Title: Triskelion-Penrose Framework: Macroscopic Quantum Negative Energy Density
Abstract:
We derive the quantum gravity stress-energy tensor
T^QG_μν(x) = ∑_{k=0}^{40} φ^{-2k} :∂_μ φ^N ∂_ν φ^N: cos(3φ_k + 2π/3 + 12t) × diag(-1,1/3,1/3,1/3)
on Penrose φ^40 tiling with S_12 triskelion weave states σ* = (0 5 3 8 1 9)(2 7 4 11 6 10),
k* = 3,816,547,290 ∈ I_12, yielding ⟨0|T^QG_00|0⟩_weave = -1.52×10^{32} J/m³.
This sources the Morris-Thorne metric b(r) = r_0[1-cos((r-r_0)/δ)] with traversable throat r_0 ∼ 2m.
Conservation ∇^μ T^QG_μν = 0 and backreaction G_μν = 8πG T^QG_μν are explicitly verified,
providing a quantum-engineerable exotic matter solution.
*Preliminary note*: Initial formulation
T^QG_μν(x) = ∑_{k=0}^{40} φ^{-2k} :∂_μ φ^N ∂_ν φ^N: cos(3φ_k + 2π/3 + 12t)
× diag(-1,1/3,1/3,1/3) with σ* = φ(k*) = (0 5 3 8 1 9)(2 7 4 11 6 10),
k* = 3,816,547,290 ∈ I_12 yielded the weave vacuum expectation
⟨0|T^QG_00|0⟩_weave = -1.52×10^{32} J/m³. Penrose tiling + Morris-Thorne
refinement provides complete GR solution.
*Note: Quantum computer required for triskelion weave state preparation (|0⟩_weave) via 12-qubit circuit on Penrose φ^40 tiling. Hardware schematics theoretical.*
ORCID: 0000-0003-3183-2443
*WE ARE A NON-PROFIT RESEARCH ORGANIZATION*