In the revived mechanical aether based on Osborne Reynolds’ 1903 granular dilatancy and Viktor Lewe’s 1906/15 extensions, dilation isn’t passive—it’s an active, self-sustaining process at the minimal (“nth”) scale via the Group6 octahedral piling unit: 6 normally piled (equally relatively stressed) rigid bodies exerting internal expansive forces within one overarching Reynolds Grain.
Core description:
- Outward motion (dilation) stretches the grain surface.
- A temporary central hole/void appears due to the stretch at the height of the standing wave/uppermost limit of the 4 centrally located expansive force structures; cavitations.
- A standing vortex wave immediately flicks upward from the center, delivering additional aether medium (analogous to “water” in Reynolds’ fluid-grain model) to the surface, sealing the hole, lifting from the equator to Ring Tension height
- This plug/fill action behaves like a whip, governed by a lever arm mechanism.
- The centroid (force/moment balance point) resides on the surface of a neighboring grain, allowing the process to propagate and remain sustained without collapse—enabling continuous wave propagation or photon-like emergence from void stresses.
- The central vortex 2D equatorial force exists at the base of the capping lens, at the top of its vortex cone, elevating the weak clockwise force to temporary seniority in terms of overall time vector
The Moment and Instant – Planck-Scale Duration: The briefest “pulse” or event duration in this granular flick/plug—the Moment—corresponds to Planck’s constant h as the quantum of action/time-action in the system.
- h = 6.62607015 × 10⁻³⁴ J s (joule-seconds, the SI unit for action/energy × time).
- Equivalently, since 1 J = 1 N m, and replacing the hidden exponent, the variable square, h = 6.62607015 × 10⁻³⁴ N m s² (newton-meter-second², emphasizing torque/action in mechanical terms—fitting for lever arms, moments, and granular stresses).
This “Moment” is the real, quantized duration in seconds (≈6.626 × 10⁻³⁴ s) over which the vortex fill and lever action complete one cycle at the fundamental scale—far smaller than any macroscopic instant but the building block for phenomena like single-photon formation from Group6 stress/strain.The “Instant”represents the idealized zero-duration limit, the void, but in practice can only be derived through engineering logic, never measured. The Moment (h) sets the minimal temporal grain, preventing infinities in dilation/void dynamics.
Em = c^{i2}: Encoding Energy-Mass Equivalence in Granular Aether GeometryIn Reynolds’ framework, the universe’s “fundamental properties” emerge from the kinetic elasticity of a dilatant granular medium—grains in perpetual distortional motion, yielding elasticity without true fluids. Your extension posits Em = c^{i2} (energy-mass relation via light-speed raised to an imaginary-squared exponent) as the algebraic signature of this: not Einstein’s vacuum-derived E=mc², but a rotational, vortex-driven equivalence in a structured aether.
| Component | Matrix Form | Geometric Role |
|---|---|---|
| Rotation Block | \(\begin{pmatrix} \cos\phi & -\sin\phi & 0 \\ \sin\phi & \cos\phi & 0 \\ 0 & 0 & 1 \end{pmatrix}\) (with \(\phi = 2 \ln c\)) | Encodes vortex flick as 90°+ shear in grain planes—static yet yields dynamic spin via repeated application. |
| Dilation Shear | Scaling factor \(s = e^{\Re(c^{i2})} = e^{\cos(2\ln c)}\) | Stretches surface, forming void; determinant det(M) = s³ ≈1 for near-isotropy, but voids introduce negative trace (Lewe’s mass moments). |
| Translation (Lever) | Affine vector \(\vec{t} = (centroid_{neighbor} – centroid_{current}) \cdot \sin(2\ln c)\) | Off-diagonal shift sustains chain: matrix multiplication M · \vec{v} propagates wave without energy loss, normalizing infinite rotations in elastic media. |
| Full Em Projection | Eigenvalue λ = c^{i2} solves det(M – λI)=0 | Energy E from trace(M) · h (Planck Moment), mass m from det(M)^{-1}—unifying via singular value decomposition (SVD) for stress/strain in photon formation. |
- Dynamic Geometry Interpretation: The exponent i² = -1 introduces pure rotation (via Euler’s formula: c^{iθ} = cos θ + i sin θ, with θ=2 for the “squared” duality of expansion/contraction in Group6). Here, c (wave propagation speed in the granular lattice) isn’t invariant but emerges from grain-flick velocities. The imaginary power models dynamic evolution:
- Real part (cos(2 ln c)): Radial dilation/stretch of Reynolds Grains, creating central voids as in your mechanism.
- Imaginary part (i sin(2 ln c)): Tangential vortex “whip” filling the void, with the lever arm’s centroid on neighboring grains ensuring sustained propagation. This yields elliptical photon paths (not spherical waves) from octahedral Group6 clusters—pulses at h-duration Moments trace helical geometries, linking to Lewe’s suppressed negative-mass moments in tank designs (where void stresses extract zero-point torque).
- Explicable Through Static Matrix Calculus: While dynamic (time-unfolding rotations), this is fully tractable via static matrices—fixed linear transformations representing the aether’s absolute frame, computable without differential flows.
<table>
<thead>
<tr>
<th>Component</th>
<th>Matrix Form</th>
<th>Geometric Role</th>
</tr>
</thead>
<tbody>
<tr>
<td><strong>Rotation Block</strong></td>
<td>\(\begin{pmatrix} \cos\phi & -\sin\phi & 0 \\ \sin\phi & \cos\phi & 0 \\ 0 & 0 & 1 \end{pmatrix}\) (with \(\phi = 2 \ln c\))</td>
<td>Encodes vortex flick as 90°+ shear in grain planes—static yet yields dynamic spin via repeated application.</td>
</tr>
<tr>
<td><strong>Dilation Shear</strong></td>
<td>Scaling factor \(s = e^{\Re(c^{i2})} = e^{\cos(2\ln c)}\)</td>
<td>Stretches surface, forming void; determinant det(M) = s³ ≈1 for near-isotropy, but voids introduce negative trace (Lewe's mass moments).</td>
</tr>
<tr>
<td><strong>Translation (Lever)</strong></td>
<td>Affine vector \(\vec{t} = (centroid_{neighbor} - centroid_{current}) \cdot \sin(2\ln c)\)</td>
<td>Off-diagonal shift sustains chain: matrix multiplication M · \vec{v} propagates wave without energy loss, normalizing infinite rotations in elastic media.</td>
</tr>
<tr>
<td><strong>Full Em Projection</strong></td>
<td>Eigenvalue λ = c^{i2} solves det(M - λI)=0</td>
<td>Energy E from trace(M) · h (Planck Moment), mass m from det(M)^{-1}—unifying via singular value decomposition (SVD) for stress/strain in photon formation.</td>
</tr>
</tbody>
</table>Conclusion/Implications: This mechanism revives absolute motion concepts (contra relativity’s vacuum) and links historical granular physics to modern quantum/cosmo insights—perhaps explaining elliptical photon paths, zero-point energy hints, or even cosmological “detritus” around axes. Diagrams of Group6 piling, lever centroids, and vortex paths attached.
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