The Spiral Structure Model (SSM) is a phenomenological model in the tradition of Bohr's early atom: confined to kinematics and geometry, it trades dynamical depth for ontological clarity and experimental exposure. Three postulates suffice. (I) The photon is a pointlike energy quantum in uniform helical motion, with axial and circulation speeds both equal to c; (II) physical space is an elastic, relativistically covariant medium that sustains vortex excitations; (III) the electron is a stable topological vortex defect of that medium. From these postulates, with every step carrying an explicit epistemic label, the model obtains the photon's circulation angular momentum mcrγ = ħ as a consistency theorem and identifies it with the photon spin; logarithmic vortex confinement with no free parameters; the two polarization states and the absence of a longitudinal mode; orbital angular momentum as an ensemble property; the electron's 720-degree periodicity and spin ħ/2 from π₁(SO(3)) = ℤ₂. The same postulates yield the fine-structure constant as a ratio of structural scales and the free radiation field as a retarded ensemble moment satisfying the wave equation exactly. They also yield a phase-coupling account of two-slit interference and a double-helix ontology of entangled pairs that reproduces the CHSH value 2√2. Three falsifiable discriminants are stated with explicit falsification criteria: a wavelength-locked on-axis void in the photon's detection profile, a spin-dependent electron form-factor window near Q = mc, and a circulation-periodic component in entangled-pair coincidence timing.
The Spiral Structure Model (SSM) is a phenomenological model in the tradition of Bohr's early atom: confined to kinematics and geometry, it trades dynamical depth for ontological clarity and experimental exposure. Three postulates suffice. (I) The photon is a pointlike energy quantum in uniform helical motion, with axial and circulation speeds both equal to c; (II) physical space is an elastic, relativistically covariant medium that sustains vortex excitations; (III) the electron is a stable topological vortex defect of that medium. From these postulates, with every step carrying an explicit epistemic label, the model obtains the photon's circulation angular momentum mcrγ = ħ as a consistency theorem and identifies it with the photon spin; logarithmic vortex confinement with no free parameters; the two polarization states and the absence of a longitudinal mode; orbital angular momentum as an ensemble property; the electron's 720-degree periodicity and spin ħ/2 from π₁(SO(3)) = ℤ₂. The same postulates yield the fine-structure constant as a ratio of structural scales and the free radiation field as a retarded ensemble moment satisfying the wave equation exactly. They also yield a phase-coupling account of two-slit interference and a double-helix ontology of entangled pairs that reproduces the CHSH value 2√2. Three falsifiable discriminants are stated with explicit falsification criteria: a wavelength-locked on-axis void in the photon's detection profile, a spin-dependent electron form-factor window near Q = mc, and a circulation-periodic component in entangled-pair coincidence timing.
The Spiral Structure Model (SSM) is a phenomenological model in the tradition of Bohr’s early atom: confined to kinematics and geometry, it exchanges dynamical depth for ontological clarity and experimental exposure. Three postulates suffice. (I) The photon is a pointlike energy quantum in uniform helical motion, its axial and circulation speeds both equal to c; (II) physical space is an elastic, relativistically covariant medium sustaining vortex excitations; (III) the electron is a stable topological vortex defect of that medium. From these — with every step carrying an explicit epistemic label — the model obtains the photon’s circulation angular momentum mcrγ = ℏ as a consistency theorem, identified with its spin; logarithmic vortex confinement with no free parameters; the two polarization states and the absence of a longitudinal mode; orbital angular momentum as an ensemble property; the electron’s 720-degree periodicity and spin ℏ/2 from π1(SO(3)) = Z2; the fine-structure constant as a ratio of structural scales; the free radiation field as a retarded ensemble moment satisfying the wave equation exactly; a phase-coupling account of two-slit interference; and a double-helix ontology of entangled pairs that reproduces the CHSH value 2√2. Three falsifiable discriminants are stated with explicit kill criteria: a wavelength-locked on-axis void in the photon’s detection profile, a spin-dependent electron form-factor window near Q = mc, and a circulation-periodic component in entangled-pair coincidence timing.
