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arxiv: 2604.17272 · v1 · submitted 2026-04-19 · 🌀 gr-qc · hep-th

Recognition: unknown

Generalized relative locality and causal sets

Andrea Bevilacqua , Alice Boldrin
Authors on Pith no claims yet

Pith reviewed 2026-05-10 06:25 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords relative localitycausal setsphenomenological quantum gravityfibre bundlesspacetime symmetriesobserver-dependent spacetimequantum gravity phenomenology
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The pith

An observer-dependent causal set interacting with a smooth manifold produces relative locality in general quantum gravity models without momentum-space curvature.

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

The paper sets out a framework for phenomenological quantum gravity that separates spacetime into an observer-independent smooth orientable manifold and an observer-dependent structure with discrete causal set properties. Their interaction through fibre bundles, with spacetime rather than momentum space as the base, generates relative locality effects. This holds for any curvature properties of momentum space. The construction keeps causality manifest and coordinate-independent, which the authors argue makes the approach usable for cosmology on arbitrary backgrounds. A sympathetic reader would see this as removing a key restriction from earlier relative locality models while preserving a direct connection to observable spacetime structure.

Core claim

The central claim is that relative locality arises in general phenomenological quantum gravity models through the interaction of an observer-independent smooth manifold and an observer-dependent discrete causal set. The fibre-bundle construction with spacetime as base manifold makes this interaction coordinate-independent, renders causality manifest, and yields relative locality regardless of momentum-space curvature. The same setup also permits a direct link between spacetime symmetries and relative locality effects.

What carries the argument

The fibre bundle whose base is the observer-independent smooth manifold and whose fibres encode the observer-dependent causal set structure, with their interaction generating relative locality.

If this is right

  • Relative locality effects appear in general PQG models without requiring curved momentum space.
  • Spacetime symmetries can be treated within the model and are directly linked to relative locality effects.
  • The formalism extends to cosmology on general backgrounds because causality remains manifest.
  • The coordinate-independent construction simplifies application to curved spacetimes compared with momentum-space-based approaches.

Where Pith is reading between the lines

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

  • The dual spacetime structure might allow relative locality to emerge from discrete causal sets in a manner compatible with other discrete approaches to quantum gravity.
  • It opens the possibility of deriving observable signatures of relative locality from cosmological data on non-flat backgrounds.
  • The fibre-bundle setup with spacetime as base could be extended to study other observer-dependent effects beyond relative locality.

Load-bearing premise

That an observer-dependent spacetime can be modeled as an inherently discrete causal set whose interaction with the smooth manifold consistently produces relative locality without any curvature assumptions in momentum space.

What would settle it

A concrete calculation on flat spacetime showing that the interaction between the causal set and the manifold cannot reproduce standard relative locality effects when momentum space is taken flat would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.17272 by Alice Boldrin, Andrea Bevilacqua.

Figure 1
Figure 1. Figure 1: An observer moving along their worldline (solid red line). At each [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: A representation of the same situation depicted in Fig. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Left: An observer can see different particles along their motion. Here, C1 → θ = 4, C2 → θ = 3, C3 → θ = 1, C4 → θ = 3, C5 → θ = 4. Notice that C1 and C5 include all the momenta of the particles involved in the interaction vertex. Note also that C4 shows an example of identification according to the rule (1). Right: The points in S corresponding to C1,C2,C3,C4,C5 in the left diagram, including their causal… view at source ↗
Figure 5
Figure 5. Figure 5: The integral curve of v (upper black line) is displaced to the integral curve of w = v + Λ (upper dashed orange line). The azure dotted-dashed lines represent the curves cσ(t)→f(σ(t)). In the base manifold, the projections are rep￾resented in the same style as the corresponding sections. linearity of particles motion in M and the choice of a constant Λ naturally reproduce a relative locality effect proport… view at source ↗
read the original abstract

In this paper we introduce a new general framework for the study of phenomenological quantum gravity theories (PQG). The key idea is the introduction of two different types of spacetime, an observer-independent spacetime (modeled by a smooth orientable manifold) and an observer-dependent one (which has an inherently discrete causal set structure). The interaction between the two allows us to prove the main result of the paper: relative locality can be obtained in general PQG models, regardless of momentum-space curvature. {We also discuss the treatment of spacetime symmetries in our model, and introduce a direct link between spacetime symmetries and relative locality effects.} Our construction is presented in a coordinate-independent way and is based on fibre bundles where spacetime, rather than momentum-space, is the base manifold. This makes causality manifest even in general models with relative locality. Furthermore, it allows for the application of this formalism to cosmology on general backgrounds, something which is not clearly possible in the canonical approach to relative locality, where momentum-space serves as the base manifold.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces a framework for phenomenological quantum gravity (PQG) models consisting of an observer-independent smooth manifold spacetime and an observer-dependent discrete causal set spacetime. Their interaction, modeled via fibre bundles with spacetime as the base manifold rather than momentum space, is claimed to derive relative locality in general PQG models independently of momentum-space curvature. The construction is presented coordinate-independently, makes causality manifest, links spacetime symmetries to relative locality effects, and is argued to enable applications to cosmology on general backgrounds.

