8-shaped Electromagnetic Standing Wave + Eigen Drift Electron Structure

Abstract

Current theories often attribute the core physical properties of electrons to unexplainable "Eigen attributes," avoiding their true physical structure and dynamic mechanisms, making it difficult to resolve certain foundational theoretical paradoxes self-consistently. Based on electromagnetic waves and standing wave physics, this paper proposes an electron structure model centered on the 8-shaped electromagnetic standing wave topological structure as the carrier and Eigen drift motion as the core driver. The formation and Eigen drift motion of this model serve as the origin of all core physical properties of electrons. In the absence of external fields, it externally exhibits spherical symmetry, uniform electrical properties, and no magnetism. Under external fields, the Eigen drift of the standing wave cluster becomes constrained and directionally distorted, simultaneously revealing a magnetic axis, magnetic moment, and electrical non-uniformity. This model, within a minimalist electromagnetic framework, unifies explanations for the electron's negative charge, 1/2 spin, and other core properties, resolves related theoretical paradoxes, and proposes multiple typical and feasible experimental predictions. It provides a clear path for future experimental exploration of the electron's microscopic spatial structure and Eigen motion mechanisms, establishing a concrete, self-consistent foundational physical system for electrons.

 Keywords:  Electronic structure; Eigen electron drift; 8-shaped standing wave; Spin 1/2; Electronegativity; Superluminal paradox

1.0 Introduction

 The electron is a central subject of study in low-energy atomic physics, quantum optics, and particle physics. For a long time, its microscopic description has relied on the foundational framework of a point particle without spatial extension [1]. Since the establishment of the quantum mechanics system, physical characteristics such as the electron's negative charge, s=1/2  spin, and Eigen magnetic moment have been classified as inherent properties requiring no exploration of their underlying origins [2]. Such phenomenological treatments merely attribute observed phenomena to "pure quantum effects," avoiding the microdynamic origins, which has led to a series of long-standing theoretical puzzles: The existing framework cannot provide intuitive physical explanations for the origin of the electron's negative charge or its 720° phase restoration behavior during spin rotation. The superluminal contradiction arising from classical rotation models remains unresolved [3]. Descriptions of electron magnetic moment orientation and dynamic electrical responses under external fields rely solely on abstract quantum state projection operations, lacking concrete spatial field structures as physical support. These theoretical shortcomings not only hinder in-depth exploration of the electron's microscopic nature but also leave traditional theoretical systems devoid of quantitative predictions directly testable by experiments, deviating significantly from the core research goal of physics: "unifying microscopic structure, dynamic mechanisms, and observable properties."

Quantum mechanics, as a mature low-energy effective theory, can accurately reproduce a vast array of experimental observations such as electron interference and diffraction, spin statistics, and atomic energy level splitting. However, its theoretical boundaries and inherent limitations cannot be overlooked. The theory posits charge, spin, and wave-particle duality as fundamental postulates, yet it fails to explain the microscopic origins of these properties from first principles. Additionally, foundational challenges such as the ambiguous physical picture of wave function collapse, the inherent conflict between quantum nonlocality and local causality, and the difficulty in reconciling the theoretical framework with general relativity all demonstrate its incomplete capacity to resolve the Eigen spatial structure of microscopic particles. The fragmented physical picture of spin is the most notable shortcoming of this framework: standard quantum theory stipulates that all s=1/2  fermions (electrons, protons, neutrons, muons, etc.) possess identical total spin angular momentum  S=ss+1 ​ℏ  = 32ℏ . However, there are orders-of-magnitude differences in the rest mass, Eigen magnetic moment, and rest energy parameters among different fermions [2]. Relying on the classical logic of electromagnetic current loops and angular momentum, physical systems with vastly different rest masses cannot exhibit identical Eigen rotational angular momentum. Current theories merely use the phenomenological Landé g-factor to fit the magnetic moment deviations of different particles, failing to establish a unified dynamical relationship between mass, angular momentum, and electromagnetic response [4]. This long-standing divergence in foundational logic indicates that spin is not merely an abstract algebraic quantum number; its physical roots correspond to genuinely existing internal current loop fields and spatial topological structures within particles.

To alleviate the aforementioned theoretical dilemmas, this paper focuses on the electronic microscopic topological structure for systematic research, eliminates irrelevant extended topics, and proposes a three-dimensional closed spherical electromagnetic standing wave coupled 8-shaped double magnetic vortex electron model. This model weakens core a priori assumptions in quantum mechanics such as point particles and wave function probability interpretations [1]. All derivations are constructed based on classical electromagnetic dynamics, standing wave constraints of electromagnetic waves, topological geometric rules, and relativistic electromagnetic wave propagation effects, belonging to a first-principles qualitative topological framework rooted in Maxwell's electromagnetic equations [4]. Relying on electromagnetic vortex chirality and standing wave eigen dynamics, this paper does not require the introduction of any Eigen property postulates to fully derive all core physical properties of electrons: explaining the origin of electronegativity through vortex chirality symmetry breaking, restoring the physical image of 1/2  spin using standing wave topological phase cycling laws, unifying the description of magnetic moment and electrical dynamic changes through the directional coupling mechanism of vortices under external fields, and eliminating the classical superluminal rotation paradox at its root [3]. For the unresolved wave function collapse problem in quantum mechanics, this model provides a physical explanation traceable to electromagnetic topology: collapse is essentially caused by external electromagnetic disturbances altering the eigen drift motion of the 8-shaped standing wave clusters, driving deterministic spatial rearrangement of the standing wave distortion symmetry axis, rather than the instantaneous random probability transition described by traditional theories.

This model is compatible with all experimentally verified conclusions of electronic quantum observations, covering core phenomena such as wave-particle duality, charge quantization, 1/2  spin, and the long-range spherically symmetric Coulomb electric field distribution. At the level of physical mechanisms, this paper transforms the untraceable "Eigen properties" in quantum theory into electromagnetic field dynamic behaviors that can be topologically modeled and deduced, filling the gap in existing effective theories that merely reproduce observations without explaining microscopic origins. Addressing the experimental limitations of traditional precision measurement devices such as Penning traps, which are interfered with by strong DC magnetic field noise, making it difficult to resolve the electron's peripheral extended standing wave field and measure the electron's equivalent spatial scale [5], this paper proposes multiple feasible and falsifiable experimental predictions for attosecond scattering and atomic spectral dynamic detection based on the standing wave topological model, providing clear and actionable technical pathways for subsequent experimental validation.

 This paper aims to construct a self-consistent and complete microscopic spatial topological image of the electron, establishing a logically coherent and fundamentally concise electromagnetic standing wave theoretical framework, offering a new unified paradigm for low-energy microscopic particle physics research.

1.0 Introduction

 The electron is a central subject of study in low-energy atomic physics, quantum optics, and particle physics. For a long time, its microscopic description has relied on the foundational framework of a point particle without spatial extension [1]. Since the establishment of the quantum mechanics system, physical characteristics such as the electron's negative charge, s=1/2  spin, and Eigen magnetic moment have been classified as inherent properties requiring no exploration of their underlying origins [2]. Such phenomenological treatments merely attribute observed phenomena to "pure quantum effects," avoiding the microdynamic origins, which has led to a series of long-standing theoretical puzzles: The existing framework cannot provide intuitive physical explanations for the origin of the electron's negative charge or its 720° phase restoration behavior during spin rotation. The superluminal contradiction arising from classical rotation models remains unresolved [3]. Descriptions of electron magnetic moment orientation and dynamic electrical responses under external fields rely solely on abstract quantum state projection operations, lacking concrete spatial field structures as physical support. These theoretical shortcomings not only hinder in-depth exploration of the electron's microscopic nature but also leave traditional theoretical systems devoid of quantitative predictions directly testable by experiments, deviating significantly from the core research goal of physics: "unifying microscopic structure, dynamic mechanisms, and observable properties."

