A model of quantum gravity with emergent spacetime
Bibliographic record
Abstract
A bstract We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial sites. In the limit that the size of the matrix is large, the sites can collectively form a spatial manifold. The manifold is determined from the pattern of entanglement present across local Hilbert spaces associated with column vectors of the matrix. With no structure of manifold fixed in the background, the spacetime gauge symmetry is generalized to a group that includes diffeomorphism in arbitrary dimensions. The momentum and Hamiltonian that generate the generalized diffeomorphism obey a first-class constraint algebra at the quantum level. In the classical limit, the constraint algebra of the general relativity is reproduced as a special case. The first-class nature of the algebra allows one to express the projection of a quantum state of the matrix to a gauge invariant state as a path integration of dynamical variables that describe collective fluctuations of the matrix. The collective variables describe dynamics of emergent spacetime, where multi-fingered times arise as Lagrangian multipliers that enforce the gauge constraints. If the quantum state has a local structure of entanglement, a smooth spacetime with well-defined dimension, topology, signature and geometry emerges at the saddle-point, and the spin two mode that determines the geometry can be identified. We find a saddle-point solution that describes a series of (3 + 1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between. The phase transitions between spacetimes with different signatures are caused by Lifshitz transitions in which the pattern of entanglement is rearranged across the system. Fluctuations of the collective variables are described by bi-local fields that propagate in the spacetime set up by the saddle-point solution.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".