Locality, Probability and the Relevance of History
Abstract
Relativistic theory and experiments teach us that causal influences are constrained by the speed of light. Deterministic theories incorporate this lesson in functional terms: whether an event occurs or not is functionally determined by events that occur in its immediate causal past. In this paper we suggest a natural generalization of this constraint that applies to probabilistic theories: the probability that an event occurs is to be functionally determined by the probability of the event-occurrences in its immediate causal past. This constraint differs from Bell's criterion of local causality and turns out to imply it only under an additional assumption that requires history to be, in a sense, irrelevant. Bell-inequality-violating quantum phenomena are thus arguably not in tension with relativity, locality, "statistical independence", nor with a supposed "realism". What they instead show is that history is, in a sense, relevant.
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BibTeX
@misc{horvat2026locality,
title = {{Locality, Probability and the Relevance of History}},
author = {Sebastian Horvat},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41944},
eprint = {2610.41944},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41944},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Locality, Probability and the Relevance of History
AU - Sebastian Horvat
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41944
UR - https://arxiv.org/abs/2610.41944
AB - Relativistic theory and experiments teach us that causal influences are constrained by the speed of light. Deterministic theories incorporate this lesson in functional terms: whether an event occurs or not is functionally determined by events that occur in its immediate causal past. In this paper we suggest a natural generalization of this constraint that applies to probabilistic theories: the probability that an event occurs is to be functionally determined by the probability of the event-occurrences in its immediate causal past. This constraint differs from Bell's criterion of local causality and turns out to imply it only under an additional assumption that requires history to be, in a sense, irrelevant. Bell-inequality-violating quantum phenomena are thus arguably not in tension with relativity, locality, "statistical independence", nor with a supposed "realism". What they instead show is that history is, in a sense, relevant.
ER -