Quantum mechanics, as a mature low-energy effective theory, can accurately reproduce a vast array of experimental observations such as electron interference and diffraction, spin statistics, and atomic energy level splitting. However, its theoretical boundaries and inherent limitations cannot be overlooked. The theory posits charge, spin, and wave-particle duality as fundamental postulates, yet it fails to explain the microscopic origins of these properties from first principles. Additionally, foundational challenges such as the ambiguous physical picture of wave function collapse, the inherent conflict between quantum nonlocality and local causality, and the difficulty in reconciling the theoretical framework with general relativity all demonstrate its incomplete capacity to resolve the Eigen spatial structure of microscopic particles. The fragmented physical picture of spin is the most notable shortcoming of this framework: standard quantum theory stipulates that all s=1/2  fermions (electrons, protons, neutrons, muons, etc.) possess identical total spin angular momentum  S=ss+1 ​ℏ  = 32ℏ . However, there are orders-of-magnitude differences in the rest mass, Eigen magnetic moment, and rest energy parameters among different fermions [2]. Relying on the classical logic of electromagnetic current loops and angular momentum, physical systems with vastly different rest masses cannot exhibit identical Eigen rotational angular momentum. Current theories merely use the phenomenological Landé g-factor to fit the magnetic moment deviations of different particles, failing to establish a unified dynamical relationship between mass, angular momentum, and electromagnetic response [4]. This long-standing divergence in foundational logic indicates that spin is not merely an abstract algebraic quantum number; its physical roots correspond to genuinely existing internal current loop fields and spatial topological structures within particles.

To alleviate the aforementioned theoretical dilemmas, this paper focuses on the electronic microscopic topological structure for systematic research, eliminates irrelevant extended topics, and proposes a three-dimensional closed spherical electromagnetic standing wave coupled 8-shaped double magnetic vortex electron model. This model weakens core a priori assumptions in quantum mechanics such as point particles and wave function probability interpretations [1]. All derivations are constructed based on classical electromagnetic dynamics, standing wave constraints of electromagnetic waves, topological geometric rules, and relativistic electromagnetic wave propagation effects, belonging to a first-principles qualitative topological framework rooted in Maxwell's electromagnetic equations [4]. Relying on electromagnetic vortex chirality and standing wave eigen dynamics, this paper does not require the introduction of any Eigen property postulates to fully derive all core physical properties of electrons: explaining the origin of electronegativity through vortex chirality symmetry breaking, restoring the physical image of 1/2  spin using standing wave topological phase cycling laws, unifying the description of magnetic moment and electrical dynamic changes through the directional coupling mechanism of vortices under external fields, and eliminating the classical superluminal rotation paradox at its root [3]. For the unresolved wave function collapse problem in quantum mechanics, this model provides a physical explanation traceable to electromagnetic topology: collapse is essentially caused by external electromagnetic disturbances altering the eigen drift motion of the 8-shaped standing wave clusters, driving deterministic spatial rearrangement of the standing wave distortion symmetry axis, rather than the instantaneous random probability transition described by traditional theories.

This model is compatible with all experimentally verified conclusions of electronic quantum observations, covering core phenomena such as wave-particle duality, charge quantization, 1/2  spin, and the long-range spherically symmetric Coulomb electric field distribution. At the level of physical mechanisms, this paper transforms the untraceable "Eigen properties" in quantum theory into electromagnetic field dynamic behaviors that can be topologically modeled and deduced, filling the gap in existing effective theories that merely reproduce observations without explaining microscopic origins. Addressing the experimental limitations of traditional precision measurement devices such as Penning traps, which are interfered with by strong DC magnetic field noise, making it difficult to resolve the electron's peripheral extended standing wave field and measure the electron's equivalent spatial scale [5], this paper proposes multiple feasible and falsifiable experimental predictions for attosecond scattering and atomic spectral dynamic detection based on the standing wave topological model, providing clear and actionable technical pathways for subsequent experimental validation.

 This paper aims to construct a self-consistent and complete microscopic spatial topological image of the electron, establishing a logically coherent and fundamentally concise electromagnetic standing wave theoretical framework, offering a new unified paradigm for low-energy microscopic particle physics research.

2.0 Blind Spots in Existing Theories Explaining Electrons

 This chapter systematically outlines the core blind spots in current mainstream theories regarding the explanation of fundamental physical properties of electrons, providing a problem-oriented background for the  8-shaped electromagnetic standing wave + Eigen drift electron structure model  proposed in this paper [1,2].

2.1 The Theoretical Nature of Charge

Dual Paradox from Eigen Attributes to Classical Models: Charge is defined as an "Eigen attribute" of electrons, providing only experimental values without clarifying the origin of electrical properties or the mechanism of quantization [1]; the classical charged sphere model suffers from the self-repulsion tearing paradox, failing to resolve the structural collapse caused by electrostatic tension [4,6].

2.2 Misconceptions in Spin Cognition

Confusion Between Externally Induced Appearance and Eigen Hidden States: It is commonly assumed that electron spin is a fixed rotational orientation that exists at all times, misinterpreting the observed phenomena under external fields as the electron's Eigen normal state. This fails to explain the physical essence of free electrons lacking definite spin orientations [2,3].

2.3 The Fallacy of Point Particles

The point particle model cannot account for the non-fragmenting nature of electrons under high-energy collisions, nor reconcile the scale contradiction between "point particles" and Compton wavelength, lacking a dynamical description of the electron's Eigen structure [1,7].

2.4 Steady-State and Lifespan Mechanisms

Fails to distinguish between the two independent physical laws of "external impact stability" and "spontaneous decay energy level stability," and does not clarify the Eigen mechanism of electrons as the lowest energy steady state[1,8].

2.5 Spin Superluminal Paradox

The classical rotation model directly conflicts with the relativistic speed of light limit. Current theories merely avoid the issue through qualitative descriptions of "spin non-classical rotation," without providing a self-consistent physical mechanism explanation[2,3].

2.6 Orientation of Electrical and Magnetic Properties Under External Fields

Existing theories treat the electron's negative charge and magnetism as independent attributes, unable to explain the coordinated dynamic process under external fields where the electron's magnetic axis manifests, magnetic moments synchronously generate, and charge distribution changes[2,4].

All the dilemmas listed above, along with others, will be perfectly explained one by one by the new theory[7].

3.0 Electron Core Structure Model

3.1 Material Basis of Electrons—Electromagnetic Waves

Numerous experiments, such as the production of electron-positron pairs and the annihilation of high-energy photons into material particles, clearly reveal the objective law of bidirectional conversion between radiant energy and material particles without a medium.

The experiment of electron pair generation by high-energy γ photons bombarding atomic nuclei is the most direct empirical evidence of this law: a single photon with energy higher than 1.022 MeV, under the influence of the Coulomb field of a heavy atomic nucleus, can directly transform into a pair of positive and negative electrons. The radiant energy originally existing in the form of electromagnetic waves directly condenses into material particles with rest mass. Conversely, during the annihilation of positive and negative electrons, the physical form of the particles completely dissolves, with all rest mass converting into two or more photon electromagnetic waves, completing the full reversion of matter into radiant energy. In high-energy accelerator collision experiments, the kinetic energy of colliding high-energy electrons and protons is largely converted into γ-ray photons and new lepton particles. Additionally, phenomena such as stellar gamma radiation in cosmic space and the frequent occurrence of particle pair generation by high-energy cosmic ray photons in interstellar fields repeatedly confirm the bidirectional conversion characteristics between field energy and material entities.

 Based on the aforementioned experimental facts, this study proposes a core hypothesis: electromagnetic waves constitute the material foundation of electrons. Electrons are not "rigid mass points" unrelated to field energy but rather localized material forms of field energy under specific conditions. This hypothesis provides a unified physical premise for subsequent explanations of the structure and characteristics of electrons.

