Quantum-Gravity Claims, Observables, and Evidence
What does a proposed quantum-gravity description actually predict? This chapter teaches you to specify its observables, states, global data, approximation regime, and possible failures before comparing calculations. The same method distinguishes a tested correspondence from a claim about a complete theory.
Enter this chapter
Section titled “Enter this chapter”Begin with Holographic Duality: Claims, Dictionaries, and Regimes to turn a proposed correspondence into a definite statement.
Helpful background. Duality claims supplies the language of dictionaries; gravitational regimes separates fixed-background, semiclassical, and quantum-gravity questions.
Topics
Section titled “Topics”- Holographic Duality: Claims, Dictionaries, and Regimes — Specify which theories, sectors, and quantities a correspondence identifies.
- Observable and Regime Matrix for Quantum Gravity — Match each observable to the regime in which it is defined.
- Relational, Boundary, and Asymptotic Observables — Locate events using physical reference systems or boundary data.
- Exact Statements, Saddle Expansions, and Conditional Derivations — Separate exact identities from saddle approximations and conditional deductions.
- Dictionary Completeness and Global Data — Identify global information that local correlators miss.
- Fixed-Theory, Ensemble, and Superselection Claims — Distinguish a state of one theory from an average over theories.
- Nonperturbative Definition and Completion Criteria — Ask what exact rules must supplement a perturbative expansion.
- Evidence Programs for Holographic Duality — Compare tests of different parts of a proposed dictionary.
- Evidence Independence, Circularity, and Double Counting — Determine which agreements share assumptions or calibration data.
- Falsifiers, Negative Results, and Counterexamples — Formulate a negative result against a precise proposition.
- Assessing Quantum-Gravity Results and Open Questions — Assess how new results change a bounded scientific conclusion.
How the ideas fit together
Section titled “How the ideas fit together”A duality dictionary and an approximation to its predictions are different ingredients. In the D3-brane construction, the proposed correspondence extends beyond the large-, strong-coupling regime in which classical supergravity is useful Maldacena 1998, § 2. A discrepancy outside that regime can invalidate the approximation without disproving the correspondence.
Tests must also be independent in the relevant sense. Fitting a normalization to one observable and recovering that observable checks implementation; predicting another observable without refitting tests additional content. Neither calculation determines global sectors that it never probes.
Claim-domain comparison
Section titled “Claim-domain comparison”Compare the assumptions and limits of these representative conclusions.
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| Claim object | State, ensemble, and conventions | Approximation, status, and evidence timing | Uncertainty and counterevidence | Falsifier | Failure condition | Licensed conclusion |
|---|---|---|---|---|---|---|
| dictionary | Declare both theories and parameter map; use the volume conventions unless the page states a local replacement. | Dictionary entry or correspondence claim. Control chain: theory pair and global data → state, algebra, and observable → claim class and regime → evidence and falsifier → bounded conclusion. Sources are cited on the destination page; literature checked through 10 August 2026. | Track omitted corrections, alternate branches, and competing definitions. A failed “round-trip one protected observable” check is counterevidence to the promoted claim. | With both theories and maps fixed, a protected observable gives incompatible values after normalization and any declared corrections are accounted for. | Inferring exact equivalence from one successful observable map. | a stated map of observables |
| saddle result | Declare state, contour, and expansion order; use the volume conventions unless the page states a local replacement. | Model-specific calculation or conditional result. Control chain: theory pair and global data → state, algebra, and observable → claim class and regime → evidence and falsifier → bounded conclusion. Sources are cited on the destination page; literature checked through 10 August 2026. | Track omitted corrections, alternate branches, and competing definitions. A failed “vary saddle and limit order” check is counterevidence to the promoted claim. | An omitted admitted saddle or remainder contributes at the claimed retained order, defeating the stated asymptotic accuracy in that regime. | Promoting a saddle expansion to a nonperturbative completion. | an asymptotic result in its regime |
| phenomenological proposal | Declare mechanism, nuisance model, and data; use the volume conventions unless the page states a local replacement. | Proposal or conditional construction. Control chain: theory pair and global data → state, algebra, and observable → claim class and regime → evidence and falsifier → bounded conclusion. Sources are cited on the destination page; literature checked through 10 August 2026. | Track omitted corrections, alternate branches, and competing definitions. A failed “compare independent alternatives” check is counterevidence to the promoted claim. | Independent data reject the specified mechanism beyond the declared nuisance and model errors; an equally successful alternative separately blocks unique identification. | Inferring evidence for a unique UV theory from sensitivity, a bound, or an anomaly. | a sensitivity, bound, or anomaly |
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Review the chapter
Section titled “Review the chapter”Two calculations agree after their normalization is fixed by the same two-point function. Does this constitute two independent tests of the full duality?
Solution
No. Both inherit the calibration and any assumptions used to identify the two-point functions. Each may still test additional interactions or kinematic dependence, but the shared input must be separated from new predictions. Untested global sectors and finite-parameter effects remain open.
Where to go next
Section titled “Where to go next”Continue to Large N and Semiclassical Bulk Criteria to determine when boundary data support a controlled gravitational approximation.