Clues
The annihilation of an electron and a positron produces only two beams of photons, which is neat and clean, with energy and momentum conserved term by term.
In the reverse process, photons with sufficient energy can generate an electron-positron pair with the "help" of a suitable environment (such as a nuclear Coulomb field or an intense field focal region), which is equally neat.
However: photons are uncharged, so how can they "create/annihilate" static charges? Electrons have both electric charge and magnetic moment, resembling "charges rotating at the speed of light". Then, where does this charge come from?
Additional Clues
1. Displacement Charge is Real
Electromagnetic waves are not "empty oscillations" but time-varying electric and magnetic fields; in media, this induces a slight separation of positive and negative charges, forming polarization/displacement charges.
Even in an intense field vacuum, there exists an equivalent "displacement/polarization response". This means that by organizing the phase and structure of electromagnetic fields, these displacement/polarization charges can be "weaved" into stable field structures.
2. Water Wave Analogy: From Zero-Mean Oscillation to "Topological Defect"
Ordinary water waves oscillate up and down, with a time integral of zero; there is no "extra or missing water". But once a vortex is formed, the center will be stably "lower"—from a distance, it looks like a persistent defect appearing on the water surface.
The same applies to electromagnetic waves: they are usually zero-mean oscillations; but under specific intense field and phase conditions, "electromagnetic vortices" can be formed. This vortex locks the "amount of displacement charge oscillating up and down" into a unidirectional net value, which appears as a positive or negative charge from the outside.
3. Locking and Quantization of Electromagnetic Vortices: From Phase to Flux
Circumferential Energy Flow and Frequency Locking
Under a suitable phase/chirality configuration, the Poynting vector in the near field forms a circumferential closed energy flow: energy circulates around the loop at the speed of light, but does not radiate outward overall (a non-dissipative closed mode, i.e., "natural frequency locking").
Topological Quantum Numbers (Integer Loops)
To maintain stability, the phase of the field must be exactly an integer multiple of 2π when traveling around the loop: Δφ = 2πn (n=±1, ±2,…). This "clips" the structure into integer states, making it a topological quantum.
Gaussian Flux Quantization
Under this locking, the electric flux through any enclosing surface is fixed to discrete values: ∮E·dS = (n·e)/ε₀. Thus, what is "read" by distant instruments is a quantized charge: n=+1→+e, n=−1→−e.
Scale and Minimum State
The minimum topological state is usually n=±1, corresponding to the minimum "charge quantum". The circumferential geometry and wavelength satisfy an approximate quantization condition: 2πr₀ ≈ λ_eff (for n=1). If the locked frequency is close to the electron Compton frequency, then r₀ ≈ λ_C/(2π) ≈ 0.386 pm.
4. Complete Image
Pair Production and Annihilation of Electron and Positron
Annihilation: The topological indices of two vortices (n=+1 and n=−1) cancel each other, frequency locking fails, and the circumferential energy flow reorganizes into two beams of free light (each about 511 keV) within an attosecond time scale, with energy and momentum conserved term by term.
Reverse process: Two beams of light with sufficient energy coherently overlap in a suitable environment (nuclear field/intense field focal region) to form a circumferential energy flow→phase locking→topological nucleation, generating a pair of closed vortices with n=+1 and n=−1—an electron and a positron.
Physical Image of Electron/Positron
It is not a "static lump of electricity" but a closed vortex composed of coherent electromagnetic energy flow circulating at the speed of light; the magnetic moment comes from the real circulation, the charge comes from the topological quantization of flux, and the positive/negative sign is determined by chirality (rotation direction).
Generation of Quantized Static Charge
Charge is not a pre-assigned point property, but a "phase-topological locking" that organizes displacement/polarization charges into a defect core that cannot be continuously removed; Gauss's law only recognizes flux, not near-field fingerprints, thus reading integer values such as ±e.
No Need for "Additional Coupling"
Except for the superposition and coherence of electromagnetic fields, there is no need to artificially specify new "couplings". Locking comes from geometric and phase conditions (integer loops) and self-consistent boundaries under intense fields, rather than externally imposed abstract rules.
No Need to "Accelerate Light to c"
The intrinsic speed of electromagnetic energy flow is c. The interior of an electron is originally a closed mode circulating at c; annihilation only unlocks the closed mode into a freely propagating wave; pair production locks freely propagating waves into a closed mode. There is no need to "accelerate photons" throughout the process.
Key Points
Conclusion: A Unified Perspective on the "Electron Image"
This approach unifies the "clean annihilation/creation" with the "charge-magnetic moment-scale" of electrons into a concise image: electrons/positrons are quantized electromagnetic vortices, charge is the topological quantum of flux, magnetic moment comes from circulation, and scale is given by the locking of wavelength and geometry.
In fact, it also provides an image of "virtual" electron-positron pairs or quantum fluctuations in quantum field theory.
Except for the superposition and coherence of fields, no artificial couplings or entities are introduced; the image is definite and real, and everything is determined by phase, boundaries, and topology. In this way, the microcosm returns from "mysterious" to an "understandable structure", and annihilation and production are merely conversions between "closed modes and traveling waves", no longer requiring a free "coupling coefficient".