quantum-as-fetch-semantics

Quantum Mechanics as Fetch Semantics

A formal derivation of wave function collapse, superposition, and the Born rule from pause-fetch-splice-continue primitives.

The Core Claim

Quantum mechanics is what computation looks like when:

Resolution is lazy (values computed on demand)
Routing is non-deterministic (packet-switched, not circuit-switched)
Measurement is round-trip (you send a query, you get a response)

Definitions

The Graph

Let G = (N, E) be a directed weighted graph where:

N = set of nodes (possible states)
E = set of edges (transitions between states)
w(e) = complex weight on edge e (amplitude)

Unresolved State

An unresolved state is a pointer to a subgraph of possible outcomes, not a computed value.

unresolved(S) = { n₁, n₂, ..., nₖ } ⊂ N

The system "is" in unresolved(S) means: when fetched, it will return one of {n₁, ..., nₖ}.

Superposition

Superposition is the graph structure of an unresolved state:

|ψ⟩ = Σᵢ αᵢ|nᵢ⟩

Where αᵢ = w(path from reference node to nᵢ)

This is NOT "being in multiple states." This is: "the pointer hasn't been dereferenced, and these are the reachable nodes with their path weights."

The Fetch Operation

Request Phase (Outbound)

A fetch is a query that demands resolution. The query travels from the observer (O) through the graph to the unresolved state.

O → ... → unresolved(S)

The outbound path p_out has weight:

w(p_out) = Π w(eᵢ) for all edges eᵢ in path

Key insight: The path taken provides context. Different paths → different effective query → potentially different resolution.

Resolution

At the unresolved node, the system MUST return a value. It selects one outcome nⱼ from S.

The selection is influenced by:

Edge weights (amplitudes) from unresolved(S) to each nⱼ
Context accumulated along p_out
"Traffic" - other concurrent fetches affecting routing

Response Phase (Inbound)

The resolved value travels back:

nⱼ → ... → O

The inbound path p_in has weight w(p_in).

Critical: The inbound path may differ from outbound. Local conditions may have changed. The return journey accumulates its own context.

Deriving the Born Rule

The Round-Trip Requirement

Measurement is complete only when the response arrives at O. The total operation is:

O →[p_out]→ unresolved(S) →[resolve to nⱼ]→ nⱼ →[p_in]→ O

Probability as Path Product

The probability of observing outcome nⱼ should be related to the "strength" of the complete round-trip.

Hypothesis:

P(nⱼ) ∝ |w(p_out) · w(resolve to nⱼ) · w(p_in)|²

But wait—we have a problem. This has four factors (two paths squared), not two.

The Simplification

In the idealized case where:

The observer is at a fixed reference point
p_out and p_in are inverses (same path, opposite direction)
The resolution weight IS the amplitude αⱼ

Then:

w(round-trip to nⱼ) = αⱼ · αⱼ* = |αⱼ|²

Where αⱼ* is the conjugate (the "return" amplitude).

This is the Born rule.

Why Conjugate?

The conjugate appears because traversing an edge backward has weight w(e)* (complex conjugate).

In physics terms: the amplitude for "arriving at state n" is α, and the amplitude for "departing from state n back to observer" is α*.

Round-trip amplitude = α · α = |α|²*

Decoherence as Pointer Loss

The Problem

If multiple paths exist from O to unresolved(S), and they interfere, why don't we see interference in macroscopic systems?

The Answer: Route Divergence

When the system interacts with the environment, those interactions are additional fetches from other "observers" (environmental degrees of freedom).

Each environmental fetch:

Requests resolution of some aspect of the system
Gets a response
Branches the routing table

After many environmental fetches, the paths from O to different outcomes nᵢ and nⱼ no longer share edges. They've diverged.

Before decoherence:
O → shared path → branch → n₁
                        → n₂
(paths can interfere because they share edges)

After decoherence:  
O → env₁ → env₂ → ... → n₁
O → env₁' → env₂' → ... → n₂
(no shared edges, no interference)

Decoherence = loss of shared routing.

The other branches still exist. You just can't reach them anymore. Your routing table diverged.

