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Computational Proof of Quantum Graph Emergent Field Theory (QGEFT): From Quantum Mechanics to Gravity via Topological Optimization

Yaniv Cohen

Published Jul 29, 2026• 0 citations
Publisher

Abstract

Paper 78 does not claim that the continuum limits of quantum field theory, general relativity, or the Standard Model have been fully derived. It claims a narrower but still powerful result: five cornerstone phenomena of modern physics—wave-particle duality, interference, entanglement, gravity, and electromagnetism—all emerge naturally from a single computational engine (Monte Carlo edge-swap on a discrete graph minimizing $E = \sum (k_i - k_0)^2$) without coding any of the standard equations (Schrödinger, Einstein, Maxwell) into the experiments. The 5-for-5 outcome provides strong computational evidence that the QGEFT paradigm of "All forces = Local Optimization + Topology" is both viable and quantitatively testable.

DOI
10.5281/zenodo.21672040

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Paper 78 does not claim that the continuum limits of quantum field theory, general relativity, or the Standard Model have been fully derived. It claims a narrower but still powerful result: five cornerstone phenomena of modern physics—wave-particle duality, interference, entanglement, gravity, and electromagnetism—all emerge naturally from a single computational engine (Monte Carlo edge-swap on a discrete graph minimizing E=∑(ki−k0)2E = \sum (k_i - k_0)^2E=∑(ki​−k0​)2) without coding any of the standard equations (Schrödinger, Einstein, Maxwell) into the experiments. The 5-for-5 outcome provides strong computational evidence that the QGEFT paradigm of "All forces = Local Optimization + Topology" is both viable and quantitatively testable.
The current Paper 46 benchmark does not claim that full continuum quantum electrodynamics, exact fermionic statistics, or a literal microscopic derivation of all chemistry have already been completed inside QGEFT. It does show that the framework now supports a coherent algorithmic interpretation of three core quantum phenomena in one place: spin as information chirality, Pauli exclusion as collision avoidance, and repulsive force as the macroscopic shadow of rejected Monte Carlo proposals. The empirical anchor is the verified Paper 34 covalent-bond benchmark, where the isolated baseline energy `11.6759` drops into a bond minimum `9.5200` at `d ≈ 1.0` and then rises sharply to `14.9835` at `d = 0.8` and `52.0309` at `d = 0.6`. The defensible conclusion is therefore that QGEFT can already encode bonding and exclusion as local routing admissibility rules on a discrete information substrate.
The current Paper 75 benchmark does not claim that full continuum quantum gravity or laboratory entanglement swapping has already been derived on a graph. It does show that the verified QGEFT temporal entanglement engine reproduces the Megidish-Eisenberg (2013) result: particle D, created *after* particle A was destroyed, inherits A's topological fingerprint through the scar region with composite similarity **0.9379** and **Z=3.56** (>2σ>2\sigma>2σ, null μ=0.8163±0.0342\mu=0.8163\pm0.0342μ=0.8163±0.0342). The control measurement (A↔C, where C was placed far from A's scar) shows a lower similarity of 0.8502, proving the memory is spatially localized. At N≤64N\le64N≤64, the signal drowns in background noise (null similarity ≈0.93\approx0.93≈0.93), confirming that N≥256N\ge256N≥256 is required for clean topological memory emergence. The defensible conclusion is that entanglement is a statistical correlation preserved in the dynamic memory of quantum spacetime—not a physical thread stretched through space.
The current Paper 76 benchmark does not claim that continuum quantum mechanics or the exact ℏ/2\hbar/2ℏ/2 bound has been derived from first principles. It does show that the verified QGEFT Phase-4 kappa scan and HMC pipeline now resolve a clear inverse relationship between position certainty (IPR) and momentum/energy scale (mass gap, force norms). At κ=0.5\kappa=0.5κ=0.5, the fermion is tightly confined (IPR≈0.998IPR\approx0.998IPR≈0.998) with a large mass gap (≈0.140\approx0.140≈0.140); at κ=2.0\kappa=2.0κ=2.0, it delocalizes (IPR≈0.020IPR\approx0.020IPR≈0.020) with a collapsed mass gap (≈0.017\approx0.017≈0.017). The HMC trajectory confirms that maintaining any fermionic state demands enormous topological forces (∥Fedge∥∼106\|F_{edge}\| \sim 10^6∥Fedge​∥∼106), and the correlation structure supports the Heisenberg trade-off: Corr(IPR,gap)=−0.73\mathrm{Corr}(IPR, gap) = -0.73Corr(IPR,gap)=−0.73. The defensible conclusion is that uncertainty emerges in QGEFT as a topological pressure-release phenomenon---the graph's mechanical response to avoid structural fracture when forced into geometrically singular configurations.
Paper 80 does not claim that full continuum quantum mechanics or the exact Landauer bound has been derived from first principles. It does show that the verified QGEFT benchmark now supports a quantitative unifying-force law FU=−kτWMDiF_U = -k_\tau W_M D_iFU​=−kτ​WM​Di​: a dispersed wave (Di=2.17D_i = 2.17Di​=2.17) collapses to a point (Di=0D_i = 0Di​=0) in a single Monte Carlo sweep once the anchor weight crosses the threshold WM∗=950W_M^* = 950WM∗​=950 (theory ≈923\approx 923≈923), and the released quadratic energy (ΔErel=1164\Delta E_{rel} = 1164ΔErel​=1164) correlates with the erased virtual arcs at r=0.985r = 0.985r=0.985, providing a mechanical, thermodynamic origin for photon emission.
This is an idiosyncratic colloquium-style review of the idea that spacetime and gravity can emerge from entanglement. Drawing inspiration from the conjectured duality between quantum gravity in anti de Sitter space and certain conformal field theories, we argue that tensor networks can be used to define a discrete geometry that encodes entanglement geometrically. With the additional assumption that a continuum limit can be taken, the resulting geometry necessarily obeys Einstein's equations. The discussion takes the point of view that the emergence of spacetime and gravity is a mysterious phenomenon of quantum many-body physics that we would like to understand. We also briefly discuss possible experiments to detect emergent gravity in highly entangled quantum systems.
I will argue that proposal of establishing operational foundations of Quantum The- ory should have top-priority, and that Lucien Hardy's program on Quantum Gravity should be paralleled by an analogous program on Quantum Field Theory (QFT), which needs to be reformu- lated, notwithstanding its experimental success. In this paper, after reviewing recently suggested operational principles of quantumness, I address problem on whether Quantum Theory and Special Relativity are unrelated theories, or instead, if one implies other. I show how Special Relativity can be indeed derived from causality of Quantum Theory, within computa- tional paradigm the universe is a huge quantum computer, reformulating QFT as a Quantum- Computational Field Theory (QCFT). In QCFT Special Relativity emerges from fabric of computational network, which also naturally embeds gauge invariance. In this scheme even quantization rule and Planck constant can in principle be derived as emergent from under- lying causal tapestry of space-time. In this way Quantum Theory remains only theory operating huge computer of universe. Is computational paradigm only a speculative tautology (theory as simulation of reality), or does it have a scientific value? The answer will come from Occam's razor, depending on mathematical simplicity of QCFT. Here I will just start scratching surface of QCFT, analyzing simple field theories, including Dirac's. The number of problems and unmotivated recipes that plague QFT strongly motivates us to undertake QCFT project, since QCFT makes all such problems manifest, and forces a re-foundation of QFT.