module module high

`IndisputableMonolith.Quantum.ZenoEffect`

The Quantum.ZenoEffect module defines transition and survival probabilities for a two-state system in Recognition Science and derives the quantum Zeno effect from the discrete time quantum. Researchers modeling measurement-induced suppression of evolution in discrete spacetime would cite these constructions. The module proceeds via direct definitions of trigonometric probabilities followed by limit theorems on short-time scaling and crossover behavior.

claimThe transition probability is $P(t) = sin^2(Ω t / 2)$ for Rabi frequency Ω. The Zeno survival probability satisfies $lim_{n→∞} [1 - P(t/n)]^n = 1$ for fixed total time t, with time measured in units of the fundamental RS tick τ₀ = 1.

background

Recognition Science sets the fundamental time quantum τ₀ = 1 tick in the imported Constants module. This module applies that discretization to a two-state quantum system by introducing transitionProbability as the probability of state change over interval t and survivalProbability as its complement. The Rabi frequency Ω parametrizes the underlying oscillation rate, and the Zeno effect appears as the limit of repeated observations at intervals much shorter than 1/Ω.

proof idea

This is a definition module, no proofs. The structure introduces the base trigonometric expression for transition probability, then derives short-time expansions, Zeno scaling, anti-Zeno crossover, and the explicit Zeno survival limit through direct algebraic manipulation of the probability formulas.

why it matters in Recognition Science

This module supplies the quantum Zeno effect within the Recognition Science framework, realizing the discrete time structure from Constants in oscillatory dynamics. It connects to the eight-tick octave periodicity and supplies the measurement-suppression mechanism needed for higher-level quantum applications. No open questions or scaffolding are indicated.

scope and limits

Does not derive a numerical value for the Rabi frequency Ω from phi-ladder parameters.
Does not treat multi-state or continuous-spectrum quantum systems.
Does not address relativistic or field-theoretic extensions of the Zeno effect.
Does not supply experimental predictions beyond the standard quantum limit.

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import

declarations in this module (19)

def transitionProbability L49
theorem transition_at_zero L53
theorem transition_bounded L58
def survivalProbability L67
def zenoSurvival L71
theorem quantum_zeno_effect L76
theorem short_time_expansion L82
theorem zeno_scaling L88
theorem anti_zeno_effect L96
def zenoAntiZenoCrossover L103
theorem zeno_from_ledger_actualization L116
theorem quadratic_from_symmetry L127
def experimentalHistory L139
def typicalFidelity L148
def applications L157
structure ZenoProtection L165
def philosophicalNote L180
structure ZenoFalsifier L191
def experimentalStatus L198