TauLib · API Book V

TauLib.BookV.Orthodox.MeasurementUnification

TauLib.BookV.Orthodox.MeasurementUnification

Measurement problem dissolved: no wavefunction collapse, address resolution instead. Quantum-to-classical transition as VM zoom level. Bell inequality recovery. Decoherence as address-resolution shadow.

Registry Cross-References

  • [V.D189] VM Representation of a Quantum State – VMQuantumState

  • [V.T134] Measurement Problem Dissolution – measurement_dissolution

  • [V.T135] Bell Inequality in tau – bell_inequality_tau

  • [V.P107] Decoherence as Address-Resolution Shadow – decoherence_shadow

  • [V.R288] Superposition in the VM – comment-only

  • [V.R289] Entanglement as Address Sharing – comment-only

  • [V.R290] The Century of Confusion – comment-only

Mathematical Content

VM Quantum State [V.D189]

A VM quantum state is a vector |psi> in the orthodox Hilbert space obtained from a boundary character chi in H_partial[omega] by the readout map: Read(chi) -> |psi_chi>. The wave function is not a physical object; it is a VM representation of a boundary character.

Measurement Problem Dissolution [V.T134]

The measurement problem is dissolved (not solved):

  • Unitary evolution = VM readout of character evolution under rho when no address resolution occurs (Read(rho^n(chi)) = U^n|psi>)

  • “Collapse” = address resolution in H_partial[omega], where a definite boundary character is selected by the resolution protocol

  • There is no physical collapse; the VM representation updates when the address is resolved

Bell Inequality [V.T135]

The CHSH inequality |S| <= 2 is violated in tau by exactly the quantum prediction |S| <= 2*sqrt(2). Boundary characters are non-local (they live on L = S^1 v S^1, which is connected). There are no hidden variables.

Decoherence [V.P107]

Decoherence is the VM description of address resolution in the boundary algebra. The environment is the collection of boundary characters not in the system’s address range.

Ground Truth Sources

  • Book V ch64: Measurement unification

  • Book IV ch20-22: Address-obstruction theorem, measurement

Tau.BookV.Orthodox.ReadoutStatus

source inductive Tau.BookV.Orthodox.ReadoutStatus :Type

Readout status of a quantum state.

  • Unresolved : ReadoutStatus Unresolved: superposition in the VM (no address resolution yet).

  • Resolved : ReadoutStatus Resolved: definite boundary character selected.

Instances For

Tau.BookV.Orthodox.instReprReadoutStatus.repr

source def Tau.BookV.Orthodox.instReprReadoutStatus.repr :ReadoutStatus → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.instReprReadoutStatus

source instance Tau.BookV.Orthodox.instReprReadoutStatus :Repr ReadoutStatus

Equations

  • Tau.BookV.Orthodox.instReprReadoutStatus = { reprPrec := Tau.BookV.Orthodox.instReprReadoutStatus.repr }

Tau.BookV.Orthodox.instDecidableEqReadoutStatus

source instance Tau.BookV.Orthodox.instDecidableEqReadoutStatus :DecidableEq ReadoutStatus

Equations

  • Tau.BookV.Orthodox.instDecidableEqReadoutStatus x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

Tau.BookV.Orthodox.instBEqReadoutStatus

source instance Tau.BookV.Orthodox.instBEqReadoutStatus :BEq ReadoutStatus

Equations

  • Tau.BookV.Orthodox.instBEqReadoutStatus = { beq := Tau.BookV.Orthodox.instBEqReadoutStatus.beq }

Tau.BookV.Orthodox.instBEqReadoutStatus.beq

source def Tau.BookV.Orthodox.instBEqReadoutStatus.beq :ReadoutStatus → ReadoutStatus → Bool

Equations

  • Tau.BookV.Orthodox.instBEqReadoutStatus.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx) Instances For

Tau.BookV.Orthodox.VMQuantumState

source structure Tau.BookV.Orthodox.VMQuantumState :Type

[V.D189] VM representation of a quantum state.

A VM quantum state is a vector psi> obtained from a boundary
character chi by the readout map Read : chi -> psi_chi>.

The wave function is NOT a physical object. It is a VM (virtual machine) representation of boundary data. “Collapse” is the VM updating when address resolution occurs at the ontic level.

  • character_count : ℕ Number of boundary characters in the superposition.

  • nonempty : self.character_count > 0 At least one character (non-empty state).

  • status : ReadoutStatus Current readout status.

  • sector_count : ℕ Sector(s) involved (up to 5).

  • sector_bound : self.sector_count ≤ 5 Sector count bounded by 5.

