A Unified 4D Euclidean Theory of Space-Time: Time as a Spatial Coordinate, Perceptual Emergence of Quantum Mechanics, Gravity and Cosmology

This preprint proposes a novel unified theory in which the universe is a 4D Euclidean dynamic manifold emergent from quantum entanglement, with the time coordinate t treated as fully spatial and symmetric to x, y, and z. There is no intrinsic arrow of time. The perceived arrow of time, Lorentz invariance, the speed of light limit c, quantum probabilities and wave-particle duality all emerge as illusions from the collective plus-t bias of our local matter grouping after the Big Bang. Particles cluster both spatially and temporally, moving “in block” along a shared direction labeled plus-t. Observations are confined to projections onto this locally biased plus-t hypersurface: we only detect worldlines that intersect our perceptual slice. Distances inherently mix spatial and temporal components. Quantum probability clouds arise as projections of deterministic worldlines oscillating in the real temporal coordinate t. Gravity is symmetric isotropic deformation across all four coordinates, perceived as spatial attraction plus time dilation. Dark matter corresponds to matter on minus-t trajectories (gravitationally active but electromagnetically invisible). The framework features elasticity emergent from entanglement entropy (K equals the second derivative of Sₑnt with respect to strain), polymer-capped curvature to resolve singularities as finite nodes, and PT-gauging plus causal-set discretization to enforce robust causality while preserving full 4D Euclidean symmetry. Forces unify geometrically: curvature gives gravity and torsion twists generate gauge fields, naturally reproducing quark masses and the CKM matrix from 4D torsional parameters (Monte Carlo fit with chi-squared per degree of freedom approximately 1. 1 using only five free parameters). The theory resolves the arrow of time, quantum measurement problem, black-hole information paradox (information preserved in finite 4D nodes and minus-t trajectories), and Hubble tension as projection effects. Subtle perceptual Lorentz invariance violations (quadratic, eta approximately 10 to the power of minus 20) are consistent with 2025 GRB 221009A data. Testable predictions include about 0. 1 arcsec sinusoidal (“wavy”) lensing arcs in JWST, gravitational-wave echoes of relative amplitude about 0. 001 (testable in LIGO O5), elevation of the GZK cutoff (greater than 10 to the power of 20 eV) consistent with IceCube 2025 data, and others. All current observations (LIGO O4, JWST, EHT) are fully consistent. Numerical simulations confirm the emergence of the speed of light c approximately 3. 00 times 10 to the power of 8 metres per second purely from 4D projections. Full derivations and figures are in the attached PDF. Ethics statement: This work was developed by the author with collaborative assistance from Grok 4. 20 (xAI) for mathematical derivations, simulations, LaTeX formatting and iterative refinement. All core scientific ideas, framework, interpretations and responsibility remain entirely with the author.