The Directed Electron and the Photon Signal in Six-Throat Spacetime

Abstract

One Electron. Two Directional Amplitudes. One Photon Field. Could the missing information be hidden in intensity itself? Can a single electron carry two simultaneous directional amplitudes without dividing into two particles? Can a single photon field preserve directional information that ordinary intensity measurements fail to distinguish? And can this hidden information be transformed into a measurable difference between two detector outputs? This research investigates these questions within Six-Throat Directed Geometry, developing a mathematical connection between directed electronic states, quantum transitions, photon-field coherence, and direction-resolved measurement. The central result establishes that one photon field can carry both unsigned intensity and signed directional information without requiring a second photon species. Through an explicitly constructed two-mode representation, directional coherence that remains inaccessible to an intensity-only measurement can be converted into a difference between two output photon counts using a coherent, number-preserving transformation. The analysis begins with the inherited six-throat spacetime metric and its directed electronic operator, preserving the established geometry and global quantum structure. A reproducible spectral investigation tracks electronic states across four Fourier cutoffs and verifies 28 inherited geometric and numerical identities. For the inherited two-route source profiles, the study obtains an exact restricted overlap of 0.9945940085424316, corresponding to a signed coherence magnitude of 0.1038400605330016. This result supplies a quantitative mathematical foundation for examining directional information within a single photon field. The paper further develops a four-class Z2 × Z2 algebraic structure linking fermionic and bosonic source sectors. Its conditional joint-covariance construction demonstrates how directional information can remain encoded in correlations even when individual measurement averages vanish. A separate quantum-transition analysis establishes precise conditions under which a single electronic state can retain simultaneous directional amplitudes while some transition measurements remain insensitive to their signed difference. The experimental significance is equally important: the research specifies an independently testable optical protocol involving coherent mode preparation, mode matching, interferometric transformation, balanced photon-count measurements, and controlled comparisons. It derives measurable predictions, coherence requirements, discrimination limits, and finite-sample precision conditions. The accompanying reproducibility package reports 13,066 successful mathematical and computational checks, together with source code, numerical data, figures, and file-integrity verification. The result is a theoretical and computational framework for investigating a fundamental possibility: directional physical information may remain concealed in total intensity while becoming accessible through coherent measurement of the same photon field. This work advances the study of directed matter–radiation coupling, quantum observability, and photon-information structure, and provides explicit mathematical predictions and experimental procedures for independent scientific examination.