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In conical spacetimes with d > 1, no superluminal signalling rules out all detectable causal loops.

2026-06-26 16:26 UTC pith:BPTMEG4Z

load-bearing objection The paper closes the open question from the (1+1) PRL by showing NSS rules out detectable causal loops in d>1 conical spacetimes, with the link being geometry-dependent. the 1 major comments →

arxiv 2606.20476 v1 pith:BPTMEG4Z submitted 2026-06-18 gr-qc quant-ph

Impossibility of superluminal signalling rules out causal loops in conical spacetimes

Maarten Grothus , V. Vilasini This is my paper
classification gr-qc quant-ph
keywords causal loopsno superluminal signallingconical spacetimesMinkowski spacetimerelativistic causalityquantum information
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Work in 1+1 Minkowski spacetime had shown that operationally detectable causal loops can exist without any superluminal signalling. This paper proves that the situation changes once the number of spatial dimensions exceeds one. Within a broad class of conical spacetimes that includes ordinary Minkowski space in d > 1, the no-superluminal-signalling condition excludes every such loop, whether the underlying theory is classical, quantum or post-quantum. The result therefore shows that the logical relationship between these two relativistic principles is fixed by the geometry of the spacetime rather than being universal.

Core claim

In a wide class of conical spacetimes, including Minkowski with d > 1, NSS does rule out all operationally detectable causal loops, in classical, quantum and post-quantum theories.

What carries the argument

The class of conical spacetimes together with the operational definition of detectable causal loops, which together force any loop to require a superluminal channel when d > 1.

Load-bearing premise

The operational definition of detectability and the precise characterization of the conical spacetime class are sufficient to exclude every possible loop construction that avoids hidden superluminal channels.

What would settle it

An explicit construction, inside (3+1)-dimensional Minkowski spacetime, of an operationally detectable causal loop that does not require superluminal signalling would falsify the claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • NSS and the absence of detectable causal loops become logically linked once spacetime has more than one spatial dimension.
  • The linkage holds uniformly for classical, quantum and post-quantum theories.
  • Whether NSS permits causal loops is therefore a geometry-dependent question rather than a universal feature of relativity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The result suggests that attempts to embed causal loops into realistic higher-dimensional models will require either superluminal channels or a departure from the conical-spacetime class.
  • Extensions of the same operational argument to other geometries, such as those with curvature or different global topology, could identify the precise dimensional or structural thresholds where loops again become possible without NSS violation.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 1 minor

Summary. The paper claims that in a wide class of conical spacetimes (including Minkowski with d>1 spatial dimensions), the no-superluminal-signalling (NSS) principle rules out all operationally detectable causal loops in classical, quantum, and post-quantum theories. This resolves an open question left by the (1+1)-dimensional Minkowski counterexample in PRL 129, 110401, where such loops were possible without NSS violation. The result is presented as geometry-dependent: the conical structure forces any detectable loop to imply a superluminal channel.

Significance. If the central claim holds, the work provides a geometric criterion distinguishing when NSS is compatible with detectable causal loops, with direct implications for higher-dimensional relativistic causality and post-quantum extensions. It strengthens the link between spacetime geometry and operational causality principles beyond the (1+1) case. The extension to post-quantum theories and the explicit contrast with the lower-dimensional counterexample are notable strengths, though significance is tempered by the need for precise operational definitions.

major comments (1)
  1. [Main theorem / conical class definition] The sufficiency of the operational detectability definition and the precise axiomatization of the conical spacetime class (likely in the main theorem or § on geometry) to exclude all loop constructions in d>1 without hidden superluminal channels is load-bearing. The manuscript must explicitly demonstrate that the geometric features absent in the 1+1 PRL counterexample are rigorously excluded here, or the post-quantum claim risks incompleteness.
minor comments (1)
  1. [Introduction] Clarify notation for 'conical' class early; ensure all references to prior work (e.g., PRL 129, 110401) include explicit geometric distinctions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the single major comment below and have revised the manuscript to strengthen the explicitness of the relevant demonstration.

read point-by-point responses

  1. Referee: [Main theorem / conical class definition] The sufficiency of the operational detectability definition and the precise axiomatization of the conical spacetime class (likely in the main theorem or § on geometry) to exclude all loop constructions in d>1 without hidden superluminal channels is load-bearing. The manuscript must explicitly demonstrate that the geometric features absent in the 1+1 PRL counterexample are rigorously excluded here, or the post-quantum claim risks incompleteness.

