scholarly journals Nonlinear quantum mechanics, the superposition principle, and the quantum measurement problem

Pramana ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. 67-91 ◽  
Author(s):  
KINJALK LOCHAN ◽  
T P SINGH
Keyword(s):  
Quantum Mechanics ◽  
Quantum Measurement ◽  
Measurement Problem ◽  
Superposition Principle ◽  
Quantum Measurement Problem ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

The build of nonlinear quantum mechancs and variations of feature of microscopic particles as well as their experimental affirmation

2014 ◽  
Vol 5 (3) ◽  
pp. 871-981 ◽  
Author(s):  
Pang Xiao Feng
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Lagrange Equation ◽  
Minimum Principle ◽  
Superposition Principle ◽  
Type Equation ◽  
Experimental Results ◽  
Traditional Concept ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

We establish the nonlinear quantum mechanics due to difficulties and problems of original quantum mechanics, in which microscopic particles have only a wave feature, not corpuscle feature, which are completely not consistent with experimental results and traditional concept of particle. In this theory the microscopic particles are no longer a wave, but localized and have a wave-corpuscle duality, which are represented by the following facts, the solutions of dynamic equation describing the particles have a wave-corpuscle duality, namely it consists of a mass center with constant size and carrier wave, is localized and stable and has a determinant mass, momentum and energy, which obey also generally conservation laws of motion, their motions meet both the Hamilton equation, Euler-Lagrange equation and Newton-type equation, their collision satisfies also the classical rule of collision of macroscopic particles, the uncertainty of their position and momentum is denoted by the minimum principle of uncertainty. Meanwhile the microscopic particles in this theory can both propagate in solitary wave with certain frequency and amplitude and generate reflection and transmission at the interfaces, thus they have also a wave feature, which but are different from linear and KdV solitary wave’s. Therefore the nonlinear quantum mechanics changes thoroughly the natures of microscopic particles due to the nonlinear interactions. In this investigation we gave systematically and completely the distinctions and variations between linear and nonlinear quantum mechanics, including the significances and representations of wave function and mechanical quantities, superposition principle of wave function, property of microscopic particle, eigenvalue problem, uncertainty relation and the methods solving the dynamic equations, from which we found nonlinear quantum mechanics is fully new and different from linear quantum mechanics. Finally, we verify further the correctness of properties of microscopic particles described by nonlinear quantum mechanics using the experimental results of light soliton in fiber and water soliton, which are described by same nonlinear Schrödinger equation. Thus we affirm that nonlinear quantum mechanics is correct and useful, it can be used to study the real properties of microscopic particles in physical systems.

scholarly journals Decoherence and its role in the modern measurement problem

2012 ◽  
Vol 370 (1975) ◽  
pp. 4576-4593 ◽  
Author(s):  
David Wallace
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Measurement ◽  
Measurement Problem ◽  
Scientific Practice ◽  
Measurement Theory ◽  
Quantum Measurements ◽  
Quantum Measurement Problem ◽  
Modern Physics ◽  
Conceptual Problems

Decoherence is widely felt to have something to do with the quantum measurement problem, but getting clear on just what is made difficult by the fact that the ‘measurement problem’, as traditionally presented in foundational and philosophical discussions, has become somewhat disconnected from the conceptual problems posed by real physics. This, in turn, is because quantum mechanics as discussed in textbooks and in foundational discussions has become somewhat removed from scientific practice, especially where the analysis of measurement is concerned. This paper has two goals: firstly (§§1–2), to present an account of how quantum measurements are actually dealt with in modern physics (hint: it does not involve a collapse of the wave function) and to state the measurement problem from the perspective of that account; and secondly (§§3–4), to clarify what role decoherence plays in modern measurement theory and what effect it has on the various strategies that have been proposed to solve the measurement problem.

scholarly journals Measured distribution of cloud chamber tracks from radioactive decay: a new empirical approach to investigating the quantum measurement problem

