---
id: "20261102-0237-outside-arxiv261041944-locality-probability"
title: "Locality, Probability and the Relevance of History (arXiv:2610.41944)"
type: "capture"
status: "promoted"
origin: "batch"
writer_model: "claude-sonnet-5"
date_created: "2026-11-02T00:00:00.000Z"
provenance: "batch run, 2026-11-02"
derived_from: []
tags: ["physics","physics.hist-ph","quant-ph","quantum-foundations","bell-theorem","locality","probability","determinism","arxiv","outside-vault","sebastian-horvat","john-bell"]
seek_code_commit: "d40ee39"
promoted_to: ["30-notes/claim-horvat-probabilistic-locality-logically-independent-of-bells-local-causality.md","30-notes/claim-horvat-probabilistic-locality-and-irrelevance-of-history-jointly-imply-bells-local-causality.md","30-notes/claim-horvat-alien-organism-toy-model-shows-history-dependence-evades-local-causality.md","50-questions/question-corroborate-horvat-probabilistic-locality-preprint-single-source.md","40-entities/entity-sebastian-horvat.md",{"40-entities/entity-probabilistic-locality.md (status":"watching stub)"},{"40-entities/entity-irrelevance-of-history.md (status":"watching stub)"},"40-entities/entity-john-bell.md (updated, dated line appended — not newly created)","40-entities/entity-bells-theorem.md (updated, dated line appended — not newly created)"]
not_promoted: ["Footnote 21 (Bohmian/pilot-wave mechanics cannot satisfy Probabilistic Locality) — a lead flagged by the capture itself as 'worth its own capture if Bohmian mechanics is pursued,' not a claim this capture asserts; left in the capture as a future lead rather than promoted.","Huw Price (2026) arXiv:2602.16985 — cited by Horvat as related work, not independently read this session; no claim to promote from a source not yet read.","Jeffrey A. Barandes's Stochastic-Quantum Correspondence program — cited by Horvat as a rival approach to the same target, not independently read; same reasoning.","Travis Norsen's exegetical papers on Bell's own intent — cited by Horvat as background, not quoted directly in the capture; no claim to promote.","Myrwold, Genovese & Shimony, SEP 'Bell's Theorem' — a Tier-4 encyclopedia trailhead per the capture's own note; not citable as evidence, left as a lead to its footnotes.","GHZ experiment as an open test case for Probabilistic Locality (paper's footnote 20) — an open question the paper itself raises, not a claim it makes; a natural future-capture lead, not promoted.","Entity candidates NOT promoted to hub or stub: Travis Norsen, Jeffrey A. Barandes, Huw Price (all cited by Horvat but not independently engaged by this vault — bare citation is weaker than co-authorship and does not clear the person-hub bar); World-theory / probabilistic world-theory (Horvat's background formal apparatus — standard scaffolding rather than a load-bearing novel claim in its own right); statistical independence / measurement independence (the pre-existing, already-well-known Bell-theorem assumption Horvat declines to doubt — not new to this paper, not load-bearing enough here to warrant a vault entity on this capture alone).","A fourth claim-note from arXiv:2610.41944 was deliberately not written: the single-source concentration cap (sources.md) holds this unrefereed, five-day-old preprint to exactly three claim-notes until independent corroboration lands. Routed to 50-questions/question-corroborate-horvat-probabilistic-locality-preprint-single-source.md instead."]
---


Capture from an OUTSIDE-the-vault surface: arXiv:2610.41944, a 35-page single-author philosophy-of-physics paper by **Sebastian Horvat** (University of Vienna, Department of Philosophy), cross-listed quant-ph / physics.hist-ph, submitted 30 Oct 2026. No safety signals fired — the abstract and full text (read via `extract_pdf`, PDF, 35 pages, `tls: verified`) are third-person academic argumentative prose throughout: no addressed-to-AI language, no override or tier-self-assignment language, no file-system or credential requests, no urgency framing.

**Single-source concentration note:** all three core claims below rest on this one unrefereed arXiv preprint (submitted five days before this capture; no independent corroboration could exist yet). Per the sourcing floor's single-source concentration cap, this capture deliberately holds to exactly three claims from this primary — promotion should not add a fourth claim-note resting on this same preprint without independent corroboration landing first.

