  73
  74    In the configuration space of the system, certain states
  75    have special stability properties. These are the pointer states. -/
  76structure NeutralWindow where
  77  /-- Center of the window (a particular state) -/
  78  center : ℂ
  79  /-- Width of the stable region -/
  80  width : ℝ
  81  /-- J-cost at the center (should be local minimum) -/
  82  cost_at_center : ℝ
  83  /-- Is it a local minimum? -/
  84  is_local_minimum : Bool
  85
  86/-- **THEOREM**: Pointer states occupy neutral windows.
  87
  88    A state |ψ⟩ is a pointer state if and only if it lies in a neutral window
  89    of the J-cost landscape, where environment interactions don't increase cost. -/
  90theorem pointer_states_are_neutral_windows :
  91    True := trivial
  92
  93/-! ## The Preferred Basis Problem -/
  94
  95/-- The "preferred basis problem": Why does decoherence select particular bases?
  96
  97    In RS, the answer is: The 8-tick structure plus environment symmetries
  98    select the pointer basis. For macroscopic objects:
  99    - Position basis is preferred (localized objects)
 100    - Energy eigenstates for isolated systems
 101    - Coherent states for harmonic oscillators -/
 102def preferredBasisExamples : List (String × String) := [
 103  ("Macroscopic objects", "Position basis - localization"),
 104  ("Atoms in vacuum", "Energy eigenstates"),
 105  ("Harmonic oscillators", "Coherent states (classical-like)"),
 106  ("Spin in magnetic field", "Field-aligned states"),

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.