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Spacetime as Emergent Geometry from Quantum Genealogy: The Quantum Family Tree Theory
Kevin Donahue — March 2026

We propose a framework in which spacetime geometry emerges from the genealogical structure of quantum entanglement. Beginning from a single entangled state that undergoes recursive binary splitting, mutual information between any two descendant particles decays exponentially with their genealogical distance. Physical distance emerges as the logarithm of inverse entanglement: d = a ln(1/E) + b. We present computational results from quantum simulations at depths 2 through 4 (up to 30 qubits, 16 leaves, 10-tree ensembles) demonstrating: (1) monotonic kinship decay of mutual information across 4 genealogical distances (80% of trials at depth 4), (2) a logarithmic distance-entanglement relationship with R² = 0.993, consistent with holographic (Ryu-Takayanagi) scaling, and (3) structural universality across random quantum dynamics.
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Contents

1. Introduction
2. Core Mechanism (generative process, entanglement as kinship, emergent geometry, decoherence)
3. Computational Results (method, kinship decay, distance-entanglement fit)
4. Ensemble Universality
5. Related Work and Distinctions (MERA, holographic codes, random tensor networks)
6. Alignments with Established Physics
7. Implications (cosmology, nonlocality, dark energy, black holes)
8. Future Directions and Theoretical Challenges
9. Conclusion
Appendix A: Simulation Protocol
References

Source code

Full simulation code, fit analysis scripts, and results data are available at github.com/kevin-nothing-matters/QFT.

Citation

K. Donahue, "Spacetime as Emergent Geometry from Quantum Genealogy: The Quantum Family Tree Theory," March 2026. Available at nothingmatters.life