Algorithmic Randomness and Physical Typicality
Abstract
Appeals to typicality are common in physics, but it is often unclear what it means for a physical state to be typical relative to a probability measure, and correspondingly unclear what a law that appeals to typicality asserts. Here we consider how one might characterize physical typicality using ideas from the theory of algorithmic randomness. As a concrete example, we show how taking a physical state to be typical relative to a computable measure when it is Martin-Löf random allows one to formulate the distribution postulate in Bohmian mechanics as a statistical constraining law of the theory. Using a toy model, we show how this constraint guarantees the standard Born statistics for computable experimental protocols. Algorithmic Bohmian mechanics (aBM) thus illustrates how algorithmic randomness may be used to provide precise content to a statistical law.
Related
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BibTeX
@misc{barrett2026algorithmic,
title = {{Algorithmic Randomness and Physical Typicality}},
author = {Jeffrey A. Barrett and Eddy Keming Chen and Josiah Lopez-Wild},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06268},
eprint = {2609.06268},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06268},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Algorithmic Randomness and Physical Typicality
AU - Jeffrey A. Barrett
AU - Eddy Keming Chen
AU - Josiah Lopez-Wild
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.06268
UR - https://arxiv.org/abs/2609.06268
AB - Appeals to typicality are common in physics, but it is often unclear what it means for a physical state to be typical relative to a probability measure, and correspondingly unclear what a law that appeals to typicality asserts. Here we consider how one might characterize physical typicality using ideas from the theory of algorithmic randomness. As a concrete example, we show how taking a physical state to be typical relative to a computable measure when it is Martin-Löf random allows one to formulate the distribution postulate in Bohmian mechanics as a statistical constraining law of the theory. Using a toy model, we show how this constraint guarantees the standard Born statistics for computable experimental protocols. Algorithmic Bohmian mechanics (aBM) thus illustrates how algorithmic randomness may be used to provide precise content to a statistical law.
ER -