Chapter 49: Cause = Prior Collapse Reference

Before there can be thunder, there must be lightning. Before there can be thought, there must be a thinker. Causation is the universe's filing system for keeping prerequisites in order.

49.1 The Genealogy of Events

Every event has ancestors—prior collapse patterns that had to occur for it to exist. We call these ancestors "causes," but they're not mysterious forces. They're simply the required prior nodes in the great directed graph of becoming.

Definition 49.1 (Causal Ancestry): $\text{Causes}(E) = \{C : \exists \text{ path } C \to E \text{ in DAG}\}$

Theorem 49.1 (Causal Necessity): An event cannot occur without its causes: $P(E | \neg C) = 0 \text{ for } C \in \text{Causes}_{\text{necessary}}(E)$

You can't have fire without fuel, oxidizer, and ignition.

49.2 The Partial Order of Reality

Causality creates a partial (not total) ordering of events—some must precede others, but many are independent.

Definition 49.2 (Causal Ordering): $A \prec B \iff A \in \text{Causes}(B)$ $A \parallel B \iff A \not\prec B \wedge B \not\prec A$

Theorem 49.2 (Concurrent Causation): Independent events can occur simultaneously: $A \parallel B \Rightarrow \text{possible}(A \wedge B)$

This is why the universe can do many things at once.

49.3 The Causal Cone

Each event has a past "light cone" of potential causes and a future cone of potential effects.

Definition 49.3 (Causal Cones):

• Past cone: $\mathcal{C}^-(E) = \{C : C \prec E\}$
• Future cone: $\mathcal{C}^+(E) = \{F : E \prec F\}$

Theorem 49.3 (Cone Intersection): Causal influence requires cone overlap: $A \text{ can influence } B \iff \mathcal{C}^+(A) \cap \mathcal{C}^-(B) \neq \emptyset$

Events outside each other's cones are causally disconnected.

49.4 Sufficient vs Necessary Causes

Not all causes are equal—some are necessary, others merely sufficient.

Definition 49.4 (Cause Types):

• Necessary: $P(E|C) > 0, P(E|\neg C) = 0$
• Sufficient: $P(E|C) = 1, P(E|\neg C) \geq 0$
• Contributing: $P(E|C) > P(E|\neg C)$

Theorem 49.4 (Causal Combinations): Most events have multiple causes: $E = f(C_1, C_2, ..., C_n)$

Real causation is multifactorial—many threads weave each event.

49.5 Quantum Causality and Superposition

In quantum mechanics, causes can exist in superposition.

Definition 49.5 (Superposed Cause): $|C\rangle = \alpha|C_1\rangle + \beta|C_2\rangle$

Theorem 49.5 (Causal Interference): Superposed causes interfere: $P(E) = |\alpha|^2 P(E|C_1) + |\beta|^2 P(E|C_2) + 2\text{Re}[\alpha^*\beta \langle C_1|C_2\rangle]$

The interference term creates purely quantum causal effects.

49.6 Retrocausation and Time Symmetry

Can future events influence the past? In the DAG picture, seemingly yes.

Definition 49.6 (Retrocausal Path): $\text{Path}_{\text{retro}}: F \dashrightarrow P$

where $\dashrightarrow$ indicates constraint propagation.

Theorem 49.6 (Weak Retrocausation): Future measurements constrain past probabilities: $P(P|F) \neq P(P)$

The future doesn't change the past but reveals which past occurred.

49.7 The Bootstrap Paradox

Some causal loops have no external origin—they cause themselves.

Definition 49.7 (Bootstrap Loop): $\mathcal{L}: A \to B \to C \to A$

Theorem 49.7 (Self-Causing Systems): Bootstrap loops can exist if: $\prod_{\text{loop}} P(\text{next}|\text{prev}) = 1$

The loop maintains itself without external input—like $\psi = \psi(\psi)$ itself.

49.8 The Forty-Ninth Echo

We have discovered that causes are not mysterious forces but simply prior requirements—nodes that must be traversed before others in the great directed graph of becoming. Causality partially orders events, creating cones of influence. Causes can be necessary or sufficient, single or multiple, classical or quantum. Even retrocausation and bootstrap paradoxes find natural explanation in the DAG structure. At the deepest level, all causation reduces to the requirements of ordered self-observation—$\psi$ must observe certain aspects before others, and this ordering is what we call cause and effect.

The Forty-Ninth Echo: Chapter 49 = Priority(Cause) = Ordering($\psi$-DAG) = Prerequisite(Effect)

Next, we explore how effects achieve stability in the turbulent flow of causation.

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Continue to Chapter 50: Effect = DAG Branch Stability →