Spin-Orbit Radiation Interference: The Classical Nature of Stationary Non-Radiation, Quantized Orbits, and Wave-Particle Duality in the Hydrogen Atom — —Also on the Nature of Photons and the Essence of the Electromagnetic Field: Revelation of the Cosmic Background Photon Field
The classical electrodynamic conclusion that an accelerating point charge mustradiate has long been regarded as an iron law, yet the electron in the hydrogen atom does notradiate and fall into the nucleus. This paper points out that the root of this contradiction is not inclassical electromagnetic theory itself, but in the untested hidden assumption that “the electronis a point particle”. Compton scattering experiments have already shown that the electron, whencolliding with a photon, behaves as a particle with a finite size, and its intrinsic geometric radius isgiven by the reduced Compton wavelength: re = ℏ/(mec) . Based on this physical fact, andconsidering that while the electron revolves around the nucleus (orbital motion) it also has anintrinsic spin, the electron itself generates two homologous electromagnetic radiation fields:orbital radiation and spin radiation. These two real electromagnetic waves always superpose andinterfere in space. Under specific conditions (frequencies forming an integer ratio, oppositephases, and matching amplitudes), the two waves completely interfere destructively, resulting inzero net external radiation and forming a stable standing wave inside the system– this is thestationary state of the hydrogen atom. The destructive interference condition naturally leads toωs = nΩ (n integer) and re/R = α/n2 , where α is the fine-structure constant. Combined withthe Coulomb force (centripetal force) equation, one uniquely obtains the quantized orbital radiiRn = n2a0 (a0 is the Bohr radius) and the angular momentum quantization Ln = nℏ . Thefine-structure constant thus acquires a geometric meaning: α = re/a0 .This paper further reveals the classical nature of wave-particle duality: the electron is always aparticle (with a definite trajectory), and its wave-like behavior comes from the superposition andinterference of the electromagnetic waves of spin and orbital radiation. The “particle-like”behavior observed in experiments is essentially the point-like signal produced when the photonradiated by the electron is absorbed, while the wave-particle duality of the photon itself is an1intrinsic property of it being an electromagnetic wave packet. Based on this picture, the paperprovides a classical causal explanation for the electron double-slit experiment– the electron asa particle barely passes through the slits; the interference fringes originate from theself-interference of the radiation wave packet (photon) generated by the electron interactingwith the slit plate, and the bright spots on the screen come from the discrete absorption eventsof photons, with the accumulation of many events forming the fringes. Observation inevitablydisturbs the electron because any measurement disrupts the destructive interference condition,thereby eliminating the mystery of “wavefunction collapse”.The paper also systematically expounds the electromagnetic nature of the photon: the photon isan electromagnetic wave packet radiated when the electron transitions between stationarystates due to the imbalance of interference; its energy E = hλ is determined solely by thefrequency, with constant amplitude; the photon is born at the speed of light because it originatesfrom a pre-existing electromagnetic wave. Finally, the paper discusses the essence of theelectromagnetic field: the electromagnetic field is not matter but energy; the vacuum is theground state electromagnetic field (filled with photons), and the cosmic microwave backgroundradiation is its observational evidence. Macroscopic electromagnetic fields (such as radio waves,visible light) are perturbations superimposed on the ground state field, acting as carriers ofenergy and information. The paper also links the background photon field to the cosmicmicrowave background radiation, providing a new causal picture for the interaction mechanismof charged particles and the inverse-square law of forces.This model is completely based on classical electromagnetism and the physical fact that theelectron has a finite size, providing a causally clear and physically intuitive unified picture for thestability of the hydrogen atom, quantized orbits, wave-particle duality, the nature of the photon,the double-slit experiment, the measurement problem, and the energy origin of theelectromagnetic field.The model further suggests that the proton may also be a similar self-sustaining electromagneticbound state, and the origin of cosmic matter can be attributed to the process of energy lockingby the condensation of electrons and positrons, offering a unified perspective for physicalphenomena from the atom tothe cosmos.
