton, for which there are natural ways to regularize topological charge to finite energy - and it seems the only approach really trying to handle this infinite energy problem: https://physics.stackexchange.com/questions/386760/the-problem-of-infinite-energy-of-electron-as-point-charge

All the answers to the questions of John A. Macken are in my book entitled Structure of Space and the Submicroscopic Deterministic Concept of Physics (2017).