Here is a formal system of equations linking the
Quantum Convergence Threshold (QCT) to
QuantumZeno Effect (QZE) dynamics, using a coherent memory-based feedback formalism:
1. Quantum Zeno Suppression
The evolution of the quantum state ψ(t) is suppressed by frequent informational measurement I(t):
dψ(t)dt=−I(t) ψ(t)\frac{d\psi(t)}{dt}= -I(t)\, \psi(t)dtdψ(t)=−I(t)ψ(t)
2. Coherence Dynamics with InformationalFeedback
The system's coherence ρ(t) (e.g. purity of the state or off-diagonal density matrix strength) decays over a timescale τ, but is reinforced by observation-like feedback I(t):
dρ(t)dt=I(t)−ρ(t)τ\frac{dρ(t)}{dt}= I(t) - \frac{ρ(t)}{τ}dtdρ(t)=I(t)−τρ(t)
3. Memory Integration (ARC Remembrance Operator)
A memory-like accumulation of coherence over time (retrocausal influence, stabilizing identity across time):
R(t)=∫0tρ(τ) dτR(t)= \int_0^t ρ(τ)\, dτR(t)=∫0tρ(τ)dτ
4. Temporal Coherence Operator (Θ)
The ARC Θ(t) operator reflects the degree of stable temporal memory integration (temporal self-reference):
θ(t)=exp(−1R(t)+ε)(with small ε to avoid singularity)θ(t)= \exp\left(-\frac{1}{R(t) + \varepsilon}\right) \quad \text{(withsmall } \varepsilon \text{ to avoid singularity)}θ(t)=exp(−R(t)+ε1)(with small ε to avoid singularity)
5. Quantum Convergence Threshold (QCT)Condition
Collapse occurs (QCT is triggered) when the system's temporal coherence reaches a critical value:
θ(t)=QCT
Interpretation and Integration
This system frames collapse as a
feedback-driven,temporally integrated phase transition:
- I(t) acts like an observer-like pressure, suppressing evolution (QZE) while enhancing coherence.
- R(t) accumulates coherence history, enabling the system to build up temporal memory.
- θ(t) functions like an order parameter, sensitive to whether the system achieves stable temporal identity.
- QCT is the critical point beyond which a single, consistent history is selected—i.e., wavefunction collapse via psychegenic selection.