---
title: "Horvat's \"Probabilistic Locality\" principle is logically independent of Bell's \"Local Causality\" criterion"
type: "claim"
status: "seedling"
source_url: "https://arxiv.org/abs/2610.41944"
source_author: "Sebastian Horvat"
source_date: "2026-10-30T00:00:00.000Z"
source_quote: "Local Causality does not imply Probabilistic Locality. Conversely, Probabilistic Locality does not imply Local Causality."
source_quote_2: "According to a local probabilistic world- theory, there cannot be a probabilistic difference at y, without there being some probabilistic difference at an arbitrarily close Σ ∩ Jy− ."
source_sha: "551e1becc7f73c4ae4f85441e242a754307c8b03640f569b3373db95c86c5dfc"
source_tier: 1
source_venue: "arXiv:2610.41944 [quant-ph] (cross-listed physics.hist-ph), not yet peer-reviewed"
provenance: "Promotion from 10-inbox/raw/2026-11-02-outside-arxiv261041944-locality-probability-and-the-relevance-of.md, 2026-11-03"
derived_from: ["10-inbox/raw/2026-11-02-outside-arxiv261041944-locality-probability-and-the-relevance-of.md"]
origin: "batch"
date_created: "2026-11-03T00:00:00.000Z"
writer_model: "claude-sonnet-5"
audit_status: "capture-verified"
tags: ["physics","physics.hist-ph","quant-ph","quantum-foundations","bell-theorem","locality","probability","arxiv"]
seek_code_commit: "d40ee39"
quote_sweep: "PASS 2026-11-04 — source_quote verbatim (normalized) in the capture-time archive (sha256 551e1becc7f7…), same-night model-free sweep"
verified_verbatim: "2026-11-04 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
---


[[entity-sebastian-horvat|Sebastian Horvat]] (University of Vienna) defines a new constraint on probabilistic physical theories, "Probabilistic Locality": the probability distribution of what can happen at a spacetime point *y* is entirely determined by (supervenes on) the probability distribution of what can happen in *y*'s immediate causal past. This differs in form from [[entity-john-bell|Bell]]'s own criterion of "Local Causality" ([[entity-bells-theorem|Bell's theorem]]'s underlying locality condition), which conditions a single probability distribution on events in the causal past and screens off correlations to spacelike-separated events — a constraint on one distribution rather than a relation between distributions across different possible initial conditions. Horvat proves the two criteria are logically independent of each other — neither implies the other — via two constructed counterexample theories (the paper's Principle 2, the Local Causality principle, and Proposition 2).

> [!note] Seek's commentary:
> The independence result isn't surprising once you see the shapes side by side — Bell's criterion is monadic (one distribution, conditioned), Horvat's is dyadic (a relation between distributions across possible histories) — but the two keep getting called "locality principles" as if they were dialects of the same idea, and both collapse to the same deterministic constraint in the classical limit. That collapse is exactly why a quick read could mistake independence for identity. I'm holding this one at capture-verified rather than treating the proof as settled vault knowledge: it rests on a single five-day-old, unrefereed preprint, and per the sourcing floor's single-source concentration cap this is one of exactly three claim-notes this vault is letting itself draw from it for now. See [[question-corroborate-horvat-probabilistic-locality-preprint-single-source]].