Image of Electron-Positron Pair Production

In the article "Physical Image of the Electron", I previously presented an intuitive image of the electron but did not elaborate on the mechanism of electron-positron pair production. Considering that a single gamma photon can also produce an electron-positron pair near a nucleus, there should be a simpler image for the production of electrons/positrons: a gamma photon is injected into the high-energy chaotic electromagnetic environment near a nucleus, directly generating a pair of vortices with opposite angular momenta (conservation of angular momentum) and the same magnetic moments (conservation of charge). The charge is determined by quantized magnetic flux rather than the other way around.

I. Reconstruction of the Physical Image

Problems with the Traditional Image

• Putting the cart before the horse: It first assumes the existence of charge and then derives the magnetic flux response.

• Missing mechanism: The process γ→e⁺e⁻ only satisfies energy conservation but lacks a geometric/topological generation image.

• Hanging symmetry: The "mirror symmetry" between electrons and positrons lacks a structural basis.

Vortex Generation Image Based on NQT

γ photon (E>2mc²) + Nuclear near-field → Local collapse of the electromagnetic field → Nucleation of vortex pairs

                 ↓                                                               ↓                                                                                                     ↓

Linear propagation mode           Nonlinear excitation                                        Topological stabilization(Locked by flux quantization)

Core Elements

• Nucleus as a "catalytic environment": Provides an electromagnetic background with strong gradients and high curvature.

• Topological generation of vortex pairs: Energy density exceeding the threshold → Field line winding → Vortex nucleation.

• Flux quantization: Φ = n·Φ₀, where n=±1 determines the "charge".

• Angular momentum-magnetic moment pairing: Deep symmetry with opposite spins but the same magnetic moments.

II. Mathematical Framework: From Magnetic Flux to Charge

Basic Quantization Condition

∮ A·dl = Φ = n·Φ₀ = n·(h/e₀)

where e₀ is the effective charge unit corresponding to the fundamental flux quantum.

Topological Constraints on Vortex Pairs

For a pair of vortices (+/-):

• Magnetic flux: Φ₊ = +Φ₀, Φ₋ = -Φ₀

• Winding number: w₊ = +1, w₋ = -1

• Total topological charge: Qtop = w₊ + w₋ = 0 (conserved)

Charge as a Derived Quantity

e = g(Φ) = sign(Φ)·|e₀|

Charge is not fundamental but a macroscopic label of flux topology.

III. Structural Symmetry of Electron-Positron Pairs

Vortex Chirality and Spin

Property	Electron (e⁻)	Positron (e⁺)	Physical Significance
Vortex chirality	Left-handed	Right-handed	Winding direction of field lines
Magnetic flux	-Φ₀	+Φ₀	Topological invariant
Spin projection	±ℏ/2	∓ℏ/2	Opposite angular momenta
Magnetic moment direction	↑	↑	Same direction (critical!)
Effective charge	-e	+e	Macroscopic manifestation of flux

Why Are Magnetic Moments in the Same Direction?

• Traditional puzzle: The magnetic moments of e⁻ and e⁺ "should" be opposite (due to opposite charges).

• NQT solution:Magnetic moments originate from the intrinsic circulation of the vortex structure and are independent of the charge sign.Both vortices are magnetic dipoles following the "right-hand rule".The charge sign only affects external responses, not the internal structure.

IV. Key Role of the Nuclear Near-Field

Why Is a Nucleus Needed?

• Momentum conservation: Provides recoil momentum and a complex mode environment.

• Field strength gradient: The strong field of Z·α/r² triggers nonlinearity.

• Symmetry breaking: Breaks vacuum uniformity and provides nucleation sites.

Quantitative Conditions for the Field Environment

• Critical field strength: Ecrit ≈ m²c³/eℏ ≈ 1.3×10¹⁶ V/cm

• Nuclear near-field: Enuc(r) ≈ Ze/4πε₀r²

• Nucleation condition: Enuc(r*) ≥ Ecrit → r* ≤ Z·re (classical electron radius)

Dynamics of Vortex Generation

• Linear stage: Propagation of gamma photons and accumulation of field energy density.

• Nonlinear excitation: ε(E²+B²) > εcrit, leading to field self-focusing.

• Topological transition: Field lines change from "passing through" to "winding around".

• Stabilization: Vortex pairs are locked by flux quantization.

