Within a realist extension of the de Broglie–Bohm framework, this work proposes aphysical interpretation of elementary particle spin as an emergent topological property of anunderlying guiding-wave structure.In previous works, a hypothetical physical wave component associated with photons wasintroduced as a possible experimentally accessible extension of the pilot-wave concept. Thisapproach was subsequently extended to entangled photons through the hypothesis of a com-mon non-separable guiding structure WAB existing in physical three-dimensional space.The present paper develops the internal dynamics of this guiding structure. We proposethat spin does not correspond to the mechanical rotation of a point-like particle, but ratherto a topological excitation of the physical guiding wave itself. The particle is interpreted as alocalized excitation embedded within a structured field W (r, t) possessing an internal phasegeometry.A nonlinear field model is introduced in which stable localized excitations can emerge astopological soliton-like structures. The quantization of spin is associated with a phase wind-ing number characterizing the topology of the guiding field around the particle excitation.The central result of this work is a generalized guiding equation combining the transla-tional guidance induced by the energy flow of the physical wave with an additional topologicalspin current. This equation provides a unified description linking particle motion, internalfield geometry, and spin quantization within a single deterministic framework.The proposed model remains phenomenological and aims at establishing a possible phys-ical ontology for quantum spin rather than replacing the standard mathematical predictionsof quantum mechanics.
Within a realist extension of the de Broglie–Bohm framework, this work proposes aphysical interpretation of elementary particle spin as an emergent topological property of anunderlying guiding-wave structure.In previous works, a hypothetical physical wave component associated with photons wasintroduced as a possible experimentally accessible extension of the pilot-wave concept. Thisapproach was subsequently extended to entangled photons through the hypothesis of a com-mon non-separable guiding structure WAB existing in physical three-dimensional space.The present paper develops the internal dynamics of this guiding structure. We proposethat spin does not correspond to the mechanical rotation of a point-like particle, but ratherto a topological excitation of the physical guiding wave itself. The particle is interpreted as alocalized excitation embedded within a structured field W (r, t) possessing an internal phasegeometry.A nonlinear field model is introduced in which stable localized excitations can emerge astopological soliton-like structures. The quantization of spin is associated with a phase wind-ing number characterizing the topology of the guiding field around the particle excitation.The central result of this work is a generalized guiding equation combining the transla-tional guidance induced by the energy flow of the physical wave with an additional topologicalspin current. This equation provides a unified description linking particle motion, internalfield geometry, and spin quantization within a single deterministic framework.The proposed model remains phenomenological and aims at establishing a possible phys-ical ontology for quantum spin rather than replacing the standard mathematical predictionsof quantum mechanics.
This paper presents a realist pilot-wave framework exploring a pos-sible physical interpretation of elementary particle spin.Rather than treating spin exclusively as an intrinsic non-spatialdegree of freedom, the model investigates the hypothesis that the mea-sured spin state emerges from the interaction between a localized par-ticle excitation and a structured nonlinear spinor-valued guiding fieldW .The guiding field is described through a multi-scale organization,represented either by discrete spatial domains or continuous high-frequencyphase modulations. These descriptions correspond to stable local con-figurations in which particle excitations may become dynamically lo-calized.The initial spin-1/2 formulation is generalized to arbitrary spin sthrough a (2s + 1)-component complex spinor field. The same guiding-wave mechanism is therefore extended to different spin representationsthrough the corresponding SU (2) generators.The framework investigates the rotational properties of the guid-ing field, the generalized Stern–Gerlach interaction, and a possible re-alist interpretation of Bell-type correlations through a common non-separable guiding configuration.A physical interpretation of the coupling mechanism is proposedthrough an analogy with structured waves composed of interacting mi-croscopic elements. This analogy illustrates how different localized ex-citations may couple differently to the same guiding structure depend-ing on their geometry, inertia, interaction properties and dynamicalresponse.The present work remains a theoretical framework requiring furthermathematical development and experimental investigation.
In a previous work, I proposed an experimental approach to investigate a hypotheticalphysical wave component associated with photons, capable of contributing to the Bohmianguidance process independently of the localized photon trajectory. In this paper, I explorea possible consequence of this hypothesis for photon entanglement. Assuming the existenceof such a hypothetical physical wave component, I propose that two entangled photonsmay be interpreted as two localized excitations of a common guiding structure rather thanas two independent particles carrying correlated properties. The purpose of this work isnot to modify the predictions of quantum mechanics, but to investigate whether quantumcorrelations may receive a realist ontological interpretation within an extended Bohmianframework. I introduce a common guiding structure WAB associated with an entangledphoton pair. The non-separability of this structure is considered as a possible physicalorigin of the observed correlations. The compatibility of this approach with Bell’s theorem,the Born rule, and relativistic constraints is discussed. At this stage, the proposal remainsphenomenological. A complete dynamical equation for the proposed wave component and aquantitative derivation of quantum statistics remain open problems.