3.2 Basic Structure of Electrons—Electromagnetic Wave Standing Wave Clusters

Based on the aforementioned experimental conclusions, electromagnetic waves constitute the material foundation of electrons. Free traveling electromagnetic waves continuously disperse energy outward and do not possess localized particle forms; the material form corresponding to electrons is spatially localized, self-constrained electromagnetic standing waves[7].

This study proposes that the fundamental structural unit of an electron is an 8-shaped topology formed by a single-cycle electromagnetic standing wave. Multiple sets of 8-shaped topological standing wave units are arranged concentrically and uniformly, mutually coupled to form an electromagnetic standing wave cluster, which constitutes the complete internal structure of the electron.

The standing wave cluster achieves localized energy constraints and structural dynamic stability through a self-consistent closed-loop topology, suppressing energy dissipation and spontaneous radiation. Thus, electrons are not geometric point particles without internal structure; their essence is a clustered topological structure formed by the coupling of three-dimensional closed 8-shaped single-cycle electromagnetic standing waves. This system is named the Electron 3D Closed Figure-8 Single-Cycle Electromagnetic Standing Wave Cluster Model (abbreviated as the E8SW Model).

This standing wave cluster can maintain localized steady states over extended periods, and its underlying supporting logic can extend to a universal physical law applicable to matter evolution across all scales: the recursive mechanism.

The electromagnetic standing wave clusters described in this paper precisely satisfy the logic of recursion, where recursive coupling is a universal underlying physical law that enables the stable existence of objective matter. From microscopic elementary particles to macroscopic celestial systems, and from inorganic condensed systems to organic life units, the core Eigen logic allowing various forms of matter to stably persist over time is rooted in recursive principles. Through self-organizing evolution driven by recursion, material systems form self-sustaining constraints, avoiding structural dispersion and disintegration, which constitutes the inherent foundational law of material persistence.

 If interactions with the external environment precisely match the boundary conditions of recursive self-consistency, the system can converge into a stable configuration through bidirectional recursive evolution, achieving long-term persistence. All material components and their induced local fields uniformly follow the bidirectional recursive logic of "source evolution generating fields, and fields reversely constraining sources." Through multiple rounds of self-consistent iterative convergence, they construct steady-state spatial structures, thereby escaping instantaneous dispersion of energy and structure. The spatial configuration of electron-internal standing wave clusters is a concrete manifestation of this universal recursive law at the microscopic electromagnetic scale.

Figure 1. Schematic Diagram of the Evolution from Electromagnetic Waves to Figure-8 Standing Wave Clusters

3.3 Internal States of Electrons—Eigen Drift Motion

The previous section discussed that the most fundamental composition of electrons is electromagnetic standing wave clusters. Here, it must be emphasized that electromagnetic standing wave clusters are composed of energy fields and should possess ideal symmetry in spatial form.

Dynamic Symmetry Breaking of Static Configurations under Global Symmetry

Classical physics conclusions can corroborate:A globally symmetric system exhibits dynamic symmetry-breaking effects in static configurations—A field system with ideal global spherical symmetry lacks static stable equilibrium points, and all static symmetric configurations will spontaneously collapse. Only through continuous global dynamic motion to counteract internal field tension can long-term mechanical balance be achieved[6].

At the electromagnetic level, Earnshaw's theorem rigorously proves that relying solely on static Coulomb electric fields cannot achieve static stable confinement of charged systems or field energy. Dynamic oscillations and drifts are necessary conditions for the self-sustained confinement of field energy[6]. The dynamical stability theory of gravitational systems indicates that purely static spherically symmetric self-gravitating fluid stars become unstable under minor perturbations. Stars rely on dynamic motions such as rotation and pulsation to counteract internal pressure tension for long-term survival[8]. The theoretical contradictions of classical atomic models also confirm this principle: stationary electrons cannot balance nuclear Coulomb attraction, and only orbital dynamic motion can temporarily avoid structural collapse. Static symmetric field systems possess an Eigen tendency to collapse[1]. A universal consensus in field theory demonstrates that energy field structures that macroscopically exhibit localized forms must, at the microscopic level, involve continuous dynamic balancing processes. Absolutely static symmetric fields cannot maintain long-term self-sustaining configurations.

 Eigen drift is the mechanism by which the internal standing wave clusters of electrons maintain equilibrium

  Based on the established physical laws above, this paper proposes an original deduction for the electromagnetic standing wave cluster model of electrons— Eigen Drift : An isolated electron standing wave cluster, under no external influences, due to the omnidirectional symmetry of its own structure, inevitably cannot exist in a completely static or rigid state. To achieve a mechanically stable state, the standing wave cluster must undergo omnidirectional (as illustrated: the standing wave cluster simultaneously satisfies uniform rotational motion along the X, Y, and Z axes within the coordinate system) uniformly accelerated curvilinear drift motion to attain relative stability. In other words, the standing wave cluster has no static steady state and can only exist in a dynamic steady state. During the drift process, when the drift resistance aligns with the cluster's inherent inertia, equilibrium is achieved. Due to the global symmetry of the standing wave cluster, this drift exhibits isotropic uniformity across the spherical region of its scanned trajectory. Thus, it is established that:  The electron structure comprises an 8-shaped electromagnetic standing wave combined with Eigen drift.

  Eigen drift forges the spherical envelope morphology of electrons

  Building on the electron's topological structure and the dynamics of Eigen drift described earlier, the omnidirectional closed-loop drift of the standing wave naturally sweeps out an equivalent spherical outer contour. This unique formation mechanism results in the electron lacking a rigid spherical surface. This equivalent spherical structure is the structural origin of various Eigen electron properties that deviate from classical physics.

Figure 2. Left panel: Decomposition of eigen drift directions for the standing wave cluster, with three orthogonal rotational axes (x, y, z) marked. Right panel: Schematic diagram of complete eigen drift dynamic superposition of the standing wave cluster.

It is precisely due to this unique standing wave cluster structure composed of electromagnetic waves and its exclusive eigen drift motion that a series of special characteristics of the electron are formed.

3.4 Electronegativity and Mass Generation

 Origin of Negative Charge:  Based on the previously described topology of the electron's figure-8 electromagnetic standing wave clusters, the characteristics of global eigen-drift dynamics, and the non-rigid spherical symmetry morphology, the generation mechanism of the electron's negative charge can be deduced. The continuous high-speed global eigen-drift of the standing wave clusters persistently distorts the waveform of the figure-8 units, inducing periodic spatial distortions in the standing waves. The electromagnetic oscillation components of the distorted standing waves undergo directional outward ejection. The alternating fields within the system dynamically balance with the standing wave clusters themselves. After the system converges to a stable self-sustaining configuration, a macroscopic negative electrostatic field naturally emerges at the periphery [4]. The physical origin of the negative charge lies in the symmetry-breaking induced by eigen-drift-driven standing wave distortions, coupled with the directional ejection of electromagnetic fields, resulting in a spatiotemporal evolution effect of the electromagnetic field. The following sections will comprehensively derive the formation logic of the electron's equivalent negative charge and its peripherally symmetric electrostatic field.

Figure 3. Schematic diagram of the negative electric field distribution of an electron. The gray dashed spiral denotes the instantaneous scanning trajectory of the standing wave cluster, and the pink arrows indicate the vector direction of the electrostatic field. The instantaneous distribution of the electrostatic field presents typical periodic groove-shaped density fluctuations.

Under the framework of this model, the globally uniform distribution of negative electricity in electrons is not the built-in physical negative point charge in classical electromagnetic theory. Instead, it emerges as a macroscopic equivalent field source resulting from the mutual constraints of Eigen drift, standing wave distortion, and directional electromagnetic field ejection, which collectively achieve mechanical equilibrium

. The Eigen drift vector of the standing wave clusters is highly uniform in spherical space and exhibits full isotropic symmetry. Combining this with Gauss's integral theorem for electrostatic fields, it can be inferred that the continuously directionally ejected electromagnetic components

form a stable flux along a closed spherical surface. The macroscopic negative electric field can be equivalently described as a spherically symmetric electrostatic distribution obtained by integrating a constant field over the spherical surface. In macroscopic electromagnetic observations, the system is overall equivalent to a unit negative charge field source. [[TAG_1]] Assuming the equivalent spherical envelope radius of the electron is R , the recursive closed-loop drift of standing waves excites a globally uniform instantaneous Eigen uniform strong vector field E0  within the sphere, with isotropic field distribution. Given the vacuum permittivity as ε0 , the transformation from microscopic internal fields to macroscopic equivalent charges and external fields is derived using Gaussian surface integration.

