Quaternion–Hypersphere Theory of Spacetime

by Norbert Nopper

A conceptual synthesis of closed FLRW cosmology, a quaternionic parameterisation of the spatial three-sphere $S^3$, and a relational account of time.

Overview

This note is a conceptual synthesis, not a new dynamical theory. It assembles four ingredients into a single self-consistent picture:

1. A quaternionic parameterisation of the spatial three-sphere $S^3$.
2. The closed ($k=+1$) branch of Friedmann–Lemaître–Robertson–Walker (FLRW) cosmology.
3. The Schwarzschild-radius identification $R \sim 2Gm/c^2$ relating the curvature radius to the total mass-energy content (an order-unity coincidence in any near-critical FLRW cosmology).
4. A relational stance in which cosmic time is defined operationally through matter-built clocks.

Each ingredient has independent precedent: quaternions on $S^3$ (Hamilton); closed FLRW (Friedmann, Lemaître); Schwarzschild-scale cosmology (Pathria, Good, Stuckey, Popławski, Melia); relational time (Mach, Barbour, Rovelli). The combination is offered as a pedagogical and philosophical reframing of standard closed $\Lambda$CDM, not as a source of new empirical predictions.

The paper

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Citation

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License

CC BY 4.0. See LICENSE.