Status: ❌ CLOSED (Oct 16, 2025)
Finding: Morris-Thorne wormholes satisfy ANEC but require impossible exotic matter
Conclusion: Quantum realizability gap of 10²⁹× makes approach infeasible
Phase C achieved ANEC satisfaction but hit fundamental quantum barrier
ANEC Results: 5/7 Morris-Thorne configurations satisfy ANEC globally (71.4% success rate)
- Best config: tanh(σ=0.1), ANEC = +8.88×10²⁷ J ✅
- Top 5 all have positive ANEC (no violations!)
- CRITICAL ISSUE: ALL require exotic matter at throat (ρ < 0)
The Fatal Problem - Quantum Realizability:
- Required: ρ(throat) ~ -10²⁶ J/m³ (negative energy density)
- Available (Casimir, 1nm gap): ρ ~ -10⁻³ J/m³
- GAP: 10²⁹× deficit — completely insurmountable with known physics
Key Insight: Proper throat-crossing integration essential
- Previous approach: stopped at l = 1.01×l₀ (avoided coordinate singularity)
- Solution: Proper coordinate mapping l(r) enables full throat crossing
- Result: Discovered configurations with ∫ T_μν k^μ k^ν dλ > 0
Comparison to Previous Phases:
Phase A (Warp Drives - FAILED):
Natário: 76.9% ANEC violations (median -6.32e38 J)
Quantum Inequality: 10²³× violations
Status: CLOSED - No-go theorem established
Phase B (Scalar-Tensor - FAILED):
Brans-Dicke: Field collapse (δφ/φ₀ ~ -10²³)
Horndeski: Screening 100× too small (R_V/R ~ 0.009)
Status: CLOSED - Screening approaches don't work
Phase C (Wormholes - CLOSED):
Morris-Thorne: 71.4% configs satisfy ANEC ✅
Best: tanh(σ=0.1), ANEC = +8.88e27 J
FAILURE: Exotic matter requirement 10²⁹× beyond quantum sourcing
Status: CLOSED - Quantum realizability impossible
Why Phase C Failed:
Despite satisfying ANEC globally (a significant achievement), all wormhole configurations require exotic matter densities that cannot be sourced by any known quantum mechanism:
- Casimir effect (strongest quantum source): ρ ~ -10⁻³ J/m³
- Squeezed vacuum states (achievable): ρ ~ -10¹⁰ J/m³
- Wormhole requirement: ρ ~ -10²⁶ J/m³
- Deficit: 10²⁹× for Casimir, 10¹⁶× for squeezed states
No plausible path to bridge this gap exists within known physics.
Phase A Result (lqg-anec-framework):
- FTL warp drives violate ANEC in pure GR (Natário: 76.9% violations)
- Quantum Inequality violations: 10²³× margin (insurmountable)
Phase B Result (scalar-tensor-ftl-analysis):
- Brans-Dicke FAILED: δφ/φ₀ ~ -10²³ (field collapse)
- Horndeski FAILED: R_V/R ~ 0.009 (screening 100× too small)
- Conclusion: Scalar-tensor theories cannot screen warp stress-energy
Phase C Question: Are wormholes fundamentally different?
