Bell’s theorem: Local realism versus quantum mechanics
M. Ferrero · T. W. Marshall · E. Santos
Summary and citation · read the original at the source
In one page
Miguel Ferrero of Oviedo, Trevor Marshall of Manchester and Emilio Santos of Cantabria wrote this for the American Journal of Physics, a teaching journal, so it is built to be followed line by line rather than admired. They first define realism and locality as physical principles in their own right, then derive from those two assumptions the expression Bell proposed for calculating correlations, and from that expression the incompatibility theorem: local realism and quantum mechanics cannot both be right about every prediction. The second half turns to the laboratory. Photomultipliers and polarizing filters are not perfectly efficient, so an experiment only ever samples the pairs it happens to detect. To get from what such an experiment measures to a verdict on local realism, the authors show, you must add a subsidiary assumption about how the detectors behave on the pairs they miss. Their conclusion is that those assumptions are not logically necessary — so in 1990 local realism stood unrefuted by experiment.
Why it matters hereChapter 1 is the evidence ladder, and this is one of the sharpest lessons on it: what an experiment establishes depends on what you assume the instruments are doing. Chapter 2 needs that lesson because the whole stochastic-electrodynamics programme — the vacuum as a real random field — lives or dies on how the photon-detection step is read.
What it claims
01Realism and locality are defined as separate, fundamental physical principles, and Bell’s expression for calculating correlations is derived from them — so the inequality that follows is a consequence of those two stated assumptions rather than a piece of quantum theory.Abstract, sentences 1 and 2; American Journal of Physics 58, 683 (1990)
Settled physics02From that expression the authors prove the theorem of incompatibility between local realism and quantum mechanics: the two cannot agree on every prediction, so an experiment able to distinguish them is possible in principle.Abstract, sentence 3
Settled physics03In the experiments performed by Aspect and others, photomultipliers and polarizing filters are not perfectly efficient, so ruling out local realism requires subsidiary assumptions about how those instruments operate on the pairs they do not register.Abstract, sentence 4
Published and peer-reviewed04Those subsidiary assumptions are not logically necessary; therefore, on the evidence available in 1990, local realism had not yet been refuted empirically. This is the argument that keeps a real-vacuum, local-realistic programme such as stochastic optics live rather than closed.Abstract, final sentence
Published and peer-reviewed05What to watch: the paper names its own decisive measurement — a Bell test whose detector efficiency is high enough that no subsidiary assumption is needed. Detection-efficient, locality-enforcing experiments were carried out in 2015 at Delft, NIST and Vienna, and the argument in this programme has since moved to the assumptions those tests still carry, contextuality among them.Abstract, sentences 4 and 5, read against the companion analysis in Physical Review A 39, 6271 (1989)
What to watch
The way in
https://doi.org/10.1119/1.16400SOURCE NOT REACHED IN FULL. The article is held closed by the publisher; OpenAlex and Unpaywall both report no repository copy, and a search of UCrea, the Universidad de Cantabria repository that holds much of Santos’s work, did not surface this paper on 2026-09-08. So the summary and the claims below are written from the authors’ own published abstract as carried by Crossref, from the Crossref bibliographic record — American Journal of Physics volume 58, issue 7, pages 683 to 688, July 1990, with Ferrero at the Departamento de Física, Universidad de Oviedo, Marshall at the Department of Mathematics, Manchester University, and Santos at the Departamento de Física Moderna, Universidad de Cantabria — and from the companion 1989 Physical Review A paper by Marshall and Santos, which this site holds in full and which contains the detector argument in its technical form. Locators therefore point to the abstract rather than to numbered sections, and no text of the article is reproduced here. REGISTRY NOTE: the record reached the library with chapters ch01, ch02, ch13, ch06 and ch03; this article treats neither energy extraction nor zero-point-field inertia, so the sheet carries chapters 1, 2 and 13.
How to cite it
M. Ferrero, T. W. Marshall, E. Santos (1990) Bell’s theorem: Local realism versus quantum mechanics. doi:10.1119/1.16400
Where it sits in the curriculum