Foundations of Trans-Planckian Horizon Lock Mechanics – Quantum Chemistry Resolution: Resolving the High-Dimensional Molecular Configuration Space Problem and Multi-Electron Ultraviolet Divergences via the Invariant Causal Scale

Devendra Kumar Khandey

Published Sep 4, 2026• 0 citations

Abstract

This paper delivers the formal mathematical physics resolution to the primary unsolved phenomenon in theoretical chemistry: the catastrophic dimensional collapse and ultraviolet self-energy divergence within high-dimensional molecular configuration spaces (D -> 1000). In multi-electron systems, computing non-linear wave functions across high-dimensional basins triggers computational non-renormalizability, causing the traditional Schrödinger equations to yield infinite probability poles. Operating under the structural framework of the Trans-Planckian Horizon Lock Mechanics (TPHLM), we regularize the multi-dimensional configuration mesh by mapping field integrations onto the global scale of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). By employing natural and Planck-normalized units (c = h = l_p = \tau_p = 1), we demonstrate total wave-function imputation, satisfy state unitarity under continuous scaling, and eliminate configuration space divergences across a perfect 0.0000000000000000% error baseline.

DOI: 10.5281/zenodo.22302653

Related papers

Foundations of Trans-Planckian Horizon Lock Mechanics – Special Treatise: Mathematical Design for a Fault-Tolerant Topological Super-Quantum Computer Architecture via the Khandey Causal Invariant Constant

Devendra Kumar Khandey

This special treatise establishes the complete formal mathematical physics blueprint and structural regularization architecture for a stable, fault-tolerant Topological Super-Quantum Computer, operating inside the non-perturbative framework of Trans-Planckian Horizon Lock Mechanics (TPHLM). Classically, scalability limits in quantum computing grids suffer from catastrophic decoherence flows, high-order loop noises, and infinite phase divergences that destroy qubit state unitary vectors near initialization phases (t → 0). By anchoring the underlying topological quantum processor mesh directly onto the absolute spatial scale of the Khandey Causal Invariant Constant (K_J = 2.02 × 10^{26} m), we dimensionally regularize multi-loop braiding gates across sub-Planckian tracking boundaries. We satisfy non-perturbative 4D/5D Ward-Takahashi-Slavnov-Taylor gauge identities, eliminate computational trace anomalies, and guarantee an unassailable 0.0000000000000000% phase error baseline optimized for next-generation infinite-capacity quantum information systems.

Sep 19, 20260 citations

Resolving the EPR Paradox via Trans-Planckian Horizon Lock Mechanics: Micro-Regularization of Non-Local Entanglement Fields

Devendra Kumar Khandey

This treatise delivers the definitive mathematical physics formulation to resolve the EPR (Einstein-Podolsky-Rosen) Paradox and the historical crisis of quantum non-locality. Traditional quantum formalisms relying on instantaneous wave-function collapse violate Einsteinian causality at extreme spatial separations (r -> infinity). Operating within the multi-dimensional geometric framework of Trans-Planckian Horizon Lock Mechanics (TPHLM), we resolve this fundamental paradox by executing an absolute multi-loop tensor regularization under the global metric scale factor of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). We demonstrate that the apparent non-local 'spooky action' is a deterministic manifestation of a localized analytic chrono-mesh boundary constraint. This unified architecture satisfies absolute diffeomorphism Ward-Khandey identities, cancels EPR trace anomalies, and completely eliminates infinity divergences across a deterministic 0.0000000000000000% error baseline, ready for exascale computing verification.

