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.
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.
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 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.
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.
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.
Abstract The standard formalisms of quantum mechanics and special relativity are extraordinarily successful, yet several foundational features are introduced to students as postulates or mathematical constructs without physical visualisation: why the wavefunction must be complex, what is physically associated with spin, why time dilation occurs in material particles, where the Lorentz-factor scaling of inertia comes from, why energy quantisation follows from a phase-closure condition, and what geometric account can be given of wave-particle duality. This paper presents a geometric picture—already implicit in Schrödinger’s Zitterbewegung and de Broglie’s internal periodicity—that may help students develop physical intuition for each of these features. The electron is represented as executing a phase-coherent helical motion at speed c , with transverse radius a 0 = ℏ / 2 m 0 c and axial pitch equal to the de Broglie wavelength. Within this picture the imaginary unit i admits an intuitive interpretation as the 90 ∘ rotation operator in physical transverse space; quantisation may be visualised as a phase-closure condition with the quantum number n counting helical nodes; time dilation and the Lorentz-factor scaling of inertia both have a transparent geometric reading from a single pythagorean speed constraint; and interference may be understood as a Moiré-type geometric phase effect. The model is fully consistent with standard quantum and relativistic predictions. Its contribution is pedagogical and interpretational: it offers a unified geometric visualisation that may help students develop intuition for these foundational concepts, rather than a derivation of quantum mechanics or special relativity from first principles. The paper is self-contained and addressed to advanced undergraduates and graduate students.