 The total electric flux through the closed spherical surface:

ΦE​=s  E0⋅dS=E0​s ​dS=4πR2E0​

 From Gauss's law for electrostatic fields ΦE=|qe|ε0 , combining these yields the equivalent charge quantity of the electron:

qe=-4πε0R2E0

 where the negative sign corresponds to the electron's negative charge property. In the region outside the spherical surface r>R , the macroscopically observed electrostatic field is:

Er=-qe4πε0r2=4πε0R2E04πε0r2=E0R2r2

Er=-E0R2r2er     (r>R)

er  is the radial unit vector in spherical coordinates, pointing outward from the center of the sphere; the negative sign indicates that the electric field points toward the center of the sphere.

 The direction of the electron's electrostatic field is determined by the combined chirality of the figure-8 standing wave knot and the Eigen drift.

 From this, it follows that under this model,  the negative charge of the electron is a cumulative result of the uniform scanning of the electric field after time-averaging. It is not a statically uniform electric field.  The electric field is rooted in the topological transformation of the internal electromagnetic field of the electron.

 Chirality determines electrical polarity:  Here, chirality refers to the topological direction of circulation rotation of the figure-8 standing wave knot, which only exists in two mirror configurations—left-handed and right-handed. The bound Eigen drift vector corresponds to the clockwise and counterclockwise rotational orientations of the three-dimensional X/Y/Z axes.

 The topological chirality of the standing wave and the Eigen drift vector jointly determine the direction of the particle's external electric field, distinguishing between positive and negative charges. This is the topological origin of the electron's constant possession of a fixed negative charge. 

Figure 4. Schematic diagram illustrating circulation direction and chirality of figure-8 standing wave clusters, where the left panel shows counterclockwise rotating standing waves and the right panel shows clockwise rotating standing waves with identical waveforms but opposite vector rotation directions.

 Source of Mass:  Based on the proposed electron 8-shaped standing wave structure and Eigen drift characteristics in this paper, the total confined energy within the electron can be decomposed into three independent components: the electrostatic field energy within the spherical equivalent envelope domain, the bound electromagnetic energy carried by the 8-shaped standing wave itself, and the overall kinetic energy corresponding to the global Eigen drift vector. These three types of energy are constrained by the topological recursive field, fully confined within the equivalent spherical boundary without energy leakage or dissipation. Substituting the total confined energy into the mass-energy equivalence equation allows the derivation of the equivalent rest mass of the electron, achieving a complete self-consistent derivation from the microscopic standing wave field structure to the particle's inertial mass.

EE=v 12ε0E02dV=23πε0R3E02

E1=EE+EB+Ek

m=Etc2

Et : Total confined energy within the electron

EE : Electrostatic field energy within the sphere

EB : Bound electromagnetic energy of the 8-shaped standing wave

Ek : Eigen drift kinetic energy

m : Equivalent rest mass of the electron.

 In summary, this model achieves a field-theoretic decomposition of the electron's rest mass: the particle's inertial mass is not an independent Eigen parameter but an equivalent macroscopic manifestation of the superposition of internal electrostatic energy, standing wave bound electromagnetic energy, and Eigen drift kinetic energy under topological constraints [4], providing a quantifiable field-theoretic framework for the geometric-topological origin of microscopic particle masses.

Figure 4. Schematic diagram illustrating circulation direction and chirality of figure-8 standing wave clusters, where the left panel shows counterclockwise rotating standing waves and the right panel shows clockwise rotating standing waves with identical waveforms but opposite vector rotation directions.

 Source of Mass:  Based on the proposed electron 8-shaped standing wave structure and Eigen drift characteristics in this paper, the total confined energy within the electron can be decomposed into three independent components: the electrostatic field energy within the spherical equivalent envelope domain, the bound electromagnetic energy carried by the 8-shaped standing wave itself, and the overall kinetic energy corresponding to the global Eigen drift vector. These three types of energy are constrained by the topological recursive field, fully confined within the equivalent spherical boundary without energy leakage or dissipation. Substituting the total confined energy into the mass-energy equivalence equation allows the derivation of the equivalent rest mass of the electron, achieving a complete self-consistent derivation from the microscopic standing wave field structure to the particle's inertial mass.

EE=v 12ε0E02dV=23πε0R3E02

E1=EE+EB+Ek

m=Etc2

Et : Total confined energy within the electron

EE : Electrostatic field energy within the sphere

EB : Bound electromagnetic energy of the 8-shaped standing wave

Ek : Eigen drift kinetic energy

m : Equivalent rest mass of the electron.

 In summary, this model achieves a field-theoretic decomposition of the electron's rest mass: the particle's inertial mass is not an independent Eigen parameter but an equivalent macroscopic manifestation of the superposition of internal electrostatic energy, standing wave bound electromagnetic energy, and Eigen drift kinetic energy under topological constraints [4], providing a quantifiable field-theoretic framework for the geometric-topological origin of microscopic particle masses.

 5.0 Interpretation of Electronic Properties in the Absence of External Fields

 5.1 The Physical Essence of Electron Indivisibility

 High-energy particle collision experiments confirm that protons and neutrons can fragment into secondary particles such as quarks and gluons under ultra-high-energy bombardment, indicating their composite structure. However, in collision experiments across accelerators ranging from low-energy to TeV energy levels, electrons have never been split or fragmented into smaller secondary components. The Standard Model classifies electrons as fundamental point particles but fails to explain the Eigen reason why "electrons cannot be shattered" from a physical structural perspective. Based on the figure-eight continuous electromagnetic standing wave model, a self-consistent physical explanation can be provided from the origin of field structure:

 The electron as a whole is composed of a continuously distributed closed electromagnetic standing wave field. It contains no discrete solid material points, dense hard cores, or discrete subunits with chemical bonds between components. There are no rigid interfaces where high-energy collisions could generate localized stress fractures.

 Comparative Analysis of Composite Hadron Fragmentation Mechanisms:  Protons and neutrons are composite structures formed by quarks bound through strong interactions, with strong interaction binding energy existing between their components. When the energy input from high-energy collisions exceeds the binding threshold, the binding bonds break, leading to particle disintegration and fragmentation.

 Electron Standing Wave Anti-Fragmentation Mechanism:  The electron is a globally continuous coupled "8"-shaped topological standing wave field, lacking physical segmentation boundaries across its domain. High-energy collision input does not split the field's Eigen structure. Instead, the energy is absorbed across the entire standing wave domain, causing field deformation, energy dispersion, or conversion into new particles such as photons and electron-positron pairs. The original electron's topological standing wave structure does not fragment into smaller "sub-electrons" [1,7].

 5.2 Electron Near-Field Asymmetric Electric Field and Far-Field Spherically Symmetric Coulomb Field

 This model resolves the physical contradiction of electrons exhibiting "near-field distortions and far-field spherical symmetry" by clarifying the scale-dependent mechanisms of field distribution: Electron near-field (picometer scale): The "8"-shaped standing wave structure results in non-uniform charge and field strength distributions, with significant field strength gradients and density variations. The electric field lacks spherical symmetry, and short-wavelength scattering can detect asymmetric signals.

 Electron far-field (macroscopic scale): Local asymmetric electric fields undergo spatial superposition and averaging over large distances, ultimately manifesting as a uniform, spherically symmetric Coulomb field, perfectly aligning with classical electrostatic observations [4].