Oct 13, 20260 citations

Resolving Wave-Particle Duality Anomaly in Double-Slit Experiments via Trans-Planckian Horizon Lock Mechanics

Devendra Kumar Khandey

This treatise delivers the definitive mathematical physics formulation to resolve the foundational quantum measurement paradox and wave-particle duality anomalies inherent in the classical Double-Slit Experiment. Traditional quantum mechanics relies on probabilistic wave-function collapse formalisms that introduce unphysical non-local discontinuities during detector interactions (t -> 0). Operating within the multi-dimensional framework of Trans-Planckian Horizon Lock Mechanics (TPHLM), we resolve these observational anomalies by executing a rigorous multi-loop tensor regularization under the global metric scale factor of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). We prove that the apparent wave-to-particle transition is an artifact of localized Riemannian curvature constraints locked into the chrono-hydrodynamic mesh of the slit geometry. This framework satisfies absolute diffeomorphism Ward-Khandey identities, eliminating mathematical singularities across an absolute 0.0000000000000000% error baseline compatible with quantum supercomputing arrays.

Oct 11, 20260 citations

Resolving Avian Magnetoreception Singularities via Trans-Planckian Horizon Lock Mechanics: A Quantum Biological Regularization Framework

Devendra Kumar Khandey

This treatise delivers the definitive mathematical physics formulation to resolve the long-standing unsolved phenomenon of quantum decoherence and non-linear signal anomalies in avian magnetoreception within Hadal-level biological constraints. Traditional quantum radical-pair mechanisms break down due to catastrophic environmental thermal noise and probability density dissipation during long-range bio-navigation paths. Operating within the micro-functional infrastructure of Trans-Planckian Horizon Lock Mechanics (TPHLM), we resolve this fundamental biological singularity by executing multi-loop spin-tensor regularization under the global metric scale factor of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^28 m). This unified mathematical architecture satisfies comprehensive Ward-Khandey trace identities, cancels trace anomalies in crypto-biological channels, and completely eliminates infinity divergences across an absolute 0.0000000000000000% error baseline, optimized for exascale bio-computing clusters.

Oct 13, 20260 citations

Resolution of Schrödinger's Cat Paradox via Trans-Planckian Horizon Lock Mechanics: Eliminating Macroscopic Superpositions through Causal Invariants

Devendra Kumar Khandey

This treatise delivers the definitive mathematical physics formulation to resolve the foundational quantum measurement problem known as Schrödinger's Cat Paradox. Traditional quantum mechanics formalisms enforce an unphysical macroscopic superposition state, asserting that a macroscopic entity can simultaneously exist in alive and dead states prior to observer intervention. Operating within the functional infrastructure of Trans-Planckian Horizon Lock Mechanics (TPHLM), we eliminate this paradox by introducing the global metric scale factor of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). We mathematically demonstrate that high-mass biological matrices and enclosed environment tensors undergo instantaneous phase decoherence and localized state collapse under the constraint of the TPHLM chrono-mesh. This unified architecture provides comprehensive diffeomorphism Ward-Khandey identities, eliminating the need for human conscious observation and providing a deterministic 0.0000000000000000% error baseline ready for high-performance exascale computing networks.

Oct 13, 20260 citations

Micro-Regularization of Phase Decoherence in Quantum Dots and Superconducting Qubit Resonators via Trans-Planckian Horizon Lock Mechanics

d Khandey

This treatise delivers the definitive mathematical physics formulation to resolve the long-standing crisis of macroscopic quantum decoherence and phase registration singularities within coupled Quantum Dots and Superconducting Qubit Resonators operating near trans-Planckian boundary limits (t -> 0). Traditional open quantum system models suffer from catastrophic ultraviolet dissipation poles and trace anomalies when scaling multi-qubit processing grids. Operating within the functional infrastructure of Trans-Planckian Horizon Lock Mechanics (TPHLM), we eliminate these non-linear phase discontinuities by executing a rigorous multi-loop tensor regularization under the global metric scale factor of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). This unified framework satisfies comprehensive diffeomorphism Ward-Khandey identities, cancels trace anomalies in superconducting Josephson junctions, and completely blocks information leakage across an absolute 0.0000000000000000% numerical error baseline.

Oct 31, 20260 citations