2021 ◽  
Author(s):  
Jonathan Schonfeld
Keyword(s):  
Spatial Distribution ◽  
Quantum Mechanics ◽  
Quantum Measurement ◽  
Measurement Problem ◽  
Radioactive Decay ◽  
Foundations Of Quantum Mechanics ◽  
Radioactive Source ◽  
Cloud Chamber ◽  
Quantum Measurement Problem ◽  
Measured Distribution

Abstract Using publically available video of a cloud chamber with a very small radioactive source, I measure the spatial distribution of where tracks start, and consider possible implications. This is directly relevant to the quantum measurement problem and its possible resolution, and appears never to have been done before. The raw data are relatively uncontrolled, leading to caveats that should guide future, more tailored experiments. Track distributions from decays in cloud chambers represent a previously unappreciated way to probe the foundations of quantum mechanics, and a novel case of wavefunctions with macroscopic signatures.

The Collapse of the Quantum State

2019 ◽  
pp. 118-142
Author(s):  
Jeffrey A. Barrett
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Quantum Measurement ◽  
Measurement Problem ◽  
Primitive Ontology ◽  
Quantum Measurement Problem

We consider Wigner’s proposal for solving the quantum measurement problem. His solution involves a strong mind-body dualism, but it is also possible to provide a purely physical collapse solution to the quantum measurement problem. To this end, we consider the GRW formulation of quantum mechanics and three ways one might interpret it: GRWr, GRWm, and GRWf. These ways of interpreting the theory differ in the metaphysical commitments one makes and, hence, in how one explains one’s measurement records and hence one’s experience. This provides an introduction to the notions of an empirical ontology and a primitive ontology. We consider some of the comparative virtues and vices of the GRW formulation of quantum mechanics.

scholarly journals Interpretive analogies between quantum and statistical mechanics

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
C. D. McCoy
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Quantum Measurement ◽  
Measurement Problem ◽  
Initial Conditions ◽  
Primitive Ontology ◽  
Quantum Measurement Problem ◽  
Classical Statistical Mechanics ◽  
Interpretive Strategies ◽  
Significant Application

AbstractThe conspicuous similarities between interpretive strategies in classical statistical mechanics and in quantum mechanics may be grounded on their employment of common implementations of probability. The objective probabilities which represent the underlying stochasticity of these theories can be naturally associated with three of their common formal features: initial conditions, dynamics, and observables. Various well-known interpretations of the two theories line up with particular choices among these three ways of implementing probability. This perspective has significant application to debates on primitive ontology and to the quantum measurement problem.

NONLINEAR QUANTUM MECHANICS WITH NONCLASSICAL GRAVITATIONAL SELF-INTERACTION

1989 ◽  
Vol 04 (13) ◽  
pp. 3229-3267 ◽  
Author(s):  
A.D. POPOVA
Keyword(s):  
Quantum Mechanics ◽  
Quantum Particle ◽  
Superposition Principle ◽  
Uncertainty Relations ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics ◽  
Stationary Gravitational Field ◽  
Quantum Operators ◽  
Original Approach ◽  
Ordinary Quantum

The original approach for the self-consistent inclusion of gravity into quantum mechanics of a particle is developed. (There are no connections with second quantization.) The nonstandard action principle is constructed for the stationary situation: the quantum particle in a stationary state creating some nonclassical stationary gravitational field and interacting with it, The accompanying problem of covariantization of quantum operators is considered. The general theory is illustrated by the Newtonian-Schrödingerian and quasi classical limiting cases. The levels of applicability of ordinary quantum mechanics and the problems of measurements and interpretation of nonclassical gravity are discussed. The “uncertainty relations” connecting uncertainties of some “local” parts of curvature and those of the particle’s position and momentum are derived. The superposition principle is generalized on the base of some approximate action.

