No violation on a generalisation of Leggett-Garg inequality and Bell-CHSH inequality with extended probability
Abstract
A generalisation of the Leggett-Garg inequality (LGI) and the Bell-CHSH inequality is proposed in this work, by replacing a classical probability notion with an extended probability notion. The extended probability serves as an underlying layer of reality to the classical probability. Within the consistent history framework, the underlying layer is so-called a non-settleable history. Hence, the bounds of the LGIs and Bell-CHSH inequalities are extended. The resulting generalised inequalities are satisfied without violation for arbitrary measurement settings. Furthermore, generalised Macro- realism and generalised Local realism are introduced and analysed within the extended probability framework without relying on an explicit measurement. This opens up further possibilities on one of the great pursuits in physics, understanding on how a quantum system can possess classical properties.
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BibTeX
@misc{kajonsombat2026violation,
title = {{No violation on a generalisation of Leggett-Garg inequality and Bell-CHSH inequality with extended probability}},
author = {Sirawit Kajonsombat and Pongwit Srisangyingcharoen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24169},
eprint = {2609.24169},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24169},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - No violation on a generalisation of Leggett-Garg inequality and Bell-CHSH inequality with extended probability
AU - Sirawit Kajonsombat
AU - Pongwit Srisangyingcharoen
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24169
UR - https://arxiv.org/abs/2609.24169
AB - A generalisation of the Leggett-Garg inequality (LGI) and the Bell-CHSH inequality is proposed in this work, by replacing a classical probability notion with an extended probability notion. The extended probability serves as an underlying layer of reality to the classical probability. Within the consistent history framework, the underlying layer is so-called a non-settleable history. Hence, the bounds of the LGIs and Bell-CHSH inequalities are extended. The resulting generalised inequalities are satisfied without violation for arbitrary measurement settings. Furthermore, generalised Macro- realism and generalised Local realism are introduced and analysed within the extended probability framework without relying on an explicit measurement. This opens up further possibilities on one of the great pursuits in physics, understanding on how a quantum system can possess classical properties.
ER -