module module moderate

`IndisputableMonolith.Quantum.NonlocalityNoSignaling`

The module defines EPR pairs and related quantum objects to formalize nonlocality and no-signaling within Recognition Science. Physicists working on quantum foundations would cite it to see how the RS ledger accounts for entanglement. The module consists of a collection of definitions and theorem statements built on the imported constants and cost structures.

claimAn EPR pair consists of two entangled particles \(A\) and \(B\). The no-signaling theorem asserts that a local measurement on one subsystem leaves the reduced density matrix of the distant subsystem unchanged.

background

The module imports the RS time quantum (\tau_0 = 1) tick from Constants and the cost definitions from the Cost module. It operates in the quantum domain of Recognition Science, where nonlocality is modeled via shared ledger entries. The setting uses the J-cost and recognition composition law to constrain correlations without superluminal signaling.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the quantum nonlocality framework that feeds the Recognition Science derivation of physics from the functional equation. It provides the no-signaling theorem and ledger explanation for Bell violations, connecting to the T5 J-uniqueness and T8 D=3 landmarks.

scope and limits

Does not derive Tsirelson or CHSH bounds from the J-cost equation.
Does not treat relativistic quantum field theory or curved spacetime.
Does not compute explicit correlation values for specific states.
Does not address experimental protocols or measurement implementations.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (17)

structure EPRPair L38
structure Measurement L49
def quantumCorrelation L68
def chshBound L72
def tsirelsonBound L75
theorem bell_violation L78
theorem no_signaling_theorem L98
theorem reduced_density_unchanged L108
theorem ledger_explains_nonlocality L126
structure SharedLedgerEntry L136
theorem reading_is_local L148
def no_signaling_reasons L161
def mutualInformationProperties L176
theorem relativity_preserved L192
def experimentalTests L207
def implications L225
structure NonlocalityFalsifier L238