Precision Tests of Quantum Mechanics
Steven Weinberg
Abstract and summary · read the original at the source · APS default licence for the version of record — no Creative Commons licence
En une page
Quantum mechanics is linear: add two solutions and you get another. Steven Weinberg asked how well that has actually been tested, and proposed a way to test it far more stringently. He writes down a generalisation in which the wave function evolves under a Hamiltonian function that need not be bilinear, only homogeneous, so that small nonlinear terms can be switched on while the theory keeps its Hamiltonian form. Then he looks for the fingerprint any nonlinear oscillator leaves: detuning. In a nonlinear system the resonant frequency depends on how strongly each mode is excited, so a slow transition driven at a fixed frequency drifts off resonance as it proceeds. The hyperfine transitions of beryllium ions used for frequency standards are driven over seconds, which makes them an extremely sensitive detector. Weinberg shows that existing measurements already bound any nonlinear share of the beryllium nucleus's energy, and names how to tighten the bound by orders of magnitude.
Pourquoi cela compte iciChapter 17's section on self-consistent loops needs to say exactly where a door could open. Standard quantum mechanics forbids signalling through entanglement, and those proofs lean on linearity. Weinberg's paper is where a small nonlinearity became a precisely stated, measurable parameter — the thing later work showed would change what entanglement can carry, and the thing precision spectroscopy can bound.
Ce qu'il affirme
01The generalisation. The wave function obeys Hamilton-form equations with a real Hamiltonian function of the wave function and its conjugate that is homogeneous of first degree in each; if it is bilinear the equation reduces to ordinary time-dependent quantum mechanics, and small non-bilinear terms produce small nonlinearities. Homogeneity guarantees that a solution multiplied by a constant is still a solution.Equations 1 and 2 and the paragraph following
Published and peer-reviewed02The signature. A nonlinear system's resonant frequency depends on the amplitudes of the modes excited, so a transition driven slowly over a time T can only go to completion if the change in resonant frequency along the way stays within a natural width of order one over T; observing the transition complete therefore bounds the nonlinearity. For a two-level system the resonance condition tuned for the full transition still equals the energy difference, as in ordinary quantum mechanics.Opening paragraphs; Equations 10 and 11
Published and peer-reviewed03The experiment. The radio-frequency hyperfine transition in beryllium ions used to set frequency standards is driven with transition times of order a second; existing measurements at the National Bureau of Standards already set a limit on the fraction of the beryllium nucleus's energy that could come from nonlinear corrections, and lengthening the transition time, using Ramsey's separated-field method with free-precession times of minutes, or line-splitting methods could improve it by orders of magnitude.Abstract; the beryllium ion analysis and closing paragraph; reference 1, Bollinger, Prestage, Itano and Wineland 1985
Published and peer-reviewed
Lisez-le · abstract
(Summary only — no text of the paper is reproduced here; see the rights note above.)
Citation
Steven Weinberg, Theory Group, Department of Physics, University of Texas, Precision Tests of Quantum Mechanics, Physical Review Letters 62, 485–488 (30 January 1989). DOI 10.1103/PhysRevLett.62.485.
The shelf this sits on
- Polchinski, Weinberg's nonlinear quantum mechanics and the Einstein–Podolsky–Rosen paradox (1991) — what the nonlinearity does to entanglement: /library/stm-0aff150da2
- Cramer, The transactional interpretation of quantum mechanics — the self-consistent picture of emission and absorption: /library/stm-57e4eb66e8
- DIRD 16, The Space Communication Implications of Quantum Entanglement and Nonlocality (2010) — the report that sets Weinberg and Polchinski in the communications context: /library/stm-e094621316
La porte d'entrée
https://doi.org/10.1103/PhysRevLett.62.485WHICH COPY WAS READ. The version of record, Physical Review Letters volume 62, number 5, pages 485 to 488, 30 January 1989, received 23 November 1988, was downloaded on 2026-09-13 from the American Physical Society full-text endpoint at harvest.aps.org/v2/journals/articles/10.1103/PhysRevLett.62.485/fulltext and read in full in text form. LICENCE CHECK. The Crossref deposit for this DOI points to link.aps.org/licenses/aps-default-license, which is not a Creative Commons licence. WHAT THIS PAGE CARRIES. No text of the paper is reproduced: the summary and claims are the site's own prose with locators. One figure is deliberately not restated: the exponent in the paper's numerical bound did not survive text extraction legibly, and a number that could not be read off the page is not printed here. The longer companion paper, Testing quantum mechanics, Annals of Physics 194, 336 to 386 (1989), is published by Elsevier without an open licence and was not read for this sheet.
Comment le citer
Steven Weinberg (1989) Precision Tests of Quantum Mechanics. doi:10.1103/PhysRevLett.62.485
Sa place dans le programme
Trous de ver, conditions d'énergie et le budget d'énergie négative