- Geometry: Static throat vs dynamic bubble
- Topology: Non-trivial (two asymptotic regions) vs trivial
- Stress Distribution: Localized at throat vs extended shell
- Time Dependence: Static vs moving at v_s ~ c
Hypothesis: Wormholes might have different ANEC violation patterns, but likely still require exotic matter (ρ < 0)
Goal: Implement traversable wormhole geometry and compute ANEC at throat
Framework:
Morris-Thorne metric (1988):
ds² = -c²dt² + dl²/(1 - b(l)/l) + l²(dθ² + sin²θ dφ²)
l: Radial "proper distance" coordinate
b(l): Shape function (throat radius at l₀)
Φ(l): Redshift function (tidal forces)
Traversability conditions:
1. b(l₀) = l₀ (throat at l₀)
2. b'(l₀) < 1 (flare-out condition)
3. Φ finite (no horizons)
The Fundamental Barrier: Every FTL/warp approach tested requires violating energy conditions or sourcing impossible exotic matter:
| Phase | Approach | ANEC | Exotic Matter | Quantum Realizability | Status |
|---|---|---|---|---|---|
| A | Warp drives | ❌ 76.9% violations | Required | 10²³× QI gap | ❌ CLOSED |
| B | Scalar-tensor | N/A | Modified coupling failed | N/A | ❌ CLOSED |
| C | Wormholes | ✅ 71.4% satisfied | Required | 10²⁹× gap | ❌ CLOSED |
Key Insight from Phase C:
- ANEC satisfaction is achievable (wormholes succeeded where warp drives failed)
- BUT exotic matter sourcing is the insurmountable barrier
- The 10²⁹× gap between Casimir and required ρ is fundamentally unbridgeable
All conventional approaches exhausted. Three options remain:
- Accept FTL impossibility within known physics
- Find new quantum exotic matter sources (requires physics beyond Standard Model)
- Change the coupling itself: Modify how curvature couples to energy-momentum
Next Research Direction: Instead of trying to source exotic stress-energy, explore whether the gravitational coupling constant G can be made field-dependent through coherence/phase effects, making curvature "cheaper" energetically.
→ See Phase D: Coherence-Modulated Gravity Coupling (if pursued)
Implemented:
- ✅ Morris-Thorne metric class (348 lines, fully tested)
- ✅ Shape function catalog: power-law, exponential, tanh
- ✅ Stress-energy tensor from Einstein equations
- ✅ Coordinate mapping system (r ↔ l for safe throat crossing)
- ✅ Throat-crossing ANEC integrator
- ✅ Configuration optimizer (60 configs tested)
- ✅ Thin-shell wormhole model (Visser cut-and-paste)
- ✅ Comprehensive comparison runner
- ✅ Tests: 18/18 passing (10 MT + 2 coord + 6 thin-shell)
Key Results:
| Configuration | ANEC (J) | Status |
|---|---|---|
| tanh(σ=0.1) | +8.88e27 | ✅ SATISFIED |
| tanh(σ=0.15) | +5.83e27 | ✅ SATISFIED |
| tanh(σ=0.2) | +4.04e27 | ✅ SATISFIED |
| exponential(λ=0.5) | +2.70e27 | ✅ SATISFIED |
| exponential(λ=1.0) | +6.43e26 | ✅ SATISFIED |
| power-law(n=0.5) | -1.33e27 | ❌ VIOLATED |
| power-law(n=0.8) | -5.23e26 | ❌ VIOLATED |
Thin-Shell Comparison:
- All 5 tested configs violated ANEC (0% success)
- Morris-Thorne approach superior for ANEC satisfaction
Deliverable: ✅ results/comprehensive_wormhole_comparison.json (12 configs analyzed)
Goal: Direct comparison of ANEC constraints between wormholes and warp drives
Tests:
- Throat crossing geodesics (radial null rays)
- Off-axis geodesics (impact parameter sweep)
- Time-like vs null geodesics
- Energy conditions: NEC, WEC, SEC, DEC
Comparison Matrix:
Wormhole (MT) Warp Drive (Natário)
─────────────────────────────────────────────────────────
ANEC violation: ??? 76.9% (median -6.32e38 J)
QI violation: ??? 10²³× margin
Exotic matter: Required at Required in shell
throat
Stress magnitude: ??? T ~ 10³⁷-10³⁹ J/m³
Deliverable: Comparative analysis document + JSON
Goal: Assess if wormholes are more/less realizable than warp drives
Questions:
- Can quantum fields source wormhole stress-energy?
- Do vacuum fluctuations satisfy exotic matter requirements?
