1. Entrance
In classical quantum mechanics, the uncertainty principle is considered an absolute and immutable law of nature. The uncertainty product of complementary quantities such as phase and current cannot fall below a certain lower limit under any circumstances.
In Ümit Arslan’s circuit-topological model, this approach changes radically. The uncertainty principle is not the necessary limit of nature; It is redefined as the measurement result based on the architecture.
2. Basic Principle
At the center of the model is the following equation:
Δφ*ΔI=Λ(φ,I,Z)=(S/N)*I0
- Δφ: Phase uncertainty
- ΔI: Current/amplitude uncertainty
- S: Phase–current mutual entropy
- N: Number of synchronized modules
- I0: Reference current scale
This equation reveals that uncertainty is determined by the entropic capacity of the system, not by a constant of nature.
3. Algebraic Framework
- Clifford algebra: The symmetric product of phase and current operators gives the constant Λ. φ̂ Î + Î φ̂ = 2Λ
- Lie group: The commutator of phase and current operators gives the constant Λ. [φ̂, Î] = iΛ
This formalization shows that Λ is not a constant of nature but an algebraic constant of the system architecture.
4. Experimental Validation
In tests with the synthetic data set, the value of Δφ · ΔI overlapped with Λ as synchronization increased and entropy decreased.
Conclusion: Uncertainty equality is verified under conditions of strong synchronization and low entropy; It deteriorates in poor conditions.
5. Consistency with Circuit Laws
- KCL/KVL: Synchronization provides ambiguity reduction without violating node and surround currents.
- Ohms and Impedance: Phase and current uncertainties can be controlled by the frequency dependence of impedance.
- Energy conservation: Power ripple scales with the number of synchronous modules; energy conservation is not violated.
6. Final Judgment
Uncertainty principle in Ümit Arslan’s circuit-topological model:
- It is not an absolute law of nature.
- It is the measurement result depending on the architecture.
- The entropic impedance is defined by Λ.
- It is expressed as a constant in Clifford and Lie algebras.
- It can be verified experimentally and by circuit laws.
7. Manifesto Statement
The uncertainty principle is not a constant of nature in this model; It is an indicator of the entropic capacity of the system. When you change the architecture, the border also changes. Uncertainty is therefore not a necessary rule of nature but a derivative of the measurement paradigm.