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

arXiv:0712.0730

Possible agreement of wave function reduction from the basic principles of quantum mechanics

Roland L. Omnes

Published Dec 5, 2007• 1 citation
arXivHTMLPDF

Abstract

Reduction is shown to be a possible consequence of the basic principles of quantum mechanics, involving no branching of the quantum state of the universe. The key feature of a measurement is attributed to the creation of macroscopic germs of ionized tracks, bubbles, sparks and so on, in a superposed quantum state, the main mechanism being a breaking and a restoration of ``classicality'' in nearby macroscopic objects and their small patterns. A new significance of quantum probabilities, involving no absolute randomness, is also proposed.

DOI
10.48550/arxiv.0712.0730

Related papers

A quantum approach to the uniqueness of Reality

Roland L. Omnes

A brief review is given of the present state of an approach to consistency between basic quantum mechanics and a unique macroscopic reality, with no assumption of branching in the state of the universe. The main new idea consists in the recognition of local properties in the growth and transport of entanglement between a macroscopic measuring quantum system and a microscopic measured one. Moving waves of entanglement from the environment arise then and carry external phases, affecting significantly the state of the measuring device. These "predecoherence" waves perturb randomly the growth of other waves, which carry entanglement with the measured system. The outcome of these wave interactions could generate random fluctuations in the quantum probabilities of different measurement channels, which could lead in turn to a collapse mechanism satisfying Born's probability rule, according to earlier works by Nelson and Pearle. A necessary randomness in the environment remains however unexplained and some suggestions regarding algorithmic complexity of the wave functions in a large quantum system e are made along that direction.

arXiv:1302.1750•Feb 7, 2013•1 citation

On the derivation of wave function reduction from Schrödinger's equation: A model

Roland L. Omnes

The possibility of consistency between the basic quantum principles and reduction (wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as a convenient tool for this investigation. A derivation of reduction from quantum mechanics is proposed on a specific example, using standard methods of statistical physics. Although these methods are valid only "for all practical purposes", arguments are given to ascribe an emerging status to reduction (or the uniqueness of physical reality), similar to the status of classical physics. Examination of measurements of the particles in an EPR pair by two space-like separated apparatuses shows that the model is consistent with the non-separable character of quantum mechanics, although both measurements are local. Quantitative estimates are given.

arXiv:1006.3227•Jun 16, 2010•2 citations

On the derivation of reduction from the Schrodinger equation. A disproof of no-go theorems and a proposal

Roland L. Omnes

The possibility of a fundamental consistency between the basic quantum principles and reduction (so-called wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as a convenient tool for this investigation. Previous no-go theorems excluding consistency are disproved on this ground, because their assumptions neglected the occurrence of organization in a real measuring apparatus. A scheme for deriving reduction from quantum mechanics is also proposed as a conjecture.

arXiv:0911.0598•Nov 3, 2009•2 citations

A realistic model for completing Quantum Mechanics

M. Baldo

In the well known Copenhagen interpretation of Quantum mechanics, advocated by N. Bohr, the physical objects and the experimental results can be described only in a macroscopic language, leaving any possible microscopic description as unspeakable. This point of view has been deepened by C. Rovelli in the relational interpretation of Quantum mechanics. Most of the alternative interpretations, which try a detailed microscopic description of physical phenomena and of their evolution, have in common the explicit introduction of the wave function as the basic element of the theory. These interpretations require the notion of quantum state as the fundamental concept of the theory, which is the typical unspeakable physical element according to the Copenhagen interpretation. The two basic physical entities are intimately bound together by the integrity of the wave function. These interpretations are usually indicated as realistic. It is well known that the use of the wave function and its time evolution in the description of the physical processes leads unavoidably to some difficulties or so-called paradoxes. The measurement problem is at the center of these difficulties, mainly because it requires the introduction of the reduction process of the wave function, which is not included explicitly within the mathematical formalism of Quantum Mechanics. In this paper we build up and propose a model which goes beyond the standard formalism and which is able to solve the measurement problem and all the other difficulties which, in a way or in another, are related to it.

arXiv:2104.12701•Apr 26, 2021•1 citation

Theory of Measurement of Quantum Mechanics: Mechanism of Reduction of Wave Packet. I

S. Machida, Mikio Namiki

New theory of measurement is presented to show that quantum mechanics can describe the whole processes of quantum-mechanical measurement leading to the so-called reduction of wave packet if applied properly to the total system of object and apparatus. We introduce a simple model, where momenta of particles are measured using a perfect rigid mirror, to yield the reduction of wave packet in a clear-cut way. Microscopic uncertainties of macroscopic quantities and the dynamical scattering theory play the essential roles. Before entering into the main part, we briefly summarize the controversial points in the theory of measurement.