The Spiral Structure Model (SSM) is a phenomenological model in Bohr’s tradition: restricted to kinematics and geometry, it trades dynamical depth for ontological clarity and experimental exposure. Three postulates suffice: (I) the photon is a pointlike energy quantum in uniform helical motion, axial and circulation speeds both equal to c; (II) physical space is an elastic, relativistically covariant medium sustaining vortex excitations; (III) the electron is a stable topological vortex defect of that medium. These yield, every step labeled: the photon’s circulation angular momentum mcrγ = ℏ as a consistency theorem identified with its spin; logarithmic vortex confinement with zero free parameters; the two polarization states and no longitudinal mode; orbital angular momentum as an ensemble property; the electron’s 720-degree periodicity and spin ℏ/2 from π1(SO(3)) = Z2; the fine-structure constant as a ratio of structural scales; the free radiation field as an ensemble statistical moment; a phase-coupling account of two-slit interference; and a double-helix ontology of entangled pairs reproducing the CHSH value 2√2. Three falsifiable discriminants are stated with kill criteria: a wavelength-locked on-axis detection void, a spin-dependent electron form-factor window near Q = mc, and a circulation-periodic component in entangled-pair coincidence timing.
A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck’s theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie’s wavelength; furthermore, Compton’s and de Broglie’s wavelengths were also differentiated.
A geometric interpretation of electron dynamics is presentedbased on phase-coherent helical motion constrained by relativistic kinematics.Building on de Broglie’s concept of internal periodicity and theHamilton–Jacobi formulation of mechanics, the electron is modeled asan intrinsic light-speed helical trajectory whose axial pitch correspondsto the de Broglie wavelength and whose transverse scale is set by thereduced Compton length. Within this framework, spin-1/2 symmetry,magnetic moment, rest energy, and bound-state quantization emerge asinterconnected consequences of phase closure and geometric constraints,rather than as independent postulates. The formal operator structure ofquantum mechanics is recovered as a statistical description of ensemblesof phase-coherent helical trajectories, with momentum and energy operatorsarising as generators of spatial and temporal phase evolution. The frameworkprovides a geometric visualization of interference, tunneling, and quantumtransitions, while remaining fully consistent with the standard probabilisticpredictions of quantum mechanics and the Lorentz invariance of specialrelativity. The helical phase interpretation is intended as a conceptualand pedagogical complement to orthodox formalisms, offering physicalintuition for otherwise abstract quantum structures without modifying theirmathematical foundations. Thus, this work does not propose a modificationof quantum theory, but offers a geometric interpretation of its formal structures aimed at clarifying their physical content.
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.
A geometric interpretation of electron dynamics is presentedbased on phase-coherent helical motion constrained by relativistic kinematics.Building on de Broglie’s concept of internal periodicity and theHamilton–Jacobi formulation of mechanics, the electron is modeled asan intrinsic light-speed helical trajectory whose axial pitch correspondsto the de Broglie wavelength and whose transverse scale is set by thereduced Compton length. Within this framework, spin-1/2 symmetry,magnetic moment, rest energy, and bound-state quantization emerge asinterconnected consequences of phase closure and geometric constraints,rather than as independent postulates. The formal operator structure ofquantum mechanics is recovered as a statistical description of ensemblesof phase-coherent helical trajectories, with momentum and energy operatorsarising as generators of spatial and temporal phase evolution. The frameworkprovides a geometric visualization of interference, tunneling, and quantumtransitions, while remaining fully consistent with the standard probabilisticpredictions of quantum mechanics and the Lorentz invariance of specialrelativity. The helical phase interpretation is intended as a conceptualand pedagogical complement to orthodox formalisms, offering physicalintuition for otherwise abstract quantum structures without modifying theirmathematical foundations. Thus, this work does not propose a modificationof quantum theory, but offers a geometric interpretation of its formal structuresaimed at clarifying their physical content.