AMPSTrilemma

formal source

  54       entangled with TWO other systems!
  55
  56    Conclusion: One of {Unitarity, No drama, Locality} is false. -/
  57structure AMPSTrilemma where
  58  unitarity : Prop        -- Hawking radiation is pure
  59  no_drama : Prop         -- Smooth horizon for infaller
  60  locality : Prop         -- Physics is local
  61  monogamy : Prop         -- Entanglement is monogamous
  62  contradiction : unitarity ∧ no_drama ∧ locality ∧ monogamy → False
  63
  64/-! ## Proposed Resolutions -/
  65
  66/-- Various proposals to resolve the firewall:
  67
  68    1. **Firewall exists**: Give up "no drama" (AMPS)
  69    2. **Complementarity**: Give up locality (Susskind)
  70    3. **ER = EPR**: Wormholes connect entangled pairs (Maldacena-Susskind)
  71    4. **Fuzzball**: No interior at all (Mathur)
  72    5. **RS Resolution**: Ledger non-locality resolves all
  73
  74    Each has strengths and weaknesses. -/
  75inductive Resolution
  76| Firewall          -- High-energy particles at horizon
  77| Complementarity   -- No single observer sees contradiction
  78| ERisEPR           -- Entanglement = wormholes
  79| Fuzzball          -- Stringy structure, no interior
  80| RS_Ledger         -- Ledger non-locality
  81deriving Repr, DecidableEq
  82
  83/-! ## RS Resolution: Ledger Non-Locality -/
  84
  85/-- In Recognition Science, the resolution is ledger non-locality:
  86
  87    The ledger is NOT local. It spans the horizon naturally.