The present paper reports an alternative solution of the measurement problem in quantum theory. The measurement problem can be characterized as that the U-procedure verses the R-procedure. The R-procedure is tested by the Yes/No measurement originally proposed by von Neuman and discussed in details by Penrose. We propose a novel stochastic sampling method to tackle the measurement paradox. Each testing sample produces a pair of Yes-number c and No-number d, which in turn generates a sample phase with respect to the exponential form of (c+id). All the sample phases forms a group GR. Taking GR as the sampling potential, combined with the dynamic phase group GU，we establish a unified model of U-procedure and R-procedure for the evolution of wavefunction. Based on the Born rule, the probability of a sample is given by the squared magnitude of （c+id）. Some metaproperties of the new U-R model, such as natural transformation, consistency, and completeness, are presented. The present work provides a new picture of quantum mechanics and alike. The measurement problem widely exists in dynamic analysis, higher cognition, and large data modeling. Thus, the work reported here has a wide range of applications. Keywords: The measurement problem; U-R procedures; the Yes/No type measurement; stochastic sampling; sample phase; Born probability.
The present paper reports an alternative solution of the measurement problem in quantum theory. The measurement problem can be characterized as that the U procedure verses the R procedure. The R-procedure is tested by the Yes/No measurement originally proposed by von Neuman and discussed in details by Penrose. We propose a novel stochastic sampling method to tackle the measurement paradox. Each testing sample produces a pair of Yes-number c and No-number d, which in turn generates a sample phase with respect to the exponential form of . All the sample phases form a group, write Taking as the sampling potential, the revised Schrödinger equation has the form . This equation has a solution , where is the dynamic phase, while is the sample phase. Based on the Born rule, the probability of a sample is given by the squared magnitude of . Some metaproperties of the new U-R model, such as natural transformation, consistency, and completeness, are presented. The present work provides a new picture of quantum mechanics and alike
This is Paper V in the AIΩN Foundations Series, establishing the dynamical principles of the AIΩN framework. While Papers I–IV established the kinematics, measurement theory, and observer geometry of deterministic rewrite systems, this work introduces the dynamical law governing how realised worldlines arise from the bundle of admissible histories. We address the "selection problem" in deterministic rewriting by equipping histories with a local action functional and an associated complex amplitude measure. We demonstrate that probabilistic behaviour, interference, and effective unitary evolution emerge from deterministic graph rewriting under observer-induced projection, without assuming intrinsic randomness or continuum postulates.