Particles Are Network Resonances: Why Electrons Are Not Little Balls

Physics’ Biggest Lie

Elementary school science tells us: Atoms are like solar systems, electrons orbit the nucleus like planets.

This is a beautiful lie.

Middle school chemistry tells us: Electrons are “clouds,” probability distributions on orbitals.

This is a lie closer to truth.

University quantum mechanics tells us: Electrons are wave functions, satisfying Schrödinger’s equation.

This is mathematically correct but physically incomplete truth.

What we reveal today is: Electrons are not “things” at all.

They are not little balls, not clouds, not even waves—they are resonance modes in information scattering networks.

Like notes on a guitar string, not “part of the string,” but “vibration patterns”.

Particles are patterns, not matter.

Act I: Scattering—The Dialogue of Everything

Before we begin, we need to understand a concept: scattering.

What Is Scattering?

Simplest example: You throw a tennis ball at a wall, it bounces back.

• You throw it: incident
• Ball hits wall: scattering
• Ball bounces back: outgoing

In the quantum world, all interactions are scattering:

• Photons hitting electrons (Compton scattering)
• Electrons hitting atomic nuclei (Rutherford scattering)
• Proton collisions (LHC Large Hadron Collider)

Scattering is quantum particles’ “dialogue”—exchange of information.

Scattering Matrix $S$

Physicists describe scattering with something called the scattering matrix (S-matrix):

$$|\text{outgoing}⟩=S\cdot |\text{incident}⟩$$

$S$ is a matrix telling you: Given incident state, what is the outgoing state.

Key properties:

• $S$ is unitary ($S^{†}S=I$), ensuring probability conservation
• $S$ is analytic (smooth function of energy), ensuring causality
• Poles of $S$ (where denominator is zero) correspond to resonances

The last point is key.

Act II: Resonance—When Waves Reinforce Themselves

Imagine a guitar string.

You pluck it, vibrations occur. But not all frequencies can persist—only resonance frequencies (fundamental and its multiples) can exist stably.

Why? Because waves reflect at both ends, forming standing waves—peaks and troughs fixed at specific positions.

Resonance = waves reinforcing themselves

In scattering theory, resonances correspond to poles of the $S$ matrix.

What Are Poles?

Consider simple scattering: particle tunneling through a potential barrier.

The scattering matrix might look like:

$$S(E)=\frac{E-E_0+i\Gamma /2}{E-E_0-i\Gamma /2}$$

When energy $E$ approaches $E_0$ (on complex plane), denominator approaches zero, $S$ tends to infinity—this is a pole.

Poles mean: Particles can “stay” near this energy for a long time.

How long? Determined by $\Gamma$ (width):

$$\tau \sim \frac{\hslash }{\Gamma }$$

If $\Gamma$ is small, residence time is long—this is quasi-steady state or resonance state.

We call this a “particle.”

Act III: Particles = Scattering Poles

Now comes the key insight:

Everything we call “particles”—electrons, photons, quarks, Higgs bosons—are poles of scattering matrices.

They are not fundamental “matter blocks,” but resonance modes in information scattering networks.

Electrons Are Not Little Balls

Traditional image: Electron is a little ball, negatively charged, moving in space.

New image: Electron is a resonance pole when electromagnetic field couples with other fields.

• Mass $m_e$ = projection of pole position on energy axis
• Infinite lifetime (stable particle) = pole on real axis ($\Gamma =0$)
• Spin 1/2 = angular momentum quantum number of pole

Electrons don’t “exist” somewhere, but when you measure, the scattering network excites this resonance mode.

What Are Photons?

Photons are more obvious: They are scattering poles of electromagnetic fields.

• Massless = pole at $E=0$
• Spin 1 = resonance of vector field
• Light-speed propagation = kinematics of massless pole

The “light” you see isn’t photons flying, but resonances of electromagnetic field scattering network propagating.

Why Is Higgs Boson Hard to Find?

Higgs boson (discovered 2012, Nobel Prize 2013) why so hard to find?

Because its pole is very wide ($\Gamma$ is large), meaning extremely short lifetime ($\sim 10^{-22}$ seconds).

It’s not a stable resonance, but transient fluctuation—a mode briefly excited by the scattering network, then immediately decays.

