Q-based, objective-field model for wave-function collapse: Analyzing measurement on a macroscopic superposition state

• URL: http://arxiv.org/abs/2601.02767v1
• Date: Tue, 06 Jan 2026 06:58:32 GMT
• Title: Q-based, objective-field model for wave-function collapse: Analyzing measurement on a macroscopic superposition state
• Authors: Channa Hatharasinghe, Ashleigh Willis, Run Yan Teh, P. D. Drummond, M. D. Reid,
• Abstract summary: Schrodinger considered a microscopic system prepared in a superposition of states which is then coupled to a macroscopic meter.<n>We show how the $Q$-based model represents a more complete description of quantum mechanics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The measurement problem remains unaddressed in modern physics, with an array of proposed solutions but as of yet no agreed resolution. In this paper, we examine measurement using the Q-based, objective-field model for quantum mechanics. Schrodinger considered a microscopic system prepared in a superposition of states which is then coupled to a macroscopic meter. We analyze the entangled meter and system, and measurements on it, by solving forward-backward stochastic differential equations for real amplitudes $x(t)$ and $p(t)$ that correspond to the phase-space variables of the Q function of the system at a time $t$. We model the system and meter as single-mode fields, and measurement of $\hat{x}$ by amplification of the amplitude $x(t)$. Our conclusion is that the outcome for the measurement is determined at (or by) the time $t_{m}$, when the coupling to the meter is complete, the meter states being macroscopically distinguishable. There is consistency with macroscopic realism. By evaluating the distribution of the amplitudes $x$ and $p$ postselected on a given outcome of the meter, we show how the $Q$-based model represents a more complete description of quantum mechanics: The variances associated with amplitudes $x$ and $p$ are too narrow to comply with the uncertainty principle, ruling out that the distribution represents a quantum state. We conclude that the collapse of the wavefunction occurs as a two-stage process: First there is an amplification that creates branches of amplitudes $x(t)$ of the meter, associated with distinct eigenvalues. The outcome of measurement is determined by $x(t)$ once amplified, explaining Born's rule. Second, the distribution that determines the final collapse is the state inferred for the system conditioned on the outcome of the meter: information is lost about the meter, in particular, about the complementary variable $p$.

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