Cohomological Obstructions to Superluminal Hamiltonian Navigation: Symplectic Field Theory and the Hofer Energy Spectrum of Acausal Lagrangian Cobordisms

Mathematical Applications of Science Fiction We present a rigorous derivation of the topological obstructions preventing superluminal transport within theframework of Hamiltonian mechanics on symplectic manifolds equipped with a Lorentzian cobordism structure.By lifting the causal structure of spacetime to the contact hypersurface of the unit cotangent bundle, weconstruct a Symplectic Field Theory (SFT) formalism that detects "acausal" Lagrangian submanifolds. Wedefine the Causal Hofer Energy Spectrum and prove that any Hamiltonian isotopy generating a trajectoryviolating the null-energy condition induces a singularity in the moduli space of J-holomorphic curves.Specifically, we demonstrate that the Gromov-Witten invariants associated with superluminal cobordismsvanish identically unless the Hofer norm of the generating Hamiltonian approaches infinity. This establishesa "Symplectic Speed of Light" as a hard cohomological limit, independent of local metric perturbations,resolving the Alcubierre paradox through non-squeezing theorems in phase space.