Dashboard Roadmap Fuchs Shell Six Slices Fell–Heisenberg Warp Factory Figures Notebooks About
Alcubierre · Boundary-Mode

1 · Existence anchor — Fuchs shell exists

Fuchs et al. 2024 (arXiv:2405.02709) construct a constant-velocity warp metric in which the Alcubierre shift βx is supported by a shell of ordinary matter modelled as a Tolman–Oppenheimer–Volkoff fluid with a smooth bump-function radial profile. At their canonical parameters

R₁ = 10 m, R₂ = 20 m, M = R₂c²/(6G), β = 0.02 c

the in-shell pass-fractions for all four energy conditions (NEC, WEC, DEC, SEC) come out identically 1.0000: the shell is positive-energy and the wall is sub-luminal everywhere. We reproduce this independently from a clean Warp Factory v1.0 install (Session 18) using the public metricGet_WarpShellComoving + evalMetric pipeline. The existence question is settled.

2 · Thickness scaling — κβ/C is universal in form, slice-valued in number

How thin can the shell be made? Holding compactness C = 2GM/(R₂c²) and shift speed β fixed, sweep the shell thickness Δ = R₂ − R₁ downward and find the smallest Δ at which DEC still holds throughout the wall. Across a 27-cell (C, R₂, β) ∈ {1/6, 1/3, 1/2} × {15, 20, 30 m} × {0.005, 0.02, 0.05} grid, evaluated at 6 inner Δ samples each (162 total Warp Factory metric builds, 140 minutes of headless MATLAB), the result is

Δmin / R2 = κ · β / C

with κ ≈ 5 typical: midpoint mean 5.33, median 6, std 1.0, range [4.0, 6.0] across 15 bracketed cells. The form of the scaling law holds across the entire surface — confirmed at decision-gate A. The numerical value κ varies systematically with β and R₂; relative spread is 18%, above the gate-A threshold of 10%, so κ is formally a slice-value rather than a universal constant. The Session-18 anchor estimate κ ∈ (4.17, 5.83] is one slice of this surface.

Geometrical-cap saturation — a new null finding

At high β + low C the κβ/C bound runs into the geometrical cap Δ < R₂ before any DEC-respecting shell exists. These cells are null configurations: no Fuchs shell exists for them regardless of mass. This adds a binding constraint on the Path-2A landscape that the analytic 2A.7 / 2A.9a derivations did not surface, and rules out high-velocity low-compactness Fuchs constructions categorically.

3 · Acceleration — ADM 4-momentum forbids self-acceleration

A static Fuchs shell is not a warp drive. To carry passengers anywhere it must accelerate. ADM 4-momentum conservation forbids self-acceleration of any isolated system in asymptotically flat vacuum (Schuster–Santiago–Visser 2023, Theorem 3). Three escape routes are catalogued in acceleration.ipynb:

  • Mass ejection (rocket-like) — viable but low-thrust, decoupled from warp physics.
  • Gravitational-wave recoil — quantitatively bounded by an HF-Jobs sweep over Fuchs-compatible parameters cross-rescaled against Varma et al. 2022 NR data: ≲ 0.25% of vwarp under the most favourable parameter combination tested. Not enough.
  • External momentum capture (interaction with cosmological exterior) — Phase 2C Slice 5 ceiling Δv ≤ 10⁻³⁶ m/s. Not enough.

This strictly strengthens Schuster–Santiago–Visser within the static-slice scope. The matter-shell route is closed under acceleration.

4 · Static infrastructure — Krasnikov tubes have no wall

The remaining classical option is a static "highway" — a network of pre-built Krasnikov tubes through which subluminal craft travel afterwards. Task 2A.13 (krasnikov_tube.ipynb) computes the Einstein tensor of the Krasnikov 4D metric symbolically with a Fuchs-class thick wall, reproducing Everett–Roman 1997 Eq. 14 to 14 decimals. The pointwise WEC minimum obeys a universal scaling

ρpmin(η, ε) = −κK(η) / ε²

with κK(η) ≈ 0.122 η at small η. Both the violation magnitude and the observable lightcone opening scale linearly with η, so their ratio is fixed: a Krasnikov tube cannot be made simultaneously useful and energy-condition-friendly. An HF-Jobs preview sweep over 300 (η, ε, n) points returns WEC pass-rate 0.0000.

This closes the static-infrastructure-network branch of the speculation/RING_NETWORK_CONCEPT.md document independently of any QFT-loophole arguments.

5 · Where this leaves the slice

Within the canonical static slice — Alcubierre βxx̂ × spherical Fuchs shell × asymptotically flat vacuum × steady-state × 4D GR — Path 2A returns:

  • Existence: yes, with positive-energy ordinary matter.
  • Thickness: bounded below by κβ/C, κ ≈ 5; high-β + low-C corner is null.
  • Acceleration: no useful classical mechanism.
  • Static infrastructure: no Krasnikov-tube wall for any η > 0.

The slice composite is "a positive-energy bubble exists, but no classical mechanism can accelerate it to useful speeds and no static infrastructure walls can be built." This is informative but not the closure of the classical question — six adjacent slices in Phase 2C all return null, and Phase 2D's Fell–Heisenberg multi-mode shift is the single largest source of positive-leaning physics still in flight.