Hard-to-find particles = wide poles = short-lived resonances.

Act IV: Secret of Fermions—Self-Referential Scattering

Now we explain the most mysterious thing: Why are there two types of particles?

Nature’s particles divide into two classes:

• Bosons (photons, gluons, Higgs…): Multiple can occupy same state
• Fermions (electrons, quarks, neutrinos…): Cannot have two in same state (Pauli exclusion principle)

Traditional answer: “God made it so.”

New answer: Fermions are resonances of self-referential scattering.

What Is Self-Reference?

Imagine information circulating in a network, then returning to start—seeing itself.

Like a camera pointing at a monitor: monitor displays what camera captures, and the image contains the monitor…

This is self-reference.

In scattering theory, self-reference corresponds to closed loops:

$$|\psi ⟩\stackrel{\text{scatter}}{\to }S|\psi ⟩\stackrel{\text{re-scatter}}{\to }{S}^2|\psi ⟩\to \cdots \to S^n|\psi ⟩$$

If $S^n|\psi ⟩=|\psi ⟩$ (returns to self), this is self-referential closed loop.

One Turn or Two Turns?

Key question: How many turns to return to self?

• If one turn (360°) returns to self: boson
• If two turns (720°) returns to self: fermion

Why “two turns”?

Because self-referential loops have square root branches (like $\sqrt{1}=\pm 1$).

Mathematically, this is ${\mathbb{Z}}_2$ uniformization—you need two turns to go around the branch point.

Spinors and Clifford Algebra

Mathematical description of fermions is called spinors, satisfying:

$$R(2\pi )\psi =-\psi$$

After 360° rotation, wave function changes sign!

This isn’t arbitrary assumption, but mathematical necessity of self-referential scattering.

Deeper structure is Clifford algebra:

$$\{{\gamma }^{\mu },{\gamma }^{\nu }\}=2g^{\mu \nu }$$

These $\gamma$ matrices (Dirac matrices) encode the algebraic structure of self-referential loops.

Fermions aren’t God’s choice, but topological necessity of self-referential networks.

Act V: Standard Model—Symmetry of Scattering Networks

Now we’re ready to understand the entire Standard Model (theory describing all fundamental particles and forces).

Gauge Group = Symmetry of Information Frames

Standard Model has a core: gauge group

$$G=SU(3)\times SU(2)\times U(1)$$

• $SU(3)$: Strong nuclear force (quark “colors”)
• $SU(2)\times U(1)$: Electroweak force (electromagnetic + weak nuclear)

Traditional view: This is the symmetry group nature chose.

New view: This is local frame symmetry of information scattering networks.

What does this mean?

Information Frames

Imagine describing the same thing in different languages at different places:

• In Beijing, you say “苹果”
• In New York, you say “apple”
• In Paris, you say “pomme”

Same information, but different encoding—this is choice of “frame”.

In quantum field theory, each spacetime point has an “internal space” (fiber), you can choose different bases (frames) to describe particle internal states.

Gauge group $G$ is all possible frame transformations.

Gauge Fields = Translation Between Frames

When information propagates from one point to another, frames may change, you need translation—this is gauge fields.

• Electromagnetic field $A_{\mu }$ is translation of $U(1)$ frame
• Gluon field $G_{\mu }^a$ is translation of $SU(3)$ frame
• Weak bosons $W_{\mu },Z_{\mu }$ are translation of $SU(2)$ frame

Forces aren’t “pull” or “push,” but constraints maintaining information consistency between different frames.

Higgs Mechanism = Spontaneous Choice of Frame

Higgs mechanism explains why some particles have mass.

Traditional explanation: Higgs field “gives” particles mass.

New explanation: Higgs mechanism is spontaneous frame breaking—system spontaneously chooses a specific frame, breaking symmetry.

Like magnets spontaneously magnetizing below Curie temperature (choosing a direction), Higgs field spontaneously chooses vacuum expectation value:

$$⟨\varphi ⟩=v\ne 0$$

This choice breaks $SU(2)\times U(1)$ symmetry, leading to:

• $W,Z$ bosons gain mass (frame locked)
• Photon remains massless (residual $U(1)$ symmetry)

Mass = energy cost of frame locking.

