Time Is Not a Dimension: Causal Accumulation in a Discrete Substrate

Time Is Not a Dimension: Causal Accumulation in a Discrete Substrate (v2. 0) This is the fifth entry in a six-part physics series introducing the ΔC (Delta-C) framework. Building on the mechanical definitions of Gravity (Paper 3) and Inertia (Paper 4), this paper presents a radical reformulation of Time itself. In this framework, Time is not a pre-existing coordinate dimension. It is an emergent measure of Causal Fracture. Time as Stress Accumulation: The substrate stores unresolved causal change as tension (). When this tension exceeds the substrate's Yield Limit (₂ₑ₈ₓ), a discrete rupture occurs. The Chronon (): The "tick" of time is defined as a single substrate fracture event. Time flows because the substrate is continuously breaking under causal stress. The Arrow of Time: Time is irreversible because fracture is irreversible. The "Past" is the record of broken symmetry; the "Future" is the accumulation of stress. What's new in Version 2. 0: This is a complete reconstruction of the original draft, integrating the "Stiffness" () and "Inertial Density" () parameters defined in the previous papers. Major updates include: The Rupture Mechanism: Formal definition of the Chronon Yield Limit (₂ₑ₈ₓ). Time dilation is reinterpreted as a "hardening" of the substrate that prevents fracture (ticks), effectively slowing time down. Thermodynamics Derived: Entropy is shown to be a consequence of Substrate Hysteresis. The vacuum "remembers" every fracture, creating a permanent historical record. Appendix C (LENR Consistency): We reinforce the "Gamma Suppression" mechanism. High-frequency events (like 24 MeV gamma rays) fail to trigger a fracture in stiffened substrates, forcing energy into thermal channels. Series roadmap: This paper provides the temporal logic required for the final unification. The series concludes with the quantum application of these principles: Paper 1: A Dynamic ΔC Substrate for Gravity and Electromagnetism Paper 2: Δ₀ — The Universal Return Field Paper 3: Gravipressure — Gravity and Time Dilation as Substrate Mechanics Paper 4: The Chronon Field — Inertia and Causal Latency Paper 5: Time as Emergent Causal Fracture Paper 6 (in development): Substrate Rupture and the Quantum Collapse Related DOIs: Paper 1: https: //doi. org/10. 5281/zenodo. 17073364 Paper 2: https: //doi. org/10. 5281/zenodo. 17073638 Paper 3: https: //doi. org/10. 5281/zenodo. 17082227 Paper 4: https: //doi. org/10. 5281/zenodo. 17089747 Paper 5: https: //doi. org/10. 5281/zenodo. 17148920 Note on mathematical notation: Full LaTeX-rendered equations are in the PDF. This description uses plain-text notation due to Zenodo's formatting constraints.