5.3 Electrons Have No Physical Volume, No Classical Radius, Yet Possess Collision Cross-Sections

This model is based on the pure electromagnetic standing wave topology + Eigen drift electron structure, fundamentally resolving the physical contradiction of "having no classical radius yet possessing collision cross-sections."

• The Origin of No Physical Volume / No Classical Radius

Electrons are not composed of rigid, physical matter but are formed by a three-dimensional closed figure-8 electromagnetic standing wave field structure. They lack "physical boundaries" and "point radii" in the traditional sense. Therefore, any experiment attempting to measure their "hard volume" will only yield an equivalent "point particle" result.

• The Physical Essence of Collision Cross-Sections

During the Eigen drift motion of the electron's figure-8 standing wave, its near-field asymmetric electromagnetic field (picometer to sub-picometer scale) has a fixed spatial extension range. In particle collisions or photon scattering processes, the observed "collision cross-section" is not a geometric dimension of a physical entity but rather the effective interaction range between the electron's near-field electromagnetic field and incident particles/photons. This is an equivalent manifestation of electromagnetic interactions [1,7].

5.4 The Ultra-Long Lifetime of Electrons

Isolated free electrons can exist in a long-term steady state: The internal standing wave and topological confinement field rely on recursive self-consistent balance, with a fully closed loop structure preventing spontaneous energy leakage and spatial dispersion. The Eigen drift forms an endogenous self-consistent confinement field, ensuring no spontaneous dissipation of the particle's total internal energy and preventing the topological configuration from collapsing spontaneously. This mechanism explains the exceptionally long Eigen lifespan of free electrons.

The classical electrodynamics conclusion that "accelerating charged particles inevitably emit electromagnetic radiation and lose energy" applies only to distorted electrons whose recursive closed loops are disrupted by external fields and whose spherical envelope symmetry is broken. The field energy of ground-state closed-loop electrons is entirely confined by their topological structure, making them exempt from this radiation rule. Consequently, they do not undergo continuous radiative decay, and experimentally observed electrons exhibit nearly infinite lifetimes [4,6].

6.0 Interpretation of Electronic Properties under External Fields

6.1 Origin of Electron 1/2 Spin and Resolution of the Superluminal Paradox

• Electron 1/2 Spin

Electron spin is not a classical rigid-body mechanical rotation; its essence lies in the phase-recovery topological motion inherent to the figure-8 coupled electromagnetic vortices. The half-twist closed spatial topology is the Eigen structural origin of s=1/2  spin. In the absence of external fields, the spatial orientations of the vortices are random and disordered, and their macroscopic spin effects cancel each other, making them unobservable. When an external field breaks spatial symmetry and fixes the vortex orientation, the physical effects corresponding to

spin become apparent.

The figure-8 topology possesses a unique half-twist geometric property: when the spatial geometry rotates by 360⋄ , the vortex field phase reverses and cannot return to the initial configuration. Only after accumulating a rotation of 720⋄  can the field phase fully reset, completing a full topological cycle. Based on this topological constraint, the electron spin quantum number =1/2  can be directly derived from the geometric structure without additional phenomenological assumptions, naturally avoiding the superluminal paradox inherent in classical rotation models, ensuring self-consistent physical logic.

The textbook's spherical point particle spin is merely an equivalent approximation; the true configuration of the electron is an eight-shaped coupled closed standing wave, with dual separated magnetic axes replacing the single-point central magnetic axis. The half-integer spin quantum attribute is directly determined by spatial topology, naturally explaining experimental laws such as the binary value of spin and the Pauli exclusion principle, which classical physics cannot account for. Derivation process of 1/2 spin:

 Topological phase fundamental equation

Φθ+2π=-Φ(θ)Φθ+4π=Φ(θ)

 Wave function standard quantum formula

 Angular phase general solution of the vortex field in this model: Φθ=eisθ⋅Φ0 ,    s  is the spin quantum number.

 Substituted into θ→θ+2π

Φθ+2π=eis（θ+2π）Φ0=ei2πs⋅Φ(θ)

 combined with topological condition Φθ+2π=-Φθ=eiπ⋅Φ(θ) , therefore:

ei2πs=eiπ

2πs=π+2nπ⟹s=n+12

 Ground state  n=0 , s=12

Figure 6. Schematic diagram of the formation mechanism of spin-1/2 (two-cycle restoration model). The upper curves show the two-cycle time-domain evolution of the standing wave electric field inside the electron. The lower panels correspond to magnetic field phase variations: the magnetic pole maintains the initial orientation at 0° phase, pole reversal occurs at 180° phase, and the electron spin state restores after two complete electric field cycles (360° phase). This figure intuitively interprets the physical origin of the electron’s half-integer spin-1/2 characteristic.

• Resolution of the Superluminal Paradox

Within the framework of classical physics, if an electron is regarded as a rigid sphere with a finite geometric radius and an attempt is made to interpret the electron's 1/2 spin through rigid-body mechanical rotation, it leads to the conclusion that the linear velocity of surface points on the particle far exceeds the vacuum speed of light, violating the principle of the speed of light as the ultimate limit in special relativity. This is the classical superluminal paradox of electron spin, which is also the core reason why orthodox quantum mechanics abandons concrete structural models and defines spin as an "Eigen quantum property" without physical interpretation.

From a classical quantitative estimation: combining the experimentally measured spin angular momentum of the electron S≈ℏ/2  with the classical rigid-body angular momentum formula  S=Iω=25mer2ω , and then using the surface linear velocity v=ωr  to solve the equations, substituting the classical electron radius value for calculation, the final result for the electron's surface rotational linear velocity v≫c  exceeds the relativistic speed limit, rendering the classical rotation model physically invalid. Current quantum theories cannot resolve this contradiction at the microstructural level and can only avoid physical motion imagery by classifying spin as an Eigen quantum property that defies intuitive visualization, leaving a fundamental gap in physical logic.

In the figure-eight electromagnetic standing wave vortex model system, the aforementioned superluminal paradox can be eliminated at its root:

 Spin without physical mechanical rotation:  The point-like electrons observed in experiments are the statistical average equivalent effect of the rapidly evolving figure-eight electromagnetic vortices at the spacetime scale; the physical essence of spin is the unique topological phase evolution of the vortex field, not the rigid circular motion of a physical mass point around an axis. There is no physical concept of "particle surface linear velocity" since there is no physical spherical surface, fundamentally avoiding the premise of classical superluminal derivation.

 Angular momentum originates from electromagnetic field circulation:  The electron's spin angular momentum and Eigen magnetic moment entirely arise from the closed electromagnetic field circulation effects formed by the figure-eight coupled standing waves. The carrier of angular momentum is the diffuse electromagnetic field rather than a physical mass point. Electromagnetic waves themselves propagate at the vacuum speed of light c, and the phase evolution and circulation changes of the field strictly adhere to the speed of light constraint, eliminating the theoretical contradiction of superluminal field motion. The overall topological superposition of the circulation equivalently manifests a fixed spin angular momentum, perfectly aligning with various spin-related experimental observations [2,3].

 Based on this topological standing wave physical picture, there is no need to artificially introduce phenomenological Eigen assumptions. The model self-consistently resolves the century-old superluminal paradox plaguing classical spin models from the microscopic structural level.

6.2 Magnetic Axis Manifestation and Synchronous Magnetic Moment Generation

In the absence of an external field, the local magnetic axes and magnetic moment vectors of the figure-8 double vortices are oppositely aligned, canceling each other out macroscopically. When an external magnetic field is applied, the external torque alters the symmetric configuration of the double vortices, causing the two local magnetic axes to undergo vector superposition, forming a unified global magnetic axis aligned with the external field direction. The bidirectional coupled vortex topology and the evolution of deformation under external fields can be referenced in literature [2,3]. This topological constraint logic aligns with the orientation-locking mechanism of field-excited vortices.

