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REVIEW 4 major objections 3 minor 119 references

Quantum Correlations and Quantum Non-locality: a review and a few new ideas

T0 review · 4 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper proposes that the tension between quantum non-locality and special relativity dissolves if wave-function collapse propagates through compactified extra dimensions, turning apparent action at a distance into ordinary…

desk verdict The review half is a serviceable survey, but the central extra-dimensional collapse field idea is a sketch that fails its own geometric premise; still worth a serious referee to put the issue on record. read the letter →

arxiv 1908.03114 v1 pith:FPGY6PGQ submitted 2019-08-08 quant-ph

Marco Genovese , Marco Gramegna This is my paper · ORCID
classification quant-ph
keywords quantumnon-localityBellinequalitiesentanglementwave-functioncollapseextradimensionscompactificationspecialrelativitymodels
open problems Quantum Gravity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reviews the landscape of quantum non-locality and closes with a proposal: the tension between nonlocal correlations and special relativity may be only apparent, because wave-function collapse could be mediated by a field that propagates through compactified extra spatial dimensions. If the extra dimensions are extremely small, events that are far apart in ordinary $3+1$-dimensional space can be connected by an extremely short effective path, so the collapse of one entangled particle can trigger the collapse of its partner through a subluminal signal in the higher-dimensional space. The paper argues that this would reduce quantum non-locality to ordinary relativistic propagation, removing action at a distance while preserving the no-signalling constraint. It also suggests the extra-dimensional collapse component could be incorporated into relativistic collapse models and might have cosmological consequences.

What carries the argument

The load-bearing object is the compactified extra-dimensional collapse field, together with the geometric observation that a space can be contracted isometrically around a point, so distances in ordinary space can be made arbitrarily small through the extra dimensions. The formal carrier is the non-unitary evolution operator $U(t) = \exp\!\left(-i \int d^4x\, d^n y\, O_I(x,y,t)\right)$, where $O_I(x,y,t)=H_I(x,t)+C_I(x,y,t)$; $H_I$ is the ordinary Hermitian Hamiltonian density in $3+1$ dimensions, while the non-Hermitian $C_I(x,y,t)$ induces collapse. Tracing over the degrees of freedom attached to $C_I$ restores the usual unitary evolution, which ties the proposal to existing ideas about finite degrees of freedom in quantum gravity.

What would settle it

A decisive test would be to search for the non-unitary collapse component $C_I$: the proposal predicts small violations of unitary evolution in isolated quantum systems, and experiments that bound such violations increasingly tightly, while Bell correlations still match quantum mechanics exactly, would falsify the existence of the proposed extra-dimensional collapse field.

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Extended reading notes

Core claim

The paper's central proposal is a concrete mechanism: add $n-4$ compactified spatial dimensions to spacetime and suppose that, while ordinary quantum fields live only in $3+1$ dimensions, the collapse process is mediated by a field that also propagates in the extra dimensions. Because a small extra-dimensional space can be contracted around a point, any two events in ordinary space lie at an extremely short effective distance through the compactified directions. The collapse of one of two remote entangled particles could therefore cause the collapse of the other by a subluminal signal in the higher-dimensional space, so quantum non-locality would no longer require action at a distance: it would be a local process in the higher-dimensional geometry that only appears nonlocal from a $3+1$-dimensional perspective. The paper sketches this with a non-unitary evolution operator whose non-Hermitian component induces collapse, with unitary evolution restored after tracing over the extra degrees of freedom.

Load-bearing premise

The load-bearing premise is that a physical collapse field actually exists and propagates through extremely small extra dimensions, so that any two events in ordinary space are connected by a very short effective path; the paper offers no direct evidence for this field, no collapse mechanism, and no size scale.