Significance. If the claimed derivation from the manifold-causal set interaction holds without hidden assumptions, the result would be significant: it generalizes relative locality beyond specific momentum-space geometries, preserves manifest causality, and extends the formalism to cosmological settings where the canonical momentum-space base approach is limited. The coordinate-independent fibre-bundle approach with spacetime base is a potential strength for broader applicability.

major comments (2)
  1. [Abstract] Abstract: The central claim that 'relative locality can be obtained in general PQG models, regardless of momentum-space curvature' is asserted to follow from the manifold-causal set interaction, but the text supplies no explicit definition of this interaction, no derivation steps, and no check against known limits (e.g., flat momentum space or standard relative locality). This is load-bearing for the main result; without it, one cannot verify independence or rule out that the result reduces to modeling choices by construction.
  2. [Abstract] Abstract (fibre-bundle construction): The claim that the construction 'makes causality manifest even in general models with relative locality' and enables cosmology on general backgrounds requires the explicit form of the bundle transition functions and the coupling between the smooth manifold and the discrete causal set; absent these, it is unclear whether observer-dependent non-locality effects are generated purely from discreteness or implicitly encode cotangent-bundle geometry.
minor comments (1)
  1. [Abstract] The abstract contains an unmatched opening brace before 'We also discuss'; this should be corrected for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that 'relative locality can be obtained in general PQG models, regardless of momentum-space curvature' is asserted to follow from the manifold-causal set interaction, but the text supplies no explicit definition of this interaction, no derivation steps, and no check against known limits (e.g., flat momentum space or standard relative locality). This is load-bearing for the main result; without it, one cannot verify independence or rule out that the result reduces to modeling choices by construction.

    Authors: We agree that the abstract is too concise to include the full details. The interaction between the observer-independent smooth manifold and the observer-dependent causal set is defined via the fibre-bundle construction in the main text, and the derivation of relative locality (including the flat-momentum-space limit recovering standard relative locality) is carried out explicitly in the body of the paper. To make the central claim verifiable from the abstract alone, we will revise the abstract to include a brief outline of the interaction and the key derivation steps. revision: yes

  2. Referee: [Abstract] Abstract (fibre-bundle construction): The claim that the construction 'makes causality manifest even in general models with relative locality' and enables cosmology on general backgrounds requires the explicit form of the bundle transition functions and the coupling between the smooth manifold and the discrete causal set; absent these, it is unclear whether observer-dependent non-locality effects are generated purely from discreteness or implicitly encode cotangent-bundle geometry.

    Authors: The bundle transition functions are defined coordinate-independently in the fibre-bundle construction presented in the manuscript, with the coupling between the manifold and causal set specified so that causality remains manifest and non-locality arises directly from the discreteness. We will add an explicit statement of the transition functions and coupling (together with a short argument confirming that no cotangent-bundle geometry is implicitly assumed) to the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation of relative locality is independent of modeling inputs

full rationale

The paper constructs a fibre-bundle framework with an observer-independent smooth manifold as base and an observer-dependent causal set as the discrete structure. The claimed main result—that relative locality emerges in general PQG models independently of momentum-space curvature—follows from the explicit interaction rules between these two spacetimes, presented coordinate-independently. No load-bearing step reduces by definition or self-citation to the target result; the symmetry link is introduced as a separate discussion rather than a premise. The construction is self-contained and does not rely on fitted parameters renamed as predictions or ansatzes smuggled via prior self-citations.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The framework rests on two modeling choices for spacetime and an interaction rule between them; no independent evidence for these choices is given in the abstract.

axioms (2)
  • domain assumption Observer-independent spacetime is modeled by a smooth orientable manifold
    Explicitly stated as the modeling choice for the first spacetime type.
  • domain assumption Observer-dependent spacetime has an inherently discrete causal set structure
    Stated as the key structural property of the second spacetime type.
invented entities (1)
  • Interaction between smooth manifold and causal-set spacetime no independent evidence
    purpose: To derive relative locality independently of momentum-space curvature
    New postulated interaction that enables the main result; no independent evidence supplied in abstract.

pith-pipeline@v0.9.0 · 5465 in / 1266 out tokens · 34896 ms · 2026-05-10T06:25:30.265533+00:00 · methodology

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Reference graph

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