Abstract We present a diagonal spacetime 4-manifold to model the wave-particle duality with two derivations of the energy ratio of wave to particle to be 1 to 3, by which we calculate the least time for an electron nutation as based on its quadrupole spin states in a 720-degree rotation of its associated electromagnetic wave in a model of Zitterbewegung.
Abstract We present a diagonal spacetime 4-manifold to model the wave-particle duality with two derivations of the energy ratio of wave to particle to be 1 to 3, by which we calculate the least time for an electron nutation as based on its quadrupole spin states in a 720-degree rotation of its associated electromagnetic wave in a model of Zitterbewegung.
The wave-particle duality is one of the most intriguing properties of quantum objects. The duality is rather pervasive in the quantum world in the sense that not only classical particles sometimes behave like waves, but also classical waves, e.g., light, may behave as point particles. In this article, motivated by the wave-particle duality, I develop a deterministic time-crystal Lorentz-covariant mechanical model for an electron with spin. In the proposed time-crystal model an electron is formed by two components: a particle-type component that transports the electric charge, and a wave component that moves at the speed of light and whirls around the massive component. Interestingly, the motion of the particle-component is completely ruled by the trajectory of the wave-component, somewhat analogous to the pilot-wave theory of de Broglie-Bohm. The dynamics of the time-crystal electron is controlled by a generalized least action principle. The model predicts that the electron stationary states have a constant spin angular momentum, predicts the spin vector precession in a magnetic field and gives a possible explanation for the physical origin of the anomalous magnetic moment. Remarkably, the developed model has nonlocal features that prevent the divergence of the self-field interactions. The classical theory of the electron is recovered as an effective theory valid on a coarse time scale. The reported results suggest that time-crystal models may be used to describe some features of the quantum world that are inaccessible to the standard classical theory.
This preprint presents a conceptual model—not a mathematical theory—of the electron as a rotating filament of spacetime: a "spacetime spaghetti" that spins, stretches, and tangles. The model offers a single, unified mechanism to explain fourteen long-standing puzzles in quantum mechanics, including wave-particle duality, wavefunction collapse, electron spin and g-factor, the double-slit experiment, the delayed-choice experiment, the Pauli exclusion principle, pair production and annihilation, photon emission, and the quantization of atomic energy levels. Core idea: The electron is not a point particle. It is a thin, rapidly rotating filament of spacetime. Its rotation—defined as spacetime torsion relative to the background fabric—creates an extended curvature well (the "cloud"). When energy is injected past a critical threshold, the filament contracts to its ground state, releasing a ripple in spacetime (the photon). This single mechanism naturally explains both wave-like and particle-like behavior. Important note: This is a conceptual framework under active development. The rigorous mathematical formulation and quantitative experimental predictions are not yet complete. The purpose of this preprint is to share the core ideas openly, establish intellectual priority, and invite collaboration from mathematicians and theoretical physicists. Testable predictions include: · A critical detector energy threshold in the double-slit experiment · A nonlinear deviation in electron interference patterns compared to photons · A critical time delay in delayed-choice experiments (temporal depth of the electron cloud) · Possible deviations from QED in strong-field regimes
This paper overall treats the timeless mind-body problem. Descartes said: “I think, therefore I am.” This suggests the existence of life in a non-material world, specifically, a spacetime that is devoid of particles, which then evokes the equally celebrated theme of the wave-particle duality, which is the foundation of quantum mechanics. Correspondingly in mathematics, there is a dichotomy of the real number 1, and the imaginary number i - - which has however presented itself as a mystery for centuries. Here, we maintain that a 1-dimensional manifold is either a line or otherwise with curvatures and any curvature can be locally fitted by a circle, i.e., either a line with unit 1 or a unit circle expressed by exp(it), such as in the contrast between a linear calendar time t and a circular clock time it, or a linear expansion versus a rotational motion as indicated by the eigenvalues of a linear operator in a dynamical system. As such, the imaginary number i is just a periodic motion, or a wave. While Maxwell’s electromagnetic wave has energy, the quantum wave is yet a probability; we unify these two treatments of the wave by equating the quantum wave with Maxwell’s electromagnetic wave. The wave-particle duality logically leads to a diagonal spacetime manifold containing {(particle, its associated electromagnetic wave)}. In literature, a particle wave has its energy E distributed into (3E/4, E/4) respectively. Experimentally, a 50/50 beam splitter has been found to split half of the E/4 into a particle-less wave, evidencing the existence of a separate but coincidental wave universe; it is here that we define a living element as a set of particle-less electromagnetic waves that adds life to a set of molecules in the particle universe. We will present the mathematical formulation of the above and examine its implications and applications.
Abstract In previous work, the Hamilton-Jacobi equation has been associated with the metrics of general relativity and shown to be a generalized Dirac equation for quantum mechanics. This lends itself to a natural definition of wave-particle duality in quantum mechanics. This theory is now further developed to show that a free spinless quantum particle moving with velocity v obeys the standard wave equation of electro-magnetism. We also discuss the implications for the zitterbewegung problem and its relationship to isotropy. Moreover, it is also shown that for the theory to be consistent, the momentum defined by the Hamilton-.!acobi function presupposes the existence of a universal parameter internal to the system. In the case of particles with mass this invariant can be defined by dX = dt/m(t) where t has the units of time and m = m(t) has the units of mass.
This paper presents a conceptual model—not a mathematical theory—of the electron as a rotating filament of spacetime: a "spaghetti" that spins, stretches, and tangles. The model proposes a single, intuitive mechanism to explain fourteen long-standing puzzles in quantum mechanics, including wave-particle duality, wavefunction collapse, spin, the double-slit experiment, the Pauli exclusion principle, and the delayed-choice experiment. Important note: This is a conceptual framework under active development. The rigorous mathematical formulation and quantitative experimental predictions are not yet complete. The purpose of this preprint is to share the core ideas openly, establish priority, and invite collaboration from mathematicians and theoretical physicists interested in developing the formalism. Keywords: electron model, wave-particle duality, spacetime filament, rotating filament, quantum foundations, double-slit experiment, threshold black hole, conceptual model, spacetime torsion, Pauli exclusion principle, delayed-choice experiment, spin, g-factor
This paper presents a conceptual model of the electron as a rotating filament of spacetime — a "spaghetti" that spins, stretches, and tangles. The model proposes a single, intuitive mechanism to address fourteen long-standing puzzles in quantum mechanics, including wave-particle duality, wavefunction collapse, spin, the double-slit experiment, the Pauli exclusion principle, and the delayed-choice experiment. Important update:A revised and extended second version of this preprint has now been published. The new version includes: · an effective Lagrangian for the filament,· derived equations of motion and normal modes,· canonical quantization,· a phenomenological mapping to the Schrödinger equation,· and falsifiable predictions for double-slit interference. This first version remains public to preserve the priority of the original conceptual framework and to document the development of the model.