Where the Schrödinger equation lives (and why)
In this framework the Schrödinger equation:
\[ i\hbar \frac{\partial}{\partial t},|\psi\rangle = \hat H |\psi\rangle \]
it is not a law of history creation. It is a law governing:
- evolution of possibilities,
- redistribution of aggregation weights,
- phase interference and compatibility,
- structure of the aggregation landscape.
That means:
- it does not advance proper time \((d\tau)\),
- it does not produce entropy,
- it does not write to the causal log,
- it does not define events.
So it cannot live in \(\mathcal C\).
It lives squarely in \(\mathcal A\).
Reinterpretation in FU terms
In Functional Universe language:
- Schrödinger evolution updates
\[ \mathcal A(f_n) ;\rightarrow; \mathcal A'(f_n) \]
- Commitment applies
\[ f_{n+1} = \mathcal C(\mathcal A(f_n)) \]
Analogy: Picture many tributary streams flowing from all directions, merging at a waterfall. The Schrödinger equation governs how the tributary aggregations interfere and interact upstream of the waterfall. Commitment governs whether the waterfall occurs at all, producing a cascade that advances proper time and creates historical events.
Why this avoids confusion
This cleanly separates things that standard QM blurs:
| Standard QM | FU resolution |
|---|---|
| “Wavefunction evolves in time” | Aggregation is parameterized, not temporal |
| “Collapse interrupts Schrödinger evolution” | Collapse = exit from \(\mathcal A\) |
| “Measurement problem” | Mixing \(\mathcal A\) and \(\mathcal C\) |
| “Unitary vs non-unitary” | Unitary in \(\mathcal A\), irreversible in \(\mathcal C\) |
There is no contradiction because they are not acting in the same ontological layer.
Seriality + Schrödinger = no conflict
Because:
- Schrödinger evolution is parallel, reversible, pre-historical
- Composition is serial, irreversible, historical
- Seriality applies only after commitment
- Schrödinger dynamics never commits anything by itself
So saying:
“Composition is serial per worldline”
and
“The Schrödinger equation lives in \(\mathcal A\)”
are not just compatible; they require each other.
Summary
The Schrödinger equation governs the evolution of possibility; serial composition governs the creation of history.