dorsal/arxiv
View SchemaOn Superselection Rules in Bohm-Bell Theories
| Authors | Samuel Colin, Thomas Durt, Roderich Tumulka |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0509177 |
| URL | https://arxiv.org/abs/quant-ph/0509177 |
| DOI | 10.1088/0305-4470/39/50/008 |
| Journal | J. Phys. A: Math. Gen. 39 (2006) 15403-15419 |
Abstract
The meaning of superselection rules in Bohm-Bell theories (i.e., quantum theories with particle trajectories) is different from that in orthodox quantum theory. More precisely, there are two concepts of superselection rule, a weak and a strong one. Weak superselection rules exist both in orthodox quantum theory and in Bohm-Bell theories and represent the conventional understanding of superselection rules. We introduce the concept of strong superselection rule, which does not exist in orthodox quantum theory. It relies on the clear ontology of Bohm-Bell theories and is a sharper and, in the Bohm-Bell context, more fundamental notion. A strong superselection rule for the observable G asserts that one can replace every state vector by a suitable statistical mixture of eigenvectors of G without changing the particle trajectories or their probabilities. A weak superselection rule asserts that every state vector is empirically indistinguishable from a suitable statistical mixture of eigenvectors of G. We establish conditions on G for both kinds of superselection. For comparison, we also consider both kinds of superselection in theories of spontaneous wave function collapse.
{
"annotation_id": "19357838-950b-4924-b87f-5bbf528750f1",
"date_created": "2026-03-02T18:02:19.952000Z",
"date_modified": "2026-03-02T18:02:19.952000Z",
"file_hash": "85c505be86344ae36757a9e85420b29cb8416515a1bb7e30eb8500928e9a76ca",
"private": false,
"record": {
"abstract": "The meaning of superselection rules in Bohm-Bell theories (i.e., quantum\ntheories with particle trajectories) is different from that in orthodox quantum\ntheory. More precisely, there are two concepts of superselection rule, a weak\nand a strong one. Weak superselection rules exist both in orthodox quantum\ntheory and in Bohm-Bell theories and represent the conventional understanding\nof superselection rules. We introduce the concept of strong superselection\nrule, which does not exist in orthodox quantum theory. It relies on the clear\nontology of Bohm-Bell theories and is a sharper and, in the Bohm-Bell context,\nmore fundamental notion. A strong superselection rule for the observable G\nasserts that one can replace every state vector by a suitable statistical\nmixture of eigenvectors of G without changing the particle trajectories or\ntheir probabilities. A weak superselection rule asserts that every state vector\nis empirically indistinguishable from a suitable statistical mixture of\neigenvectors of G. We establish conditions on G for both kinds of\nsuperselection. For comparison, we also consider both kinds of superselection\nin theories of spontaneous wave function collapse.",
"arxiv_id": "quant-ph/0509177",
"authors": [
"Samuel Colin",
"Thomas Durt",
"Roderich Tumulka"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/39/50/008",
"journal_ref": "J. Phys. A: Math. Gen. 39 (2006) 15403-15419",
"title": "On Superselection Rules in Bohm-Bell Theories",
"url": "https://arxiv.org/abs/quant-ph/0509177"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "30ce8d09-9460-43ec-b6a5-3cf37254e44f",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}