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Chapter 23: ψ-Implication and Collapse Causality

23.1 The Arrow of Collapse​

Classical implication "if P then Q" is static logical relationship. In collapse logic, implication becomes dynamic process—observation of P triggers cascade collapse forcing Q's truth value. Causality emerges from collapse propagation.

Principle 23.1: Implication is collapse propagation from antecedent to consequent.

23.2 The Implication Operator​

Definition 23.1 (Collapse Implication): ∣P→Q⟩=∣F⟩P⊗∣∗⟩Q+∣T⟩P⊗∣T⟩Q|P \rightarrow Q\rangle = |F\rangle_P \otimes |*\rangle_Q + |T\rangle_P \otimes |T\rangle_Q

Where |*⟩_Q represents unconstrained Q when P is false.

23.3 Causal Collapse Chains​

When P collapses to true:

  1. Entanglement activates
  2. Q's state constrained
  3. Must collapse to true
  4. Causality established

This creates temporal ordering in logical space.

The Causal Collapse: When you think "if P then Q," you're not stating static relationship but creating collapse channel. Observing P's truth sends causal wave through logical space, forcing Q to align. This explains why implications feel directional—they encode actual causal flow in the quantum field of meaning.