Projective geometry for relativistic quantum physics

James Thomas Wheeler

Young, Charles

This paper presents a geometric reinterpretation of the Dirac equation within the Dimensional Evolution (DE) framework. Without modifying the mathematical structure or empirical predictions of relativistic quantum mechanics, the Dirac equation is reformulated as a constraint on relativistic identity formation rather than as a purely kinematic wave equation. In this interpretation, the Dirac spinor encodes internal resonance structure required for relativistic coherence, while gamma matrices act as directional collapse operators mediating between internal geometry and spacetime constraints. The intrinsic doubling of solutions is explained as a structural duality between verse-domain localization and inverse-domain harmonic support, providing a physical account of antimatter without violating CPT symmetry or energy positivity. Spin, Zitterbewegung, and relativistic measurement are reinterpreted as consequences of resonance geometry rather than unexplained algebraic features. Measurement and localization are treated as local geometric stabilization processes consistent with Lorentz covariance, extending the collapse-geometry account developed in DE-SP6 (Mott) to relativistic systems. This work is interpretive and foundational in scope. It preserves full compatibility with quantum field theory and established relativistic quantum mechanics while clarifying the physical meaning of the Dirac equation’s most enigmatic structures. --- Project website: https://de-theory.com This work is part of the Dimensional Evolution research program. Additional materials, updates, and contact information will be made available via the project website as the work expands.

Itsuma Kochi

This work proposes a unified structural interpretation in which time is treated not as a physical dimension, but as a dimensional activation axis (Z-axis) that projects a two-dimensional quantum informational domain into a three-dimensional relativistic spacetime. By distinguishing the dimensional rules governing quantum nonlocality and relativistic causality, the model explains why both regimes appear incompatible when interpreted within the same dimensional framework. The proposed activation mechanism reframes wavefunction collapse, the speed of light, and the emergence of classical spacetime geometry as consequences of projection from a lower-dimensional substrate. This framework does not modify existing physics but organizes quantum and relativistic behavior within a coherent geometric hierarchy.

F. T. Falciano, M. Novello, Jose M. Salim

Anatolii Mukha

Abstract We develop an operator‑geometric framework in which relativistic and quantum dynamics arise as projections of a deeper χ‑structured space. The construction begins with χ‑space, defined as an operator manifold equipped with a χ‑spectral algebra and a χ‑topological structure. Within this setting, Zitterbewegung is interpreted as a χ‑spectral cycle, and we prove that χ‑cycles generate discrete spectral data corresponding to physical mass and spin. A χ‑projection operator is introduced as a map from χ‑geometry to observable spacetime. We show that (i) relativistic kinematics emerges from χ‑metric projections, and (ii) quantum operators arise from χ‑spectral projections. Three main results are established: (1) χ‑spectrality implies quantization of χ‑cycles; (2) χ‑projections generate the standard quantum operator algebra; (3) mass and spin correspond to invariants of χ‑cycles. An explicit example—the χ‑structure of the electron—demonstrates how χ‑frequency, χ‑spin, and χ‑stability arise from the operator‑geometric formalism. The framework provides a unified mathematical mechanism linking relativistic and quantum structures through χ‑projections, suggesting a new direction for operator‑geometric approaches to fundamental physics.

Dave Pandres