We propose a geometric interpretation of the wavelengths associated with the dynamics of a confined structure. This approach is based on a distinction between impulse, associated with the intrinsic dynamics of the phase, and momentum, associated with the translation of the structure in the coherence landscape from the point of view of the reference observer. The construction gives rise to two wavelengths with distinct statuses : impulse leads to the Compton wavelength, while momentum leads to the de Broglie wavelength. These two wavelengths thus result from the same decomposition of the dynamics of the confined structure, applied to two contributions of different nature.
We propose a geometric interpretation of the wavelengths associated with the dynamics of a confined structure. This approach is based on a distinction between impulse, associated with the intrinsic dynamics of the phase, and momentum, associated with the translation of the structure in the coherence landscape from the point of view of the reference observer. The construction gives rise to two wavelengths with distinct statuses : impulse leads to the Compton wavelength, while momentum leads to the de Broglie wavelength. These two wavelengths thus result from the same decomposition of the dynamics of the confined structure, applied to two contributions of different nature.
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.
This work revisits the kinematic foundations of wave–particle duality by re-examining the logic originally proposed by Louis de Broglie within the framework of Special Relativity developed by Albert Einstein. Starting from the assumption that a massive particle possesses an intrinsic periodic degree of freedom associated with its rest energy, the study explores how Lorentz covariance acts on such periodicity. By representing the internal phase on a transverse cylindrical manifold, it is shown that the relativity of simultaneity naturally converts temporal periodicity into a spatial helical phase structure when observed from a moving frame. Within this geometric representation, the longitudinal phase gradient is fixed by relativistic kinematics, leading directly to the relation kz=p/ℏkz=p/ℏ which reproduces the well-known de Broglie relation. In this framework, particle momentum appears as the torsional density of the helical phase field, while the transverse radius forms a Lorentz-invariant geometric seat for the intrinsic structure. The analysis further shows that this transverse scale naturally aligns with the characteristic length Rc=ℏ/mcRc=ℏ/mc previously identified as a structural scale in the author's earlier work on helical phase-field models. The resulting picture suggests a geometric convergence in which the de Broglie wavelength and the characteristic particle radius emerge as the longitudinal and transverse signatures of a single relativistic phase structure. This work is purely kinematic and does not attempt to resolve the detailed dynamical origin of the internal energy partition. The dynamical mechanism responsible for the transverse stabilization and the associated energy coefficients will be addressed in subsequent studies.
Relativity is reframed in an “object-centric” description that takes the object’s Compton frequency as primary and treats observer-dependent kinematics as alternative decompositions of a single underlying motion. Compton and de Broglie wavelengths are treated as coupled consequences of motion in an expanding, globally four-dimensional hyperspherical cosmos. A fundamental quantum action step is assumed, so the discrete proper-time interval defines an intrinsic Compton stride, the distance an object is carried with the expanding cosmic hypersurface during each update. The de Broglie wavelength then arises as the relational projection of that same stride into coherent patterning along the locally three-dimensional hypersurface. The associated traveling-wave form, sourced on the past light cone, parallels the structure of free-space electromagnetic traveling fields, and in quasi-static limits naturally yields inverse-square behavior. Implications for intrinsic spin and zitterbewegung are outlined, and connections to entanglement are noted. A new ontological account of time is proposed.
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.
We suggest that momentum should be redefined in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy–momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation leads us to a new relativistic wave equation and a new and likely better QM. Further, we show that Minkowski space-time is unnecessarily complex and that a simplified, special case of Minkowski space-time is more consistent with the quantum world. Also, we show how the Heisenberg principle breaks down at the Planck scale, which opens this area of physics up for hidden variable theories once again. Many of the mystical interpretations in modern QM are rooted in the development of an unnecessarily complex theory that drives much speculation and is therefore subject to many different and even conflicting interpretations.
We present a structural formulation of physical dynamics based on discrete unitary propagation, in which the time evolution is directly described by a unitary operator W^=f(H^) associated with a self-adjoint structural operator H^. Starting from the relationship between action and phase, ϕ=S/ℏ, and the variational construction of structural operators, we show that the propagation can be written exactly as the action of a bilocal kernel W(x,y) on the state, in continuity with recent developments of the Action-Phase program. We show that the spectral decomposition of H^ induces a diagonalization of the unitary propagation, in which the state evolution becomes multiplicative in the eigenvector basis of the structural operator. Consequently, the spectral structure organizes the propagation modes of the system, providing a description in which the dynamics is expressed in a decoupled manner between modes. It is evidenced that the distinction between nodal representation and spectral representation emerges naturally from the operator structure, corresponding to different decompositions of the same state in distinct bases of the same Hilbert space. In the case of translational invariance, the decomposition into Fourier modes is recovered as a particular situation. The results presented do not constitute a complete reconstruction of quantum mechanics nor a general gravitational theory. In particular, aspects of measurement, multiparticle structures, or complete covariant formulations are not treated. The objective of this work is more restricted and precise: to establish a formulation in which the dynamics is determined by the propagation operator and organized by its spectral decomposition, providing a structural layer from which more complete physical descriptions can be developed.