dorsal/arxiv
View SchemaConditional probabilities in quantum theory, and the tunneling time controversy
| Authors | Aephraim M. Steinberg |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9502003 |
| URL | https://arxiv.org/abs/quant-ph/9502003 |
| DOI | 10.1103/PhysRevA.52.32 |
| Journal | Phys.Rev.A52:32-42,1995 |
Abstract
It is argued that there is a sensible way to define conditional probabilities in quantum mechanics, assuming only Bayes's theorem and standard quantum theory. These probabilities are equivalent to the ``weak measurement'' predictions due to Aharonov {\it et al.}, and hence describe the outcomes of real measurements made on subensembles. In particular, this approach is used to address the question of the history of a particle which has tunnelled across a barrier. A {\it gedankenexperiment} is presented to demonstrate the physically testable implications of the results of these calculations, along with graphs of the time-evolution of the conditional probability distribution for a tunneling particle and for one undergoing allowed transmission. Numerical results are also presented for the effects of loss in a bandgap medium on transmission and on reflection, as a function of the position of the lossy region; such loss should provide a feasible, though indirect, test of the present conclusions. It is argued that the effects of loss on the pulse {\it delay time} are related to the imaginary value of the momentum of a tunneling particle, and it is suggested that this might help explain a small discrepancy in an earlier experiment.
{
"annotation_id": "d1b899db-9b9b-4ea3-a4af-c119c0c82a90",
"date_created": "2026-03-02T18:02:38.139000Z",
"date_modified": "2026-03-02T18:02:38.139000Z",
"file_hash": "742b934e09f6aa985578bfb74d6c66da065609b9f39f8919aece38c45377131d",
"private": false,
"record": {
"abstract": "It is argued that there is a sensible way to define conditional probabilities\nin quantum mechanics, assuming only Bayes\u0027s theorem and standard quantum\ntheory. These probabilities are equivalent to the ``weak measurement\u0027\u0027\npredictions due to Aharonov {\\it et al.}, and hence describe the outcomes of\nreal measurements made on subensembles. In particular, this approach is used to\naddress the question of the history of a particle which has tunnelled across a\nbarrier. A {\\it gedankenexperiment} is presented to demonstrate the physically\ntestable implications of the results of these calculations, along with graphs\nof the time-evolution of the conditional probability distribution for a\ntunneling particle and for one undergoing allowed transmission. Numerical\nresults are also presented for the effects of loss in a bandgap medium on\ntransmission and on reflection, as a function of the position of the lossy\nregion; such loss should provide a feasible, though indirect, test of the\npresent conclusions. It is argued that the effects of loss on the pulse {\\it\ndelay time} are related to the imaginary value of the momentum of a tunneling\nparticle, and it is suggested that this might help explain a small discrepancy\nin an earlier experiment.",
"arxiv_id": "quant-ph/9502003",
"authors": [
"Aephraim M. Steinberg"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.52.32",
"journal_ref": "Phys.Rev.A52:32-42,1995",
"title": "Conditional probabilities in quantum theory, and the tunneling time controversy",
"url": "https://arxiv.org/abs/quant-ph/9502003"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "349512f2-71f6-463b-8397-2693ea23e38a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}