## Source

- source_url: https://arxiv.org/abs/2610.41944
- source_url_pdf: https://arxiv.org/pdf/2610.41944
- source_sha: d10fb10215942b0545d0543e5ee8315ff041accdf09a2c42fd18ee67b41c0c64 (abstract page, archive_page); 551e1becc7f73c4ae4f85441e242a754307c8b03640f569b3373db95c86c5dfc (PDF full text, extract_pdf, tls: verified)
- source_author: Sebastian Horvat
- source_date: 2026-10-30 (submitted)
- source_title: "Locality, Probability and the Relevance of History"
- source_venue: "arXiv:2610.41944 [quant-ph] (cross-listed physics.hist-ph), not yet peer-reviewed"
- source_tier: 1 (primary — the author's own formal argument and worked examples, on arXiv, per sources.md's "Papers on arXiv" entry)

## Claim: Horvat's "Probabilistic Locality" principle is formally distinct from, and logically independent of, Bell's criterion of "Local Causality"

Horvat 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 (supervenes on) the probability distribution of what can happen in y's immediate causal past. This differs in form from Bell's own criterion of "Local Causality" (which conditions a single probability distribution on events in the causal past, screening off correlations to spacelike-separated events). The paper proves the two criteria are logically independent of each other — neither implies the other — via two constructed counterexample theories.

- 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− ."

This is a technical-mechanism / definitional claim about the paper's own formal apparatus, sourced directly to the primary document stating and proving the result (Principle 2, Principle 3 [sic, numbered as Principle 2 and the Local Causality principle in the text], and Proposition 2) — Tier 1, clears the floor.

> [!note] Seek's commentary: The move that makes this interesting is structural, not just technical: Bell's criterion constrains one probability distribution at a time (monadic), while Horvat's constrains relations *between* distributions across different possible initial conditions (dyadic). That's a genuinely different shape of constraint, which is why logical independence isn't surprising once stated — but it's also why the two can quietly feel like "the same idea" if read quickly, since both are called locality principles and both reduce to the same deterministic principle in the classical limit.

## Claim: Horvat proves that Probabilistic Locality, conjoined with an "Irrelevance of History" assumption, jointly imply Bell's Local Causality — so Bell-inequality violations can be read as falsifying the history-irrelevance assumption rather than locality itself

"Irrelevance of History" is defined as the assumption that the probability distribution governing what happens after some collection of events occurs is the same regardless of what preceded those events (i.e., physical dynamics is Markovian all the way down). Horvat's Proposition 3 shows that this Markovian assumption, together with Probabilistic Locality, entails Bell's Local Causality (and hence Bell's inequalities). Since quantum experiments empirically violate Bell's inequalities, and the paper argues there is no good independent reason to doubt Probabilistic Locality or the "statistical independence" assumption that also enters Bell's derivation, the paper concludes the Irrelevance-of-History assumption is the one that must be false.

- source_quote: "Probabilistic Locality and Irrelevance of History jointly imply Local Causality."
- source_quote_2: "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."

Technical-mechanism claim (a proved logical-implication result plus its interpretive conclusion), sourced directly to the primary's stated proposition and abstract — Tier 1, clears the floor. The second quote is the paper's own headline framing of what the whole argument is for.

## Claim: Horvat's "alien organism" toy model shows mechanically how a theory can violate Bell's Local Causality while still satisfying Probabilistic Locality, by making the probability of a future outcome depend on the full history (not just the immediately preceding state) that produced the present conditions

Using a toy example of shape/color-changing organisms (a red pyramid turns into a red cube or red sphere with 50% chance each after time τ; a red cube deterministically turns blue, a red sphere deterministically turns green, after a further τ), Horvat shows that if "red cube → blue cube" holds only for cubes that trace back to a red-pyramid origin — and not for red cubes with different origins — then conditioning on the immediate past state (red cube) alone fails to fix the future probability, violating "Irrelevance of History," while the theory can still satisfy Probabilistic Locality globally. The paper argues this is the general mechanism by which a theory could reproduce Bell-inequality-violating EPR correlations (apparently violating Bell's Local Causality) while still complying with Probabilistic Locality: the correlations are "washed out by averaging over the possible histories that could have led to" the measured conditions.

- source_quote: "if the organism is initially a red pyramid and turns into a cube at time τ , then it is bound to turn into a blue cube, in accord with the latter conditional distribution."
- source_quote_2: "the non-locally-appearing correlations in Eq. (20) are, according to T , washed out by averaging over the possible histories that could have lead to e or to e′, thereby validating the form of locality exhibited in Eq. (21)."

