Emergent gravity from relatively local Hamiltonians and a possible resolution of the black hole information puzzle
Bibliographic record
Abstract
A bstract In this paper, we study a possibility where gravity and time emerge from quantum matter. Within the Hilbert space of matter fields defined on a spatial manifold, we consider a sub-Hilbert space spanned by states which are parameterized by spatial metric. In those states, metric is introduced as a collective variable that controls local structures of entanglement. The underlying matter fields endow the states labeled by metric with an unambiguous inner product. Then we construct a Hamiltonian for the matter fields that is an endomorphism of the sub-Hilbert space, thereby inducing a quantum Hamiltonian of the metric. It is shown that there exists a matter Hamiltonian that induces the general relativity in the semi-classical field theory limit. Although the Hamiltonian is not local in the absolute sense, it has a weaker notion of locality, called relative locality : the range of interactions is set by the entanglement present in target states on which the Hamiltonian acts. In general, normalizable states are not invariant under the transformations generated by the Hamiltonian. As a result, a physical state spontaneously breaks the Hamiltonian constraint, and picks a moment of time. The subsequent flow of time can be understood as a Goldstone mode associated with the broken symmetry. The construction allows one to study dynamics of gravity from the perspective of matter fields. The Hawking radiation corresponds to a unitary evolution where entanglement across horizon is gradually transferred from color degrees of freedom to singlet degrees of freedom. The underlying quantum states remain pure as evaporating black holes keep entanglement with early Hawking radiations in the singlet sector which is not captured by the Bekenstein-Hawking entropy.
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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".