Threshold-Based Decoherence in Quantum Measurement

This work proposes a threshold-based picture of decoherence in quantum measurement. Microscopic quantum dynamics remain fully continuous and unitary, but real detectors implement thresholded amplification and nonlinear gain boundaries that partition continuous microscopic inputs into discrete macroscopic outcomes. Within this framework, discreteness and irreversibility arise from scale asymmetry between a continuous microscopic energy distribution and a finite macroscopic threshold ΔE_threshold, without invoking fundamental collapse, branching, or uncontrolled environmental decoherence.

The measurement apparatus effectively performs an analog-to-digital conversion: it maps a continuous input distribution ρ(E) to a binary output variable X_eff ∈ {0,1} according to
P(event) = ∫_{ΔE_threshold}^{∞} ρ(E) dE,
while the recording layer irreversibly erases phase information by structural codomain restriction. This threshold-based decoherence model preserves standard quantum mechanics, provides an operational bridge across major interpretations of quantum theory, and locates the origin of discrete outcomes in the architecture of measurement rather than in quantum ontology itself.

In short, this paper views discrete measurement outcomes as emerging from threshold detector architecture rather than from any fundamental discreteness of the quantum substrate.