    Authors: We thank the referee for underscoring the importance of this point. The conical spacetime class is axiomatized in the manuscript via the metric structure and light-cone properties that preclude the specific causal identifications permitting the (1+1)-Minkowski counterexample of PRL 129, 110401. The main theorem then shows that, under this geometry, any operationally detectable causal loop (defined via the same theory-independent operational framework as the PRL paper) necessarily induces a superluminal channel. Because the argument invokes only the no-signalling condition and the operational notion of detectability, it applies directly to post-quantum theories without additional assumptions. Nevertheless, to address the request for greater explicitness, we have added a new paragraph in the geometry section that directly contrasts the excluded features of the d>1 conical case with those present in the (1+1) counterexample. revision: yes

Circularity Check

0 steps flagged

No circularity; geometric distinction from 1+1 case provides independent content

full rationale

The abstract and description frame the result as a geometric proof that NSS excludes detectable causal loops in a defined class of conical spacetimes for d>1, explicitly distinguishing from the (1+1) counter-example in prior work. No equations, definitions, or self-citations are supplied that reduce the central claim to a fit, self-definition, or load-bearing self-citation chain. The operational detectability notion and conical class are presented as sufficient to exclude loops without hidden channels, and the derivation is described as extending rather than presupposing the target result. This is the expected non-finding for a self-contained geometric argument.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the NSS principle and the geometric definition of conical spacetimes; no free parameters or invented entities are visible from the abstract.

axioms (2)
  • domain assumption No superluminal signalling (NSS) is a fundamental principle that must be preserved
    Invoked as the constraint that rules out causal loops in the target geometries.
  • domain assumption Conical spacetimes form a well-defined class that includes Minkowski space for d>1
    The result is stated for this class; the precise metric or symmetry properties are not detailed in the abstract.

pith-pipeline@v0.9.1-grok · 5651 in / 1272 out tokens · 32249 ms · 2026-06-26T16:26:25.325669+00:00 · methodology

0 comments
read the original abstract

In PRL 129, 110401 it was shown that it is theoretically possible to have operationally detectable causal loops without violating the principle of no superluminal signalling (NSS) in (1+1)-Minkowski spacetime. Whether or not such causal loops are also possible in $d > 1$ spatial dimensions, has remained a key open question. We resolve this question by showing that in a wide class of "conical" spacetimes, including Minkowski with d > 1, NSS does rule out all operationally detectable causal loops, in classical, quantum and post-quantum theories. This establishes that the relationship between the relativistic principles of NSS and no causal loops depends inherently on the geometry of spacetime.

Figures

Figures reproduced from arXiv: 2606.20476 by Maarten Grothus, V. Vilasini.

Figure 1
Figure 1. Figure 1: Let X, Y, Z, A, B ∈ S. Consider X ⊨ Y, Y ⊨ AB, A ⊨ X, Z ⊨ AB, B ⊨Z. (a) No matter the underlying causal model, the affects relations allow to infer that a causal loop will always be present. Here, ↠ denotes causal relations between two RVs, while its dashed version stands for alternative causal relations, e.g. Y ↠ AB being equivalent to (Y ↠ A or Y ↠ B), so at least one of the dashed arrows from Y must be … view at source ↗
Figure 2
Figure 2. Figure 2: Representation of light cones in Minkowski spacetime for d spatial dimensions. (a) For d = 1 Minkowski spacetime does not show conicality. This is because L1 := {a, b} and L2 := {x, y} are distinct, yet share the same joint future. (b) For d = 2, Minkowski spacetime is conical. As can be seen from the figure which shows one particular time slice, the joint futures are distinct between L1 and L2 (and the re… view at source ↗

discussion (0)

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