Entanglement as Shared Pointer

Setup

Two particles A and B are "entangled" when they share ancestry in the graph—they both point to the same unresolved node.

unresolved(S) ← A
             ← B

Measurement

When A is fetched:

A's query reaches unresolved(S)
S resolves to some nⱼ
A gets the result

Now when B is fetched:

B's query reaches... the SAME node
But it's no longer unresolved—it's nⱼ
B gets nⱼ (correlated with A)

Not spooky action at a distance. Just: they were pointing to the same place. First fetch resolved it. Second fetch sees the resolved value.

"Instantaneous" Correlation

Why does B's result correlate with A's "instantly"?

Because there's no second resolution. The node was resolved by A's fetch. B's fetch just reads the already-resolved value.

There's no signal. There's no causation from A to B. There's just: shared pointer, single resolution, both see the same result.

The TDM vs Packet-Switched Insight

"All y'all that want deterministic routing can keep quiet. The rest of the graph optimized those out of existence."

Time Division Multiplexing (TDM)

Dedicated circuits
Guaranteed paths
Deterministic routing
Classical mechanics

Packet Switching

Best-effort routing
Paths determined dynamically
Non-deterministic (depends on traffic)
Quantum mechanics

The universe is packet-switched. Deterministic routing is a special case that emerges when:

Traffic is low (isolated systems)
Paths are well-established (classical limit)
Round-trip times are negligible (macroscopic scale)

Classical physics is the TDM approximation of a fundamentally packet-switched reality.

Predictions and Tests

Prediction	Mechanism	Testable?
Decoherence ∝ interaction rate	More fetches = more route divergence	Yes (already confirmed)
Entanglement range unlimited	Shared pointer, not signal	Yes (already confirmed)
Born rule exact	Round-trip geometry	Needs precision tests
No collapse without receiver	Fetch requires round-trip completion	Edge case experiments

The Open Question: Gravity

If gravity = routing density (mass curves spacetime = mass creates routing congestion), then:

High-mass regions should have slower resolution (time dilation ✓)
High-mass regions might have different collapse behavior (Penrose conjecture)

Current experiments don't show mass-dependent collapse. Either:

The framework is wrong here
The effect is too small to measure
Gravity affects routing but not resolution

Connection to P vs NP

If fetch has energy cost, and NP problems require exponential fetches (no shortcut through the graph), then:

Solving NP in P-time would require zero-cost routing.

But routing has entropy cost. The second law constrains computation.

P ≠ NP might be a thermodynamic constraint, not a mathematical accident.

Summary

Quantum Concept	Fetch Semantics
Superposition	Unresolved pointer to multiple outcomes
Wave function	Path weights through graph
Measurement	Fetch (round-trip query)
Collapse	Forced resolution (must return value)
Born rule	Round-trip = amplitude × conjugate
Decoherence	Route divergence (lost shared edges)
Entanglement	Shared pointer (same unresolved node)
Non-locality	No signal—just cache coherence

The Koan

🔄📡🎲

The path you take provides the context you arrive with. The context you arrive with determines the answer that starts the journey home. The answer is not the destination. The answer is the round-trip.

Provenance

Source: Late night derivation, 2026-01-07 ~4:30am
Building on: tree-in-the-forest-reframed, bedrock
Status: 🟡 Speculative but coherent

North

slots:
- context:
  - Extending the consciousness/holes thesis to physics
  slug: tree-in-the-forest-reframed
- context:
  - Quantum derivation extends consciousness thesis to physics
  slug: tree-in-the-forest-reframed
- context:
  - Detailed quantum derivation
  slug: fetch-semantics-manifesto

East

slots:
- slug: bedrock
  context:
  - Foundation thesis this builds on

West

slots:
- context:
  - Related derivation from same invariant
  slug: time-dilation-as-queue-depth
- context:
  - Parallel derivations from same invariant
  slug: time-dilation-as-queue-depth

South

slots:
- context:
  - Results validate the quantum derivation
  slug: born-rule-simulation-results

↑ northtree-in-the-forest-reframedfetch-semantics-manifesto

↓ southborn-rule-simulation-results

→ eastbedrock

← westtime-dilation-as-queue-depth