Scale-Time Theory

Scale-Time Theory 10.0: The Pre-Geometry of Scale Space presents a hypothetical pre-ordinary-geometric framework in which quantum-like uncertainty, classical stability, motion-like appearance, gravity-like organization, and relativistic-looking phase-lapse are explored as connected regimes of one signal-processing-like scale-space. The framework begins from one global phasor sweep with invariant frequency fp, invariant carrier speed cφ ≡ c, and phasor travel step ℓp = c/fp. Scale-space is described through an interpretative radar-screen grammar: nested scale-slice horizons, scale angles, system baselines, observer baselines, sampling, aliasing, standing scale modes, and stroboscopic lock. A selected scale relation has physical scale radius ℛσ = ρσℓp, outer horizon path Lσ = 2πℛσ, dimensional scale address σ = πℛσ², and dimensionless sampling address sσ = σ/ℓp² = πρσ². In this version, scale does not change the carrier speed; it changes the path opened under that speed. Larger scale radii contain longer path distance per shared angular phasor cycle, while the carrier relation remains invariant. The central stabilizing mechanism is stroboscopic lock: coherent phase-overlay relative to a chosen baseline. Residual phase mismatch appears as aliasing. In the ideal dyadic sampling ladder, RA = 2 marks the first Nyquist-compatible relation, RA = 128 marks deep alias suppression, and RA = 256 marks stable octave-lock. Nyquist-proximal aliasing is associated with quantum spin-like ambiguity, while higher-oversampled coherent aliasing is associated with stable spin-like and rotation-like appearance. The framework distinguishes native scale position from scale-shift. Native scale position, σA,0 = πℛA,0², gives rest-mass-like invariant structure. A scale-shift factor ΛA moves the whole system into a longer synchronized path lane, σA(t) = ΛA(t)σA,0, giving energy-like and acceleration-like appearance without changing cφ. Motion-like appearance arises from changing observer-relative baseline separation. Gravity-like appearance is modeled as baseline drift organized around a dominant stroboscopic focus, with an inverse-square-like weak-field correspondence emerging from dilution over an expanding area-like scale domain. Observer selection establishes a local reference plane, now-baseline, and four-sector phase environment. Distance and delay arise from path multiplicity plus selected-baseline separation; containment occurs when observer-relative path clearance exceeds a system’s scale radius; observable size is the footprint of that radius on the observer’s baseline. Phase-lapse near the orthogonal boundary produces redshift-like, clock-slowdown-like, and horizon-like appearance. Spherical appearance and the Earth-scale mapping are treated as selected-reference outcomes of the same baseline, sector, scale-radius, and phase-lapse grammar. Scale-Time Theory 10.0 is not presented as a replacement for quantum field theory, general relativity, thermodynamics, standard cosmology, or established physical models. Its purpose is to provide a coherent hypothetical language in which sampling, aliasing, stroboscopic lock, scale address, standing scale modes, scale-shift, baseline drift, containment, spherical mapping, complexity, and phase-lapse can be explored as connected regimes of one phasor-ordered scale-space. The next intended step is constructive simulation: testing whether simple phasor-sampling models can generate stable lock nodes, aliasing regimes, standing scale-mode behavior, and transitions from weakly resolved to deeply oversampled structure.