The classical electrodynamic conclusion that an accelerating point charge mustradiate has long been regarded as an iron law, yet the electron in the hydrogen atom does notradiate and fall into the nucleus. This paper points out that the root of this contradiction is not inclassical electromagnetic theory itself, but in the untested hidden assumption that “the electronis a point particle”. Compton scattering experiments have already shown that the electron, whencolliding with a photon, behaves as a particle with a finite size, and its intrinsic geometric radius isgiven by the reduced Compton wavelength: re = ℏ/(mec) . Based on this physical fact, andconsidering that while the electron revolves around the nucleus (orbital motion) it also has anintrinsic spin, the electron itself generates two homologous electromagnetic radiation fields:orbital radiation and spin radiation. These two real electromagnetic waves always superpose andinterfere in space. Under specific conditions (frequencies forming an integer ratio, oppositephases, and matching amplitudes), the two waves completely interfere destructively, resulting inzero net external radiation and forming a stable standing wave inside the system– this is thestationary state of the hydrogen atom. The destructive interference condition naturally leads toωs = nΩ (n integer) and re/R = α/n2 , where α is the fine-structure constant. Combined withthe Coulomb force (centripetal force) equation, one uniquely obtains the quantized orbital radiiRn = n2a0 (a0 is the Bohr radius) and the angular momentum quantization Ln = nℏ . Thefine-structure constant thus acquires a geometric meaning: α = re/a0 .This paper further reveals the classical nature of wave-particle duality: the electron is always aparticle (with a definite trajectory), and its wave-like behavior comes from the superposition andinterference of the electromagnetic waves of spin and orbital radiation. The “particle-like”behavior observed in experiments is essentially the point-like signal produced when the photonradiated by the electron is absorbed, while the wave-particle duality of the photon itself is an1intrinsic property of it being an electromagnetic wave packet. Based on this picture, the paperprovides a classical causal explanation for the electron double-slit experiment– the electron asa particle barely passes through the slits; the interference fringes originate from theself-interference of the radiation wave packet (photon) generated by the electron interactingwith the slit plate, and the bright spots on the screen come from the discrete absorption eventsof photons, with the accumulation of many events forming the fringes. Observation inevitablydisturbs the electron because any measurement disrupts the destructive interference condition,thereby eliminating the mystery of “wavefunction collapse”.The paper also systematically expounds the electromagnetic nature of the photon: the photon isan electromagnetic wave packet radiated when the electron transitions between stationarystates due to the imbalance of interference; its energy E = hλ is determined solely by thefrequency, with constant amplitude; the photon is born at the speed of light because it originatesfrom a pre-existing electromagnetic wave. Finally, the paper discusses the essence of theelectromagnetic field: the electromagnetic field is not matter but energy; the vacuum is theground state electromagnetic field (filled with photons), and the cosmic microwave backgroundradiation is its observational evidence. Macroscopic electromagnetic fields (such as radio waves,visible light) are perturbations superimposed on the ground state field, acting as carriers ofenergy and information. The paper also links the background photon field to the cosmicmicrowave background radiation, providing a new causal picture for the interaction mechanismof charged particles and the inverse-square law of forces.This model is completely based on classical electromagnetism and the physical fact that theelectron has a finite size, providing a causally clear and physically intuitive unified picture for thestability of the hydrogen atom, quantized orbits, wave-particle duality, the nature of the photon,the double-slit experiment, the measurement problem, and the energy origin of theelectromagnetic field.The model further suggests that the proton may also be a similar self-sustaining electromagneticbound state, and the origin of cosmic matter can be attributed to the process of energy lockingby the condensation of electrons and positrons, offering a unified perspective for physicalphenomena from the atom tothe cosmos.
We study the energy conversion laws of the macroscopic harmonic LC oscillator, the electromagnetic wave (photon) and the hydrogen atom. As our analysis indicates that the energies of these apparently different systems obey exactly the same energy conversion law. Based on our results and the wave-particle duality of electron, we find that the atom in fact is a natural microscopic LC oscillator. In the framework of classical electromagnetic field theory we analytically obtain, for the hydrogen atom, the quantized electron orbit radius rn=a0n2, and quantized energy En=−RHhc/n2, (n=1,2,3,...), where a0 is Bohr radius and RH is Rydberg constant. Without any adaptation of the quantum theory, we present a reasonable explanation of the Zeeman effect, Selection rules and Pauli exclusion principle. Our results show that the concept of electron spin is not the physical reality and should be replaced by the intrinsic characteristic of the helical moving electron (Left-hand and Right-hand). In addition, a possible physical mechanism of superconductivity is also provided.