Instances For

Tau.BookV.Orthodox.instReprVMQuantumState.repr

source def Tau.BookV.Orthodox.instReprVMQuantumState.repr :VMQuantumState → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.instReprVMQuantumState

source instance Tau.BookV.Orthodox.instReprVMQuantumState :Repr VMQuantumState

Equations

  • Tau.BookV.Orthodox.instReprVMQuantumState = { reprPrec := Tau.BookV.Orthodox.instReprVMQuantumState.repr }

Tau.BookV.Orthodox.VMQuantumState.is_resolved

source def Tau.BookV.Orthodox.VMQuantumState.is_resolved (s : VMQuantumState) :Bool

A resolved VM state has a definite boundary character. Equations

  • s.is_resolved = (s.status == Tau.BookV.Orthodox.ReadoutStatus.Resolved) Instances For

Tau.BookV.Orthodox.VMQuantumState.is_superposition

source def Tau.BookV.Orthodox.VMQuantumState.is_superposition (s : VMQuantumState) :Bool

An unresolved VM state is in superposition (VM language). Equations

  • s.is_superposition = decide ((s.status == Tau.BookV.Orthodox.ReadoutStatus.Unresolved) = true ∧ s.character_count > 1) Instances For

Tau.BookV.Orthodox.MeasurementDissolution

source structure Tau.BookV.Orthodox.MeasurementDissolution :Type

The three-part dissolution of the measurement problem.

  • unitary_is_readout : Bool Part 1: unitary evolution = character evolution readout.

  • collapse_is_address_resolution : Bool Part 2: collapse = address resolution (not physical).

  • born_from_pythagorean : Bool Part 3: Born rule = Pythagorean theorem on characters.

  • all_parts : Bool All three parts hold.

Instances For

Tau.BookV.Orthodox.instReprMeasurementDissolution

source instance Tau.BookV.Orthodox.instReprMeasurementDissolution :Repr MeasurementDissolution

Equations

  • Tau.BookV.Orthodox.instReprMeasurementDissolution = { reprPrec := Tau.BookV.Orthodox.instReprMeasurementDissolution.repr }

Tau.BookV.Orthodox.instReprMeasurementDissolution.repr

source def Tau.BookV.Orthodox.instReprMeasurementDissolution.repr :MeasurementDissolution → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.canonical_measurement_dissolution

source def Tau.BookV.Orthodox.canonical_measurement_dissolution :MeasurementDissolution

[V.T134] The measurement problem is dissolved.

There is no wavefunction collapse in the ontic layer. There is address resolution in H_partial[omega], which the VM readout functor describes as “collapse.”

Formally:

  • Read(rho^n(chi)) = U^n psi_chi> (unitary evolution)
  • Read(resolve(chi)) = P_a |psi_chi> / ||P_a|psi_chi>|| (address resolution -> “collapse” in VM)

The Born rule ||^2 is the Pythagorean theorem: the squared projection of one boundary character onto another. Equations

  • Tau.BookV.Orthodox.canonical_measurement_dissolution = { } Instances For

Tau.BookV.Orthodox.measurement_dissolution

source theorem Tau.BookV.Orthodox.measurement_dissolution :canonical_measurement_dissolution.all_parts = true

Tau.BookV.Orthodox.canonical_dissolution

source def Tau.BookV.Orthodox.canonical_dissolution :MeasurementDissolution

The canonical dissolution structure. Equations

  • Tau.BookV.Orthodox.canonical_dissolution = { } Instances For

Tau.BookV.Orthodox.unitary_is_readout

source theorem Tau.BookV.Orthodox.unitary_is_readout :canonical_dissolution.unitary_is_readout = true

Unitary evolution is a readout.

Tau.BookV.Orthodox.collapse_is_address_resolution

source theorem Tau.BookV.Orthodox.collapse_is_address_resolution :canonical_dissolution.collapse_is_address_resolution = true

Collapse is address resolution.

Tau.BookV.Orthodox.BellInequality

source structure Tau.BookV.Orthodox.BellInequality :Type

[V.T135] Bell inequality in tau: the CHSH bound is 2*sqrt(2), exactly matching the quantum prediction (Tsirelson bound).

Boundary characters are non-local: they live on the connected space L = S^1 v S^1. The crossing point of L enables correlations that exceed the CHSH classical bound |S| <= 2.

There are no hidden variables because boundary characters are not factorable over space-like separation. The “hidden variable” is the boundary character itself, which is shared across the lemniscate – but sharing a boundary character is not the same as a classical hidden variable (it respects Tsirelson).

  • classical_bound : ℕ Classical CHSH bound (|S| <= 2).

  • tsirelson_numer : ℕ Quantum Tsirelson bound numerator (2*sqrt(2) ~ 2828/1000).

  • tsirelson_denom : ℕ Tsirelson bound denominator.

  • tsirelson_denom_pos : self.tsirelson_denom > 0 Denominator positive.

  • reproduces_tsirelson : Bool tau reproduces Tsirelson (not classical).

  • no_hidden_variables : Bool No hidden variables.