Progress of Theoretical Physics•May 1, 1980•131 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
Reduction is shown to be a possible consequence of the basic principles of quantum mechanics, involving no branching of the quantum state of the universe. The key feature of a measurement is attributed to the creation of macroscopic germs of ionized tracks, bubbles, sparks and so on, in a superposed quantum state, the main mechanism being a breaking and a restoration of ``classicality'' in nearby macroscopic objects and their small patterns. A new significance of quantum probabilities, involving no absolute randomness, is also proposed.
A brief review is given of the present state of an approach to consistency between basic quantum mechanics and a unique macroscopic reality, with no assumption of branching in the state of the universe. The main new idea consists in the recognition of local properties in the growth and transport of entanglement between a macroscopic measuring quantum system and a microscopic measured one. Moving waves of entanglement from the environment arise then and carry external phases, affecting significantly the state of the measuring device. These "predecoherence" waves perturb randomly the growth of other waves, which carry entanglement with the measured system. The outcome of these wave interactions could generate random fluctuations in the quantum probabilities of different measurement channels, which could lead in turn to a collapse mechanism satisfying Born's probability rule, according to earlier works by Nelson and Pearle. A necessary randomness in the environment remains however unexplained and some suggestions regarding algorithmic complexity of the wave functions in a large quantum system e are made along that direction.
The possibility of consistency between the basic quantum principles and reduction (wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as a convenient tool for this investigation. A derivation of reduction from quantum mechanics is proposed on a specific example, using standard methods of statistical physics. Although these methods are valid only "for all practical purposes", arguments are given to ascribe an emerging status to reduction (or the uniqueness of physical reality), similar to the status of classical physics. Examination of measurements of the particles in an EPR pair by two space-like separated apparatuses shows that the model is consistent with the non-separable character of quantum mechanics, although both measurements are local. Quantitative estimates are given.
The possibility of a fundamental consistency between the basic quantum principles and reduction (so-called wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as a convenient tool for this investigation. Previous no-go theorems excluding consistency are disproved on this ground, because their assumptions neglected the occurrence of organization in a real measuring apparatus. A scheme for deriving reduction from quantum mechanics is also proposed as a conjecture.
In the well known Copenhagen interpretation of Quantum mechanics, advocated by N. Bohr, the physical objects and the experimental results can be described only in a macroscopic language, leaving any possible microscopic description as unspeakable. This point of view has been deepened by C. Rovelli in the relational interpretation of Quantum mechanics. Most of the alternative interpretations, which try a detailed microscopic description of physical phenomena and of their evolution, have in common the explicit introduction of the wave function as the basic element of the theory. These interpretations require the notion of quantum state as the fundamental concept of the theory, which is the typical unspeakable physical element according to the Copenhagen interpretation. The two basic physical entities are intimately bound together by the integrity of the wave function. These interpretations are usually indicated as realistic. It is well known that the use of the wave function and its time evolution in the description of the physical processes leads unavoidably to some difficulties or so-called paradoxes. The measurement problem is at the center of these difficulties, mainly because it requires the introduction of the reduction process of the wave function, which is not included explicitly within the mathematical formalism of Quantum Mechanics. In this paper we build up and propose a model which goes beyond the standard formalism and which is able to solve the measurement problem and all the other difficulties which, in a way or in another, are related to it.
New theory of measurement is presented to show that quantum mechanics can describe the whole processes of quantum-mechanical measurement leading to the so-called reduction of wave packet if applied properly to the total system of object and apparatus. We introduce a simple model, where momenta of particles are measured using a perfect rigid mirror, to yield the reduction of wave packet in a clear-cut way. Microscopic uncertainties of macroscopic quantities and the dynamical scattering theory play the essential roles. Before entering into the main part, we briefly summarize the controversial points in the theory of measurement.
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.