- Casimir effect magnitude vs throat requirements
- Stability analysis (perturbative)
Expected Outcome:
- Wormholes likely also violate ANEC/QI (different pattern, same impossibility)
- Combined with Phases A & B → comprehensive FTL no-go theorem
wormhole-anec-analysis/
├── src/
│ ├── metrics/
│ │ └── morris_thorne.py # MT wormhole metric
│ ├── geometry/
│ │ ├── throat.py # Throat geometry calculations
│ │ └── shape_functions.py # b(l) catalog
│ ├── stress_energy/
│ │ └── einstein_solver.py # T_μν from Einstein equations
│ └── anec/
│ └── wormhole_integrator.py # ANEC for throat crossing
├── tests/
│ ├── test_morris_thorne.py
│ ├── test_throat_geometry.py
│ └── test_anec_integrator.py
├── examples/
│ └── demo_throat_crossing.py
├── run_wormhole_anec_sweep.py # Main analysis script
└── docs/
└── week1_mt_results.md # Results documentation
ds² = -e^{2Φ(l)} c²dt² + dl²/(1 - b(l)/l) + l²(dθ² + sin²θ dφ²)
Φ(l): Redshift function (controls tidal forces)
b(l): Shape function (determines throat geometry)
- No horizons: Φ(l) finite everywhere
- Throat exists: b(l₀) = l₀ at minimum radius l₀
- Flare-out: b'(l₀) < 1 (wormhole opens up from throat)
# Power-law shape function
b(l) = l₀ × (l₀/l)^n for l ≥ l₀
n > 0: flare-out rate
l₀: throat radius (e.g., 1 m)From Einstein equations G_μν = 8πG T_μν:
ρ(l₀) = -b'(l₀)/(8πG l₀²) # Energy density
p_r(l₀) = ρ(l₀) # Radial pressure
p_t(l₀) = ... # Tangential pressure
Flare-out condition b'(l₀) < 1 → ρ(l₀) < 0
→ Exotic matter REQUIRED at throat
- Throat crossing geodesics: ∫ T_μν k^μ k^ν dl < 0
- Similar to warp drives (different geometry, same physics)
- Exotic matter requirements comparable to QI bounds
Conclusion: Wormholes also impossible via same mechanism as warp drives
- Throat ANEC integral positive (averaged)
- But quantum stress-energy fluctuations violate QI
- Still impossible (same as Alcubierre in Phase A)
Conclusion: Different failure mode, same impossibility
- Would require exotic matter that violates energy conditions but satisfies ANEC
- Physically inconsistent (NEC violation usually implies ANEC violation)
Conclusion: Would need completely new physics (not expected)
Phase A (Warp Drives):
- Moving bubbles (v_s ~ 0.1c - 0.9c)
- Extended stress-energy shell
- ANEC violations: Natário 76.9%, Alcubierre 0% (but causality violated)
Phase B (Scalar-Tensor):
- Attempted to screen warp stress via scalar fields
- Both BD and Horndeski failed (coupling/screening issues)
Phase C (Wormholes):
- Static geometry (no v_s)
- Localized stress at throat
- Different geodesic structure (throat crossing vs bubble transiting)
Common Thread: All require exotic matter (ρ < 0)
Minimum Viable Analysis:
- ✅ MT metric implementation validated
- ✅ Throat stress-energy computed from Einstein equations
- ✅ ANEC integral for radial geodesics
- ✅ Exotic matter quantification
- ✅ JSON output with violation statistics
Complete Analysis (if time permits):
- 🔲 Off-axis geodesics (impact parameter sweep)
- 🔲 All energy conditions (NEC, WEC, SEC, DEC)
- 🔲 Quantum field theory stress-energy (renormalized)
- 🔲 Casimir effect estimate vs throat requirements
- 🔲 Stability analysis
Week 1 (Oct 15-22): MT implementation + throat ANEC Week 2 (Oct 22-29): Wormhole vs warp comparison Week 3 (Oct 29-Nov 5): Physical realizability + final report
Decision Point (Nov 5):
- If wormholes also fail → Comprehensive FTL no-go theorem
- If wormholes show promise → Extended analysis (Phase C+)
Wormhole Theory:
- Morris & Thorne (1988): "Wormholes in spacetime and their use for interstellar travel"
- Visser (1995): "Lorentzian Wormholes: From Einstein to Hawking"
- Hochberg & Visser (1997): "Geometric structure of the generic static traversable wormhole throat"
Energy Conditions:
- Hawking & Ellis (1973): "The Large Scale Structure of Space-Time"
- Wald (1984): "General Relativity"
- Visser (2002): "Energy conditions in the epoch of galaxy formation"
Phase A/B:
- lqg-anec-framework: Pure GR warp drive ANEC analysis
- scalar-tensor-ftl-analysis: BD/Horndeski screening attempts
MIT License
Current Status: Repository initialized. Starting Week 1 implementation.