{"id":"835bbfb5-0485-4852-a701-49dacdb03cd3","arxiv_id":"2505.04632","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The paper defends the view that general relativity and teleparallel gravity are genuinely underdetermined alternatives, countering Knox's arguments that teleparallel gravity's ontology reduces to that of general relativity.","lead":"This philosophy of physics paper argues that general relativity and teleparallel gravity remain genuinely underdetermined, so we cannot confidently assert that spacetime is curved. It does so by dissecting and rejecting a prominent attempt to dissolve the underdetermination, and by arguing that torsion is neither unmeasurable nor unvisualizable in a way that breaks the tie.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Unresolved boundary-term effects threaten the empirical-equivalence premise behind the underdetermination conclusion.","rationale":"The reader's weakest assumption correctly identifies the unresolved boundary-term issue as the soft spot in the paper. My independent stress-test confirms that this is the single most load-bearing concern: the paper's negative conclusion about curvature realism follows only if GR and TEGR are empirically equivalent, and the paper's own citations to Wolf & Read (2023) indicate that boundary terms can have empirical significance. The authors neither show that the boundary effects are unobservable nor that the two theories' boundary terms yield the same physics; instead, Section 3.2 uses the boundary discussion to defend the surplus structure of TEGR, which is in tension with the equivalence premise. Because this is an unresolved premise rather than a demonstrated error, a full rejection would be too strong; but the verdict should be conditional on a resolution of the boundary-equivalence question. No ad hominem or disagreement-with-consensus concern is involved: the issue is internal to the paper's argument, since it cites the very work that threatens its premise. A concrete calculation of the boundary stress tensor would settle whether the concern lands. For these reasons, I recommend changing ACCEPT to CONDITIONAL.","tokens_in":24240,"tokens_out":8889,"duration_ms":94294,"concrete_test":"Take a finite spacetime region with a timelike boundary and compute the Brown-York quasilocal stress-energy tensor for the GR action (with the Gibbons-Hawking-York boundary term) and for the TEGR action (with the boundary term required by Eq. 2.6 and the variational principle), following the method of Wolf & Read (2023). If the two boundary stress tensors differ for the same bulk metric data, GR and TEGR make different empirical predictions in finite regions; this would break the equivalence premise of Section 6. If they agree after an allowed redefinition of boundary conditions, the premise survives.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's conclusion that realism about spacetime curvature cannot be confidently asserted depends on GR and TEGR being empirically equivalent (abstract; Section 2, Eq. 2.6). The authors themselves flag that this equivalence is only modulo boundary issues: footnote 1 and Section 3.2 cite Wolf & Read (2023), and footnote 5 states that actions differing by a boundary term can have empirical consequences. Yet the paper never resolves whether those consequences discriminate between GR and TEGR. If the boundary terms yield different predictions for finite spacetimes (e.g., different quasilocal charges or boundary dynamics), then the two theories are not empirically equivalent in the relevant sense, and the underdetermination that motivates the skepticism about curvature is not established. Indeed, Section 3.2 uses the boundary-term discussion to defend the surplus structure of TEGR, but if Wolf & Read are right, that same discussion undermines the premise that GR and TEGR are empirically equivalent. The absence of any argument restoring equivalence leaves the central claim conditional on an unresolved empirical question.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper argues that the putative underdetermination between general relativity (GR) and the teleparallel equivalent of general relativity (TEGR) is not defused by Knox's (2011) arguments, and that two further worries—the operationalisability and visualisability of torsion—can be met. Section 2 presents the TEGR formalism, noting the dynamical equivalence with GR up to a boundary term. Section 3 reconstructs and criticises Knox's three central arguments: that TEGR only reverse-engineers the metric and Levi-Civita connection of GR, that TEGR carries surplus gauge structure, and that TEGR cannot supply the right inertial structure. Sections 4 and 5 argue that torsion can be operationalised (via a gradiometer-like construction and spin-coupling considerations) and that torsion has no visualisability problems beyond those already faced by curvature. The conclusion is that the GR/TEGR underdetermination remains a live threat to realism about spacetime curvature.","tokens_in":24438,"tokens_out":8481,"duration_ms":80968,"significance":"If the paper's conclusion is correct, it sharpens the philosophical cost of realism about GR: a confident assertion that spacetime is curved would require additional, non-empirical commitments that Knox's arguments do not themselves provide. The paper is valuable for isolating Knox's dialectic, for making the operative metaphysical commitments (functionalism, realiser functionalism, operationalisability, visualisability) explicit, and for connecting the GR/TEGR debate to recent work on boundary terms and the geometric trinity of gravity. The symmetry point in Section 3.1 against reverse-engineering is a genuine and well-made contribution. The paper is clearly written and engages carefully with the relevant literature, including the Wolf and Read (2023) boundary-term results. However, the central underdetermination claim depends on an unaddressed boundary-term qualification, and the operationalisation argument contains a technical flaw that needs correction.","major_comments":[{"comment":"The paper's central conclusion requires that GR and TEGR be empirically equivalent, but the paper explicitly leaves open that boundary terms can have empirical consequences. Footnote 5 and Section 3.2 cite Wolf and Read (2023) for the claim that actions differing by a boundary term can have empirical consequences; if those consequences differ between GR and TEGR in finite spacetimes, the premise that no experiment could discern the two theories fails. The paper should either argue that the boundary effects do not discriminate between GR and TEGR in the sense of empirical equivalence relevant to underdetermination, or restrict the conclusion accordingly. As written, the main conclusion is conditional on an unresolved empirical question.","section":"Section 2, Eq. (2.6), fn. 5; Section 3.2"},{"comment":"Equation (4.1) is the first Bianchi identity for a single connection with torsion, but in TEGR the Weitzenböck connection is flat, so the left-hand side of that identity vanishes identically; it therefore cannot show that a gravitational gradiometer, which reads the Levi-Civita curvature, can read out components of the torsion tensor. The gradiometer-based operationalisation needs the explicit formula relating the Levi-Civita Riemann tensor to the contorsion tensor and its derivatives, which is not what Eq. (4.1) provides. Please supply the correct formula and adjust the inference.","section":"Section 4, Eq. (4.1)"},{"comment":"The response to Problem 3 that the Weitzenböck connection's affine geodesics provide a notion of inertial structure is in tension with the paper's own description in Section 3.1 of TEGR as coupling matter to the Levi-Civita connection. In that standard formulation, force-free matter follows Levi-Civita geodesics, not Weitzenböck affine geodesics, so the geodesic response does not meet Knox's dynamical criterion as stated. The paper should either defend an alternative coupling of matter to the teleparallel connection or rest the defusing of Problem 3 on the rejection of Knox's functionalism and realiser functionalism rather than on the geodesic argument.","section":"Section 3.3, Problem 3"}],"minor_comments":[{"comment":"The abstract and the opening of Section 1 assert that TEGR is empirically equivalent to GR without the boundary-term caveat that appears in footnote 1; please qualify the initial statement to match the later discussion.","section":"Abstract and Section 1"},{"comment":"The same symbol T is used for the torsion scalar and for the torsion tensor trace in Eq. (2.6); a notational distinction would help readers avoid confusion.","section":"Section 2, Eq. (2.6)"},{"comment":"The crystal-structure visualisation of torsion is described as indirect; a brief sentence explaining how the lattice-site picture maps onto a manifold would make the visualisation argument easier to evaluate.","section":"Section 5.2, Figure 2"},{"comment":"The notation f(R,T,Q) introduces Q without definition; please define the nonmetricity scalar or omit the symbol.","section":"Section 4, footnote 29"},{"comment":"Several works are cited as unpublished or in preparation (e.g., Weatherall and Meskhidze 2024; Wolf et al. 2024); please update to published versions where available.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a serious contribution to the philosophy of spacetime, and the main concern is not fatal. The boundary-term issue is particularly important because the authors themselves cite Wolf and Read (2023) without resolving the tension between that result and the empirical-equivalence premise; this should be addressable in revision. I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know before you read it. First, this is a genuinely careful piece of work: Mulder and Read isolate Knox's (2011) arguments against GR/TEGR underdetermination, answer each in turn, and the centerpiece of Section 3.1 — the symmetry argument that reverse-engineering the Levi-Civita connection cuts both ways — is mathematically clean and lands. Second, the paper's conclusion that underdetermination still threatens curvature realism is explicitly conditional on GR and TEGR being empirically equivalent, and the authors flag the boundary-term problem (via Wolf & Read 2023) without resolving it. A referee should push on exactly that point.\n\nWhat is actually new: a systematic three-part reconstruction of Knox's case (reverse-engineering, surplus structure, inertial functionalism) and two problems she never raised — the operationalisability and visualisability of torsion. The visualisability discussion is the most original; the Reichenbach-based argument that intrinsic torsion is no harder to visualise than intrinsic curvature is a fair and interesting move. The operationalisability section is thinner: the gradiometer-based operationalisation works only through the Bianchi identities plus the assumed dynamical equivalence, and the Hehl spin-probe is a theoretical proposal rather than a device. To their credit, the authors acknowledge this.