Three Regimes

[STRUCTURAL — the complete picture of quantum-to-classical]

You have seen two faces of Axiom R so far. Measurement: the now writes one record, and the outcome is definite. Unitary evolution: the now writes no record, and the pre-state drifts.

But the world is not made of isolated measurements and perfect isolation. The world is made of things touching other things, constantly, everywhere.

There is a third regime — and it is the one you actually live in.

1.1 — The two regimes already derived

AP09 established two regimes:

Unitary evolution: Between measurements, no record is written. The pre-state evolves smoothly. The Schrödinger equation governs (AP09 7.3). Superpositions persist. Interference is possible. The pre-state is intact.

Measurement: The now writes a record. One degree of freedom is distinguished. The break occurs. The outcome is definite, irreversible (Axiom R), and probabilistic (Born rule, AP09 6).

The pre-state for that degree of freedom is broken.

The question is: what happens in between?

What happens when a system is not isolated (no record-writing) and not directly measured (one definite record), but is interacting with a complex environment that is itself writing records?

1.2 — The third regime: decoherence

A quantum system — say, an electron in superposition of two positions — is not isolated.

It interacts with air molecules, photons, the electromagnetic field, the gravitational condensate (the architecture’s term for the gravitational sector; see AP08).

These are ordinary physical degrees of freedom, described in the language of the axioms: each is a record-writing system (a degree of freedom capable of establishing correlations via Axiom R).

Each interaction between the electron and an environmental particle is a coupling event: the now writes a record for that particular environmental degree of freedom.

No single environmental record determines the electron’s state. Each environmental particle that scatters off the electron writes a partial record — it gains a tiny amount of information about the electron’s position.

But there are vast numbers of environmental particles, each writing their own record, each gaining their own fragment of information.

The result: the information about the electron’s superposition is not destroyed. It is dispersed — spread across an enormous number of environmental records.

The coherence — the phase relationship between the two superposed states that allows interference — is now encoded in correlations between the electron and every environmental particle that has interacted with it.

To recover the coherence, you would need to gather every one of those environmental records and reverse every one of those interactions. Axiom R says you cannot reverse them: the monoid has no inverse.

The coherence is gone — not destroyed, but rendered irrecoverable.

Decoherence is the dispersal of coherence into the environment via irreversible record-writing (Axiom R).