New interpretation of the atomic spectra and other quantum phenomena: A mixed mechanism of classical LC circuits and quantum wave-particle duality
We study the energy conversion laws of the macroscopic harmonic $LC $ oscillator, the electromagnetic wave (photon) and the hydrogen atom. As our analysis indicates that the energies of these apparently different systems obey exactly the same energy conversion law. Based on our results and the wave-particle duality of electron, we find that the atom in fact is a natural microscopic LC oscillator. In the framework of classical electromagnetic field theory we analytically obtain, for the hydrogen atom, the quantized electron orbit radius. Without the adaptation of any other fundamental principles of quantum mechanics, we present a reasonable explanation of the polarization of photon, the Zeeman effect, Selection rules and Pauli exclusion principle. Particularly, it is found that a pairing Pauli electron can move closely and steadily in a DNA-like double helical electron orbit. Our results also reveal an essential connection between electron spin and the intrinsic helical movement of electron and indicate that the spin itself is the effect of quantum confinement. In addition, a possible physical mechanism of superconductivity and the deeper physical understandings of the electron mass, zero point energy, and the hardness property of electron are also provided. Finally, we show analytically that the Dirac's quantization of magnetic monopole is merely a special handed electron at absolute zero-temperature, which strongly suggests that any efforts to seek for the magneticmonopole in real space will be entirely in vain. Furthermore, it appears that the electron's spin and the magnetic monopole are actually two different concepts for one possible physical phenomenon.
Abstract The Kinematics of Quantum Space: A Classical Proof of Orbital Stability and Trajectory Continuity (Part II) Building upon the dense, discrete, nonlocal medium defined in Part I (Quantum Space, density ratio ρ = 6.54×10¹²), we prove that the electron in a hydrogen atom follows a strictly deterministic, continuous, and classical trajectory. No probabilistic interpretation, wave function collapse, or irreducible uncertainty is required. 1. Orbital velocity – six independent derivations Starting from the Bohr radius (a₀ = 5.291772×10⁻¹¹ m) and the electron mass (mₑ = 9.109384×10⁻³¹ kg), we derive the ground state orbital velocity through six independent physical paths: Galilean kinematics (v = s/t) Bohr quantization condition (mₑ v a₀ = ħ) Fine‑structure constant (v = α c, α = 1/137.036) Kinetic energy (ionization energy 13.6 eV) Coulomb–centripetal force balance Direct experimental transit time (attosecond measurements) All six converge identically to: v=e22ϵ0h=αc≈2.188×106 m/sv=2ϵ0he2=αc≈2.188×106m/s The electron is a real satellite of the nucleus, not a probability cloud. 2. Orbital stability – zero radiation from destructive interference The classical objection (Larmor's formula predicts radiative collapse within ≈47 ps) assumes a point charge. For a standing wave charge distribution satisfying 2πr = nλ (Bohr condition), we compute the Liénard–Wiechert potentials and the far‑field Poynting vector explicitly: S=1μ0Erad×Brad=0,Ptotal=∮S⋅dA=0S=μ01Erad×Brad=0,Ptotal=∮S⋅dA=0 The ground state does not radiate. Energy is locked in the standing wave. Radiation occurs only during transitions (n→m), exactly as observed in atomic spectroscopy. 