scholarly journals On Collapse of Quantum State on Measurement

2021 ◽  
Author(s):  
Basudev Nag Chowdhury ◽  
Sanatan Chattopadhyay
Keyword(s):  
Quantum Measurement ◽  
Measurement Problem ◽  
Current Model ◽  
Superposition Principle ◽  
Weak Measurement ◽  
Measuring Apparatus ◽  
Physical Systems ◽  
Quantum Measurement Problem ◽  
Classical Systems ◽  
Classical World

Abstract In the context of the century-long debate on quantum measurement problem, the current work proposes a model that describes the process of collapse of state by quantum interaction, which resolves the controversies of the framework of quantum mechanics and describes the entire domain of quantum-to-classical world including the weak measurement and partial collapse. ‘Measurement’, being the process of physically interacting with a system in order to extracting information from it, is theorized in the current model by synthesizing the quantum interaction between system and measuring apparatus with the information entropy of such process. The model assumes Schrödinger equation to be the only guiding equation for all physical systems including the measuring apparatus, and does not presuppose ‘superposition principle’, rather derives it theoretically from the formulation. The superposed state is shown to be independent of the choice of measurement operator (observable) or basis states (pointers) of the measuring apparatus. Most interestingly, the current model explains the non-observance of ‘superposition principle’ by classical systems as the classical limit of such quantum description of measurement. Along with solving the quantum measurement problem, the work also explains weak measurement and partial collapse, which can be further extended to investigate such several emerging critical phenomena.

The Quantum Measurement Problem

2019 ◽  
pp. 105-117
Author(s):  
Jeffrey A. Barrett
Keyword(s):  
Quantum Mechanics ◽  
Quantum Measurement ◽  
Physical System ◽  
Measurement Problem ◽  
Standard Theory ◽  
Standard Formulation ◽  
Logical Consistency ◽  
Quantum Measurement Problem ◽  
Logical Inconsistency ◽  
Wigner’S Friend

We use the Wigner’s friend story to characterize the quantum measurement problem. On the standard formulation of quantum mechanics, whether a physical system is measured determines which of the theory's two dynamical laws obtains. For this reason, the logical consistency of the theory depends on one specifying strictly disjoint conditions for when when each law obtains, which means that one needs to say precisely what constitutes a measurement. But since the term measurement occurs in the standard theory as an undefined primitive term, the theory is at best incomplete. We see precisely how this conceptual incompleteness threatens the logical inconsistency of the theory and why, on even the most charitable reading, it entails that the theory is empirical incomplete. We end by considering why its empirically incompleteness is extremely difficult to test.

scholarly journals On Collapse of Quantum State on Measurement

2021 ◽  
Author(s):  
Basudev Nag Chowdhury ◽  
Sanatan Chattopadhyay
Keyword(s):  
Quantum Measurement ◽  
Measurement Problem ◽  
Current Model ◽  
Superposition Principle ◽  
Weak Measurement ◽  
Measuring Apparatus ◽  
Physical Systems ◽  
Quantum Measurement Problem ◽  
Classical Systems ◽  
Classical World

Abstract In the context of the century-long debate on quantum measurement problem, the current work proposes a model that describes the process of collapse of state by quantum interaction, which resolves the controversies of the framework of quantum mechanics and describes the entire domain of quantum-to-classical world including the weak measurement and partial collapse. ‘Measurement’, being the process of physically interacting with a system in order to extracting information from it, is theorized in the current model by synthesizing the quantum interaction between system and measuring apparatus with the information entropy of such process. The model assumes Schrödinger equation to be the only guiding equation for all physical systems including the measuring apparatus, and does not presuppose ‘superposition principle’, rather derives it theoretically from the formulation. The superposed state is shown to be independent of the choice of measurement operator (observable) or basis states (pointers) of the measuring apparatus. Most interestingly, the current model explains the non-observance of ‘superposition principle’ by classical systems as the classical limit of such quantum description of measurement. Along with solving the quantum measurement problem, the work also explains weak measurement and partial collapse, which can be further extended to investigate such several emerging critical phenomena.

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