Quantum Mechanics
Why does quantum measurement give probabilistic outcomes? What causes
wavefunction collapse? Why is P(k) = |⟨k|ψ⟩|² and not some other formula?
In the GTE framework, these are not postulates — they are theorems,
two of them machine-certified in Lean 4 with zero sorry.
What you'll understand after this path
PSC requires the universe to contain its own measurement mechanism — no external apparatus, no observer. Transputation is that mechanism, forced by the structure of the theory.
Quantum measurement sits at exactly Turing degree 0′ — one level above ordinary computation, two-sided certified: not easier, not harder.
P(k) = |ck|² is derived by four independent routes, two machine-certified (CatAL). No circular reasoning — the Born rule is output, never input.
Lessons
Transputation: Quantum Measurement from MDL
What the measurement problem is, why Copenhagen and many-worlds fail, and how the GTE framework derives a third answer: transputation — a lawful but non-algorithmic internal adjudicator at exactly Turing degree 0′.
The Born Rule as a Theorem
P(k) = |⟨k|ψ⟩|² — Max Born's 1926 postulate — derived by four independent routes. Two are machine-certified in Lean 4 with zero sorry. The Born rule is a structural consequence of PSC, not an axiom.
Prerequisites and connections
- Path 1 — Foundations: the PSC principle (L02), MDL selection, the GTE orbit (L06)
- Path 2 — Selection: what self-containment requires
- Path 3 (Particles): kinks as the physical entities being measured
- Path 5 (Gravity): the shared clock τc used in the Page-Wootters route