Physical extension of quantum mechanics in the SGDM model by Yuri A. Chesnokov: electron as a stable 3D standing wave ($\vec{E} \perp \vec{B}$, $\Delta\varphi = 90^\circ$, $\langle\vec{S}\rangle \equiv 0$), graviton nucleus ($N_{\text{grav}} = A$, $\rho_0 \approx 3 \cdot 10^{17}\text{ kg/m}^3$), resolution of wave-particle duality, quantum numbers, and material properties.
The SGDM model resolves the century-old wave-particle duality paradox and bridges microphysics with relativistic GR gravity. The electron in a stable atom is not a point particle, but a closed 3D standing wave resonator anchored to the Kerr graviton nucleus ($N_{\text{grav}} = A$).
Only continuous wave fronts propagate through space at velocity $c$. A quantum ($E = \hbar\omega$) arises strictly as a local resonant absorption/emission act by the atom's graviton nucleus.
In an unexcited $1s$ atom, the radial $\vec{E}$ and azimuthal $\vec{B}$ spin vortex fields are shifted by $\pi/2$. Poynting vector $\langle\vec{S}\rangle \equiv 0$ — zero radiation, eternal stability.
$n$ — number of de Broglie wavelengths; $l$ — nodal planes ($s, p, d, f$); $m$ — $90^\circ$ phase orthogonality; $s = \pm 1/2$ — Pauli spin magnetic lock (2 electrons $\uparrow\downarrow$ per mode).
The $1057\text{ MHz}$ shift arises from direct contact of the $2s_{1/2}$ mode with the Kerr graviton ($r_g \approx 0.84\text{ fm}$), unlike the nodal $2p_{1/2}$ mode. Mass $m_e$ is standing wave energy in $a_0$.
In SGDM, the spin-2 massive graviton with rest mass $M_g \approx 2.6 \times 10^{-68}\text{ kg}$ is the primary topological metric node. Nucleons condense onto pre-existing quantum graviton nodes of space.
Hydrogen: 1 node, Helium-4: 4 nodes (tetrahedron), Iron-56: 56 nodes, Gold-197: 197 nodes, Uranium-238: 238 nodes.
Due to energy density $\rho_0 c^2 \sim 3 \times 10^{34}\text{ J/m}^3$, nonlinear curvature generates attractive force $F \sim 10^4 - 10^6\text{ N}$ ($10 - 200\text{ tons of force!}$), binding quarks and nucleons together.
Over chemical bond distances, direct gravitational pull falls by $1/r^2$ by a factor of $10^{46} - 10^{48}$ ($F \sim 10^{-44}\text{ N}$), strictly negligible compared to Van der Waals forces.
In the SGDM framework, the concept of "Gravitational Nuclear Force" does not contradict standard Quantum Chromodynamics (QCD) with its gauge gluon fields $SU(3)_c$, but rather models the dual geometric spacetime framework of confinement. At $r \le 1\text{ fm}$, spin-2 graviton nodes establish metric tension $\sigma \sim c^4/G_{\text{eff}} \sim 10^5\text{ N}$, inside which gauge quark-gluon flux tubes naturally close into color-singlet hadrons without singularities.
The primordial black hole swarm (95% of cosmic mass) populates the spherical galactic halo, through which the Solar System traverses at $v \sim 230 - 300\text{ km/s}$. At local halo density $\rho_{\text{DM}} \approx 0.4\text{ GeV/cm}^3$, the mean inter-PBH separation is $L \sim 1.5 - 3.0\text{ AU}$ ($200 - 450\text{ million km}$).
| Target Body / Scale | Cross-Section $\sigma$ | Direct Collisions (500 Myr) | Orbital Transits (500 Myr) |
|---|---|---|---|
| Earth ($R = 6\,371\text{ km}$) | $1.27 \times 10^8\text{ km}^2$ | $\sim 5 \times 10^{-6}$ (rare event) | — |
| Jupiter ($R = 70\,000\text{ km}$) | $1.5 \times 10^{10}\text{ км}^2$ | $\sim 10^{-4}$ | — |
| Sun ($R = 696\,340\text{ km}$) | $1.5 \times 10^{12}\text{ km}^2$ | $\approx 10^{-2}$ ($\sim 1\%$) | — |
| Earth's Orbit ($r = 1\text{ AU}$) | $7.0 \times 10^{16}\text{ km}^2$ | — | $\mathbf{\sim 500 - 1000\text{ transits}}$ |
| Kuiper Belt ($r = 50\text{ AU}$) | $1.7 \times 10^{20}\text{ km}^2$ | — | $\mathbf{> 1\,000\,000\text{ transits}}$ |
In SGDM, black holes remain stable in vacuum. When traversing dense planetary matter ($\rho \approx 3 - 13\text{ g/cm}^3$) at hypersonic speed $v \approx 300\text{ km/s}$, asymmetric Bondi–Hoyle accretion transfers rotational torque ($\frac{da^*}{dx} > 0$), leading to two outcomes:
With modest initial spin ($a_0^* < 0.85$), the micro-BH traverses Earth in $\approx 42\text{ seconds}$, absorbing only micrograms of matter and leaving a narrow plasma ionization trail.