Act VI: WScat^+ Framework—Category of Scattering

Now, the deepest unification: WScat^+ framework (Windowed Scattering Plus).

This is a mathematical framework completely unifying scattering, information, and geometry.

Core Idea

The universe is a scattering category:

• Objects: Quantum states
• Morphisms: Scattering processes $S:|{\psi }_1⟩\to |{\psi }_2⟩$
• Composition: Sequential scattering $S_2\circ S_1$

Category theory ensures:

• Associativity: $(S_3\circ S_2)\circ S_1=S_3\circ (S_2\circ S_1)$
• Identity: Identity scattering $I$

Information Fiber Bundle

Each spacetime point $x$ attaches an “information fiber” (internal space).

Together forming principal bundle $P(\mathcal{M},G)$:

• Base manifold $\mathcal{M}$: Spacetime
• Fiber: Internal frame space
• Structure group $G$: Frame transformation group (Standard Model gauge group)

Physics is scattering networks on principal bundles.

BRST Quantization

To ensure gauge invariance (frame choice doesn’t affect physics), need BRST quantization:

Introduce “ghost fields” and anti-ghost fields, define BRST operator $Q$, satisfying:

$$Q^2=0$$

Physical states are $Q$’s cohomology:

$${\mathcal{H}}_{\text{phys}}=\frac{\ker Q}{\text{im}Q}$$

Physics = BRST cohomology = gauge-invariant information.

From WScat^+ to Standard Model

Amazingly, from WScat^+ framework axioms (scattering, information, causality), can derive:

1. Principal bundle reduction → Higgs mechanism
2. Pole extraction → Particle mass spectrum
3. IGVP → Einstein equation + Yang-Mills equations
4. BRST cohomology → Physical Hilbert space

The entire Standard Model is inevitable emergence of scattering network categories.

Act VII: Where Does Mass Come From?

Let’s return to a simple question: What is the electron’s mass?

Experimental measurement: $m_e=0.511\text{ MeV}/c^2$

But where does this number come from?

Traditional Answer

Quantum field theory says: Electron mass is a parameter in Lagrangian, needs experimental determination.

This is unsatisfactory—why exactly this value?

New Answer: Pole Extraction

WScat^+ gives a procedure:

1. Write scattering matrix $S(E)$ (depends on energy)
2. Calculate determinant $\det S(E)$
3. Find poles on complex plane $E=E_0-i\Gamma /2$
4. Real part $E_0$ is particle mass

Mass isn’t a parameter, but pole position of scattering network resonance.

Why this value? Because:

• Field coupling constants (from IGVP)
• Vacuum expectation value (Higgs field)
• Quantum corrections (loop contributions)

Together determine pole position.

Birman-Kreĭn Formula

Remember the Trinity Mother Ruler?

$$\frac{\phi (E)}{\pi }={\rho }_{\text{rel}}(E)=\frac{1}{2\pi }\mathrm{tr}\mathsf{Q}(E)$$

Phase $\phi$ relates to scattering matrix determinant:

$$\det S(E)=e^{-2\pi i\xi (E)},\xi (E)=\frac{\phi (E)}{\pi }$$

Poles correspond to zeros (or infinity) of $\det S$, which exactly are resonance peaks of state density.

So: $$\text{particle mass}\leftrightarrow \text{scattering pole}\leftrightarrow \text{state density peak}\leftrightarrow \text{phase jump}$$

This is again manifestation of Trinity Mother Ruler.

Act VIII: Virtual Particles Are Not Virtual

Quantum field theory has a concept: virtual particles.

For example, two electrons produce electromagnetic force by exchanging virtual photons.

Textbooks say: “Virtual particles cannot be directly observed, just calculation tools.”

New View: Virtual Particles = Non-Pole Scattering Modes

In scattering network picture:

• Real particles = poles of scattering matrix (resonances)
• Virtual particles = non-pole components of scattering matrix (non-resonances)

Virtual particles don’t “not exist,” but cannot exist long-term—they are transient scattering modes, immediately decaying into other modes.

But in short time (allowed by Heisenberg uncertainty), they truly carry energy and momentum.

Virtual particles are “high-frequency fluctuations” of scattering networks.

Every dashed line in Feynman diagrams encodes a transient scattering process.

Act IX: What Are Antiparticles?

