| _version_ | 1866901153471528960 |
|---|---|
| author | Bell, Jules |
| author_facet | Bell, Jules |
| contents | <p>Formal Papers I and II established a covariant multivector scaffold for Helical Scalar Theory (HST) and supplied a constitutive interpretation of the effective inertia parameter as confinement energy. The purpose of the present paper is to develop the kinematic isomorphism of the field equation and explicitly derive its principal limiting regimes. Starting from the stabilized excitation equation, we establish the structural algebraic isomorphism to the Dirac-Hestenes kinematics. By applying the Kinematic Isomorphism (q ≡ m³), structurally established as the Bell QED-Fluid Duality, we provide a constitutive continuum ontology for the geometric spinor, mathematically verified by the strict SI translation of electrodynamic units into fluid-dynamic pressure and impedance. Furthermore, we formally derive the nonrelativistic reduction (Schrödinger limit) via slow-phase envelope factoring. We constitutively subsume recent dynamic-vacuum acoustic models, deterministically deriving the Bohr radius (a₀) as a primary acoustic trap of the lattice, independent of primitive mass inputs. This is physically validated by pilot-wave hydrodynamics, and we define the macroscopic coarse-grained limit utilizing Lattice Scalar Impedance (LSI). We demonstrate physical regularization in the macroscopic limit via the Vacuum Elastic Modulus snap-point constraint. Finally, we establish the geometric derivation of the Neutron Mass Gap (1.293 MeV), confirming that the HST excitation equation replaces probabilistic point-particle kinematics with a strictly deterministic, continuous mechanics of the vacuum.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19123849 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Helical Scalar Theory III: Kinematic Isomorphisms and the Dirac-Schrödinger Limits Bell, Jules Helical Scalar Theory, Structured Scalar Medium, Kinematic Isomorphism, Counter-Rotating Helical Pairs, Helical Unit Cell, Bell QED-Fluid Duality, Topological Solitons, Superfluid Vacuum Theory, Continuum Mechanics, Spacetime Algebra, Clifford Algebra Cl(1,3), Fluid Dynamics, Quantum Mechanics, Dirac-Hestenes Kinematics, Schrödinger Limit, Nonrelativistic Reduction, Deterministic Bohr Radius, Pilot-Wave Hydrodynamics, Lattice Scalar Impedance, Neutron Mass Gap, Born's Rule, Attosecond Quantum Delay <p>Formal Papers I and II established a covariant multivector scaffold for Helical Scalar Theory (HST) and supplied a constitutive interpretation of the effective inertia parameter as confinement energy. The purpose of the present paper is to develop the kinematic isomorphism of the field equation and explicitly derive its principal limiting regimes. Starting from the stabilized excitation equation, we establish the structural algebraic isomorphism to the Dirac-Hestenes kinematics. By applying the Kinematic Isomorphism (q ≡ m³), structurally established as the Bell QED-Fluid Duality, we provide a constitutive continuum ontology for the geometric spinor, mathematically verified by the strict SI translation of electrodynamic units into fluid-dynamic pressure and impedance. Furthermore, we formally derive the nonrelativistic reduction (Schrödinger limit) via slow-phase envelope factoring. We constitutively subsume recent dynamic-vacuum acoustic models, deterministically deriving the Bohr radius (a₀) as a primary acoustic trap of the lattice, independent of primitive mass inputs. This is physically validated by pilot-wave hydrodynamics, and we define the macroscopic coarse-grained limit utilizing Lattice Scalar Impedance (LSI). We demonstrate physical regularization in the macroscopic limit via the Vacuum Elastic Modulus snap-point constraint. Finally, we establish the geometric derivation of the Neutron Mass Gap (1.293 MeV), confirming that the HST excitation equation replaces probabilistic point-particle kinematics with a strictly deterministic, continuous mechanics of the vacuum.</p> |
| title | Helical Scalar Theory III: Kinematic Isomorphisms and the Dirac-Schrödinger Limits |
| topic | Helical Scalar Theory, Structured Scalar Medium, Kinematic Isomorphism, Counter-Rotating Helical Pairs, Helical Unit Cell, Bell QED-Fluid Duality, Topological Solitons, Superfluid Vacuum Theory, Continuum Mechanics, Spacetime Algebra, Clifford Algebra Cl(1,3), Fluid Dynamics, Quantum Mechanics, Dirac-Hestenes Kinematics, Schrödinger Limit, Nonrelativistic Reduction, Deterministic Bohr Radius, Pilot-Wave Hydrodynamics, Lattice Scalar Impedance, Neutron Mass Gap, Born's Rule, Attosecond Quantum Delay |
| url | https://doi.org/10.5281/zenodo.19123849 |