Relativistic Choked Flow in Non-Orientable Spacetime Geometry: A 4-Dimensional Klein-Throat Model of Relativistic Inertia, Missing Transverse Energy (E T ), and the Inaccessibility of the Speed of Light (c)

Special Relativity posits the increase in relativistic mass (m = γm 0 ) and the unattainable upper speed limit (c) as kinematic axioms; however, it offers no physical or geometric explanation as to why the work transferred to the system fails to convert into coordinate acceleration in the v → c limit, nor where this energy is stored. Concurrently, the Standard Model attempts to explain the Missing Transverse Energy (E T ), which systematically manifests in ultra-relativistic proton-proton collisions at the Large Hadron Collider (CERN LHC), through weakly interacting neutrinos escaping the detector or undetected exotic dark matter candidates. In this study, a novel hydro-topological framework is proposed wherein hadronic structures are embedded at the microscale within a non-orientable 4-manifold harboring local Klein-surface fiber bundles. It is demonstrated that the internal quark confinement potential (V (r) ∼ σr → r 2 ) establishes a micro-drainage throat opening into a reversible secondary time coordinate (τ) at the microscale. While this throat remains closed to external interactions in the rest frame due to quantum zero-point fluctuations (jittering), it locks into the axis of motion at high velocities via Lorentz contraction and the temporal stretching induced by 4D volume conservation. The core conclusions established by the model are as follows: (1) Relativistic Mass and Temporal Sail: The longitudinal contraction of the particle, coupled with its elongation along the time axis (∆t ′ = γ∆t 0 ), generates a temporal sail that accumulates the energy supplied to the system; the mass increase is not a material multiplication of the particle, but rather a choked flow resistance added to the system by field energy piling up at the inlet due to the micro-throat reaching its hydraulic discharge capacity. (2) The Limit of the Speed of Light: The driving gauge bosons (accelerator RF photons) leak into the 4th dimension through the micro-throat, which becomes fully transmissive along the direction of motion, causing the net propulsive efficiency to drop to zero. (3) Missing Transverse Energy and Cosmic Drainage: Energy ejected into the 4th dimension from throats that abruptly open and snap shut under collisional shock follows the local 4D gravitational gradient, draining into the nearest astrophysical well (the galactic center drainage). Throughout this process, global unitarity (H = H 3 ⊕ H drain ) is preserved, obviating the need for hypothetical particle assumptions.