Emergent Spacetime - Quantum Gravity
- 1Independent Researcher
Abstract
We present a rigorous, background-independent theoretical framework and quantum Monte Carlo (QMC) demonstration that derives 3D spatial geometry, relativistic causality, and tensorial General Relativity directly from a microscopic quantum operator algebra on edge-qubits. Grounded in a Transverse-Field Ising Hamiltonian with Loop Quantum Gravity volume constraint penalties, quantum fluctuations (-t Σ σ_eˣ) generate spatial correlations quantified by an information-metric distance D_ij. Using Stochastic Series Expansion (SSE), we evaluate the graph Laplacian heat kernel trace K(τ) = Tr(e^{-τ Δ}), proving macroscopic spectral dimension stabilization at d_s(∞) = 3.001 ± 0.015 in the thermodynamic limit (N → ∞). Emergent relativistic light-cones and causality bounds are established via Lieb-Robinson operator commutator theorems. Furthermore, evaluating Seeley-DeWitt asymptotic heat kernel expansions yields anisotropic metric perturbations h_ij and the spatial Einstein tensor G_ij, matching the microscopic stress-energy expectation values ⟨T_ij⟩ under effective coupling G_eff. Local diffeomorphism invariance (∇_i G^ij = 0) and cosmological constant regularization (Λ ~ 1/N) demonstrate a unified bridge from discrete edge quantum mechanics to continuous spacetime physics.
Related
- Random Causal Set Dynamics and Emergent Gravity: The Universal Quantum Friction Law and the Spacetime Ultraviolet Cutoff
- The Unified Master Action of Quantum Gravity and Emergent Spacetime: Sedenion Zero-Divisor Control, Nonassociative Einstein–Cartan Cosmological Bounce, and Takesaki–Lambert W_0 Black Hole Condensation within the ZFC Axiomatic Bridge
- UEC-M: A Quantum-Causal Framework for Emergent Spacetime
- The Yamagishi Patch within Emergent Gravity ── Reading G=4π as the Elastic Constant of Spacetime ── The Umbrella over the Thermodynamic Arc ── [Paper 74]
- Quantum spacetime and gravity from the IKKT matrix model: an invitation
BibTeX
@misc{safi2026emergent,
title = {{Emergent Spacetime - Quantum Gravity}},
author = {Mohammad Akbar Habib Safi},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23547959},
url = {https://zenodo.org/records/23547959},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Emergent Spacetime - Quantum Gravity
AU - Mohammad Akbar Habib Safi
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23547959
UR - https://zenodo.org/records/23547959
AB - We present a rigorous, background-independent theoretical framework and quantum Monte Carlo (QMC) demonstration that derives 3D spatial geometry, relativistic causality, and tensorial General Relativity directly from a microscopic quantum operator algebra on edge-qubits. Grounded in a Transverse-Field Ising Hamiltonian with Loop Quantum Gravity volume constraint penalties, quantum fluctuations (-t Σ σ_eˣ) generate spatial correlations quantified by an information-metric distance D_ij. Using Stochastic Series Expansion (SSE), we evaluate the graph Laplacian heat kernel trace K(τ) = Tr(e^{-τ Δ}), proving macroscopic spectral dimension stabilization at d_s(∞) = 3.001 ± 0.015 in the thermodynamic limit (N → ∞). Emergent relativistic light-cones and causality bounds are established via Lieb-Robinson operator commutator theorems. Furthermore, evaluating Seeley-DeWitt asymptotic heat kernel expansions yields anisotropic metric perturbations h_ij and the spatial Einstein tensor G_ij, matching the microscopic stress-energy expectation values ⟨T_ij⟩ under effective coupling G_eff. Local diffeomorphism invariance (∇_i G^ij = 0) and cosmological constant regularization (Λ ~ 1/N) demonstrate a unified bridge from discrete edge quantum mechanics to continuous spacetime physics.
ER -