Photons Running along Their Own N-Level Quantum Wells and the Electron-Like Structure near the Black-Hole Photon Ring —— Anomalous Radiation, the Photon Falling into the Black Hole, and the Cause of the Thin Photon Ring —— A Special-Topic Volume of the Parent Monograph "The Dual-Channel Quantum-Well Annihilation-Field Model: A Self-Consistent Derivation from Underlying Postulates to Macroscopic Phenomena"

Photons Running along Their Own N-Level Quantum Wells and the Electron-Like Structure near the Black-Hole Photon Ring —— Anomalous Radiation, the Photon Falling into the Black Hole, and the Cause of the Thin Photon Ring —— A Special-Topic Volume of the Parent Monograph “The Dual-Channel Quantum-Well Annihilation-Field Model: A Self-Consistent Derivation from Underlying Postulates to Macroscopic Phenomena” Author: Lu Weihui Date: November 2026 Note: This volume is a written record of one special-topic discussion. Following the order in which the discussion proceeded, each section gives three parts: a summary of that section of the discussion (what was said in it), the analysis and calculation under that summary (what was done, step by step), and what that section resolved. No new postulate is introduced; all criteria follow Postulates I–VI and the postulate-level laws L1–L5 of the parent monograph “The Dual-Channel Quantum-Well Annihilation-Field Model: A Self-Consistent Derivation from Underlying Postulates to Macroscopic Phenomena”; whatever is extrapolated is labelled “special-topic extrapolation / current understanding”. Only structural formulas and criteria are given; numerical values await calibration, and no numerical assertion is made. Contents Section 1 Modification of the photon's mode of running 1.1 Summary 1.2 Analysis and calculation 1.3 What this section resolves Section 2 The electron-like layer and the positive-quantum-well core: the two-layer structure and its properties 2.1 Summary 2.2 Analysis and calculation 2.3 What this section resolves Section 3 The formation region, the scales and the radiation 3.1 Summary 3.2 Analysis and calculation 3.3 What this section resolves Section 4 The photon falling into the black hole and the maintenance of the thin photon ring 4.1 Summary 4.2 Analysis and calculation 4.3 What this section resolves Conclusion Section 1 Modification of the photon's mode of running 1.1 Summary This section makes two modifications and raises one question. The first modification concerns the photon's mode of running: a photon runs within its own N-level quantum well, runs within a negative quantum well, and also runs within the negative quantum well that lies inside a neutral quantum well. The second modification is the recognition that light carries a structure resembling a dynamic electron, that is, a quantum-well structure (a negative quantum well surrounding the photon's own dynamic positive annihilation pair, forming the structure); its mass may be far less than that of an electron (an electron is regarded as having a negative quantum well on the outside and a positive-quantum-well structure in the middle). The question that arises is this: when such a photon is under the powerful gravitation of a black hole — previously it was generally held that the photon merely circles the black hole — can it happen, under some condition, that the photon's kinetic energy turns into temporary positive annihilation pairs, and these temporary positive annihilation pairs increase the density of positive quantum wells (temporary is also acceptable), so that the photon approaches a dynamic electron and shifts into the mode of a dynamic electron; and further, in which region of the black hole such a situation can form, and whether it is possible at all. 1.2 Analysis and calculation Following this formulation, the work proceeds step by step as follows. · First step: write “shifting into the mode of a dynamic electron” as a criterion. Let E_γ be the photon's kinetic energy at that orbit, and let E_sep be the minimum energy required for the photon to combine with the neutral quantum wells along its path (this combination being precisely the electron-like structure); then the criterion for the shift is: E_γ ≥ E_sep (1-1) · That is to say, only when the photon's kinetic energy at that place suffices to combine with the neutral quantum wells along its path (this combination being precisely the electron-like structure) does the photon shift from a “pure photon” into an “electron-like mode”. · Second step: settle the composition of the electron-like mode. The inner layer is the positive annihilation pair carried by the photon itself, and the outer layer steps along within the negative quantum wells — isomorphic to what the parent monograph defines as “an electron = a positive-quantum-well core + a surrounding negative quantum well”. · Third step: circle out the candidate regions. By (1-1), only a region where gravity is strong enough for the photon to circle along a stable orbit and where the density of the neutral quantum wells along the path is high enough can satisfy it. Around a black hole there