Abstract
The quantum measurement problem asks how the smooth, unitary evolution of a superposition gives way to a single, definite outcome when a macroscopic detector interacts with a quantum system. This paper presents a geometric toy model of this interaction, with a deterministic factorization stage and a probabilistic selection step. The entangled state of a quantum system and a detector is embedded into semi-structured complex (ℍ) state space, where newly introduced projection operators, called trigger transformations, factorize the entangled state into a tensor product of two identical subsystems: one describing the quantum system and one describing what the detector registers. This mirrored factorization is shown to reduce exactly to the original entangled state on projection back to standard Hilbert space. Branch-indexed selector operators R, also introduced here, then return the state to Hilbert space and retain a single branch (or measurement outcome), with the standard quantum probabilities acting as structural weights of the branches. The model thereby confines the non-unitary step of measurement to a single, explicitly defined selection operation, offering an alternative to an ad-hoc wave function collapse. In its present form, the outcome rule and the Born weights are stated as an explicit postulate rather than derived, and a possible coupling to background vacuum fluctuations is identified as a route to future experimental tests.