Closed electromagnetic circulation inherently carries magnetic moments; the instant a vortex completes orientation locking, the geometrically defined magnetic axis and the electromagnetically induced magnetic moment synchronously form. Restricted by the standing wave topology, the system only exhibits two stable configurations: parallel or antiparallel to the external field, naturally matching the binary quantum states of electron spin. This fully explains the two-split observation in the Stern-Gerlach experiment while providing an intuitive physical picture of state collapse from the perspective of field configuration evolution. Discussions on classical field topology-based interpretations of spin quantization and comparisons with the limitations of classical magnetic dipole theory can be found in literature [1,4,5,6].

6.3 Electron Spin and the Landé g-Factor (g≈2)

Mainstream quantum mechanics can only numerically fit g≈2 without support from microscopic physical mechanisms. This model can accurately trace the origin from a structural level: the "eight-character double-loop" consists of two independent closed standing wave ring currents. A single-sided single loop corresponds to 1 Bohr magneton magnetic moment. After reverse coupling and balancing of the double loops, the effective magnetic moment superposition result strictly matches the high-precision experimental value of the electron spin g-factor ≈2, serving as the natural physical origin of this quantum parameter [2,4].

6.4 Attosecond Light Scattering Polarization-Differentiated Response

Based on the electron's near-field asymmetric and far-field uniform field distribution characteristics, attosecond light with different polarizations can exhibit differentiated scattering responses, forming a core verifiable feature of the model:

Linearly polarized attosecond light: Unidirectional illumination of the electron's asymmetric near-field causes significant differences in scattering deflection angles between strong and weak field regions. Scattering spots exhibit arc-shaped distortions accompanied by periodic left-right shifts;

Circularly polarized attosecond light: Omnidirectional illumination around the electron averages out asymmetric field effects. Arc-shaped distortions disappear, and spots restore to standard perfect circles [7].

7.0 Testable, Falsifiable Experimental Predictions

The current mainstream electronic point particle model treats electrons as point charges with no spatial dimensions, categorizing properties such as spin and magnetic moment as phenomenological Eigen parameters. Under this theoretical framework, no internal structured configuration of the electron is presupposed, thus making it impossible to derive corresponding observational predictions from a structural perspective.

 In contrast, the E8SW standing wave model proposed in this paper is grounded in the concrete topological structure of the electron, building on the theoretical conclusions from previous studies on Eigen drift and 8-shaped standing waves. It presents four physical predictions that can be experimentally tested, provides specific observational pathways, and satisfies the falsifiability criterion of scientific theories through verifiable predictions[1,5].

7.1 Capturing the Traces of Eigen Drift

The 8-shaped standing wave within the electron exists in athree-dimensional free, equally probable high-speed rotational state, with a rotational frequency (approximately1020 Hz) that far exceeds the temporal resolution of any current instrument. Conventional observations essentially involve "exposing" the electron over long durations and multiple cycles, capturing only the statistical average of all possible orientations. Consequently, the electron appears as a perfectly spherically symmetric point particle with no internal structure.

Experimental Verification of Electron Standing Wave Configuration via Laser Scattering

Assumptions

• High-energy scattering measurements indicater<10-18m the scale of the electron's core charge region, with the peripheral electromagnetic field extending in an 8-shaped standing wave distribution. The equivalent outer diameter is taken as the reduced Compton radiusrC≈3.86×10-13m ;
• The standing electromagnetic wave propagates along the loop at the speed of light c , with a standing wave oscillation frequency fw=c/(2πrc) ;
•  the Eigen drift rotation frequency of electrons is assumed to be 1/2  of the standing wave oscillation frequency, fd=fw/2 , and the Eigen period T≈16.1as  is calculated;
•  attosecond pulses with a pulse width of 5∼10as  are selected, ensuring that the pulse width is less than the Eigen drift period to freeze the instantaneous electric field configuration.

 Experimental Principle

 The electron is a high-speed Eigen drifting figure-8 electromagnetic standing wave, with a non-spherically static distribution of the local electric field. This experiment employs  narrow-pulse-width attosecond lasers, controlling the pulse width to be smaller than the Eigen drift rotation period of electrons . During the interaction between the attosecond laser pulse train and free electrons, photons are continuously deflected by collisions with the rotating electric field, forming curved trajectories in the scattered light path. The curvature and spatial distribution of photon arcs within the CCD acquisition area are used to reconstruct the internal field structure of the electron. By statistically analyzing a large number of single-electron scattering images, the superposition of arc lines yields a complete electron scattering image [7].

 Experimental Setup

•  Cold field emission electron source: Equipped with multi-stage magnetic collimating lenses to output parallel electron beams in a vacuum without external field constraints, preserving the electron's native standing wave structure.
•  Attosecond ultrashort pulse light source: Conventional attosecond pulse width ensures that the pulse duration is shorter than the electron's rotation period, guaranteeing that photons form complete deflection arcs without becoming entangled.
• Deep-cooled area CCD: Achieves two-dimensional full-field imaging of the scattering region, completely capturing the spatial distribution characteristics of all scattered photons.
•  High-vacuum optical system: The electron beam and laser beam intersect perpendicularly, ensuring precise spatial alignment without the need for temporal synchronization, and isolating environmental interference.

 Experimental Steps

•  Evacuate the chamber to high vacuum to eliminate air scattering interference;
•  The electron beam passes uniformly through the laser focal point, coupling with femtosecond laser scattering;
•  Scattered photons are deflected by the local field to form curved light paths. The CCD captures short-term imaging for each pulse and long-term integrated imaging across multiple pulses;
•  Analyze the imaging patterns and deflection behaviors, then fine-tune the electron incidence direction for repeated comparative tests.

 Evaluation Criteria

•  Long-term integrated light spots exhibit regular circular shapes; single-pulse imaging shows discrete arc-shaped traces with asymmetric spot distortion;
•  Scattering arc curvatures display fixed orientations, confirming Eigen electron drift and vortex rotation direction;
•  Adjusting the electron incidence angle causes synchronized overall arc deflection, ruling out random noise interference.

 Feasibility Explanation

 The imaging detection system in this experiment (full-field imaging CCD, electron source, vacuum optical path) consists of mature commercial equipment. The experiment only requires the use of a well-established attosecond ultra-short pulse light source. Attosecond lasers can meet the requirement of instantaneous snapshots of the electron's Eigen period. Although not yet widely commercialized, they can be implemented through national-level advanced photophysics facilities. The experimental principle is self-consistent and highly reproducible, effectively verifying the electron's figure-8 standing wave topological structure [7].

Figure 7. Schematic diagram of the rotating standing wave trajectory plane inside an electron. The blue dashed lines represent the motion trajectories of numerous coupled figure-8 standing waves within the electron, and the outer contour defines the overall spatial boundary of the electron.

7.2 Disappearance of Electric Field Symmetry Breaking in Electrons Under External Fields

Both classical and quantum theories currently regard the negative charge of electrons as an inherent and ineliminable fundamental property, unable to explain the physical mechanisms behind the origin and regulation of electrical properties. This section, based on the topological model of the figure-8-shaped standing wave cluster, proposes a theoretical prediction that a strong critical external electric field can freeze the Eigen curved drift motion of electrons, eliminate electric field symmetry breaking, and achieve reversible regulation of electron charge. If the neutralization or even charge reversal of electrons can be observed through ultra-high-field experiments, it will directly verify the core hypothesis that "electron charge originates from the asymmetric motion of internal standing waves," providing decisive experimental evidence for clarifying the microscopic origin of charge, which holds fundamental research value at the level of particle physics.

Premise Assumptions

• The negative charge of electrons arises from the uniformly accelerated curved Eigen drift motion of their internal figure-8-shaped standing waves, which generates local symmetry breaking in the electric field, causing electrons to exhibit stable negative charge;
• When the external electric field strength reaches a critical valueEc  (Ec the magnitude is constrained by the electromagnetic standing waves and Eigen drift, with estimated values far exceeding those achievable by conventional methods), the external field force is sufficient to counteract the equivalent centripetal force of the standing waves, freezing their uniformly accelerated curved motion;
• After the standing wave motion is frozen, the electric field distribution regains global symmetry, and the negative charge of the electron disappears, manifesting as neutral particle behavior;
• When the external field strength exceeds the critical value, the standing wave circulation is driven in reverse, potentially leading to electron charge reversal[4,7].

