Scale-Time Theory

Scale-Time Theory: The Geometry of Scale-Space is motivated by one central interpretative question: why do quantum mechanics and general relativity appear so difficult to reconcile at the level of ordinary spacetime description? The framework approaches this divide by treating quantum-like and relativistic-like behavior not as two final foundations that must be forced together, but as downstream readout regimes of a deeper scale-time substrate. In this view, the apparent tension between quantum discreteness, measurement, localization, time, and relativistic geometry may arise because both theories describe different operating regimes of the same underlying stroboscopic readout structure. Scale-Time Theory 8.1 presents a pre-physical framework in which experienced geometry, timing, objecthood, and physical-like behavior arise from stroboscopic sampling of closed two-dimensional scale-time planes. The framework begins with a global rotational phasor at the source (0,0)₀, carried through scale-space by an invariant light-carrier. A scale-slice is defined as a point in scale-space, specified by scale radius and phase-position, that establishes its own local closed scale-time plane ΠΣ = σy × σx. Each local plane is finite but boundaryless: opposite coordinate polarities connect at maximal scale radius. From this closed-plane structure follow the core laws LΣ = πCΣ for closed coordinate-radius path depth and 𝒪Σ = AΣ = πCΣ² for closed-plane scale order, oversampling depth, and bit-depth capacity. The global phasor input clock remains invariant for all scale-slices, while local scale-clock differences arise only as completed output cadences: fΣ,out = fp / 𝒪Σ and TΣ,out = 𝒪Σ / fp. Smaller scale-slices complete rapidly with low rendered depth; larger scale-slices accumulate deeper phasor exposure and complete more slowly. The theory treats closed-plane order as the oversampling domain of a filterless stroboscopic sampling system. Dyadic and triadic scale harmonics describe lock-compatible closure depths within that domain. The completed dyadic octave-lock ΩD = 2⁸ = 256 and the completed triadic shell harmonic ΩT = 3⁶ = 729 define a candidate scale-harmonic core-shell ratio χH = 729/256 ≈ 2.84765625. Together with the scale-space to spherical-readout bridge CΣ = πrΣ and SΣ = 4𝒪Σ/π², this yields a cautious inverse-square completion-rate law ΓΣ ∝ 1/rΣ² as a possible route toward gravity-like shell behavior. Experienced three-dimensional space is modeled as reference-selected readout of closed scale-slice planes. Phase distance gives observer-relative spatial distance, while a stroboscopically locked spin-like relation gives stable normal direction. In this version, phase distance is clarified as a baseline-delay relation between the observer now-baseline βA and the system phase-baseline βΣ. The system phase-baseline is not a separate phasor source or independent clock; it is the system’s own stroboscopic focus / now-baseline position within the shared phasor-rotation rhythm. Thus, 3D-looking space arises from phase distance plus stable normal direction, organized into nested systems of sphere-like readouts. Physical terms such as spin, charge, mass, gravity, space, and time are used in qualified form. They are treated not as primitive assumptions, but as possible readout characters of stroboscopic scale-time order. Appendix A records a cautious candidate sketch for translational motion as dynamic phase-baseline drift. In this sketch, a system at native scale-lock has no persistent baseline drift and reads as rest-mass-like. Energy absorption may shift the system toward a larger dynamic scale position, changing its output-cadence relation and producing an unwrapped phase-baseline drift around the global phasor. This changing baseline-delay relation is treated as a candidate route toward translational motion-like readout, not as a completed mechanics. The framework remains speculative and does not yet attempt to replace quantum field theory, general relativity, or established physical models. Its purpose is to present a coherent mathematical and conceptual architecture for exploring how a physical-looking universe may arise from deeper scale-time order, and how the quantum / relativistic divide might be reinterpreted as a difference between readout regimes rather than an irreconcilable conflict between final foundations.