Editorial extensions

If this is right

  • Nonlocal correlations would become compatible with relativistic causality, because the full higher-dimensional process is subluminal even though the $3+1$-dimensional description looks instantaneous.
  • The disagreement between observers who see different temporal orders for the two collapses would be resolved by a definite propagation order fixed in the higher-dimensional space.
  • Relativistic collapse models could be constructed by generalizing existing formulations to include the extra-dimensional collapse field, and the non-Hermitian term would restore standard unitary evolution when the extra degrees of freedom are traced out.
  • The no-signalling theorem remains intact: even though the correlations are tied by a physical mediator, they still cannot be used to transmit messages at superluminal speed.
  • The proposal gives a concrete place to look for new physics, since the extra-dimensional collapse component could in principle contribute to dark matter and dark energy, as the paper itself notes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the mechanism is right, the apparent speed of the nonlocal influence observed in $3+1$ dimensions becomes an effective quantity set by the compactification radius and the collapse-field speed; existing lower bounds on hidden influences, around $\beta > 5 \times 10^6 c$, would then translate into a first constraint on the extra-dimensional geometry.
  • A natural testable extension is to look for tiny non-unitary effects in isolated systems, since the $C_I$ term would slightly violate unitary evolution before decoherence washes it out; precision experiments on quantum superpositions could bound this term independently of any Bell test.
  • The same compactified-mediator logic could in principle be applied to other nonlocal phenomena such as steering and contextuality, asking whether they share one mediator or require separate mechanisms.
  • If no collapse field is ever found, the paper still sharpens the question: the relativity problem of collapse is a problem about which foliation is physical, and extra dimensions are one way to make that foliation dynamical rather than postulated.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The manuscript is a review of quantum non-locality, covering Bell inequalities, entanglement-nonlocality relations, steering, PR boxes, Tsirelson's bound, and related resource-theoretic results, followed by a short speculative section (Section 3) proposing that wave-function collapse might be mediated by a field propagating in compactified extra dimensions. The authors suggest that if extra dimensions are small, spacelike-separated events in 3+1 dimensions could be connected by short effective distances, so that the collapse of one entangled particle could influence the other via a subluminal signal. They illustrate this with a non-Hermitian evolution operator in Eq. (10) and suggest tracing over the non-Hermitian part to restore unitarity.

Significance. If the proposed mechanism were quantitatively established, it would offer a concrete route to reconciling quantum non-locality with special relativity by replacing apparent action at a distance with ordinary relativistic propagation in higher dimensions. However, the proposal is presented only as a sketch: no concrete metric, collapse rule, or derivation is given, and the geometric justification offered in Section 3 is flawed. The review portions are mostly accurate summaries of known results and may serve as a useful bibliography, but the new idea is not developed to the point of making testable predictions. The paper therefore has value mainly as a literature survey plus an untested speculation, rather than as a completed research contribution.

major comments (4)
  1. [Section 3, paragraph starting 'Since every n-dimensional space can be "contracted"...'] The geometrical justification for the extra-dimensional shortcut is incorrect. The claim that a plane can be 'wrapped as tied as one wishes around a single point in 3 dimensional space' while the contraction 'is an isometry and leaves invariant gaussian curvature' is contradicted by the Gauss Theorema Egregium: a flat plane has zero Gaussian curvature and cannot be isometrically embedded as a closed surface of positive curvature. Moreover, contracting a space around a point changes distances by definition, so it cannot be an isometry. Since the entire proposed mechanism relies on the existence of short effective paths through extra dimensions, this is a load-bearing error.
  2. [Section 3, Eq. (10) and the following paragraph] Equation (10) is a symbolic expression with no concrete content: the non-Hermitian operator C_I(x,y,t) is not defined, no metric on the extra-dimensional space is specified, and no dynamics or collapse rule is given. Consequently the claim that 'when one traces over the degrees of freedom corresponding to the not Hermitian component... the usual unitary evolution is eventually restored' is unsupported. Without a defined model, there is no way to compute a signal velocity, an effective distance, or any observable consequence, so the central claim cannot be tested or even checked for consistency with known quantum predictions.
  3. [Section 3, compactified dimensions argument] For the standard compactification M^{1,3} x K, the geodesic distance between two events with the same compact coordinate is simply their 3+1 dimensional distance, independent of the compactification radius; shrinking the extra dimensions does not shorten the 4D separation. The manuscript does not provide any concrete non-product metric (e.g., a warped metric) that would make distant 3+1 events close in the full higher-dimensional space. Without such a metric, the assertion that 'every event of the 3+1 dimensional space could be connected with any another event in an extremely short effective distance' is not established.
  4. [Section 3, general framework] Even granting the existence of a collapse field in extra dimensions, the manuscript does not address how the proposed mechanism would resolve the relativistic frame-dependence of the collapse order: it does not specify a foliation or a covariant collapse rule, and no comparison to known relativistic collapse models (e.g., Tumulka's) is worked out beyond a one-line reference. The central claim therefore remains an assertion rather than a derived consequence.
minor comments (3)
  1. [Throughout] There are numerous typographical errors and malformed sentences (e.g., 'qiuantum', 'leaving' instead of 'living', 'und predectability', 'entangeld', 'forementioned'). A thorough proofreading pass is needed.
  2. [References [3], [49], [63]] Several references are incomplete or inconsistently formatted (e.g., [3] lists multiple arXiv identifiers without a single paper title; [49] begins '4.F. Buscemi'; [63] is listed both as 'B.Christensen et al., PRX 5, 041052 (2015)' and in [43] as 'PRX 041052 (2015)'). The bibliography should be unified.
  3. [Eq. (10)] The display of Eq. (10) is garbled in the manuscript; the intended mathematical form should be typeset correctly and should define the integration variables and the domain of integration explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reasoning found: the extra-dimensional collapse proposal is an explicitly exploratory suggestion, not a derivation from its conclusion, and the self-citations are not load-bearing.