are two candidate regions: the photon ring (light circle, at about 1.5 Schwarzschild radii) and the inner edge of the accretion disk (at about 3 Schwarzschild radii). · Fourth step: compare these two candidate regions (Table 1). Candidate region Position Kinetic-energy condition (1-1) Can it form Photon ring (light circle) ≈1.5 Schwarzschild radii The photon moves in a stable circular orbit; kinetic energy and gravitational strength are just at the threshold, satisfying E_γ ≥ E_sep A stable electron-like layer can form Inner edge of the accretion disk ≈3 Schwarzschild radii Further out, the density of neutral quantum wells falls; the kinetic energy is insufficient to form a complete combination with the neutral quantum wells No stable electron-like structure forms The comparison shows that the region satisfying (1-1) is the photon ring; further out at the inner edge of the accretion disk the density of neutral quantum wells falls, the kinetic energy is insufficient to form a complete combination with the neutral quantum wells, and no stable electron-like structure forms. 1.3 What this section resolves · It turns “the photon shifting into an electron-like mode” from an idea into the criterion (1-1); · It settles the formation region as the black hole's photon ring (light circle); · It gives the two-layer composition, inner and outer, of the electron-like structure, isomorphic to the electron definition of the parent monograph. Section 2 The electron-like layer and the positive-quantum-well core: the two-layer structure and its properties 2.1 Summary This section adds three premises and settles the two-layer structure. · First: the photon runs within the negative quantum well, in particular within a neutral quantum well; in the black hole's photon ring such a situation should be possible, and the photon ring is taken as existing by default. · Second: whether the electron-like structure together with this vacuum (that is, the neutral quantum well) and the positive-quantum-well part can form a matter-like structure and form mass (that is, the mass of this motion); it cannot form a cone-like compact structure but is a loose structure, and it will form two layers: one is the electron-like layer that the photon-like entity has become, in motion, and the other is itself made of positive quanta. · Third: what properties the thing made of these two layers has — it certainly has mass and also atom-like properties; not only is it in motion, it may also be luminous — and therefore it will produce more light, or that kind of unusual radiation. 2.2 Analysis and calculation · First step: match these two layers to the electron definition of the parent monograph (Table 2). Layer Composition Origin Correspondence Inner layer (core) The positive annihilation pair carried by the photon itself The photon's own quantum-well structure The positive core of an atom (an atom-like nucleus) Outer layer Stepping along within the negative quantum wells The photon runs within the negative quantum wells and, along its path, combines with the neutral quantum wells The electron orbiting the nucleus (an electron-like layer) · Second step: give the geometrical scale of this structure. The radius of an atom-like structure is inversely proportional to the core mass; let m_γ be the equivalent core mass of the electron-like layer, m_e the electron mass and a₀ the Bohr radius of the hydrogen atom; then a_γ ≈ a₀ · (m_e / m_γ) (2-1) · Since m_γ ≪ m_e, a_γ is far larger than the radius of an ordinary atom. Taking “a mass far less than the electron's” to mean m_γ between one thousandth and one millionth of the electron mass, a_γ lies roughly between 10⁻⁷ and 10⁻⁴ m — that is, on the scale of a hundred nanometres to a hundred micrometres — a loose, “fluffy” structure. · Third step: settle the position of this structure. The place where it can form and be briefly maintained is a thin spherical shell at the photon ring (because this photon has now turned into an electron-like, quantum-well-like structure, its speed is accordingly an electron-like speed, slower than the speed of light), and it can only be a very thin layer — once it thickens slightly it falls into the black hole (see Section 4): r ≈ 1.5 R_s, R_s = 2GM/c² (2-2) · Inside the photon ring the photon has no stable orbit, and outside it the density is insufficient; only at the photon ring can this thin shell form and be briefly maintained. · Fourth step: list the properties of this structure. It has mass — the mass of motion brought by the aggregation of positive quantum wells, though the structure is loose and far smaller than a real electron–atom system; it has atom-like properties — the positive core + negative outer layer is isomorphic to “nucleus + electron layer”; it is luminous and emits unusual radiation (see Section 3). 2.3 What this section resolves · It settles the loose two-layer structure of “positive-quantum-well core + negative-quantum-well outer layer”, making clear that it is isomorphic to the electron definition of the parent monograph; · It gives the scale criterion (2-1) of this str