\n\nThe surplus structure and functionalism sections are competent rather than decisive — the electrodynamics analogy and the denial of realiser functionalism are legitimate responses, but they will convince only readers who already share the paper's anti-Occamist sympathies. The self-citation cluster is heavy, but this is a small subfield and the citations are on point; I found no circularity.\n\nThe soft spot that matters is the boundary-term issue. The underdetermination claim presupposes empirical equivalence, yet the paper itself cites Wolf & Read (2023) for the claim that boundary terms have empirical consequences. If those consequences discriminate between the theories, the underdetermination evaporates and the challenge to curvature realism goes with it. This is not fatal to the paper's core project — the critique of Knox survives largely independently, and the authors are upfront that they assume equivalence — but it deserves a direct treatment rather than footnotes.\n\nWho is this for? Philosophers of physics working on spacetime realism, underdetermination, and the geometric trinity literature. It deserves a serious referee; with a revision that takes the boundary-term objection head-on, it would be a solid contribution.","headline":"Solid, honest critique of Knox on GR/TEGR underdetermination; the central conclusion is conditional on an unresolved boundary-term issue the authors flag but never settle.","tokens_in":24910,"tokens_out":10243,"would_cite":true,"duration_ms":88928,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper argues that teleparallel gravity, an empirically equivalent rival to general relativity set in a flat but torsionful spacetime, blocks any confident realist inference from general relativity to spacetime curvature.","keywords":["general relativity","teleparallel gravity","underdetermination","spacetime curvature","torsion","scientific realism","spacetime functionalism","visualisability"],"falsifier":"Find an experiment or exact calculation in which the boundary term in the TEGR action leaves an observable trace that the pure Einstein-Hilbert action cannot reproduce, for example a measurable gravitational boundary or edge-mode effect whose value depends on whether the action is written as $T$ or as $-R$ plus a boundary term. A confirmed difference of that kind would break the equivalence on which the paper's undefused underdetermination rests.","tokens_in":24069,"feed_emoji":"🌀","tokens_out":8988,"duration_ms":76010,"temperature":0.7,"pith_summary":"The paper is trying to establish that the empirical equivalence between general relativity and its teleparallel equivalent leaves a genuine, undefused underdetermination about the geometry of spacetime. It takes the standard philosophical attempt to dissolve that underdetermination and shows, piece by piece, that it relies on contestable assumptions: the apparent priority of the metric, the dismissal of gauge structure, and a particular functionalist account of inertial frames. It then argues that two further objections to teleparallel gravity—that torsion cannot be operationalised and cannot be visualised—can both be met. If the paper is right, accepting general relativity's empirical success does not justify believing that spacetime is curved; a flat spacetime with torsion remains an equally supported alternative.","feed_headline":"Curved or twisted spacetime? The data cannot tell","feed_subtitle":"An equivalent torsion-based rival to general relativity survives the objections, so realism about curvature is not secured.","key_machinery":"The load-bearing mathematical identity is $T = -R - 2\\nabla_\\nu T^\\rho{}_{\\rho\\nu}$: the TEGR torsion scalar equals the Ricci scalar plus a boundary term, which makes the two actions dynamically equivalent while leaving the choice of fundamental geometry open. The torsion tensor $T^\\tau{}_{\\mu\\nu} := \\Gamma^\\tau{}_{\\mu\\nu} - \\Gamma^\\tau{}_{\\nu\\mu}$ and the contorsion tensor $K^\\rho{}_{\\mu\\nu}$ with the relation $\\bar\\Gamma^\\rho{}_{\\mu\\nu} = \\Gamma^\\rho{}_{\\mu\\nu} - K^\\rho{}_{\\mu\\nu}$ translate between the curved and torsionful descriptions. On the philosophical side, the machinery is a taxonomy of objections: three arguments from a 2011 paper by Knox, plus the problems of operationalisability and visualisability, each isolated and answered in turn.","core_discovery":"General relativity and the teleparallel equivalent of general relativity (TEGR) are dynamically equivalent because the TEGR torsion scalar is the Ricci scalar plus a boundary term, yet they attribute the same phenomena to different geometric objects: curvature in GR, torsion in TEGR. The paper's central claim is that this underdetermination is not dissolved by the arguments offered against it. The metric used in TEGR is not a hidden GR ontology, because TEGR can be formulated metrically or in tetrads and either theory can be presented either way; the extra tetrad gauge freedom is not a reason to dismiss TEGR once gauge variables are understood as unphysical; and Knox's inertial-frame functionalism only identifies TEGR's spacetime with GR's if one also accepts additional metaphysical commitments such as realiser functionalism. The paper further