| 2026-09-17 | Classically Quantised Vacuum Electrodynamics, Part III: Vortical Photons as Maximally Entangled Pairs
A. Vrba
Maxwell's 1865 field equations are built entirely on bipolar, laboratory-sourced quantities: displacement as a response to field, sourced and terminated at a remote potential difference. We show that Maxwell's own equations --- prior to Heaviside's later reduction to curl-equation form --- admit a second, monopole reading: an excitation sector in which displacement is itself the primitive, quantised excitation of a single quantised spatial volume (voxel), identified with the elementary disturbance of the companion article's algebraic closure $\mathfrak{M}$. Constructing this excitation sector requires, and thereby supplies, a Beltrami-field representation of $\mathfrak{M}$'s transverse solutions and a general electric--magnetic symmetry law absent from Maxwell's own system. Because the companion article already fixes the speed of light $c$ and Planck's constant $h$ as ratios of the vacuum's own primitive quantities, not as imported empirical constants, every quantum relation built on this recast system follows as a theorem rather than a postulate: the Einstein--Planck relation $\mathcal{E}=h\nu$ is derived, not assumed, and a Planck-shaped spectral envelope is obtained for resistive decay, without identifying that envelope with a temperature. The same resistive mechanism yields a specific, falsifiable prediction: a hyperbolic frequency redshift in a static, non-driven resistive medium, distinct from known plasma and collisional effects. We show vortical photons produced by a Ca two photon cascade are maximally entangled Full abstract ... BibLaTeX@Online{Vrba-2026-2142, |
| 2026-09-17 | Classically Quantised Vacuum Electrodynamics, Part II: Maxwell’s 1865 Monopole Recast and a Classical Derivation of the Einstein–Planck Relation
A. Vrba
Maxwell's 1865 field equations are built entirely on bipolar, laboratory-sourced quantities: displacement as a response to field, sourced and terminated at a remote potential difference. We show that Maxwell's own equations --- prior to Heaviside's later reduction to curl-equation form --- admit a second, monopole reading: an excitation sector in which displacement is itself the primitive, quantised excitation of a single quantised spatial volume (voxel), identified with the elementary disturbance of the companion article's algebraic closure $\mathfrak{M}$. Constructing this excitation sector requires, and thereby supplies, a Beltrami-field representation of $\mathfrak{M}$'s transverse solutions and a general electric--magnetic symmetry law absent from Maxwell's own system. Because the companion article already fixes the speed of light $c$ and Planck's constant $h$ as ratios of the vacuum's own primitive quantities, not as imported empirical constants, every quantum relation built on this recast system follows as a theorem rather than a postulate: the Einstein--Planck relation $\mathcal{E}=h\nu$ is derived, not assumed, and a Planck-shaped spectral envelope is obtained for resistive decay, without identifying that envelope with a temperature. The same resistive mechanism yields a specific, falsifiable prediction: a hyperbolic frequency redshift in a static, non-driven resistive medium, distinct from known plasma and collisional effects. The Maxwell 1865 equations are recast to the excitation or vortical sector and define a Maxwellian monopole (not magnetic), $E=hf$ emerges. Full abstract ... BibLaTeX@Online{Vrba-2026-2136, |
| 2026-09-17 | Classically Quantised Vacuum Electrodynamics, Part I: Maxwellian Vortices and an Emergent EM-Mass Gap
A. Vrba
We introduce an algebraic vector closure $\mathfrak M$ set within a complex vector space $\mathcal{S}\subset\mathbb{C}^3$ equipped with a non-Hermitian symmetric bilinear product: \[ \mathfrak M[\mathbf{v}, \mathbf{B}, \mathbf{E}] := \left\{ \mathbf{v}, \mathbf{B}, \mathbf{E} \in \mathcal{S} \;\middle|\; \frac{\mathbf{B} \cross \mathbf{E}}{\mathbf{B} \vdot \mathbf{B}} - \mathbf{v} = 0, \quad \frac{\mathbf{E} \cross \mathbf{v}}{\mathbf{v} \vdot \mathbf{v}} - \mathbf{B} = 0, \quad \mathbf{v} \cross \mathbf{B} - \mathbf{E} = 0 \right\}. \] Under a Maxwell-compatible transport law, this closure reconstructs the source-free Maxwell--Heaviside curl equations while leaving the transport speed $v$ as an initially free parameter. Consequently, $\mathfrak M$ acts as a structural constraint on the underlying d'Alembert wave operator $\Box = \nabla^2 - v^{-2}\partial_t^2$. While the standard d'Alembert equation permits arbitrary linear wave packets, the non-linear algebraic requirements of $\mathfrak M$ restrict allowable field configurations to continuous 3D spatial-phase rotations $R = R_{\rm x}R_{\rm y}R_{\rm z}$. This constraint unlocks non-trivial vortical and helical wave solutions across 1, 2, and 3 spatial dimensions—such as travelling vortices and helical centreline structures—that are unobtainable through d'Alembert's equation alone. The vacuum itself is classically quantised: an elementary voxel $l_o^3$ with axial length $l_o$ and an elementary time $t_o$ carries a quantised disturbance, whose electric displacement is not a response to an applied field but the primitive excitation agent generating the fields. Defining a quantised displacement as $D_{\rm E}:=e/l_o^2$ constrains a charge density and charge tensity, providing a propagation modulus $\mathcal T=l_o^2/t_o^2$ which autonomously establishes $c=\sqrt{\mathcal T}$ and thereby fixes the previously free transport speed in $\mathfrak M$ to $v=c$ before any constitutive parameter is derived. A parameterisation theorem then derives explicit expressions for the quantities $(\phi,\psi,\epsilon_0,\mu_0)$, and the elementary scales $l_o$ and $t_o$. A second, structurally parallel construction introduces an action modulus $\mathcal{H}$ built from the same primitive charge variables to fix Planck's constant $h$. Consequently, both fundamental constants of vacuum electrodynamics ($c$ and $h$) emerge not as independent empirical inputs, but as numerical calibrations of closure-native moduli within the algebraic framework. Furthermore, the elementary time scale bounds the excitation spectrum: the upper bound eliminates the classical Rayleigh--Jeans divergence while aligning with ultra-high-energy photon limits from the Pierre Auger and Telescope Array observatories, and the lower bound yields an emergent, strictly positive electromagnetic mass gap $\Delta_{\mathrm{EM}}$, read as a vortex-nucleation threshold above an otherwise gapless excitation branch. These results establish $\mathfrak M$ as a fundamental framework for vacuum electrodynamics. We define the vacuum, quantise space and time and obtain explicit expressions for an elementary length and elementary time Full abstract ... BibLaTeX@Online{Vrba-2026-2128, |