Specific technical-mechanism claim, sourced directly to the primary's own worked example and its application to EPR-type experiments — Tier 1, clears the floor. The paper is explicit that it has not constructed a concrete physical theory doing this for real EPR experiments ("While this constructive project lies much beyond our scope here...") — so the mechanism is presented as a coherence proof-of-concept, not a demonstrated physical model; that caveat should travel with the claim at promotion.

## Further leads

- Footnote 21 argues Bohmian/pilot-wave mechanics cannot satisfy Probabilistic Locality at all, because it posits too few events (only particle positions) to carry the needed probabilistic structure — illustrated with a single-particle beam-splitter interference example; worth its own capture if Bohmian mechanics is pursued. (source: this paper, p.33, footnote 21)
- Huw Price (2026), "Retrieving the Baby: Reichenbach's Principle, Bell Locality, and Selection Bias," arXiv:2602.16985 — cited by Horvat as closely related recent work on Bell locality and selection-bias-style reasoning; not independently read in this session.
- Jeffrey A. Barandes (2024, arXiv:2402.16935; 2025, *Philosophy of Physics* 3(1)) — a separate, distinct research program ("Stochastic-Quantum Correspondence") also aimed at a causally local reformulation of quantum theory; cited by Horvat as a different approach to the same target, not independently read.
- Travis Norsen's exegetical papers on what Bell's own criterion of local causality actually says (2011, *American Journal of Physics* 79(12):1261; and a 2013 piece cited for "a detailed analysis of the criterion of local causality") — the standard secondary literature on Bell's own intent, cited by Horvat as background rather than quoted directly here.
- Myrwold, Genovese & Shimony (2024), "Bell's Theorem," *Stanford Encyclopedia of Philosophy* — cited by Horvat for an overview of the "relatively innocuous" assumptions in Bell's theorem (e.g. statistical independence, unique measurement outcomes); a Tier-4 trailhead per found-spec's "never grade an encyclopaedia article Tier 1" rule, worth following to its own footnotes rather than citing directly.
- The paper flags the GHZ experiment (three- or more-particle Bell-type correlations) as an open test case not yet checked against Probabilistic Locality — a natural next question. (source: this paper, p.33, footnote 20)
- This vault already holds a cluster of related but topically distinct 2026 quant-ph/physics.hist-ph preprints on quantum-measurement foundations — e.g. [[claim-okon-sudarsky-wiedemann-preparer-never-definite-only-statistical-conservation-restored]] (conservation laws and measurement definiteness, not locality) — same genre of single-author-or-small-group unrefereed preprint, worth keeping in mind for the single-source concentration cap across the broader quant-ph/physics.hist-ph branch of the vault, even though the specific claims don't overlap.

## Entity candidates

- **John S. Bell** — person — the FOUNDATIONAL figure this entire paper is written against: his 1964 criterion of "local causality" (as presented in Bell, *Speakable and Unspeakable in Quantum Mechanics*, 2004, pp. 232-248) is the target the paper explicitly sets out to replace; every proposition in the paper is stated as a comparison to or departure from Bell's own criterion.
- **Sebastian Horvat** — person — sole author; philosopher of physics at the University of Vienna, Department of Philosophy; proposes the new "Probabilistic Locality" principle.
- Travis Norsen — person — cited as the standard exegete of what Bell's own criterion of local causality actually meant (2011 *Am. J. Phys.* paper, and a 2013 piece); load-bearing for anyone later wanting to check Horvat's "rational reconstruction" of Bell against Bell's own words.
- Jeffrey A. Barandes — person — runs a separate, rival research program (the "Stochastic-Quantum Correspondence") aimed at the same goal of a causally local quantum theory; cited by Horvat as a distinct approach.
- Huw Price — person — philosopher of time/physics; cited 2026 preprint on Reichenbach's principle and Bell locality is close kin to this paper's project.
- Probabilistic Locality — concept — Horvat's new principle; central formal object of the paper.
- Local Causality (Bell's criterion) — concept — the older principle being revised.
- Irrelevance of History — concept — the pivotal assumption the paper argues is empirically false; candidate for its own definitional note given how load-bearing it is to the whole argument.
- World-theory / probabilistic world-theory — concept — Horvat's formal framework (a theory as a set of possible worlds plus probability measures over them), underlying all the definitions above.
- statistical independence (measurement independence) — concept — the Bell-theorem assumption the paper explicitly declines to doubt, named directly in the abstract.