Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, with randomness emerging from deterministic irregular dynamics of the detectors, shown to be just as non-signaling as noise-based collapse models are: it fully reproduces quantum statistical predictions, while being still vulnerable to signaling in individual events. The model is based on a minimally nonlinear von Neumann equation for a Stern-Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. Following Pearle's gambler's ruin scheme, the model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Outcome probabilities obey Born's rule under a no-drift or fair-game condition, implying that collapse must run to conclusion during the metastable pre-firing period of the detector system. Hidden signaling in individual events remains to be handled by future research; what is reached here is to put deterministic nonlinear models and noise-based collapse models on equal footing.
Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, with randomness emerging from deterministic irregular dynamics of the detectors, shown to be just as non-signaling as noise-based collapse models are: it fully reproduces quantum statistical predictions, while being still vulnerable to signaling in individual events. The model is based on a minimally nonlinear von Neumann equation for a Stern-Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. Following Pearle's gambler's ruin scheme, the model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Outcome probabilities obey Born's rule under a no-drift or fair-game condition, implying that collapse must run to conclusion during the metastable pre-firing period of the detector system. Hidden signaling in individual events remains to be handled by future research; what is reached here is to put deterministic nonlinear models and noise-based collapse models on equal footing.
Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, in which randomness - instead of being universally present - emerges in the measurement process, from deterministic irregular dynamics of the detectors. The treatment is based on a minimally nonlinear von Neumann equation for a Stern-Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a self-adjoint skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. The model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Environmental decoherence has no role in the scenario. Through stochastic modelling, based on Pearle's gambler's ruin scheme, outcome probabilities are shown to obey Born's rule under a no-drift or fair-game condition. This fully reproduces quantum statistical predictions, implying that the proposed non-linear deterministic model satisfies the non-signaling requirement. Our treatment is still vulnerable to hidden signaling in individual events, which remains to be handled by future research.
Abstract Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, in which randomness—instead of being universally present—emerges in the measurement process, from deterministic irregular dynamics of the detectors. The treatment is based on a minimally nonlinear von Neumann equation for a Stern–Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a self-adjoint skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. The model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Environmental decoherence has no role in the scenario. Through stochastic modelling, based on Pearle’s ‘gambler’s ruin’ scheme, outcome probabilities are shown to obey Born’s rule under a no-drift or ‘fair-game’ condition. This fully reproduces quantum statistical predictions, implying that the proposed non-linear deterministic model satisfies the non-signaling requirement. Our treatment is still vulnerable to hidden signaling in individual events, which remains to be handled by future research.
This paper describes a simple, causally deterministic model of quantum measurement based on an amplitude threshold detection scheme. Surprisingly, it is found to reproduce many phenomena normally thought to be uniquely quantum in nature. To model an N -dimensional pure state, the model uses N complex random variables given by a scaled version of the wave vector with additive complex noise. Measurements are defined by threshold crossings of the individual components, conditioned on single-component threshold crossings. The resulting detection probabilities match or approximate those predicted by quantum mechanics according to the Born rule. Nevertheless, quantum phenomena such as entanglement, contextuality, and violations of Bell’s inequality under local measurements are all shown to be exhibited by the model, thereby demonstrating that such phenomena are not without classical analogs.
Abstract This is an extended discussion of Ref. [1], presenting a nonlinear dynamical model of quantum collapse, with randomness emerging from self-generated noise. Here we focus on a few issues: 1) the way chaos theory explains “deterministic but unpredictable” as a generic feature of nonlinear dynamics; 2) a new argument about why Bell-CHSH and GHZ experiments confirm quantum mechanics; 3) a discussion of why the heating effect predicted by CSL-type theories is not expected to happen according to our approach; 4) in looking for direct-product solutions of our nonlinear Von Neumann equation, we use a parametrization different from that used in Ref. [1], allowing better insight to the locality issue.
In this article, we introduce a new form of quantum selective measurement in which the von Neumann projection postulate is replaced by quasilinear evolution, governed by a nonlinear generalization of the von Neumann equation. We demonstrate that this equation preserves the equivalence of quantum ensembles and, consequently, satisfies the no-signalling principle, ensuring consistency with both quantum mechanics and Einstein causality. Our approach eliminates the need for instantaneous, discontinuous state collapse and provides a unified description of the postmeasurement quantum state reduction as a form of quantum state evolution. Notably, it does not require invoking concepts such as the quantum state assigned to a classical apparatus. At the same time, the stochastic character of selective measurement and the Born rule remain unchanged. We present several numerical solutions of the evolution equation for quasilinear selective measurement in two-level quantum systems and compare them with the standard von Neumann projection. The results demonstrate agreement between the two measurement schemes in their fundamental properties. Furthermore, we investigate phenomena associated with the structural instability of the evolution equation and identify very narrow parameter regions in which the outcomes deviate from those predicted by the von Neumann projection. These regions may offer opportunities to test the proposed approach experimentally. Finally, using specific analytical solutions, we discuss the Stern-Gerlach experiment within the framework of quasilinear measurement.
Abstract The quantum measurement problem arises from the coexistence of unitary Schr¨odinger evolution with the apparent nonunitary collapse of quantum states during observation. Despite extensive theoretical development, no consensus has been reached on a microscopic physical mechanism for state reduction within standard quantum theory. In this work, we present a complete dynamical theory of quantum measurement in which wavefunction collapse emerges from irreversible information transfer and entropy production in realistic system–detector–environment interactions. Starting from microscopic Hamiltonian models, we derive a stochastic nonlinear evolution equation for conditioned quantum states without introducing additional axioms or phenomenological parameters. We demonstrate that the effective collapse rate is uniquely determined by environmental entropy production and remains well-defined in thermal, non-Markovian, chaotic, and zero-temperature regimes. Using stochastic calculus and martingale theory, we establish the dynamical emergence of the Born probability rule and prove almost-sure convergence of measurement trajectories to definite outcomes. The theory exhibits robust many-body amplification, universal behavior in nonlinear detectors, and mathematical well-posedness in both finite- and infinite-dimensional settings. Compatibility with algebraic quantum field theory, renormalization theory, and stochastic semiclassical gravity is established, ensuring consistency with relativistic and high-energy physics. Extensive numerical simulations confirm analytical predictions, and a comprehensive experimental program is proposed, together with rigorous validation and replication protocols. Logical analysis demonstrates compatibility with Bell nonlocality, resolution of Wigner’s friend and Frauchiger–Renner paradoxes, and compliance with information-theoretic constraints. These results provide a unified physical explanation of quantum measurement as an emergent nonequilibrium process governed by universal thermodynamic and informational principles, integrating state reduction into the standard dynamical framework of physics.