Instances For

Tau.BookV.Orthodox.instReprBellInequality

source instance Tau.BookV.Orthodox.instReprBellInequality :Repr BellInequality

Equations

  • Tau.BookV.Orthodox.instReprBellInequality = { reprPrec := Tau.BookV.Orthodox.instReprBellInequality.repr }

Tau.BookV.Orthodox.instReprBellInequality.repr

source def Tau.BookV.Orthodox.instReprBellInequality.repr :BellInequality → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.bell_data

source def Tau.BookV.Orthodox.bell_data :BellInequality

The canonical Bell inequality data. Equations

  • Tau.BookV.Orthodox.bell_data = { tsirelson_denom_pos := Tau.BookV.Orthodox.bell_data._proof_2 } Instances For

Tau.BookV.Orthodox.bell_inequality_tau

source theorem Tau.BookV.Orthodox.bell_inequality_tau :bell_data.reproduces_tsirelson = true ∧ bell_data.no_hidden_variables = true

tau reproduces the Tsirelson bound, not the classical bound.

Tau.BookV.Orthodox.tsirelson_exceeds_classical

source theorem Tau.BookV.Orthodox.tsirelson_exceeds_classical :bell_data.tsirelson_numer > bell_data.classical_bound * bell_data.tsirelson_denom

The quantum bound exceeds the classical bound.

Tau.BookV.Orthodox.DecoherenceShadow

source structure Tau.BookV.Orthodox.DecoherenceShadow :Type

[V.P107] Decoherence as address-resolution shadow.

Decoherence is the VM description of address resolution in the boundary algebra. The “environment” is the collection of boundary characters not in the system’s address range.

Decoherence rate is determined by:

  • The number of environment characters

  • The cross-coupling between system and environment sectors

  • The refinement depth of the address resolution

Decoherence is NOT fundamental: it is the readout-layer description of the ontic address-resolution process.

  • system_chars : ℕ Number of system characters.

  • env_chars : ℕ Number of environment characters.

  • total : ℕ Total characters = system + environment.

  • total_eq : self.total = self.system_chars + self.env_chars Total is sum.

  • is_fundamental : Bool Decoherence is NOT fundamental.

Instances For

Tau.BookV.Orthodox.instReprDecoherenceShadow

source instance Tau.BookV.Orthodox.instReprDecoherenceShadow :Repr DecoherenceShadow

Equations

  • Tau.BookV.Orthodox.instReprDecoherenceShadow = { reprPrec := Tau.BookV.Orthodox.instReprDecoherenceShadow.repr }

Tau.BookV.Orthodox.instReprDecoherenceShadow.repr

source def Tau.BookV.Orthodox.instReprDecoherenceShadow.repr :DecoherenceShadow → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.decoherence_example

source def Tau.BookV.Orthodox.decoherence_example :DecoherenceShadow

Canonical decoherence example. Equations

  • Tau.BookV.Orthodox.decoherence_example = { system_chars := 1, env_chars := 1000, total := 1001, total_eq := Tau.BookV.Orthodox.decoherence_example._proof_2 } Instances For

Tau.BookV.Orthodox.decoherence_shadow

source theorem Tau.BookV.Orthodox.decoherence_shadow :decoherence_example.is_fundamental = false

Decoherence is a VM shadow, not fundamental.

Tau.BookV.Orthodox.decoherence_total

source theorem Tau.BookV.Orthodox.decoherence_total (d : DecoherenceShadow) :d.total = d.system_chars + d.env_chars

The total character count is the sum of system and environment.

Tau.BookV.Orthodox.QuantumClassicalTransition

source structure Tau.BookV.Orthodox.QuantumClassicalTransition :Type

The quantum-classical transition is a change of VM zoom level, not a physical boundary.

At fine resolution: individual boundary characters visible (quantum regime) At coarse resolution: averaged over many characters (classical regime)

There is no physical “Heisenberg cut.”

  • fine_sees_individual : Bool Fine resolution sees individual characters.

  • coarse_sees_average : Bool Coarse resolution sees averages.

  • no_heisenberg_cut : Bool No physical Heisenberg cut.

Instances For

Tau.BookV.Orthodox.instReprQuantumClassicalTransition.repr

source def Tau.BookV.Orthodox.instReprQuantumClassicalTransition.repr :QuantumClassicalTransition → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.instReprQuantumClassicalTransition

source instance Tau.BookV.Orthodox.instReprQuantumClassicalTransition :Repr QuantumClassicalTransition

Equations

  • Tau.BookV.Orthodox.instReprQuantumClassicalTransition = { reprPrec := Tau.BookV.Orthodox.instReprQuantumClassicalTransition.repr }

Tau.BookV.Orthodox.canonical_qc_transition

source def Tau.BookV.Orthodox.canonical_qc_transition :QuantumClassicalTransition

Canonical quantum-classical transition. Equations

  • Tau.BookV.Orthodox.canonical_qc_transition = { } Instances For

Tau.BookV.Orthodox.no_heisenberg_cut

source theorem Tau.BookV.Orthodox.no_heisenberg_cut :canonical_qc_transition.no_heisenberg_cut = true

No Heisenberg cut in tau.

Tau.BookV.Orthodox.example_superposition

source def Tau.BookV.Orthodox.example_superposition :VMQuantumState

Example: two-state system in superposition. Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.example_resolved

source def Tau.BookV.Orthodox.example_resolved :VMQuantumState

Example: resolved (measured) state. Equations

  • One or more equations did not get rendered due to their size. Instances For