Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics

Cat Paradox for C*-Dynamical Systems

Masanao Ozawa

Published Dec 1, 1992• 8 citations
Publisher

Abstract

In the algebraic approach to the quantum physics, the notion of a macroscopic observable has been well established. This paper examines a program for the unification of classical mechanics and quantum mechanics based on the macroscopic observable and the algebraic description of a dynamical system such as a C*-dynamical system. It is proved quite generally that in this approach we cannot describe the measuring interaction between a microscopic system and a macroscopic apparatus by a C*-dynamical system, or any similar frameworks, as long as the time reversibility of the dynamics of isolated systems is assumed.

DOI
10.1143/ptp.88.1051

Related papers

Cat Paradox for C*-Dynamical Systems

Masanao Ozawa

In the algebraic approach to the quantum physics, the notion of a macroscopic observable has been well established. This paper examines a program for the unification of classical mechanics and quantum mechanics based on the macroscopic observable and the algebraic description of a dynamical system such as a C*-dynamical system. It is proved quite generally that in this approach we cannot describe the measuring interaction between a microscopic system and a macroscopic apparatus by a C*-dynamical system, or any similar frameworks, as long as the time reversibility of the dynamics of isolated systems is assumed.

Progress of Theoretical Physics•Dec 1, 1992•9 citations

Reconstruction of Schrödinger's Cat in Many Worlds 2; Structural Stability of the Quantum–Classical Boundary: A Non-Interpretational Resolution of Schrödinger's Cat Paradox

changzheng zhou, ZIQING zhou

This paper proposes a quantum measurement framework based on structuralstability theory, aiming to resolve the logical dilemma of the quantum–classicaltransition in Schrödinger’s cat paradox. Traditional quantum mechanics relies onexternal mechanisms such as “observer introduction” or “decoherence” to explainmacroscopic reality, leading to vague ontological commitments. We argue that thefundamental reason macroscopic quantum states cannot maintain coherent superpositions lies in the self-organizing critical behavior constrained by the system’sinternal structural stability. The core mechanism is: when a quantum system couples with a classical measuring device, its Hilbert space representation is forced toproject from a high-dimensional unitary representation onto a low-dimensional classical representation, a process driven by the extremization of a structural stabilityfunctional, not by external observation. We rigorously prove that when the system’sstructural information density exceeds a critical threshold, the quantum superposition state cannot satisfy self-consistency constraints mathematically; the systemmust select a classical eigenstate through an “algebraic filtration” mechanism. Thetheory yields three testable predictions: (1) a microscopic entropy production pulseat the moment of coupling between the measuring device and the quantum system,of order 10−21 J/K; (2) a deviation of the quantum Zeno suppression factor fromstandard quantum mechanical predictions on microsecond scales; (3) a scaling-lawdivergence of the decoherence time of macroscopic superpositions at critical parameters. These effects can be tested in coupled superconductor qubit–mechanicalresonator systems. The framework does not modify unitary evolution, does not relyon many-worlds assumptions, and does not introduce collapse postulates; instead,it transforms the measurement problem into a question of compatibility betweenquantum information structure and geometric–topological constraints.

•Mar 4, 2026•0 citations

Quantum Mechanics with Spontaneous Localization

T. Weber

One of the fundamental conceptual difficulties in quantum mechanics arises from the fact that two of the axioms of the theory concerning the evolution of a microscopic system are contradictory. The first axiom assumes that the state of a quantum system evolving undisturbed by any observer obeys a linear deterministic law expressed by the SchrSdinger equation. The second one (wave-packet reduction principle) states that, when the quantum system interacts with an apparatus devised to measure some of its dynamical variables, its state changes abruptly and stochastically, jumping into a normalized eigenstate of the measured variable. This evolution is not deterministic nor linear and cannot be accounted for by the SchrSdinger equation. As a consequence the internal coherence of the theory becomes questionable. On one side the influence of the apparatus on the quantum system cannot be described as an interaction of the quantum constituents of the measuring macroscopic apparatus with the measured quantum system. On the other side, the impossibility of considering a macroscopic object as made by quantum constituents, i .e . the difficulty of quantum mechanics in describing the behaviour of macroscopic systems, is even more dramatic if we consider the evolution of the closed system consisting of the macroscopic apparatus and of the microscopic system. In such a case the appearance of superpositions of macr0scopically distinguishable states related to the apparatus cannot be avoided. These superpositions contradict both our classical experience and wave-packet reduction principle, which provides for statistical mixtures.

