Although the standard model treats the electron as a point-like particle, its rest energy (~0.511 MeV) necessarily implies that it must occupy a certain physical space—i.e., that it is confined within some kind of volume.
Physics has estimated various values for its “effective size,” such as the so-called classical electron radius (~2.82 × 10⁻¹⁵ m), although experimental bounds place its actual size below 10⁻²² m. In any case, if the electron has energy and that energy is quantized, then it cannot be perfectly homogeneously distributed within its confinement, regardless of the specific volume.
Quantized energy implies discrete distribution, which in turn suggests that the electron must have some kind of internal structure. This structure might not be mechanical in the classical sense, but rather energetic or spatial—such as an internal distribution of layers or regions with varying energy densities.
Would it be reasonable to consider that such an internal energetic structure could be related to properties like electric charge or spin?
I would greatly appreciate any critical thoughts or references on this idea, especially if there are current approaches exploring similar questions from other perspectives.
Not necessarily — but possibly.
In standard quantum mechanics, energy quantization arises from boundary conditions on wavefunctions, not necessarily from any internal structure of the particle itself. For example:
• In a hydrogen atom, quantized energy levels come from the electron’s wave nature, constrained by the electrostatic potential of the nucleus.
• Similarly, in a quantum well or harmonic oscillator, quantization reflects how solutions to the Schrödinger equation fit spatial constraints.
In this view, the electron is still pointlike — with no substructure — and quantization emerges from the wavefunction behavior, not the particle itself.
But here’s the deeper question:
If quantization keeps appearing universally, and in ways not fully explained by external constraints…
Could it be a shadow of an internal periodicity — a structure beneath the current model?
Some advanced models explore this idea:
• De Broglie’s double-solution theory proposed that particles have an internal clock or “internal vibration.”
• Zitterbewegung models (e.g. by Hestenes, Barut) suggest that the electron’s spin and mass might emerge from internal circulatory motion at the speed of light.
• Even string theory treats particles like the electron as vibrational modes of extended structures — internal by definition.
So, does quantization imply internal structure?
In mainstream physics: No, quantization arises from external conditions and wave equations.
In deeper theories: It might — especially if quantization is tied to stable, intrinsic dynamics of a particle’s field or geometry.
In context of foundational theories:
If the wavefront of a quantum particle isn’t abstract but a real evolving object (as proposed in Quantum Wavefront Dynamics), then quantized energy could reflect stable curvature modes — similar to resonant standing waves on a string or in an optical cavity.
That doesn’t necessarily mean “internal parts” — but it could mean internal behavior. A distinction worth noting.
Conclusion:
Energy quantization doesn’t require internal structure.
But it could be the first visible hint of one.
Yes, the electron does have an internal structure but in the background of our current understanding of Nature, it is very difficult to explain it.
Physical space or the good old aether is well known for more than a century, to support propagation of transverse waves. It is also well known that transverse waves can propagate only through an elastic solid or an elastic continuum and certainly not through any fluid medium. Still, NO SCIENTIST is prepared to accept the physical space or aether to be an elastic solid or elastic continuum just because it is extremely difficult to imagine the existence of matter, our own existence and motion of matter particles through any solid like elastic continuum. And this deadlock is persisting - propagation of transverse waves demands the physical space to be a solid like elastic continuum, with modulus of elasticity and density like inertial constant included in its bulk properties and where equations of elasticity will be applicable. But NO SCIENTIST is mentally prepared to accept it.
Physical Space
Whereas the metric scaling property is only associated with coordinate space, the physical measurable properties of permittivity ε0, permeability μ0 and intrinsic impedance Z0 are only associated with physical space. In reality, various notions of physical space, empty space, vacuum, aether and their modern reincarnation, the quantum vacuum, all mean the same entity – call it by any name. A significant point to be highlighted here is that just like the intrinsic impedance Z0=Sqrt(μ0/ε0), the speed of strain wave propagation c=Sqrt(1/(μ0.ε0))is also a measurable property of the physical space. Since these four parameters are inter-related, only two of these are independent. Characteristic parameters ε0 and μ0 of Physical Space also represent mechanical properties of Physical Space. The propagation of transverse waves in a continuous media is essentially a feature of mechanical phenomenon, because of which we interpret these physical properties in mechanical terms as elastic constant 1/ε0 and inertial constant μ0. That is why we prefer to view Physical Space as an 'Elastic Space Continuum'.
Status of Matter and Fields.
Let us now examine the next pertinent question as to how exactly particles of matter could move through an elastic space continuum without any resistance. At subatomic scale the primary constituents of matter, namely the electrons and nuclear particles are known to occupy an extremely small volume fraction of the order of 10-12 percent of the physical volume of any material body. As such we need to view material particles as a sort of lumped up strain energy, or, a sort of localized strain wave packets. For the elastic space continuum, the equilibrium equations of elasticity can be shown to be identical to the vector wave equation. The study of dynamic deformations in the space continuum, through a detailed study of time dependent displacement vector U, along with corresponding strain tensor and stress tensor fields, provides a more fundamental level of investigation into the workings of Nature, in comparison to the fields currently employed for the purpose.
Particular solutions of these equilibrium equations as functions of space-time coordinates, satisfying appropriate boundary and stability conditions within a bounded region, can be shown to represent various strain wave fields and strain wave packets. The electromagnetic field as well as all other forms of energy and matter can be shown to exist in the the elastic space continuum as strain wave fields or strain wave packets. The energy density associated with these stress/strain waves in any particular region of the space continuum will be proportional to the square of the intensity of such waves. The matter particles essentially exist in this elastic space continuum as packets of standing strain wave oscillations whose total strain energy remains conserved in the absence of any interaction with other strain waves or packets. Hence matter and EM field do not have any independent existence separate from the characteristic dynamic deformations of the Physical Space.
