complementarityPrinciple
The declaration defines the complementarity principle as the statement that no single observer experiences both the exterior and infalling descriptions of a black hole horizon. Quantum gravity researchers addressing the AMPS firewall paradox would cite it as the Recognition Science resolution via non-local ledger mediation. The definition is a direct string assignment with no computational reduction or tactic steps.
claimIn the Recognition Science ledger framework, the complementarity principle states that no single observer experiences both the exterior description (particle never crosses the horizon) and the infalling description (smooth horizon crossing).
background
The module addresses the firewall paradox (AMPS 2012) as a trilemma among unitarity of Hawking radiation, smooth horizon for infalling observers, and locality outside the horizon. Recognition Science resolves it by making the ledger fundamentally non-local, so that ledger connections span the horizon and support both descriptions simultaneously. The supplied doc-comment states: 'Different observers, different slicings: Outside observer: Never sees particle cross horizon; Infalling observer: Smoothly crosses horizon; Both descriptions are valid (complementarity). In RS: The ledger supports BOTH descriptions!' Upstream results supply supporting structures such as vantage projection (Vantage.get) and ledger edge definitions, but the declaration itself is a pure string constant.
proof idea
The declaration is a one-line definition that directly assigns the string value 'No single observer experiences both descriptions'. No lemmas are applied and no tactics are used.
why it matters in Recognition Science
It supplies the explicit statement of complementarity that the module uses to close the firewall trilemma, allowing unitarity and no-drama to coexist because the ledger is non-local. The module doc positions this as the core of a potential Nature paper on firewall resolution. It sits alongside sibling declarations such as ledger_resolves_firewall and er_equals_epr_from_ledger, completing the RS account of horizon smoothness without invoking drama. No open scaffolding remains at this node.
scope and limits
- Does not derive the principle from the T0-T8 forcing chain or Recognition Composition Law.
- Does not supply quantitative predictions or testable observables.
- Does not prove that the ledger actually mediates information transfer.
- Does not address higher-dimensional or rotating black-hole cases.
formal statement (Lean)
156def complementarityPrinciple : String :=
proof body
Definition body.
157 "No single observer experiences both descriptions"
158
159/-! ## Information Preservation -/
160
161/-- How does information get out?
162
163 1. Hawking radiation is entangled with interior
164 2. As BH evaporates, entanglement is transferred
165 3. Late radiation becomes entangled with early (via BH mediation)
166 4. Final state: All info encoded in radiation correlations
167
168 In RS: The ledger mediates this transfer. Ledger is conserved. -/