Data Light Speed Relation

The Data Light Speed Relation says light and data take the same step, the Pulse Length, on different clocks: light once a local frame, data once a Zinf cycle, so light speed is the Pulse Length times the Frame Rate, data speed is the Pulse Length times Zinfinity, and their ratio, s = (2f)^L, is what it costs data to build light. It holds in two frames, local and UniSpheral. Data builds light, and building costs time: one step of light takes s Zinf cycles of data, about 2.361 × 10⁶² in our universe, so data runs ahead of its light by s, v_ↁ = 𝒞→·(2f)^L; at the Zinf s = 1 and data and light are one. Everything physical, light included, is capped at 𝒞→: no message crosses space faster, and the correlations of entangled data run through their shared source. A pattern is never faster than the rule that builds it, as in a cellular automaton, whose patterns move at a fraction of the rule's one cell a tick; light is the fastest pattern data can build. In the local frame, a universe's Pulse Length and Frame Rate are its own ruler and clock, and every observer in it measures 𝒞→; up the typical ladder both grow by 2f a level, so 𝒞→ is the same in every such universe, and off the ladder it differs only between universes compared in one frame. Clock speed is not light speed: a lower universe pulses faster, with more frames a second, each reaching a shorter step by the same factor. In the UniSpheral frame, counted in pixels crossed and Zinf cycles, data moves one pixel every Zinf Rhythm in every universe, the one speed the whole UniSphere shares, and light moves 1/s of that, faster in faster universes. Physics draws the same distinction within one universe, light's locally measured speed always c and its speed in shared coordinates varying (the Shapiro delay), and a frame no inside observer can detect is consistent with special relativity (Lorentz's preferred-frame theory predicts what Einstein's does), so the UniSpheral frame is tested only through its consequences, such as s. How a lattice of data gives a light speed the same in every direction and for every moving observer stays an open problem of discrete spacetime. Formally, 𝒞→ = ①⥂⦜⌂·𝓕⟳(L) and v_ↁ = ①⥂⦜⌂·ℨ∞ = 𝒞→·(2f)^L, with u_ↁ = 1 ⊕/ↁℨ⧖ and u_𝒞 = u_ↁ/s in the UniSpheral frame, where 𝒞→ is light speed measured within a universe [𝕃·𝕋⁻¹], ①⥂⦜⌂ the Pulse Length, the distance of one full cycle [𝕃], 𝓕⟳(L) the Frame Rate, one frame per Tempo [𝕋⁻¹], ℨ∞ Zinfinity, 1/ℨ [𝕋⁻¹], v_ↁ data speed [𝕃·𝕋⁻¹], s = (2f)^L the Universal Scaling Factor, the cost of one step of light [∅], u_ↁ and u_𝒞 data and light speed in pixels per Zinf Rhythm [𝕋⁻¹], ⊕ one pixel, a local Pulse Diameter, and ↁℨ⧖ the Zinf data rhythm, ℨ/2 [𝕋]: [𝕃·𝕋⁻¹] = [𝕃]·[𝕋⁻¹] and [∅] = [𝕋⁻¹]/[𝕋⁻¹]. It connects to UniSpheral Light Speed Limit, BPT Pulse Critical Velocity, UniSpheral Speed of Light, Constants of a Child Universe, Open and Closed Data, Universal Scaling Factor, Zinfinity, One Pixel = One Zinf and Effective Light Speed.

Category: Manuscript

Chapter: Chapter 1

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