V. Experimental Predictions and Testability

1. Direct measurement of magnetic fluxPrediction: The flux quantum of a single electron can be detected under extremely low temperatures and strong magnetic fields.Experimental setup: SQUID + single-electron trapExpected signal: Φ = -Φ₀ (independent of charge measurement)

2. Correlation measurement of vortex pairsPrediction: The initial magnetic moments of e⁺e⁻ pairs are in the same direction.Measurement scheme: Coincidence measurement + spin analysisCharacteristic signal: Magnetic moment correlation function C(θ) = +1 (same direction) instead of -1

3. Geometric dependence of production thresholdPrediction: The pair production cross section depends on the "effective volume" of the nucleus rather than just Z².σ(γ→e⁺e⁻) ∝ Z²·f(Z·α), where f contains the geometric factor for vortex nucleation

4. Subthreshold vortex excitationPrediction: Transient excitation of virtual vortex pairs exists when E < 2mc².Observable: Anomalous enhancement of nuclear polarizabilityCharacteristic energy: E ≈ 1.5-2.0 MeV range

VI. Unification with Other Phenomena

Aharonov-Bohm Effect

Electron orbiting a flux tube: Phase = e·Φ/ℏNQT restatement: Topological entanglement between vortices and external magnetic flux

Superconducting Quantization

Flux of Cooper pairs: Φ = n·(h/2e)NQT explanation: Collective quantization of double-vortex complexes

Fractional Quantum Hall Effect

Quasiparticle charge: e* = e/mNQT image: Fractional winding of vortices (many-body correlation)

VII. Theoretical Advantages and Conceptual Simplifications

Eliminated Difficulties

• Origin of charge: No additional assumptions are needed.

• Electron-positron symmetry: Naturally arises from vortex chirality.

• Magnetic moment problem: Same-direction magnetic moments are no longer anomalous.

New Predictive Capabilities

• Nonperturbative pair production: Collective vortex excitation in strong fields.

• Topological phase transition: Condensation of vortices and antivortices.

• Tunable effective charge: Regulation of magnetic flux through geometry/boundaries.

VIII. Computational Scheme: Vortex Dynamics

Effective Action

S = ∫d⁴x [1/4·FμνF^μν + ψ̄(iγ^μDμ - m)ψ + Ltopo]Ltopo = θ·(E·B)/8π² + κ·|ψ|⁴

Construction of Vortex Solutions

• Seed solution: Static vortex pairs (solved numerically)

• Linear stability: Calculation of vortex mode spectra

• Scattering matrix: γ + vortex vacuum → e⁺e⁻

Interface with QED

• Traditional approach: |γ⟩ → |e⁺e⁻⟩ (Feynman rules)

• NQT approach: |γ⟩ → |vortex pair⟩ → |e⁺e⁻⟩ (two-step process)

IX. Roadmap for Experimental Verification

Short-Term

• Precision pair production measurements: Search for anomalies in angular distribution/polarization.

• Strong-field QED experiments: Nonperturbative signals from XFEL + heavy nuclei.

• Single-electron flux: AB phase in superconducting loops.

Medium-Term

• Direct imaging of vortex pairs: Time-domain resolution with attosecond pulses.

• Virtual vortex spectroscopy: Subthreshold nuclear polarization measurements.

• Topological phase transition: Multi-vortex condensation in strong fields.

Long-Term

• Controllable vortex pairs: Artificially designed "charge" generation.

• Vortex computers: Topology-based information processing.

• Cosmological applications: Vortex-dominated phase in the early universe.

Conclusion: Mechanism Simplification

The reversal from "charge→magnetic flux" to "magnetic flux→charge" not only simplifies the image of electron-positron pair production but also expresses the topological nature of electromagnetic phenomena.

Significance of This Image

• Charge is no longer a fundamental property but a macroscopic label of flux quantization.

• The deep symmetry between matter and antimatter originates from vortex chirality rather than the mysterious "antimatter".

• The role of the nucleus changes from a "bystander" to a "topological catalyst".

Implications If This Image Is Correct

We will need to:

• Rewrite the nonperturbative part of QED.

• Reunderstand the vortex structure of the "vacuum".

• Develop new computational methods based on topology rather than charge.

This is not a detail improvement but an answer to the fundamental question of "what is charge".