dorsal/arxiv
View SchemaThe Counterfactual Meaning of the ABL Rule
| Authors | Louis Marchildon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307082 |
| URL | https://arxiv.org/abs/quant-ph/0307082 |
| Journal | Proc. of QTRF-2 meeting (Vaxjo University Press, Vaxjo, Sweden, 2004), pp. 403-412 |
Abstract
The Aharonov-Bergmann-Lebowitz rule assigns probabilities to quantum measurement results at time t on the condition that the system is prepared in a given way at t_1 < t and found in a given state at t_2 > t. The question whether the rule can also be applied counterfactually to the case where no measurement is performed at the intermediate time t has recently been the subject of controversy. I argue that the counterfactual meaning may be understood in terms of the true value of an observable at t. Such a value cannot be empirically determined for, by stipulation, the measurement that would yield it is not performed. Nevertheless, it may or may not be well-defined depending on one's proposed interpretation of quantum mechanics. Various examples are discussed illustrating what can be asserted at the intermediate time without running into contradictions.
{
"annotation_id": "511533b1-7981-430e-9c4e-1a94a1028276",
"date_created": "2026-03-02T18:01:59.748000Z",
"date_modified": "2026-03-02T18:01:59.748000Z",
"file_hash": "11617dc309c2087a2d1c93aeafdb834e4d9bb3bc17e7ced0476cf5290b7f063a",
"private": false,
"record": {
"abstract": "The Aharonov-Bergmann-Lebowitz rule assigns probabilities to quantum\nmeasurement results at time t on the condition that the system is prepared in a\ngiven way at t_1 \u003c t and found in a given state at t_2 \u003e t. The question\nwhether the rule can also be applied counterfactually to the case where no\nmeasurement is performed at the intermediate time t has recently been the\nsubject of controversy. I argue that the counterfactual meaning may be\nunderstood in terms of the true value of an observable at t. Such a value\ncannot be empirically determined for, by stipulation, the measurement that\nwould yield it is not performed. Nevertheless, it may or may not be\nwell-defined depending on one\u0027s proposed interpretation of quantum mechanics.\nVarious examples are discussed illustrating what can be asserted at the\nintermediate time without running into contradictions.",
"arxiv_id": "quant-ph/0307082",
"authors": [
"Louis Marchildon"
],
"categories": [
"quant-ph"
],
"journal_ref": "Proc. of QTRF-2 meeting (Vaxjo University Press, Vaxjo, Sweden,\n 2004), pp. 403-412",
"title": "The Counterfactual Meaning of the ABL Rule",
"url": "https://arxiv.org/abs/quant-ph/0307082"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "8b197c90-48bd-4213-81e8-58c083b4b90a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}