dorsal/arxiv
View SchemaAll quantum observables in a hidden-variables model must commute simultaneously
| Authors | James D. Malley |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0402126 |
| URL | https://arxiv.org/abs/quant-ph/0402126 |
| DOI | 10.1103/PhysRevA.69.022118 |
Abstract
Under a standard set of assumptions for a hidden-variables model for quantum events, we show that all observables must commute simultaneously. And, despite Bell's complaint that a key condition of von Neumann's was quite unrealistic, we show these these conditions are entirely equivalent to those later introduced by Bell, Kochen and Specker. As is it known that these conditions are also equivalent to those under which the Bell-Clauser-Horne inequalities are derived, we see that any experimental violations of the inequalities demonstrate only that quantum observables do not commute.The same conclusion applies to the collection of elegant inequality-free no-go proofs of Greenberger-Horne-Zeilinger, Mermin and Peres. Otherwise expressed, the usual hidden-variable models have assumptions that are collectively too strong to be interesting, and hence need modification or deletion.
{
"annotation_id": "3dc4b79f-acb0-489c-af59-92424f177d3e",
"date_created": "2026-03-02T18:02:06.456000Z",
"date_modified": "2026-03-02T18:02:06.456000Z",
"file_hash": "71090a35bb9537b58958eaf161d8d70d4d99168cabe72f487c6c438d57f97f25",
"private": false,
"record": {
"abstract": "Under a standard set of assumptions for a hidden-variables model for quantum\nevents, we show that all observables must commute simultaneously. And, despite\nBell\u0027s complaint that a key condition of von Neumann\u0027s was quite unrealistic,\nwe show these these conditions are entirely equivalent to those later\nintroduced by Bell, Kochen and Specker. As is it known that these conditions\nare also equivalent to those under which the Bell-Clauser-Horne inequalities\nare derived, we see that any experimental violations of the inequalities\ndemonstrate only that quantum observables do not commute.The same conclusion\napplies to the collection of elegant inequality-free no-go proofs of\nGreenberger-Horne-Zeilinger, Mermin and Peres. Otherwise expressed, the usual\nhidden-variable models have assumptions that are collectively too strong to be\ninteresting, and hence need modification or deletion.",
"arxiv_id": "quant-ph/0402126",
"authors": [
"James D. Malley"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.69.022118",
"title": "All quantum observables in a hidden-variables model must commute simultaneously",
"url": "https://arxiv.org/abs/quant-ph/0402126"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "df830dc8-c776-472b-8925-f2e5fb7f6512",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}