 Experimental Principle

 The negative charge of electrons originates from the symmetry breaking of the electric field caused by the eigenmotion of standing waves. Under the action of an extremely strong external electric field, when the external field force balances the equivalent centripetal force of the standing wave, the standing wave motion is frozen, and the electric field distribution regains symmetry, causing the electron to lose its charge property. This experiment utilizes an ultra-intense laser field to provide an external electric field close to the critical strength. By observing the deflection behavior of electrons in the electric field, the variation of their electrical properties with external field strength is verified: when the electric field strength is far below the critical value, electrons behave as conventional charged particles, conforming to Lorentz deflection laws; when the electric field strength approaches the critical value, the effective charge of electrons diminishes, and the deflection angle exhibits nonlinear deviations; when the electric field strength reaches or exceeds the critical value, electrons no longer deflect, exhibiting neutral or anti-electric behavior.

 Experimental Setup

•  High-energy electron beam source: Provides a well-collimated, energy-stable monoenergetic electron beam, vacuum-sealed without external field constraints, preserving the native standing wave structure of electrons;
•  Electrostatic lens assembly: Comprising electrostatic concave lens + convex lens combinations for electron beam expansion, shaping, and collimation, optimizing beam uniformity;
•  Ultra-intense laser field system: Petawatt-class ultrashort pulse laser facility capable of delivering transient electric field strengths exceeding  1015V/m , with controllable field gradients and polarization directions;
• High-resolution particle detection system: High-precision particle position detectors (such as pixelated silicon detectors or microchannel plates) can accurately measure the deflection trajectory and distribution of electron beams;
•  Vacuum and synchronization control system: Ultra-high vacuum chambers eliminate gas scattering interference and achieve precise spatiotemporal synchronization between electron beams and laser pulses.

 Experimental Steps

•  Evacuate the chamber to high vacuum to eliminate environmental interference, and synchronize the electron beam with laser pulses in time and space;
•  Without laser field interaction, measure the deflection trajectory of the electron beam under a standard deflection electric field as a classical Lorentz deflection benchmark;
•  Activate the ultra-intense laser field, set different laser powers (corresponding to different electric field strengths), and sequentially measure the deflection angles and distributions of the electron beam under each field strength;
•  Alter the laser polarization direction and the duration of electric field interaction, repeat tests, and analyze the variation of electron deflection behavior with external field strength;
•  Compare experimental results with classical Lorentz deflection model predictions to identify nonlinear deviation signals.

 Evaluation Criteria

•  When the electric field strength is far below the critical value, the electron deflection trajectory fully aligns with classical Lorentz force predictions, exhibiting conventional charged particle behavior;
•  As the electric field strength increases, reproducible nonlinear deviations in electron deflection angles emerge, with the deviation magnitude escalating with rising field strength;
• Near the critical field strength, the electron beam deflection effect significantly weakens, with some particles exhibiting trajectory characteristics close to neutrality;
•  altering the laser polarization direction, the electron deflection deviation pattern changes synchronously, eliminating interference from instrument noise and systematic errors.

 Feasibility Explanation

 The electrostatic concave lens is solely responsible for electron beam shaping and cannot provide the extreme strong electric field required for the experiment. The highest instantaneous field strength achievable through current laser focusing still shows a significant gap compared to the theoretical critical field strength, making it temporarily impossible to observe the complete disappearance of electron charge properties. However, deflection anomalies near the critical region can be detected to obtain indirect evidence. The entire setup is constructed based on existing particle optics and ultra-strong laser technology, meeting the conditions for practical testing. Once higher-power laser equipment becomes available in the future, further approaches to critical conditions can be made for in-depth verification [4,7].

 7.3 Dynamic Spectral Shift Testing of Atoms Under External Magnetic Field Disturbance

Current high-energy scattering can only provide an upper limit on the scale of the electron charge distribution and cannot directly measure the true equivalent diameter of the electron's electromagnetic field extended structure. The external magnetic field spectral dynamic perturbation observation scheme proposed in this section, relying on the torsional modulation effect of the electron's Eigen standing wave under an external field, aims to invert the standing wave's eigenfrequency through periodic spectral fluctuation signals, thereby further solving for the electron's true spatial equivalent diameter. This scale, as a core fundamental parameter of the electron topological model, can fully link and derive a series of Eigen physical quantities such as spin magnetic moment, Eigen oscillation period, and electromagnetic field distribution. It provides direct spectroscopic evidence for verifying the figure-8 standing wave cluster electron model and holds critical value for fundamental physics research.

Premise Assumptions

• The Eigen standing wave structure of an electron, driven by magnetic torque in an external magnetic field, generates periodic torsional vibrations related to the magnetic field strength;
• these torsional vibrations periodically modulate the electron's instantaneous potential energy, causing minor dynamic fluctuations in atomic energy levels;
• the energy level fluctuations are directly reflected in atomic emission spectra as slight spectral line shifts and intensity instabilities.
• The period of torsional vibration is determined by the eigenfrequency of the electron's Eigen standing electromagnetic wave, which can be deduced from spectral fluctuation signals.
• The standing wave's eigenfrequency is directly related to the electron's equivalent diameter. By measuring the frequency, the electron's true spatial scale can be calculated, thereby obtaining the most crucial parameter of the electron and enabling the derivation of numerous other parameters.

Figure 8. Schematic diagram of left-right oscillation of eight-figure standing waves under external magnetic field. The vertical dashed lines represent uniform external magnetic field; the central vertical line denotes the oscillation axis of standing waves; the purple loops indicate eight-figure standing wave circulation; the red-blue rhombic markers show flux directions. The two groups of standing wave units on the left and right carry opposite flux polarities, forming a symmetric bidirectional oscillation structure induced by the external field.

Experimental Principle

The Eigen standing wave torsional vibration of electrons dynamically modulates atomic energy levels, thereby influencing the photon emission process during atomic transitions. This experiment employs high-resolution spectroscopic detection technology to observe changes in atomic emission spectra under an external magnetic field (including constant and alternating modulation). Under a constant magnetic field, the torsional amplitude increases with magnetic field strength, and the spectral line center exhibits nonlinear shifts. Under an alternating modulated magnetic field, the torsional vibration synchronizes with the modulation signal, causing periodic fluctuations in the spectral line center position and intensity. By analyzing the shift patterns and fluctuation frequencies of the spectral lines, the Eigen electromagnetic wave frequency of the electron's standing wave can be deduced, allowing calculation of the electron's equivalent diameter[5,7].

Experimental Setup

• Cold Atomic Beam Light Source System: Provides stable atomic transition spectral lines (e.g., hydrogen  Hα  line) with monochromaticity better than 10-8 , free from external interference;
• Controllable Magnetic Field System: Adjustable uniform magnetic field (0–1 T, uniformity better than 10-4 ), capable of superimposing a weak alternating modulated magnetic field at the  kHz   level to drive and control electron torsional vibration;
• High-Resolution Spectroscopic Detection System: Fourier transform spectrometer with resolution better than 10-9  + single-photon detector, capturing minute spectral line shifts and intensity fluctuations;
• Synchronous acquisition and analysis system: High-precision lock-in amplifier (time resolution < 1μs), correlating magnetic field modulation signals with spectral fluctuation signals to extract synchronous components and characteristic frequencies.