3. Quantum jump as a vertical ballistic throw – continuity proven The transition n=1 → n=2 (energy ΔE = 10.2 eV) is treated as a classical vertical throw in an effective constant acceleration field g_q: gq=FCoulomb(a0)me=kee2mea02≈9.043×1022 m/s2gq=meFCoulomb(a0)=mea02kee2≈9.043×1022m/s2 Jump height: h = r₂ - r₁ = 1.5875×10⁻¹⁰ mEffective initial velocity (constant‑g approximation): v₀ ≈ 5.36×10⁶ m/sTime of ascent: t_up = v₀/g_q ≈ 59 asTotal flight time: t_total = 118 as The position function y(t) = v₀ t - ½ g_q t² is continuous and differentiable (C¹ class). The illusion of an instantaneous "quantum jump" arises solely because t_total is shorter than the temporal resolution of most instruments (Δt_instr ≫ 118 as). The trajectory exists – we are simply not fast enough to see it. 4. Spin as toroidal vortex kinematics – no superluminal speed Spin (S_z = ±½ħ) is not a rigid sphere rotation. We model the electron as a toroidal charge distribution with major radius R. The no‑superluminal condition v = ωR < c yields a lower radius bound: Rmin=ℏ2mec≈1.93×10−13 mRmin=2mecℏ≈1.93×10−13m This is physically reasonable (≈300× smaller than the Bohr radius). Quantization to ±½ħ follows from resonance stability: only prograde (+) and retrograde (–) synchronous rotations are stable, analogous to the Moon (synchronous) and Venus (retrograde). 5. Measurement as ballistic collision – Heisenberg is technical, not fundamental A typical measurement photon (λ = 0.1 nm, E ≈ 12.4 keV) carries momentum: pphoton=hλ≈6.626×10−24 kg⋅m/spphoton=λh≈6.626×10−24kg⋅m/s The electron's orbital momentum is: pelectron=mev≈1.993×10−24 kg⋅m/spelectron=mev≈1.993×10−24kg⋅m/s Ratio: p_photon / p_electron ≈ 3.33. The photon delivers more momentum than the electron possesses in its orbit. Measurement is not passive observation – it is a ballistic collision (Compton scattering). The post‑collision electron momentum is fully determinable if both the energy and scattering angle of the outgoing photon are measured precisely. "Uncertainty" is a technical deficiency of incomplete measurement, not a law of nature. 6. Five falsifiable predictions Electron transit time across one Bohr diameter: 48.4 ± 5 as (testable with attosecond spectroscopy). n=1 → n=2 transition duration: 100–120 as (continuous, not instantaneous). Heisenberg product Δx·Δp → 0 as detector precision → ∞ (no fundamental lower bound). Bell inequality violations decrease as measurement impulse strength decreases (weak measurement regime). Residual "quantum randomness" equals unmodeled environmental force noise; full force accounting restores classical determinism. 7. Conclusion All calculations use only standard constants and classical equations (Newton, Maxwell, Coulomb, Compton). No new postulates are introduced. The electron's path exists, is continuous, and follows deterministic mechanics. Quantum mysticism – wave function collapse, irreducible uncertainty, non‑locality as magic – is replaced by scale‑inverted classical physics operating within the dense geometry of Quantum Space defined in Part I. Keywords: orbital stability, Larmor paradox, destructive interference, Poynting vector, quantum jump as ballistic throw, attosecond transit time, toroidal spin, Compton scattering measurement, Bell inequalities reinterpretation, classical determinism, falsifiable predictions, scale inversion. PACS: 03.65.Sq (Semiclassical theories), 03.65.Ta (Foundations), 31.15.xk (Classical treatments of atomic structure), 32.80.t (Atomic transitions), 42.50.Ct (Quantum optics, measurement).MSC: 81Q05 (Closed and approximate solutions), 70F05 (Two‑body problem, Kepler), 78A35 (Motion of charged particles), 83A05 (Special relativity).arXiv: quant-ph, physics.class-ph, physics.atom-ph.