•Jan 1, 1991•0 citations

The Schrödinger Cat Paradox as a Stability Problem in a Coercive Vacuum;

Maillot François

The Schrödinger cat paradox is often presented as evidence that quantum mechanics fundamentally conflicts with macroscopic reality. This short conceptual paper proposes a resolution based on the TUO–NS (Theory of the Universe as an Operator – Navier–Stokes–like) framework. In this approach, physical states are interpreted as elastic deformations of a coercive vacuum field. The linear superposition principle is shown to be an effective property, valid only in the regime of small, linearized perturbations around a stable background configuration: $$\mathcal{L}[\delta\psi_1 + \delta\psi_2] \approx \mathcal{L}[\delta\psi_1] + \mathcal{L}[\delta\psi_2]$$ At macroscopic scales, the vacuum energy functional $\mathcal{E}[\Psi]$ is coercive and admits only isolated local minima. Superpositions of distinct macroscopic configurations correspond to energetically unstable states: $$\mathcal{E}[\Psi_{dead} + \Psi_{alive}] \gg \mathcal{E}[\Psi_{dead}] + \mathcal{E}[\Psi_{alive}]$$ These states relax dynamically toward one of the admissible minima. The apparent “collapse of the wave function” is thus reinterpreted as a physical relaxation process, rather than an observer-dependent or probabilistic axiom. This framework provides a physically grounded explanation for the absence of macroscopic superpositions, without invoking external observers, measurement postulates, or modifications of quantum dynamics. This document is intended as a conceptual clarification complementary to the main TUO–NS technical papers, rather than as a replacement for standard quantum mechanics.

•Jan 12, 2026•0 citations

Macroscopic Limit of Quantum Systems

János Polonyi

Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the time-dependent expectation value of the coordinate. The emergence of the classical trajectory can be followed for the average of an observable over a large set of independent microscopical systems, and the deterministic classical laws can be recovered in all practical purposes, owing to the largeness of Avogadro’s number. This result refers to the observed system without considering the measuring apparatus. The emergence of a classical trajectory is followed qualitatively in Wilson’s cloud chamber.

arXiv:2107.13594•Universe•Aug 26, 2021•3 citations

On the Classical Limit of Quantum Mechanics

M. Baldo

One of the main unsolved question in Quantum Mechanics (QM) is its compatibility with classical mechanics. The laws of QM, which describe the microscopic world, must merge into the classical ones for large enough physical systems, but it is still unknown at which point, if any, the transition occurs and if the transition is smooth or sudden as the size increases. Furthermore, a strict extension of QM to the macroscopic world leads to well known 'paradoxes', which is not straightforward to solve. This question is tightly connected with the measurement problem, since any measurement apparatus must give a response which can be described at classical level. Many experiments have been performed to answer to this question. They mainly try to find to which extent the number of particles can be increased in order to observe clear evidence of violation of standard QM. In this paper we argue that the macroscopicity parameter is not the number of particles but the number of independent degrees of freedom, as proposed in a recent model for the completion of QM. This introduces a sort of change of paradigm. To support this claim a representative set of well known experiments are analyzed from this point of view. This brings to a new interpretation of the experiments. A general scheme for the quantum-classical transition is discussed in some details.

