The Collapse Is a Single Actualisation Event

Alice measures her particle. This is an actualisation event — the break (AP09). A record is written.

When does the break happen? Actualisation occurs when the interaction between the quantum system and the measurement apparatus creates an irreversible record — a record that cannot be unwritten (Axiom R).

This is not a matter of conscious observation. It is the point at which the interaction becomes thermodynamically irreversible: when the measurement apparatus undergoes a state change that constitutes a record.

The break happens when the record is written.

But Alice’s detector interacts locally with subsystem A. How does a local interaction actualise the global state |AB⟩?

Lemma 1 (Local Interaction, Global Actualisation). If |AB⟩ is entangled (non-separable), then any interaction that creates an irreversible record involving subsystem A necessarily actualises |AB⟩ as a whole.

Proof. Alice’s measurement is represented by an operator M_a acting on subsystem A. But because |AB⟩ is entangled, the measurement acts on the global state as (M_a ⊗ I_B):

ρ′_AB(a) = (M_a ⊗ I_B)|AB⟩⟨AB|(M†_a ⊗ I_B) / Tr[(M_a ⊗ I_B)|AB⟩⟨AB| (M†_a ⊗ I_B)]

The record “a” (Alice’s outcome) is a property of this global update, not a standalone update of A alone. The measurement map is defined on |AB⟩ ⟨AB|, not on ρ_A.

The reduced density matrix ρ_A = Tr_B(|AB⟩⟨AB|) is a marginal of the global state — it is not an independent state in its own right, and it is not a record target (see Notation).

Actualisation writes a record for the state on which the measurement acts. That state is the global state |AB⟩. Therefore local interaction with any subsystem of an entangled state necessarily actualises the global state. ∎

Note: The reduced state ρ_A is an improper mixture — it arises from tracing out the entangled partner, not from classical ignorance over a definite pure state.

The distinction between record targets (pure states) and reduced marginals (improper mixtures) is an ontological commitment: the reduced state of an entangled subsystem is not a standalone physical state eligible for actualisation, because it is derived from (and dependent on) the global entangled state.

You have pulled one thread in a woven fabric. The entire weave responds — not because a signal runs along the thread, but because the threads were never separate. They were one fabric.

Lemma 1 is the formal statement of this: the entangled state is one fabric, and pulling any thread actualises the whole.

Example: Singlet state under projective measurement

Consider the singlet state |AB⟩ = (1/√2)(|↑↓⟩ − |↓↑⟩). Alice measures σ_z on subsystem A with projectors P_↑ = |↑⟩⟨↑| and P_↓ = |↓⟩⟨↓|.

If outcome is ↑: (P_↑ ⊗ I)|AB⟩ = (1/√2)|↑↓⟩. Normalised post-measurement state: |↑↓⟩. One record is written. Both outcomes are determined: Alice gets ↑, Bob gets ↓.

If outcome is ↓: (P_↓ ⊗ I)|AB⟩ = (−1/√2)|↓↑⟩. Normalised post-measurement state: |↓↑⟩. One record is written. Both outcomes are determined: Alice gets ↓, Bob gets ↑.

In both cases, the global state collapses to a product state with both subsystem outcomes determined. One measurement, one record, one event. The single-record mechanism matches the standard collapse mathematics exactly.

Proposition 1 (Single Record). Let |AB⟩ ∈ ℋ_A ⊗ ℋ_B be an entangled (non-separable) state. Then the actualisation of |AB⟩ is a single record-writing event. The record determines the outcomes for all subsystems simultaneously.

No signal propagates between subsystems during actualisation.

Proof. By Lemma 1, any local interaction triggering actualisation actualises the global state |AB⟩. By Axiom R, actualisation writes one record for the state being actualised. The state is |AB⟩ (one mathematical object).

Therefore one record is written. The record determines the outcomes for all subsystems (A and B) simultaneously, because the state being actualised contains both.

No intermediate step exists in which A’s outcome is determined and a signal must propagate to determine B’s.

Signal propagation (Axiom C) governs records on the manifold; actualisation is the creation of a record, not the propagation of one. Creation is not propagation. ∎

Corollary (Separable states). If |AB⟩ = |A⟩ ⊗ |B⟩ (a product state), then subsystem A has a well-defined pure state |A⟩ independent of B.

The measurement map (M_a ⊗ I_B) factors: the update of A does not depend on B. Subsystem A can be actualised independently. Two separate records may be written.

The single-record mechanism applies only to entangled states.

Note on multipartite entanglement. The same argument applies to entangled states of N > 2 subsystems. If |ABC…⟩ is non-separable with respect to any partition, then local interaction with any subsystem actualises the global state.

The single-record mechanism scales: one record writes all N outcomes simultaneously.

The spatial localisation of the outcomes follows from prior records.

Before the entangled state collapses, the trajectories of A and B have been written to the manifold as separate records — A is at Alice’s location, B is at Bob’s.

The single actualisation event projects the global outcome onto these pre-existing spatial records. Alice finds spin-up at her location because that is where A’s prior records place it.

Bob finds spin-down at his location for the same reason. The spatial distribution of outcomes inherits from the spatial distribution of prior records, not from the collapse itself.

There is no signal from Alice’s particle to Bob’s particle. There is no propagation across space. The single probability state becomes a single record.

The “flip” of Bob’s particle is instantaneous because it is not a separate event. It is the same event. One pop. One record.