Weinberg's Nonlinear Quantum Mechanics and the Einstein-Podolsky-Rosen Paradox
Joseph Polchinski
Abstract and summary · read the original at the source · APS copyright; the Crossref deposit for this DOI carries no licence entry, so no open licence is assumed
En una página
In ordinary quantum mechanics two entangled systems are correlated, yet nothing done to one can send a message to the other. Joseph Polchinski asked whether that survives Weinberg's proposal to let quantum mechanics be slightly nonlinear. A nonlinear theory has more observables than the linear one, which suggests the wave function carries more usable information, and so the question is sharp: could an Einstein–Podolsky–Rosen apparatus become a telephone? Polchinski works out the exact condition under which a distant system receives no signal. Every observable in that system must depend only on its own density matrix. Weinberg's original treatment of separated systems does not satisfy this, and so allows EPR communication. Polchinski then shows that the only way to forbid it opens a different, equally unusual channel: communication between different branches of the wave function, demonstrated with a four-step Stern–Gerlach thought experiment. Nonlinearity changes what quantum correlations can carry; the question is which way.
Por qué importa aquíChapter 17 teaches why self-consistent time loops are a real subject rather than a puzzle for fiction. The door to signalling through entanglement is precisely the linearity of quantum mechanics, and this paper states exactly what a small nonlinearity would do to that door. It turns an argument about paradoxes into a statement about a measurable property of nature.
Qué afirma
01The no-signal condition. Assuming the observables include all the usual linear Hermitian observables, the necessary and sufficient condition for an isolated system not to receive information through EPR correlations is that every observable in that system depends only on the density matrix for that system.The first main result, following equations 6 to 9
Published and peer-reviewed02Weinberg's separated systems. The nonlinear observables Weinberg originally proposed for separated systems are not functions of the density matrix alone, except when linear, and therefore allow communication through EPR correlations.Following equation 10
Published and peer-reviewed03The other channel. Nonlinear observables that do satisfy the no-signal condition lead to communication of another sort, between different branches of the wave function, shown with a four-step process in which a spin-one-half ion passes a Stern–Gerlach device, a macroscopic observer acts on the outcome, the ion meets a field coupled to a nonlinear observable, and the observer measures again. Forbidding EPR communication in nonlinear quantum mechanics therefore necessarily produces this second kind.Introduction; the four-step process and the partial density matrices that follow it
Published and peer-reviewed
Léelo · abstract
(Summary only — no text of the paper is reproduced here; see the rights note above.)
Citation
Joseph Polchinski, Theory Group, University of Texas, and Institute for Theoretical Physics, University of California, Santa Barbara, Weinberg's Nonlinear Quantum Mechanics and the Einstein-Podolsky-Rosen Paradox, Physical Review Letters 66, 397–400 (28 January 1991). DOI 10.1103/PhysRevLett.66.397.
The shelf this sits on
- Weinberg, Precision Tests of Quantum Mechanics (1989) — the nonlinear framework and how to bound it: /library/stm-06e5a27568
- DIRD 16, The Space Communication Implications of Quantum Entanglement and Nonlocality (2010): /library/stm-e094621316
La puerta de entrada
https://doi.org/10.1103/PhysRevLett.66.397WHICH COPY WAS READ. The version of record, Physical Review Letters volume 66, number 4, pages 397 to 400, 28 January 1991, received 18 June 1990, was downloaded on 2026-09-13 from the American Physical Society full-text endpoint at harvest.aps.org/v2/journals/articles/10.1103/PhysRevLett.66.397/fulltext and read in full in text form. WHAT THIS PAGE CARRIES. No text of the paper is reproduced: the summary and claims are the site's own prose with locators. The related paper by Gisin, Weinberg's non-linear quantum mechanics and supraluminal communications, Physics Letters A 143, 1 to 2 (1990), is published by Elsevier without an open licence and was not read for this sheet; it is mentioned only because Polchinski discusses it.
Cómo citarlo
Joseph Polchinski (1991) Weinberg's Nonlinear Quantum Mechanics and the Einstein-Podolsky-Rosen Paradox. doi:10.1103/PhysRevLett.66.397
Dónde encaja en el currículo
Agujeros de gusano, condiciones de energía y el presupuesto de energía negativa