arXiv:2607.09735•Jul 2, 2026•0 citations
In the algebraic approach to the quantum physics, the notion of a macroscopic observable has been well established. This paper examines a program for the unification of classical mechanics and quantum mechanics based on the macroscopic observable and the algebraic description of a dynamical system such as a C*-dynamical system. It is proved quite generally that in this approach we cannot describe the measuring interaction between a microscopic system and a macroscopic apparatus by a C*-dynamical system, or any similar frameworks, as long as the time reversibility of the dynamics of isolated systems is assumed.
In the algebraic approach to the quantum physics, the notion of a macroscopic observable has been well established. This paper examines a program for the unification of classical mechanics and quantum mechanics based on the macroscopic observable and the algebraic description of a dynamical system such as a C*-dynamical system. It is proved quite generally that in this approach we cannot describe the measuring interaction between a microscopic system and a macroscopic apparatus by a C*-dynamical system, or any similar frameworks, as long as the time reversibility of the dynamics of isolated systems is assumed.
This paper proposes a quantum measurement framework based on structuralstability theory, aiming to resolve the logical dilemma of the quantum–classicaltransition in Schrödinger’s cat paradox. Traditional quantum mechanics relies onexternal mechanisms such as “observer introduction” or “decoherence” to explainmacroscopic reality, leading to vague ontological commitments. We argue that thefundamental reason macroscopic quantum states cannot maintain coherent superpositions lies in the self-organizing critical behavior constrained by the system’sinternal structural stability. The core mechanism is: when a quantum system couples with a classical measuring device, its Hilbert space representation is forced toproject from a high-dimensional unitary representation onto a low-dimensional classical representation, a process driven by the extremization of a structural stabilityfunctional, not by external observation. We rigorously prove that when the system’sstructural information density exceeds a critical threshold, the quantum superposition state cannot satisfy self-consistency constraints mathematically; the systemmust select a classical eigenstate through an “algebraic filtration” mechanism. Thetheory yields three testable predictions: (1) a microscopic entropy production pulseat the moment of coupling between the measuring device and the quantum system,of order 10−21 J/K; (2) a deviation of the quantum Zeno suppression factor fromstandard quantum mechanical predictions on microsecond scales; (3) a scaling-lawdivergence of the decoherence time of macroscopic superpositions at critical parameters. These effects can be tested in coupled superconductor qubit–mechanicalresonator systems. The framework does not modify unitary evolution, does not relyon many-worlds assumptions, and does not introduce collapse postulates; instead,it transforms the measurement problem into a question of compatibility betweenquantum information structure and geometric–topological constraints.
One of the fundamental conceptual difficulties in quantum mechanics arises from the fact that two of the axioms of the theory concerning the evolution of a microscopic system are contradictory. The first axiom assumes that the state of a quantum system evolving undisturbed by any observer obeys a linear deterministic law expressed by the SchrSdinger equation. The second one (wave-packet reduction principle) states that, when the quantum system interacts with an apparatus devised to measure some of its dynamical variables, its state changes abruptly and stochastically, jumping into a normalized eigenstate of the measured variable. This evolution is not deterministic nor linear and cannot be accounted for by the SchrSdinger equation. As a consequence the internal coherence of the theory becomes questionable. On one side the influence of the apparatus on the quantum system cannot be described as an interaction of the quantum constituents of the measuring macroscopic apparatus with the measured quantum system. On the other side, the impossibility of considering a macroscopic object as made by quantum constituents, i .e . the difficulty of quantum mechanics in describing the behaviour of macroscopic systems, is even more dramatic if we consider the evolution of the closed system consisting of the macroscopic apparatus and of the microscopic system. In such a case the appearance of superpositions of macr0scopically distinguishable states related to the apparatus cannot be avoided. These superpositions contradict both our classical experience and wave-packet reduction principle, which provides for statistical mixtures.
The Schrödinger cat paradox is often presented as evidence that quantum mechanics fundamentally conflicts with macroscopic reality. This short conceptual paper proposes a resolution based on the TUO–NS (Theory of the Universe as an Operator – Navier–Stokes–like) framework. In this approach, physical states are interpreted as elastic deformations of a coercive vacuum field. The linear superposition principle is shown to be an effective property, valid only in the regime of small, linearized perturbations around a stable background configuration: L[δψ1+δψ2]≈L[δψ1]+L[δψ2]\mathcal{L}[\delta\psi_1 + \delta\psi_2] \approx \mathcal{L}[\delta\psi_1] + \mathcal{L}[\delta\psi_2]L[δψ1​+δψ2​]≈L[δψ1​]+L[δψ2​] At macroscopic scales, the vacuum energy functional E[Ψ]\mathcal{E}[\Psi]E[Ψ] is coercive and admits only isolated local minima. Superpositions of distinct macroscopic configurations correspond to energetically unstable states: E[Ψdead+Ψalive]≫E[Ψdead]+E[Ψalive]\mathcal{E}[\Psi_{dead} + \Psi_{alive}] \gg \mathcal{E}[\Psi_{dead}] + \mathcal{E}[\Psi_{alive}]E[Ψdead​+Ψalive​]≫E[Ψdead​]+E[Ψalive​] These states relax dynamically toward one of the admissible minima. The apparent “collapse of the wave function” is thus reinterpreted as a physical relaxation process, rather than an observer-dependent or probabilistic axiom. This framework provides a physically grounded explanation for the absence of macroscopic superpositions, without invoking external observers, measurement postulates, or modifications of quantum dynamics. This document is intended as a conceptual clarification complementary to the main TUO–NS technical papers, rather than as a replacement for standard quantum mechanics.
Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the time-dependent expectation value of the coordinate. The emergence of the classical trajectory can be followed for the average of an observable over a large set of independent microscopical systems, and the deterministic classical laws can be recovered in all practical purposes, owing to the largeness of Avogadro’s number. This result refers to the observed system without considering the measuring apparatus. The emergence of a classical trajectory is followed qualitatively in Wilson’s cloud chamber.
One of the main unsolved question in Quantum Mechanics (QM) is its compatibility with classical mechanics. The laws of QM, which describe the microscopic world, must merge into the classical ones for large enough physical systems, but it is still unknown at which point, if any, the transition occurs and if the transition is smooth or sudden as the size increases. Furthermore, a strict extension of QM to the macroscopic world leads to well known 'paradoxes', which is not straightforward to solve. This question is tightly connected with the measurement problem, since any measurement apparatus must give a response which can be described at classical level. Many experiments have been performed to answer to this question. They mainly try to find to which extent the number of particles can be increased in order to observe clear evidence of violation of standard QM. In this paper we argue that the macroscopicity parameter is not the number of particles but the number of independent degrees of freedom, as proposed in a recent model for the completion of QM. This introduces a sort of change of paradigm. To support this claim a representative set of well known experiments are analyzed from this point of view. This brings to a new interpretation of the experiments. A general scheme for the quantum-classical transition is discussed in some details.