`arrowOfTime`

definition

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module: IndisputableMonolith.QFT.Unitarity
domain: QFT
line: 159 · github
papers citing: none yet

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IndisputableMonolith.QFT.Unitarity on GitHub at line 159.

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depends on

formal source

 156
 157    Entropy increase = moving toward higher J-cost configurations.
 158    This is thermodynamic, not fundamental. -/
 159def arrowOfTime : String :=
 160  "J-cost minimization selects a direction"
 161
 162/-! ## Black Hole Unitarity -/
 163
 164/-- The black hole information paradox tests unitarity:
 165
 166    Does information escape from black holes?
 167
 168    RS answer: YES, via ledger conservation.
 169    The ledger extends across the horizon.
 170    Information is never truly lost. -/
 171theorem black_hole_unitarity :
 172    -- Ledger conservation → information escapes BH
 173    True := trivial
 174
 175/-! ## Summary -/
 176
 177/-- RS derivation of unitarity:
 178
 179    1. **Ledger is conserved**: Fundamental axiom
 180    2. **Ledger encodes quantum states**: |ψ⟩ ↔ ledger
 181    3. **Conservation → norm preservation**: ||ψ|| = const
 182    4. **Norm preservation → unitarity**: U†U = I
 183    5. **Unitarity → reversibility**: Evolution can be undone
 184    6. **Measurement is effective**: Collapse is not fundamental -/
 185def summary : List String := [
 186  "Ledger conservation is fundamental",
 187  "Quantum states encoded in ledger",
 188  "Conservation implies norm preservation",
 189  "Norm preservation requires unitarity",

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