If initial spin was near-critical ($a_0^* \ge 0.95$), at depths of $1/3, 1/2$ or $2/3$ Earth diameter ($x \sim 4\,000 - 8\,000\text{ km}$), spin-up hits $v_{\text{eq}} \to c$. Centrifugal overpressure ($K \equiv 1.04$) violently detonates core $\rho_0$, releasing $10^{14}-10^{17}\text{ tons}$ into ultra-hot quark-gluon plasma and pure hydrogen!
Micro-BH detonation or hypersonic passage generates localized shockwaves exceeding $P > 50 - 200\text{ GPa}$ and $T > 5\,000^\circ\text{C}$, producing vertical diatremes and ultra-high-pressure mineral phases:
Ultra-dense silica with octahedral silicon coordination lining the crustal penetration channel.
Synthesized during instantaneous shock compression of graphite, $58\%$ harder than cubic diamond.
Lower mantle high-pressure phases produced directly along upper crustal fracture zones.
Vertical cylindrical conduits of explosive mantle degassing propelling diamonds to the surface.
Newtonian ballistic theory yields deflection angle $\theta_{\text{Newton}} = \frac{2GM}{c^2 b}$. In SGDM graviton theory, tensor metric distortion doubles the total angle:
$\theta_{\text{time}} = \frac{2GM}{c^2 b}$ due to refractive time slowing.
$\theta_{\text{space}} = \frac{2GM}{c^2 b}$ due to spin-2 3D spatial warping.
In wave optics, single-slit diffraction is characterized by beam divergence $\theta \approx \lambda / d$ as slit width approaches wavelength $d \to \lambda$. In SGDM, this phenomenon is driven by the transverse metric gradient $\nabla h_{\mu\nu}(y)$ generated by graviton nodes ($N_{\text{grav}} = A$) along the slit boundaries.
As slit width $d$ narrows, the entire photon beam encounters the steep metric distortion zone near the edges, bending light trajectories into the classical diffraction fringe pattern.
Low mass $\implies$ sharp central peak, standard Fresnel diffraction.
Optimal nucleus $\implies$ moderate 1st-order side lobe enhancement.
Heavy relativistic core $\implies$ metric wave front retardation and brighter side fringes.
When white light traverses a prism at angle $\alpha$, it disperses into a rainbow spectrum. In SGDM, refractive index dispersion $n(\lambda)$ originates from the quantum-metric interaction of photon energy $E = \hbar\omega$ with the spin-2 graviton lattice of the medium ($N_{\text{grav}} = A$).
$\lambda \gg l_{\text{grav}} \sim 0.2\text{ nm}$. Photons average over atomic metric wells $\implies$ minimal phase retardation $\implies$ $n(\text{red})$ is minimal, lowest deflection angle.
Higher quantum energy ($1.75\times$) and spatial localization $\implies$ deeper probe of graviton wells $\implies$ $n(\text{violet})$ is maximal, largest deflection angle.
In classical and quantum optics, the predominant contribution to the macroscopic refractive index $n(\lambda)$ and diffraction patterns ($>99.99\%$) arises from electromagnetic polarizability of electronic shells and surface plasmon modes. The term $\beta_{\text{grav}}$ in SGDM represents an ultra-fine quantum-metric topological vacuum polarization correction ($h^{\mu\nu}T_{\mu\nu}$), linking crystal lattice geometry directly with spacetime metric fluctuations at the Planck-nuclear boundary.
For gamma and hard X-rays ($\lambda \le R_{\text{core}} \sim 1 - 7\text{ fm}$, $E > 1\text{ MeV}$), radiation interacts directly with nuclear graviton nodes ($N_{\text{grav}} = A$) via pair production ($\sigma_{\text{pair}} \propto Z^2 \propto N_{\text{grav}}^2$) and Compton scattering.
Linear single scattering $I(x) \approx I_0(1 - \mu x)$ with negligible flux loss.
Exponential shielding ($e^{-\mu x} \to 0$): $9\text{ cm}$ of Lead ($^{208}\text{Pb}$) reduces gamma flux by 1000-fold ($10 \cdot d_{1/2}$), equivalent to $1\text{ km}$ of air or $1.1\text{ m}$ of water.