experimentalTests
This definition enumerates four empirical tests for the Ryu-Takayanagi formula derived from Recognition Science ledger projections. Quantum gravity and holography researchers would cite it when mapping ledger entropy to black-hole thermodynamics and tensor-network observations. The body is a direct list construction with no lemmas or reductions.
claimThe experimental tests for the entanglement entropy equaling geometric area are: black hole entropy equals area over 4 in Planck units, tensor networks obey an area law, AdS/CFT calculations reproduce the Ryu-Takayanagi formula, and quantum entanglement experiments confirm the relation.
background
The module QG-008 derives the Ryu-Takayanagi formula S_A = Area(γ_A)/(4 G_N ℏ) from Recognition Science ledger structure. Ledger entries are 2D surfaces; shared entries between a region and its complement count as boundary area, so entanglement entropy scales with area rather than volume. Upstream, InitialCondition.entropy defines entropy as total defect with zero defect as the minimum state, while LedgerFactorization.of calibrates the J-cost on the positive reals.
proof idea
This is a direct definition that hardcodes the four-item list of test descriptions. No lemmas are applied and no tactics are used; the body simply returns the string array matching the doc-comment avenues.
why it matters in Recognition Science
The definition supplies the experimental checklist for the entanglement-area relation and is referenced by the experimentalTests declarations in ThreeGenerations, NonlocalityNoSignaling, and StrongCP. It completes the QG-008 target of obtaining the Ryu-Takayanagi formula from ledger projection, reinforcing the holographic principle and the black-hole information paradox within the Recognition framework.
scope and limits
- Does not derive the Ryu-Takayanagi formula or prove its equivalence to ledger counting.
- Does not supply quantitative predictions, error bars, or required precision for any listed test.
- Does not detail protocols for the analog quantum systems still marked under development.
- Does not reference phi-ladder rungs, J-cost, or the eight-tick octave.
formal statement (Lean)
211def experimentalTests : List String := [
proof body
Definition body.
212 "Black hole entropy = A / 4 (Bekenstein-Hawking)",
213 "Tensor networks exhibit area law",
214 "AdS/CFT calculations match RT",
215 "Quantum entanglement experiments"
216]
217
218/-! ## Implications -/
219
220/-- Major implications of S = Area:
221 1. **Holographic principle**: Information is 2D
222 2. **Black hole information paradox**: Info on horizon
223 3. **Quantum gravity**: Geometry from entanglement
224 4. **Error correction**: Holographic codes -/