Final puzzle: antiparticles.

Every fermion has an antiparticle (positron, antiquark…), why?

Dirac Sea (Outdated but Beautiful)

Dirac’s original explanation: Vacuum is a “sea” filled with negative-energy electrons, holes are positrons.

This picture is wrong (leads to infinite vacuum energy), but has aesthetic value.

Modern Explanation: Field Excitations

Quantum field theory says: Positrons are “negative frequency excitations” of electron field.

But this is still phenomenological description.

WScat^+ Explanation: Dual of Scattering

In category theory, every morphism (scattering process) has a dual morphism (inverse process).

If particles are scattering poles, antiparticles are dual poles—poles under transpose or conjugate of scattering matrix.

Mathematically:

$$\text{poles of }{S}^{†}(E)=\text{conjugate poles of }S(E)$$

Antiparticles are mirrors of particles in dual structure of scattering networks.

This also explains why:

• Particle + antiparticle = annihilation (pole + dual pole = cancellation)
• Energy conservation (dual morphisms preserve category structure)

Philosophical Reflection: World Is Not Composed of “Things”

Let’s pause and think about the deep meaning of this picture.

Ontological Revolution

Since ancient Greece, philosophers asked: “What is the world composed of?”

• Democritus: Atoms (indivisible particles)
• Aristotle: Four elements (earth, water, fire, air)
• Newton: Mass points and forces
• Einstein: Spacetime and fields

But now we know: World is not composed of “things,” but “patterns”.

Particles aren’t matter blocks, but resonances in information scattering networks.

Like music isn’t “fragments of strings,” but “vibration patterns”.

No Fundamental Particles, Only Fundamental Processes

Traditional physics searches for “fundamental particles”—quarks, leptons, bosons…

But this is wrong pursuit.

No fundamental particles, only fundamental processes—scattering.

Particles are emergence of processes, not starting points of processes.

Role of Observers

Deeper question: If particles are scattering poles, then without scattering there are no particles.

And scattering requires observers (at least measurement apparatus).

So, particles need observers to emerge.

This doesn’t mean “your consciousness creates particles,” but: Observation (measurement) excites scattering networks, emerging particle patterns.

Unobserved electrons aren’t “somewhere but you don’t know,” but haven’t yet emerged from scattering networks as definite resonance modes.

Measurement doesn’t “discover” where particles are, but “excites” particle emergence.

Real Applications: Seeing Scattering Networks

Example 1: LHC (Large Hadron Collider)

What is LHC doing?

Traditional answer: Smash protons, see what’s inside.

New answer: Excite high-energy scattering networks, observe emerging resonance modes.

Higgs boson isn’t “hidden in protons,” but resonance excited by network during high-energy scattering.

Example 2: Quantum Entanglement

Two electrons entangle, measuring one instantly affects the other (EPR paradox).

Traditional puzzle: How does information travel faster than light?

New understanding: Entanglement isn’t “connection between two particles,” but global pattern of scattering networks.

Measurement doesn’t propagate information, but selects global configuration of network.

Particles aren’t independent entities, but nodes of network—cut network, particles lose definition.

Example 3: Vacuum Fluctuations

Vacuum isn’t “empty,” but full of fluctuations: virtual particle pairs constantly created and annihilated.

What is this?

Vacuum is ground state of scattering networks—not static, but dynamic equilibrium full of transient resonances.

Casimir effect (attraction between two parallel metal plates), Lamb shift (tiny shift in hydrogen energy levels) are all observable effects of vacuum scattering networks.

Take-Home Thoughts

Next time when you:

• See a beam of light (photons)
• Use electronic devices (electrons)
• Think about your body (composed of quarks and electrons)

Remember: These aren’t “little balls moving,” but resonance modes of scattering networks.

You aren’t “collection of atoms,” but an extremely complex, continuously emerging resonance structure in information scattering networks.

When your heart beats, brain operates, scattering networks continuously excite, decay, re-excite…

You are a never-ending symphony, not a pile of static instruments.

And the deepest insight is:

Matter is not fundamental, processes are.

Existence is not a noun, but a verb.

Next: “The Geometric Definition of Life: How Negative Entropy Pumps Emerge”

We will see that life is not special matter, but geometric steady state of open systems under non-equilibrium constraints.