Hyper-Spacetime Dynamics: From Compact Lorentz Geometry to Relational Causal Quantum Geometry

This paper develops a geometric framework for causality and quantum observation within four-dimensional real spacetime, without invoking additional degrees of freedom or external measurement mechanisms. Promoting the bounded Lorentz angle to an intrinsic kinematic flow activates a spatial-vector ↔ temporal-bivector duality linking the Euclidean and Minkowski domains. Complementary manifolds, tangent spaces, and spinors become geometrically reciprocal, forming a closed, self-sustained intrinsic cyclic symmetry. Anchoring this flow to an observer’s local rest frame, without privileging any admissible timelike direction, establishes past-to-future causal ordering within a finite causal interaction volume whose boundary is double-covered by reflection symmetry. The geometric product of momentum and causal separation yields a Lorentz-invariant action defining a dynamical phase, motivating a 4π-periodic causal-boundary standing-wave interpretation. Spacetime event reflections generate four Dirac-related boundary eigenstates with geometric CPT closure, weighted by causal-boundary amplitudes to form a generalized wavefunction. Under semiclassical uncertainty and gravitational stability constraints, the Planck length emerges as a conditional minimum causal distance scale. Quantum observation is formulated as relational causal-boundary mode selection, registering spin orientation and matter–antimatter identity, rather than as wavefunction collapse.