Strain Waves and Elementary Particles.
A matter particle moving in the space continuum will always be accompanied by a localized strain wave field, something like De Broglie waves, or induced EM fields. Kinetic energy of a particle in motion in the elastic space continuum can be viewed as the strain energy stored in the accompanying strain wave field. These 'material particles' concentrated in a small volume fraction of entire space, consist of so called 'elementary particles' and are essentially characterized by their 'mass', 'charge' and interaction properties. In the parlance of strain bubbles existing in the Elastic Space Continuum, the clusters of pure and composite strain bubbles depicting 'elementary particles' are essentially characterized by their 'strain energy content', 'strain wave fields' if any, and their interaction properties. In principle, there could be a large number of different types of strain bubbles occurring in the Space Continuum, that may be correlated with equally large number of stable and unstable elementary particles.
I am currently writing a research paper titled, "Strain Wave Structure of a Photon and an Electron" which I hope to submit for publication in a month or two.
Meanwhile you may have a look at my following two papers.
Article Wrong Potential Energy Term in Schrödinger’s Equation for Hy...
Article Dynamic Electron Orbits in Atomic Hydrogen
Dear Ricard Desola Mediavilla ,
a very good and likewise important question, however if answered from state of the art current existing knowledge on it also a highly political one … as iSpace theory on exact constants of nature and integer geometry clearly is able to show with its derivation of 4 simple first order multiplicative integer geometric entities (for by now 50+ constants of nature, like c, e, h, QHR, KJ, FSC alpha, me, a0, re, R, …, G, H0, …)
Just as some examples the true inner geometric nature of speed of light c, electron charge e - and with respect to your question - the exact electron mass me from iSpace theory (ime) and its (mathematically - geometric) 6D reasoning of an overall 10D spacetime is clearly shown (simply follow the 40+ simple multiplicative equations in the following breakthrough paper of iSpace theory, with derivation and necessary proof of existence of the quantum of time (!):
Method iSpace - Quick check of α and Φ0 from Markoulakis & Antonidakis
Preprint iSpace - Quantization of Time in iSpace-IQ Unit-System by 1/...
Also checkout the following brief poster and its link, leading to TEGS 2025 Budapest conference (where it happens myself to have been invited to be the keynote speaker on iSpace theory of exact constants of nature having recently derived and present a 1:1 Volt unit replacement for the Boltzmann constant kB Kelvin unit changing a lot - if not everything):
Poster TEKNET CONFERENCE Budapest Hungary
Poster TEKNET EARTH GLOBAL SCIENCE CONFERENCE 2025
Dear Adam Nasser, thank you very much for your response and for taking the time to analyze the question so thoroughly. I especially appreciate the clarity with which you explain the standard position and the openness with which you mention other possible interpretations. I truly value your comments.
For Gurcharn Singh Sandhu:
Thank you very much for your clear and thought-provoking response. I found your model of the electron as a rotating solitonic wave in a quantum medium especially interesting, as well as the way you explain properties such as spin and the electric and gravitational fields based on this structure. I also truly appreciate the articles you’ve shared — I will read them carefully to better understand your approach. I sincerely value the time and depth with which you’ve contributed to this discussion.
For Christian G. Wolf:
Thank you very much for your response and for taking the time to share such a rich and well-documented perspective. I also appreciate the articles and materials you linked — I will read them with interest to better understand the foundations of iSpace theory. Although I personally tend to favor explanations based on the fewest possible assumptions, I find it especially interesting that your model aims to derive universal constants from a mathematical basis. I truly value your contribution to this exchange of ideas.
Ricard Desola Mediavilla „I find it especially interesting that your model aims to derive universal constants from a mathematical basis.“ … iSpace doesn‘t just „aim“ to derive exact value and integer geometry of (by now 50+) constants of nature - it *did* so - and long ago as published at Wolfram NKS-2012 and prague IMS-2015 conferences.
And it did so identifying and referring to the following 4 base quanta in the 4 electrical base units one will physically ever need:
1) GoldenRatio iSpaceAmpere - the quantum of iSpaceAmpere (and Ampere!)
2) 1/6961 iSpaceSecond - the quantum of time (effectively discretizing everything else)
3) 6 iSpaceVolt - the quantum of iSpaceVolt
4) GoldenRatio iSpaceMeter - the quantum of distance (not at all the same as a quantum of length, like say assumed SI Planck-length by most others, actually being unphysical and not even defined precisely enough before).
And simple multiplicative powers of these four base quanta is all one needs to derive all (?, by now 50+) constants of nature including Planck-constants (!) in multiple unit systems like physical 1:1 native iSpace-IQ or 100% lab value compatible iSpace-SI units, yet with a first of zero unit pressure - ever - so far, possible due to iSpace model intrinsic unique zero error bar base quanta (multiplied), of course including all prominent FSC alpha and most important likewise exact Newtonian G:
Conference Paper iSpace - Deriving G from α, e, R∞, μ0 and Quantum of Gravita...
Conference Paper iSpace - Exact Symbolic Equations for Important Physical Con...
Preprint Hubble constant H0 is derived from Newtonian gravitational c...
Article New novel physical constants metric and fine structure const...
- Badges
- Science topic
- Similar topics
- Mathematics