This paper shows that particle-like excitations can emerge naturally within classical wave physics as topological defects of an effective wavefield. Focusing on a two-dimensional elastic medium whose envelope dynamics reduces to an effective Schrödinger equation, we demonstrate that phase singularities—points where the wave amplitude vanishes—behave as robust, localized objects carrying conserved topological charge. These defects follow deterministic trajectories governed by a guidance equation formally identical to that of de Broglie–Bohm pilot-wave theory, yet derived entirely from classical continuum mechanics without invoking quantum postulates. The central result is that defect cores move with velocityv=(ℏeff/meff)∇S,\mathbf{v} = (\hbar_{\mathrm{eff}}/m_{\mathrm{eff}})\nabla S,v=(ℏeff/meff)∇S,where S is the phase of the emergent wavefunction. This wave-guided dynamics arises as a kinematic constraint: the defect must remain a zero of the evolving field. The paper presents an asymptotic analysis of defect structure and motion, and discusses both the parallels with quantum particle dynamics and the fundamental limitations of the analogy, including the absence of superposed trajectories, entanglement, and quantum statistics. Overall, the work provides a concrete example of how topology and dispersion in classical systems can give rise to quantum-like behavior without quantization, illustrating a physically transparent route to emergent particle dynamics. Keywords: emergent dynamics; topological defects; phase singularities; pilot-wave theory; classical analogs of quantum mechanics; Schrödinger equation; guidance equation; elastic waves
The physical origin of the de Broglie wavelength remains one of the central interpretive questions in quantum mechanics. This work is developed within the Zero-field framework, a phenomenological model in which space is treated as a continuous medium containing localized regions of inward energy flow toward particle-centered Zero-fields. Within this framework, moving particles generate rotation-induced guiding structures referred to as Frontal Waves. These waves are proposed to accompany particle motion and provide a geometric interpretation of the de Broglie wavelength and wave–particle duality. The proposed Frontal Wave wavelength reproduces the standard de Broglie relation and is interpreted as the physical guiding structure associated with matter-wave behavior. The framework is applied to the Double Slit Experiment and the Mach–Zehnder interferometer, where Frontal Waves propagate through multiple paths and form interference structures that guide particle trajectories toward regions of constructive interference. Connections with Bohmian mechanics are discussed, emphasizing that the model serves as a phenomenological interpretation rather than a modification of the mathematical formalism of quantum mechanics. The Frontal Wave concept provides a geometric picture of matter-wave behavior and offers a unified interpretation of particle guidance, interference phenomena, and the de Broglie wavelength within the broader Zero-field framework.
This work proposes a geometric representation of quantum phase fields motivated by the long-standing tension between localized particle cores and dispersive wave propagation in quantum mechanics. Following the original insight of Louis de Broglie's phase harmony, the quantum phase is reinterpreted as a helical structure surrounding a localized core. The construction is developed using an inverse methodology: instead of deriving the structure dynamically from first principles, a candidate geometry is postulated and tested for internal consistency with the kinematic constraints of quantum mechanics. At the matching boundary defined by the Compton radius Rc = ħ/(mc), the phase field acquires a quantized azimuthal winding, forming a helical structure that connects the localized core with the extended navigation wave. Within this framework, the de Broglie wavelength λ = h/p emerges naturally as the geometric pitch of the helical phase surface. The analysis demonstrates that this helical configuration satisfies three essential requirements for a double-solution structure:topological phase quantization, velocity matching between wave and particle, and the correct decomposition of rest and kinetic energy. The work is presented as a proof-of-existence for a geometrically consistent phase structure that could support a localized vortex-like particle guided by a continuous phase field. It forms part of a broader research program exploring the mechanical and topological origins of quantum phenomena.
In my previous works, I explored the possibility that photons may be associated with aphysically existing guiding wave component capable of influencing their trajectories withina Bohmian framework. In this paper, I introduce a further hypothesis: the possibility thatthis guiding structure originates from a more fundamental physical field, which I denote byΩ. I propose that the quantum wave function, elementary particles, and spacetime geometryare not fundamental entities, but effective descriptions emerging from the physical proper-ties of this underlying field. The central hypothesis introduced in this work is the Ω-BornRelation, which expresses the square of the wave function as the normalized physical energydensity of the Ω field. Under this hypothesis, the Born probability distribution emergesfrom the energetic structure of a physically existing field. I investigate the possible conse-quences of this framework for Bohmian guidance, photon dynamics, quantum entanglement,and the emergence of gravitational geometry. The present work does not claim to provide acomplete theory of quantum gravity. Instead, I propose a phenomenological research frame-work exploring whether quantum phenomena and spacetime geometry could originate froma common physical substrate.