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:quant-ph/9904016

Nonlocality in Nonlinear Quantum Mechanics

W. Lücke

Published Apr 6, 1999• 9 citations
arXivHTMLPDF

Abstract

A general method for testing essential nonlocality of nonlinear modifications of quantum mechanics is presented and applied to show the inconsistency of I. Bialynicki-Birula's and J. Mycielski's nonlinear quantum theory.
DOI
10.48550/arxiv.quant-ph/9904016

Related papers

Investigation of the basis aspects of an axiomatic nonlinear quantum mechanics and the phenomenon of nonlocality

Diederik Aerts, Bart D’Hooghe

•Jan 1, 2004•0 citations

Remarks on a Nonlinear Quantum Theory

H. D. Doebner

Motivated by recent proposals (Bialynicki-Birula, Mycielski; Haag, Bannier; Weinberg; Doebner, Goldin) for nonlinear quantum mechanical evolution equations for pure states some principal difficulties in the framework of usual quantum theory, which is based on its inherent linear structure, are discussed. A generic construction of nonlinear evolution equations through nonlinear gauge transformations is indicated.

arXiv:quant-ph/9803011•Mar 4, 1998•1 citation

Generalized Quantum Mechanics and Nonlinear Gauge Transformations

P. Nattermann

Motivated by the problems of interpretation of a nonlinear evolution equation in quantum mechanics we discuss in this contribution the concept of nonlinear gauge transformations, that has recently been introduced in joint work with Doebner and Goldin, in the framework of Mielnik's Generalized Quantum Mechanics. Using these gauge transformations we construct linear quantum systems in a ``nonlinear disguise'', and a gauge generalization of these (in analogy to the minimal coupling of orthodox quantum mechanics) leads to a unification of Bialynicki-Birula--Mycielski and Doebner--Goldin evolution equations for the quantum system. The notion of nonlinear observables introduced by Lücke is finally discussed in the same framework.

arXiv:quant-ph/9703017•Mar 12, 1997•0 citations

Nonlocality and quantum mechanics

Saverio Pascazio

A class of nonlocal hidden variable theories is shown to be incompatible with quantum mechanics.

arXiv:1012.5810•Dec 28, 2010•1 citation

Nonlocality in quantum theory understood in terms of Einstein's nonlinear field approach

David Böhm, Basil J. Hiley

Foundations of Physics•Aug 1, 1981•26 citations

Gauge transformations in quantum mechanics and the unification of nonlinear Schrödinger equations

H. D. Doebner, Gerald A. Goldin, P. Nattermann

Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum theories physically equivalent to linear quantum mechanics through nonlinear gauge transformations. We show that under two physically motivated assumptions, these transformations are uniquely determined: they are exactly the group of time-dependent, nonlinear gauge transformations introduced previously for a family of nonlinear Schrödinger equations. The general equation in this family, including terms considered by Kostin, by Bialynicki-Birula and Mycielski, and by Doebner and Goldin, with time-dependent coefficients, can be obtained from the linear Schrödinger equation through gauge transformation and a subsequent process we call gauge generalization. We thus unify, on fundamental grounds, a rather diverse set of nonlinear time evolutions in quantum mechanics.

arXiv:quant-ph/9709036•Journal of Mathematical Physics•Jan 1, 1999•61 citations
Motivated by the problems of interpretation of a nonlinear evolution equation in quantum mechanics we discuss in this contribution the concept of nonlinear gauge transformations, that has recently been introduced in joint work with Doebner and Goldin, in the framework of Mielnik's Generalized Quantum Mechanics. Using these gauge transformations we construct linear quantum systems in a ``nonlinear disguise'', and a gauge generalization of these (in analogy to the minimal coupling of orthodox quantum mechanics) leads to a unification of Bialynicki-Birula--Mycielski and Doebner--Goldin evolution equations for the quantum system. The notion of nonlinear observables introduced by Lücke is finally discussed in the same framework.
Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum theories physically equivalent to linear quantum mechanics through nonlinear gauge transformations. We show that under two physically motivated assumptions, these transformations are uniquely determined: they are exactly the group of time-dependent, nonlinear gauge transformations introduced previously for a family of nonlinear Schrödinger equations. The general equation in this family, including terms considered by Kostin, by Bialynicki-Birula and Mycielski, and by Doebner and Goldin, with time-dependent coefficients, can be obtained from the linear Schrödinger equation through gauge transformation and a subsequent process we call gauge generalization. We thus unify, on fundamental grounds, a rather diverse set of nonlinear time evolutions in quantum mechanics.