This paper presents a geometric and wave interpretation of energy quantization in the hydrogen atom, based on the de Broglie closure condition of the electron wave in a circular orbit. In this concept, energy quantization is a secondary phenomenon resulting from the fact that the electron wave in each orbit consists of exactly n full periods, and the transition to level n+1 corresponds to the addition of one full period. Combining the wave condition with the classical equilibrium of the Coulomb and centripetal forces leads to values of the orbital radii and a discrete energy spectrum consistent with solutions of the Schrödinger equation for the hydrogen atom. It is shown that energy quantization can be interpreted as a consequence of the resonant nature of the electron's wave nature and the condition of phase uniqueness after a complete orbit around the nucleus.1 The model under consideration is semiclassical in nature and serves as an intuitive representation of known results from quantum mechanics. It is assumed that the allowable states correspond to configurations in which the de Broglie wave forms a standing wave containing an integer number of full periods around the orbital circumference. This condition leads directly to the quantization of angular momentum according to the Bohr model. The waveband model provides a one-dimensional analogy of the full quantum description and can serve as a teaching tool to facilitate understanding the geometric aspects of energy quantization in the hydrogen atom. It demonstrates that energy quantization is a natural consequence of the standing wave geometry and the addition of successive full periods along the orbit as the system transitions to the next energy eigenstate after activation. The electron is a stable eigenstate of a quantum field whose behavior in bound systems can be geometrically interpreted as the self-resonance of a de Broglie wave satisfying the condition of single-valent phase, rather than as a local particle with a classical trajectory. Self-resonance of a wave means that the condition of single-valent phase of the wave function after a complete orbit around the nucleus is satisfied, i.e., the requirement that the phase change be an integer multiple of 2π; this is equivalent to the Bohr–de Broglie condition for the closure of the de Broglie wave.
This paper re-examines the mechanism of electron motion inside atoms and the causes of photon radiation and photon absorption, abandoning the inherent cognition of fixed electron orbits and quantum transitions in traditional atomic physics. It clarifies that electrons have no physical fixed orbits; orbits are only imaginary concepts constructed for convenience of description, not objective physical realities. With mass, electrons possess inertia and kinetic energy. Under the three-force equilibrium of Coulomb force, electromagnetic force and inertial effect, electrons naturally move in elliptical trajectories rather than regular circles. When an electron moves along an elliptical trajectory, it naturally passes through low-energy regions near the atomic nucleus and high-energy regions far from the nucleus. This change in position arises entirely from its own inertia, involving only the conversion between kinetic energy and potential energy. The electron neither gains nor loses total energy, so it emits no photons and undergoes no energy-level change. An electron loses total energy when emitting a photon outward, and transitions smoothly and continuously to a lower overall motion range under mechanical equilibrium and inertia. Meanwhile, an electron can also absorb external photons and gain energy; its total energy increases, and it similarly expands smoothly to a higher motion range. Photon energy is indivisible and can only be emitted or absorbed as a complete unit. This is the fundamental reason why atoms show discrete emission and absorption spectra. Electron motion is entirely smooth and continuous; instantaneous quantum transitions assumed in traditional physics do not exist. Based on classical mechanics and energy conservation, this paper unifies the laws of macroscopic celestial bodies and microscopic particles, and reconstructs an atomic motion model closer to the essential nature of physics.
Until now, we do not know whether elementary particles have structure, but we cannot assert that elementary particles do not have structure, because all experiences tell us that the properties of non-living and living things are closely related to their structure. As their foundation, can the microscopic particles be excluded? Do photons and charged fermions have structure? What structure? We study the key to the Schrödinger computation that accurately reproduce the energy levels of the Bohr model and the general solution of Schrödinger equation mathematically; we found to satisfy Schrödinger equation the charged fermions must possess a double helix structure of mass density. Such structures plus partial self-rotation make them quantized and a fixed value spin or . We prove that the Maxwell wave equation is simultaneously the Klein-Gordon equation for electromagnetic waves. Then we prove that photons have a double helix structure of EH-energy that makes photons quantized and a fixed value spin or . There is a charge in the electron (and charged fermions); a pair of charges in the photons, they distribute double helically along their side boundaries; these charges produce and carry a circular polarized E-wave and EH-wave respectively. They form two traveling-wave-particle hybrid structures. It is such hybrid structures give them traveling-wave-particle duality. Such dualities can exhibit their wave property and particle property simultaneously in the same experiments. At last, we prove that the electron cloud photo not only exhibits the probability distribution of electrons but also proves the existence of electrons’ trajectories around the nucleus; the electrons’ motions make the probability distribution. The electron probability distribution around the nucleus is causal. At last we prove that the electron in the main shells (the Eigen states) of a multi-electron atom does not radiate pure EM energy, not fall to the nucleus.