full rationale

The paper is primarily a review of quantum non-locality, and the new idea in Section 3 is explicitly framed as a suggestion to be explored rather than as a derived prediction. The proposal posits that a collapse field propagating in compactified extra dimensions could make spacelike-separated events effectively close, so that collapse correlations are mediated by a subluminal signal; this is a physical hypothesis, not a quantity fitted from data and then renamed as a prediction. Equation (10) is only sketched as an illustration of a possible non-unitary evolution operator, and it is not derived from the conclusion it is meant to support. The self-citations present in the paper, such as reference [2] for definitions and GRW models and reference [19] for quantum technologies, are contextual review citations and are not load-bearing for the extra-dimensional proposal. Any mathematical or physical objections to the compactification argument concern correctness and plausibility, not circularity. No step in the paper reduces by construction to its own input, so the appropriate circularity score is 0.

Assumptions & free parameters 0 free parameters · 4 assumptions · 1 invented entities

The central claim rests on several unproved assumptions: the existence of extra dimensions, the existence of a collapse field, the geometric claim that compactified dimensions make any two 3+1D events close, and the idea that tracing over the non-Hermitian part restores unitarity. No free parameters are fitted, and the collapse field is an invented entity with no independent evidence.

assumptions (4)
  • domain assumption There exist n greater than 4 spacetime dimensions with n - 4 compactified spatial dimensions.
    Section 3: 'Let us consider a n > 4 space-time with n - 4 more spatial dimensions.' This is borrowed from higher-dimensional theories and is not proven here.
  • ad hoc to paper Wave-function collapse is a real physical process mediated by a field propagating in all dimensions.
    Section 3: 'the collapse is mediated by some field propagating also in the other dimensions.' This is the core postulate of the proposal.
  • domain assumption Compactified extra dimensions can make any two points in 3+1 dimensions arbitrarily close, so a subluminal signal through them connects spacelike separated events.
    Section 3: 'every event of the 3+1 dimensional space could be connected with any another event in an extremely short effective distance through the compactified dimensions.' This geometric statement is assumed without proof.
  • ad hoc to paper Tracing over the non-Hermitian collapse component restores the usual unitary evolution.
    Section 3: 'When one traces over the degrees of freedom corresponding to the not Hermitian component, CI(x, y, t), the usual unitary evolution is eventually restored, as in 't Hooft finite degrees of freedom model.'
invented entities (1)
  • Collapse field CI(x,y,t) propagating in extra dimensions
    purpose: Mediates wave-function collapse between spacelike separated entangled particles, reconciling nonlocality with relativity.
    Section 3, Eq. (10): the operator is not specified, no Lagrangian or coupling is given, and no falsifiable prediction is made outside the paper.

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Pith. "Pith review of Quantum Correlations and Quantum Non-locality: a review and a few new ideas." pith.science (2026). https://pith.science/paper/FPGY6PGQ

@misc{pith2026190803114,
  author       = {Pith},
  title        = {Pith review of: Quantum Correlations and Quantum Non-locality: a review and a few new ideas},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FPGY6PGQ}},
  note         = {Machine review of arXiv:1908.03114}
}
read the original abstract

In this paper we make an extensive description of quantum non-locality, one of the most intriguing and fascinating facets of quantum mechanics. After a general presentation of several studies on this subject, we consider if quantum non-locality, and the friction it carries with special relativity, can eventually find a "solution" by considering higher dimensional spaces.

Discussion (0). Continue with ORCID to comment.

Reference graph

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