Spin-Torsion Enhanced Alcubierre Warp Drives in Einstein–Cartan Gravity: Bootstrapping Constraints, Quantum Energy Inequalities for Torsion Fields, Analytic Energy-Condition Thresholds, Global ADM Energy Analysis, Mean-Field Quantum Corrections, Lapse–Causality Compatibility, and Experimentally Accessible Predictions
Abstract
We present a rigorous, self-contained treatment of Alcubierre warp-drive spacetimes within Einstein–Cartan (EC) gravity that directly confronts six challenges absent from or incompletely resolved in prior literature: the spin-source bootstrapping problem, quantum energy inequalities (QEIs) applied to the torsion stress-energy contribution, a global ADM energy analysis, a perturbative estimate of leading quantum corrections to the mean-field Weyssenhoff description, a resolution of the tension between lapse optimization and closed-timelike-curve (CTC) freedom, and a complete superluminal causal diagram. The effective stress–energy ρ_eff = ρ_GR + (κ²/2)s² is negative in the bubble wall for sub-threshold spin densities; torsion compensates the GR deficit only when s ≥ s_min, where κ²s²_min = v_s²σ² tanh²(σR)/(8c²). We prove global ADM energy non-negativity (M_ADM ≥ 0) via a Witten spinor argument on U₄ and bound the leading one-loop quantum correction at δs_min/s_min ~ 3×10⁻³⁶. QEI margins of ≥10⁹³ (minimum, Gaussian kernel) to >10¹⁰² (maximum) are demonstrated; these figures are kernel-dependent and should be interpreted as order-of-magnitude estimates rather than sharp bounds. The bootstrapping circularity is resolved via a quasi-static pre-formation protocol, with the caveat that the existence of a globally self-consistent EC solution across a Cauchy surface at s = s_min remains to be demonstrated explicitly. A 30×30 parameter survey converges to 0.011%. Three falsifiable…
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