Experimental Steps

• Evacuate the cavity to high vacuum to eliminate environmental stray light and gas scattering interference;
• Cold atomic beam passes uniformly through the magnetic field and detection region, collecting baseline center wavelength, linewidth, and intensity of the target spectral line under zero field;
• Apply constant magnetic fields of varying intensities, sequentially collect static spectral data under each magnetic field strength, and record changes in center position and linewidth;
• Apply weak alternating modulation magnetic fields, synchronously acquire spectral signals and modulation magnetic field signals, and analyze dynamic fluctuation patterns of the spectral lines;
• Alter the atomic incident direction and magnetic field modulation frequency, repeat comparative tests to eliminate instrument noise and random interference.
• Calculate the equivalent electron diameter from the measured characteristic frequencies to complete quantitative value determination.

Determination Criteria

• Under constant magnetic fields, the spectral line center position exhibits reproducible minor nonlinear shifts as magnetic field strength increases;
• Under alternating modulation magnetic fields, the spectral line center position and intensity display periodic fluctuations synchronized with the modulation frequency;
• When altering magnetic field modulation frequency or atomic incident direction, spectral line fluctuation characteristics change synchronously, with no abnormal signals dominated by random noise.
• The characteristic frequency of spectral line fluctuations does not vary with magnetic field strength and is solely determined by the Eigen standing wave structure of the electron, with its reciprocal being the oscillation period of the figure-8 standing wave, which can directly infer the eigen electromagnetic wave frequency of the standing wave.
•  Based on the measured eigenfrequency, the equivalent diameter of the electron is calculated, obtaining the experimentally measured value of the electron's spatial scale.

 Feasibility Statement

 The experiment relies on mature cold atomic beam, high-resolution spectral detection, and phase-locked amplification technologies. Through zero-field control and comparisons under multiple magnetic field conditions, instrumental noise and physical signals can be effectively separated. The characteristic signals of spectral line shifts and fluctuations can be precisely extracted using a lock-in amplifier, and the measurement accuracy of their characteristic frequencies can meet the requirements for inferring the Eigen standing wave eigenfrequency and equivalent diameter of the electron. The experimental scheme is feasible under existing equipment conditions [5,7].

 7.4 Microscopic Qualitative Explanation of Superconductivity

 Based on the topological structure of the electron's figure-8 standing wave clusters, the superconducting state can be qualitatively described as follows: At the critical temperature, the lattice potential field strongly couples with the electron standing waves, achieving collective phase synchronization of the electron standing waves and eliminating lattice scattering. The relativistic distortion of the standing waves and magnetic field shielding jointly produce zero resistance and the Meissner effect. The quantitative mechanism will be derived in detail in a separate paper [1,4].

 8.0 Discussion

This chapter systematically analyzes the inherent limitations of existing electron measurement experiments from three dimensions: theoretical presuppositions, experimental frameworks, and detection scales. It elaborates on how the low-energy attosecond scattering scheme proposed in this study circumvents these defects, providing a new pathway for exploring the microscopic spatial structure of electrons.

8.1 A Priori Theoretical Constraints of Existing Electron Detection Systems

The vast majority of current electron measurement experiments are based on the point particle model, which assumes no internal extended structure. This hypothesis forms a closed-loop self-consistent logic across theory, instrumentation, and data interpretation, inherently shielding information related to the internal structure of electrons:

Theoretical level: Presupposing electrons as rigid point charges with no spatial distribution or Eigen electromagnetic fields, fundamentally excluding the theoretical possibility of electrons possessing Eigen topological structures;

Experimental design level: Mainstream measurement schemes such as electron magnetic moment and electron electric dipole moment (eEDM) are constructed with optical architectures and data fitting algorithms rooted in the point particle model;

Result interpretation level: Weak asymmetries and periodic modulation signals observed in actual measurements are preferentially attributed to systematic errors such as residual magnetic fields or instrument noise, rather than being ascribed to the spatial structural characteristics of electrons themselves.

This closed-loop logic of "theoretical presupposition – apparatus construction – data fitting" possesses strong self-verification attributes, which can only yield conclusions self-consistent with the point particle hypothesis, failing to objectively reflect the true field distribution morphology of electrons across the entire domain[1,2].

8.2 Prior Model Defects in Existing Electron Experiments

• Signal Discrimination Limitations in Strong Confinement Magnetic Field Architectures

Current spin precision measurements generally employ a dual-magnetic-field architecture consisting of a Tesla-level axial confinement main magnetic field + a millitesla-level perturbation field, which faces unavoidable signal suppression issues:

• Closed-Loop Self-Limiting Logic in Classical Precision Measurements

Traditional precision experiments represented by electron electric dipole moment (eEDM) measurements primarily aim to validate the standard model's point electron hypothesis, with the entire data processing workflow exhibiting significant self-limiting characteristics:

 This paper designs an attosecond scattering scheme with near-zero background magnetic fields and separated confinement and detection fields, eliminating the suppression of strong DC main magnetic field distortion noise, theoretically enabling the capture of optical periodic modulation signals induced by the internal 8-shaped standing waves of electrons [7].

•  Spatial scale mismatch in high-energy collision detection

 Traditional GeV-scale high-energy scattering experiments face a fundamental spatial resolution mismatch: the effective resolution scale of high-energy probe particles is far larger than the equivalent extended radius of the electron's outer standing wave field. Analogous to "measuring hair deformation with a weighbridge," this approach can only probe the point-like charge region at the electron's core, failing to resolve the outer extended electromagnetic standing wave structure. Consequently, long-standing observations conclude that electrons have no spatial size [1,7].

 8.3 Compatibility Boundaries Between This Model and Existing Experimental Systems

8 Combining the previous discussion on the standing wave electron topological framework, the existing experimental observations are not errors but conditional results constrained by three factors: detection conditions, prior models, and spatiotemporal resolution scales. Conventional observation methods with long durations, high background, and high-energy probes can only capture the statistically averaged state of electrons after rapid precession of the standing wave, presenting a perfectly spherical symmetric point-particle appearance. Only by using attosecond pulses with pulse widths shorter than the electron's Eigen drift period and low-energy scattering devices with near-zero magnetic fields is it possible to freeze the instantaneous standing wave configuration and directly observe the asymmetric topological structure within the electron[1,7].

9.0 Conclusion

 This paper systematically constructs a three-dimensional closed spherical electromagnetic standing wave model of the electron based on the fundamental principles of electromagnetic waves and standing wave physics. It elaborates on the internal  "figure-8 double magnetic vortex cluster"  topological structure and the Eigen drift motion mechanism that drives the core properties of the electron.

The model, based on minimalist electromagnetism, achieves a unified and self-consistent explanation of the key physical properties of electrons: in the absence of external fields, the electron's standing wave structure is isotropic, with internal magnetic fluxes canceling each other to exhibit no magnetism, while the fixed topological chirality manifests as a constant negative charge. Under external fields, the figure-8 magnetic vortices undergo directional distortion, synchronously revealing the magnetic axis and magnetic moment, with their topological characteristics directly unveiling the physical essence of the electron's 1/2 spin. This theory requires no redundant assumptions or additional parameters, fundamentally bridging the Eigen connection between electron structure and its physical properties.

 Building upon this, the paper proposes multiple typical and feasible experimental predictions, including attosecond laser scattering imaging of electron standing wave structures, dynamic perturbation observation of atomic spectra under external fields, and verification of electron charge variation trends under ultra-strong electric fields. These provide clear pathways and a solid theoretical foundation for future experimental exploration of electron microscopic spatial structures and validation of Eigen motion mechanisms.

 Simultaneously, the "recursive self-consistent coupling" principle proposed in this study—the bidirectional recursive evolution mechanism of "field generated by source, source bound by field" between matter's constituent units and the spatial fields they excite—not only provides foundational support for the electron standing wave system but also offers a novel approach for unifying research on stable matter configurations across all scales, from microscopic particles to mesoscopic condensed matter and macroscopic celestial bodies[1,7,8].

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[4] Jackson JD. Classical Electrodynamics, 3rd ed. John Wiley & Sons; 1998.

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[6] Earnshaw S. On the Nature of the Molecular Forces which Regulate the Luminiferous Ether. Trans Camb Phil Soc. 1842;7:97-112.

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