Indexing the archive…
Your Universe of Digital Possibilities
A watched pot, proven: an unstable quantum state on a live Bloch sphere that decays if you leave it alone and freezes if you keep looking. One lever sets how often the stage looks; the survival curve, built from honest runs, climbs toward one as the cadence rises. And at the wrong cadence, the dark twin: watching hastens the death.
Every quantum decay starts flat: the survival is 1 − (t/τ_Z)² before it is ever e−t/τ. Look n times in a time t and each look catches the state still at the top of the parabola — the product of n near-ones climbs to one as n grows. Asked often enough, it never decays.
Looks every τ broaden the state’s line to a width ~1/τ (F_τ), and the decay rate is the reservoir’s spectrum G(ω) seen through that window. A very short τ smears it thin — Zeno, Γ_eff → 0; a τ that slides the window onto a peak of G lifts Γ_eff above the unwatched rate — anti-Zeno. Which one you get is the environment’s choice.
Each look finds the state alive with the squared amplitude since the last look, and the state becomes what was found. The Qubit’s collapse, asked again and again.
A process with a constant hazard survives a span t with probability e−t/τ — and having already waited s changes nothing about the wait ahead. The bus you just missed never existed; a queue’s arrivals and services forget; a metastable state has a half-life and no age. The one law under every Zeno wait.
How long a quantum state survives depends on how often you ask. The Qubit owns the Bloch sphere and the measurement postulate — this stage asks its question on a schedule. The Metastable builds the exponential decay this wait suppresses out of noise; The Proton stretches the same law past the age of the universe. The anti-Zeno band is the environment’s — staged with one Lorentzian pole, it would move with a different reservoir; the Zeno limit would not.