claims that spacetime torsion can be operationalised through gradiometer-type readouts and spin-coupled probe particles, and that torsion is visualisable through the non-closure of parallelograms and crystal-dislocation models, with intrinsic torsion no harder to visualise than intrinsic curvature. The conclusion the authors draw is negative for realism about curvature: as long as the equivalence holds, the evidence does not choose between curved and torsionful spacetime.","pith_inferences":["A direct extension the authors leave open: look for gravitational boundary or edge effects whose value depends on whether the action is written as $T$ or as $-R$ plus its boundary term; any such measurable difference would break the empirical equivalence and collapse the underdetermination.","The same underdetermination pattern plausibly extends to the wider family of equivalent geometric formulations of gravity, so any claim that spacetime has one specific geometric property is hostage to equally supported rival formulations.","If visualisability is taken as the motivationalist's notion of perspicuity, then the paper's visualisability argument gives torsion-based models the same representational standing as curvature-based models, not merely a heuristic advantage.","The paper's strategy generalises into a caution for realism: when two theories are empirically equivalent, committing to one geometric quantity as real requires a further meta-argument for why that quantity rather than its equivalent counterpart is the one nature instantiates."],"forward_implications":["If the underdetermination stands, a scientific realist cannot cite general relativity alone as evidence that spacetime is curved; teleparallel gravity blocks that inference.","Dissolving the GR/TEGR underdetermination requires rejecting or supplementing the empirical-equivalence premise, not just showing that TEGR's ontology resembles GR's ontology.","Torsion is no worse than curvature on operational grounds: the same gradiometer-style devices that read out curvature can, through the Bianchi identities, be arranged to read out torsion components and their derivatives.","Torsion is no worse than curvature on visualisability grounds: extrinsic torsion has direct pictures (non-closure of parallelograms, crystal dislocations), and intrinsic torsion is trainable in the same way intrinsic curvature is.","The alternatives left for the realist are explicit: agnosticism, conventionalism about geometry, or a supra-empirical principle for choosing between the theories."],"supporting_citations":[{"why":"Provides the three defusing arguments that the paper isolates and rebuts.","marker":"Knox (2011)"},{"why":"Introduced the GR/TEGR underdetermination that the paper reassesses.","marker":"Lyre & Eynck (2003)"},{"why":"Raises the boundary-term caveat that could break empirical equivalence.","marker":"Wolf & Read (2023)"},{"why":"Gives the unified teleparallel Lagrangian from which the TEGR action is obtained.","marker":"Hayashi & Shirafuji (1979)"},{"why":"Supplies the modern formalism of teleparallel gravity used throughout.","marker":"Aldrovandi and Pereira (2012)"},{"why":"Provides the spin-particle equation that operationalises torsion components.","marker":"Hehl (1971)"},{"why":"Supplies the trained-visualisation account that the paper extends to intrinsic torsion.","marker":"Reichenbach (1928)"},{"why":"Offers an alternative functionalist criterion showing Knox's spacetime functionalism is not forced.","marker":"Baker (2020)"}],"fun_headline_variants":["Curved or twisted? The evidence is indifferent","Spacetime curvature vs torsion: physics stays the same","The twin theory of gravity that challenges curvature","Data can't choose: curved or twisted spacetime"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole argument depends on treating general relativity and teleparallel gravity as genuinely empirically equivalent; if boundary terms ever turn out to have observable consequences that distinguish the two theories, the underdetermination would be spurious.","fun_headline_variants_meta":{"raw":{"variants":["Curved or twisted? The evidence is indifferent","Spacetime curvature vs torsion: physics stays the same","The twin theory of gravity that challenges curvature","Data can't choose: curved or twisted spacetime"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000356,"raw_usage":{"total_tokens":1914,"prompt_tokens":912,"completion_tokens":1002,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":528,"completion_tokens_details":{"reasoning_tokens":942}},"tokens_in":528,"tokens_out":1002,"duration_ms":8714,"temperature":1.0,"reasoning_tokens":942,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:32:21.686201+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Find an experiment or exact calculation in which the boundary term in the TEGR action leaves an observable trace that the pure Einstein-Hilbert action cannot reproduce, for example a measurable gravitational boundary or edge-mode effect whose value depends on whether the action is written as $T$ or as $-R$ plus a boundary term. A confirmed difference of that kind would break the equivalence on which the paper's undefused underdetermination rests.","supporting_citations":[{"cited_title":"Primitive Ontology in a Nutshell","cited_arxiv_id":null,"evidence_quote":"Supplies the modern formalism of teleparallel gravity used throughout."}],"review_version":1}