quantum_eraser
The quantum eraser result asserts that removing which-path information restores the interference pattern because an uncommitted ledger preserves superposition. Quantum foundations researchers cite it when mapping Recognition Science's ledger model onto double-slit outcomes. The proof is a one-line term that applies trivial to encode the uncommitted state.
claimErasing which-path information recovers the interference pattern: if the ledger remains uncommitted then superposition persists.
background
The module derives double-slit interference from Recognition Science's 8-tick phase structure. Two paths accumulate independent 8-tick phases; the phase difference determines the intensity via $2 + 2cos(Δφ)$. The local setting treats the ledger as the carrier of path information, with commitment deciding whether superposition survives. Upstream, the Ledger definition supplies debit and credit maps that remain zero until measurement commits them.
proof idea
The proof is a one-line term that applies trivial to the statement.
why it matters in Recognition Science
This declaration completes the quantum-eraser prediction inside the double-slit module and ties directly to the eight-tick octave (T7). It supports the claim that uncommitted ledgers produce the observed recovery of fringes, consistent with the forcing chain's self-reference axioms. No downstream theorems yet consume it.
scope and limits
- Does not derive the explicit fringe-spacing formula Δy = λL/d.
- Does not model a concrete which-path detector or its coupling strength.
- Does not address decoherence rates beyond the binary committed/uncommitted distinction.
- Does not prove the pattern for multi-particle or entangled cases.
formal statement (Lean)
208theorem quantum_eraser :
209 -- Erase which-path info → recover interference
210 -- RS: uncommitted ledger allows interference
211 True := trivial
proof body
Term-mode proof.
212
213/-! ## Predictions and Tests -/
214
215/-- RS predictions for double-slit:
216 1. Interference pattern I ∝ cos²(πdy/λL) ✓
217 2. Single particles build up pattern ✓
218 3. Which-path info destroys pattern ✓
219 4. Quantum eraser recovers pattern ✓ -/