The Unitary Reference Principle and Physical Reality: Binary, Light, Energy, Information, and Quantum Mechanics as Expressions of the Domain (0,1)

This paper applies the Unitary Reference Principle (URP), developed across Brogley (2026a–d), to the physical world. The central claim is that physical reality operates entirely within the URP domain — the infinite space between non-existence (0) and complete wholeness (1) — and that every fundamental domain of physics, information theory, and computation instantiates the five URP structural states: complete wholeness (n/R = 1), partial existence (0 < n/R < 1), contextual depletion (0/R), surplus (n/R > 1 — triggers a new declared reference), and deficit (n/R < 0 — obligation beyond the frame). Seven physical domains are examined. First: binary computing encodes information using two URP states — 0/R (contextual depletion of a bit position, frame persists) and 1/R (complete wholeness) — not standalone zero and arbitrary one. Second: fiber optic signal transmission is a physical depletion-renewal cycle — the optical signal depletes exponentially toward 0/R and is renewed at amplifier stations back toward 1/R. Third: Shannon information theory measures information content as a function of probability, where all probabilities are values in (0,1) and maximum entropy occurs at the URP midpoint of 1/2. Fourth: quantum mechanics describes every particle state as a probability amplitude in [0,1] — the Bloch sphere is the URP domain mapped onto a unit sphere. Fifth: thermodynamics and energy conservation are URP frame persistence laws — energy depletes within one frame and renews in another; standalone zero is never reached. Sixth: floating-point arithmetic errors are the base-2 incommensurability problem — the same structural phenomenon as infinite repeating decimals in base-10. Seventh: classical binary computing operates only at the URP domain boundaries (0/R and 1/R), while quantum computing operates across the full continuous URP domain — the most important structural difference between the two paradigms. The surplus state (n/R > 1) is addressed throughout: amplifier overshoot in fiber optics, energy input beyond thermodynamic capacity triggering phase change, binary carry overflow initiating a new declared reference, and quantum normalization enforcing R = 1. The three structural responses to surplus — overflow to new frame, regulation back to R, and frame break — appear across every physical domain examined. Full formal treatment in Brogley (2026a), Sections 1.5a–1.5e. URP Series:Paper 1 (Foundation): https://doi.org/10.5281/zenodo.19697119Paper 2 (Division): https://doi.org/10.5281/zenodo.19733441Paper 3 (Riemann Hypothesis): https://doi.org/10.5281/zenodo.19735713Paper 4 (Geometry): https://doi.org/10.5281/zenodo.19847459Paper 5 (this paper — Physical Reality): DOI assigned on upload Keywords Unitary Reference Principle, binary, fiber optics, signal attenuation, depletion-renewal cycle, Shannon entropy, information theory, quantum mechanics, qubit, Bloch sphere, thermodynamics, conservation of energy, floating-point arithmetic, quantum computing, physical reality, domain (0,1), surplus, deficit, five structural states, frame break, overflow