Heisenberg Uncertainty as Domain Incompatibility: Resolving Fundamental Limits Through Dual Regulator Framework

This paper reinterprets the Heisenberg uncertainty principle as a consequence of domain incompatibility within the Dual Regulator Framework. Rather than treating uncertainty as measurement disturbance, wavefunction spread, or a purely formal commutation constraint, the framework assigns conjugate quantities to distinct physical domains:

• Real-domain observables (e.g., position and measured energy) regulated by the Resolution Gap RGRGRG, and

• Virtual-domain observables (e.g., momentum and evolution-time duration) regulated by the finite invariant Λφ\Lambda_\varphiΛφ.

Because conjugate variables inhabit incompatible domains, they cannot be simultaneously definite in a single measurement context. The uncertainty principle is therefore treated as an ontological constraint arising from the structure of the measurement interface, not merely an epistemic limit.

The paper explores regulator-dependent modifications to standard uncertainty relations for position–momentum and energy–time, and proposes experimentally testable implications for resolution limits, decay lifetimes, and atomic linewidths. Numerical prefactors are treated as a subject for further refinement, while the central result remains: complementarity follows naturally from domain separation, and “measurement disturbance” is reinterpreted as forced domain selection.

This work forms part of a planned sequence addressing foundational inconsistencies in quantum field theory using finite regulator structure derived from {π,φ,e}\{\pi,\varphi,e\}{π,φ,e}.

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