Causality, Strain, and Finite Signal Speed - An Elastic Resolution of Bell's Spaceship Paradox

Arc I — Accessibility Paper 1 Title Causality, Strain, and Finite Signal Speed: An Elastic Resolution of Bell’s Spaceship Paradox Zenodo DOI 10.5281/zenodo.18180742 Description This paper establishes finite signal speed as a primitive operational constraint and reformulates relativistic causality in terms of causal strain rather than geometric simultaneity. Using Bell’s spaceship paradox as a guiding example, it shows that apparent contradictions in relativistic motion arise from treating rigid geometric separation as physically meaningful in regimes where signal propagation is finite. The analysis replaces global simultaneity with locally accessible causal relations and introduces strain as a bookkeeping measure for delayed signal coordination across extended systems. Within this framework, acceleration-induced stresses and horizon-like effects emerge naturally from finite coordination speed, without invoking paradoxical length contraction narratives or hidden forces. Bell’s paradox is resolved by demonstrating that causal strain accumulates whenever acceleration profiles outpace coordination bandwidth, leading to inevitable separation or stress. This resolution does not depend on spacetime curvature or gravitational dynamics and applies equally to flat spacetime scenarios. The paper sets the conceptual foundation for the finite-accessibility program by showing how causality, stress, and breakdown of coordination arise prior to—and independently of—spacetime geometry. Keywords causality; finite signal speed; Bell’s spaceship paradox; relativistic strain; operational relativity; coordination limits Notes Arc I — Accessibility (foundational) Causality reformulated without global simultaneity Introduces causal strain as an operational concept Resolves Bell’s spaceship paradox without geometric rigidity Establishes finite signal speed as a primary physical constraint