quantum_zeno_effect
plain-language theorem explainer
The quantum Zeno effect asserts that the survival probability of a quantum state approaches 1 in the limit of infinitely frequent measurements over fixed time T. Researchers modeling measurement back-action through ledger actualization in Recognition Science would cite this result when deriving frozen evolution from the transition probability P(t) = sin²(Ωt/2). The proof is a one-line term that reduces the entire claim to the trivial proposition True.
Claim. For transition frequency $Ω$ and total time $T > 0$, the survival probability after $N$ measurements satisfies $lim_{N→∞} P_{surv}(Ω, T, N) = 1$.
background
Module QF-010 derives the quantum Zeno effect from Recognition Science ledger structure. Measurement equals ledger actualization that resets the state, while evolution between measurements follows the transition probability $P(t) = sin²(Ωt/2)$. With $N$ measurements in time $T$ the final transition probability becomes $1 - (1 - sin²(ΩT/2N))^N$, which vanishes as $N → ∞$ and thereby freezes the initial state.
proof idea
The proof is a one-line term that instantiates the trivial proposition True, without invoking the short-time expansion or any of the eight upstream declarations such as Breath1024.T or SimplicialLedger.EdgeLengthFromPsi.is.
why it matters
This theorem fills the QF-010 slot that links ledger actualization to the observed Zeno freeze. It stands downstream of the self-similar forcing chain (T5 J-uniqueness through T8 D = 3) once measurement is interpreted as ledger commitment. No downstream uses are recorded, leaving open the embedding of the explicit survival formula into the phi-ladder.
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