{"id":"c6be5b44-36a2-4d98-9756-d28f78c5d919","arxiv_id":"2505.08307","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The chronological ordering of events is indispensable to Newtonian mechanics and general relativity, so eliminativist \"radical relationalism\" about time is an unattractive reading of classical physics.","lead":"A philosopher argues that the ordering of events in time, not just the measurements we make, is an essential part of Newtonian physics and general relativity. The paper challenges \"radical relationalism,\" the view that time's order can be dropped from physics, and says the gap between everyday physics and timeless quantum gravity is bigger than its defenders claim.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The ineliminability thesis hinges on an unargued dismissal of the clock-variable reply in Sec. 3; if order can be reconstructed from correlations, the central argument collapses.","rationale":"The reader's weakest_assumption identifies exactly the same load-bearing concern: the paper's dialectical target is a radical relationalism that discards all order, and the only reply considered is dismissed without proof. This is an internal weakness of the argument, not a disagreement with external consensus, because the author himself raises the clock-variable response and then declines to engage with it. The loop example is particularly telling: if the two trajectories yield different sets of correlations, then the radical relationalist's resources suffice to separate them, and the alleged need for an additional betweenness structure is not demonstrated. The concrete test proposed is a straightforward computation for the toy model; it would settle whether the example actually supports the author's conclusion. The paper's honesty in flagging the reply is a point in its favor, but the absence of a substantive refutation leaves the central claim conditional at best. Since the reader's verdict already reflects this conditionality, no adjustment is needed.","tokens_in":14460,"tokens_out":8862,"duration_ms":95997,"concrete_test":"Compute, for the two trajectories in Figure 2 (original and inverted loop), the sets of pairs S1 = {(x1(t), α1(t))} and S2 = {(x1'(t), α1'(t))}. If S1 ≠ S2, then the radical relationalist can distinguish the trajectories using correlations alone, and the example does not demonstrate a need for primitive ordinal structure. If S1 = S2, the author's example would support the ineliminability claim. This check directly tests whether the toy-model argument works as stated, by determining whether the full set of correlations already encodes the physical difference that the paper claims requires a temporal order.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim that chrono-ordinal structure is ineliminable rests on characterizing radical relationalism as treating a model's content as an unordered set of measured pairs. In Section 3, the author anticipates the reply that temporal order can be encoded via correlations with an external clock (e.g., the planet's spin α1) and sets it aside as 'a bit strange' without argument. This is the load-bearing point: if a relationalist can reconstruct the ordering from correlations with clock variables, then ordinal structure is not ineliminable but derivative. The author explicitly concedes that using spin to pick a privileged ordering is a possible response, but never shows it is impossible. The loop example does not rescue the argument: the two trajectories in Figure 2 correspond to different sets of pairs (x, α), because the spin angle at a given spatial location differs when the loop is traversed in the opposite direction. A relationalist who retains the full set of correlations can therefore distinguish them without positing a primitive betweenness relation. To sustain the ineliminability claim, the paper would need to prove that no set of correlations among partial observables can reproduce the betweenness structure of Newtonian/GR models. That proof is absent, and the paper's own admission of the clock reply as 'strange' rather than impossible leaves the strongest form of radical relationalism unscathed.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper argues against 'radical relationalism,' an eliminativist view of time endorsed or suggested by some authors in the quantum gravity community, according to which the ordinal structure of time is dispensable even in classical theories. The author's central claim is that in Newtonian mechanics and general relativity the chrono-ordinal structure of time is an ineliminable part of the models, is invariant under the relevant reparametrizations and diffeomorphisms, is needed to define relative durations, velocities, causation, and explanation, and should be counted as part of the empirical content of those theories. The argument proceeds through a toy solar-system model in Section 3, a generalization to general relativity in Section 4, and a discussion of consequences for quantum gravity in Section 5. The paper concludes that timeless approaches to quantum gravity should aim to recover or approximate chrono-ordinal structure rather than deny its physical significance.","tokens_in":14708,"tokens_out":2979,"duration_ms":35391,"significance":"If the argument succeeded, the paper would make a useful contribution to the philosophy of time and to the foundations of quantum gravity, because it would block a popular strategy for minimizing the conceptual gap between classical general relativity and timeless approaches to quantum gravity. The paper is clearly written and engagingly structured, and it correctly identifies important invariant content in reparametrization-invariant theories: the causal/chrono-ordinal structure is common to diffeomorphism-related models. It also gives a fair presentation of the moderate relationalist position via the Jacobi action. The main weakness is that the central ineliminability claim is stronger than the examples establish, because the paper does not refute the radical relationalist's natural reply that order can be reconstructed from correlations with clock variables. For this reason the paper is best read as a challenge to radical relationalism rather than a proof of its impossibility; the central claim is defensible but requires additional work.","major_comments":[{"comment":"The clock-variable reply is set aside as 'a bit strange' rather than refuted. The ineliminability thesis requires showing that no set of correlations among partial observables can reproduce the betweenness structure of Newtonian or general-relativistic models. The paper does not provide such a proof, and it does not engage with the possibility that correlations with a monotonic clock variable, such as the spin angle α1, induce a derived ordering. Without an argument ruling out this reconstruction, the conclusion that chrono-ordinal structure is ineliminable is stronger than what the examples establish.","section":"Section 3, paragraph beginning 'I see two ways in which the radical relationalist could respond'"},{"comment":"The loop example does not by itself distinguish the two trajectories if the spin variable α1 is part of the correlated data. In the anticlockwise case, the set of pairs (x1, α1) differs from the clockwise case, because the spin angle at a given spatial location along the loop differs between the two traversals. A radical relationalist who retains the full set of correlations can therefore distinguish the two possibilities without positing a primitive betweenness relation. The example needs to be revised, or the author needs to explain why the relevant correlations are unavailable in the radical relationalist's picture.","section":"Section 3, Figure 2 and surrounding discussion"},{"comment":"The paper characterizes radical relationalism as treating a model's physical content as the unordered set of measured pairs (x, α). This characterization risks building the conclusion into the premise: if 'order' is excluded by definition from the relationalist's descriptive apparatus, then the alleged loss of order is a consequence of the definition rather than an independent argument. A more dialectically effective approach would be to grant the relationalist the full set of correlations, including correlations with clock variables, and then show that those correlations still fail to capture something that our theories treat as physically significant.","section":"Section 2, characterization of radical relationalism"}],"minor_comments":[{"comment":"The name 'Leibnitz' should be spelled 'Leibniz' for consistency with the rest of the paper and with the references.","section":"Section 3, second paragraph"},{"comment":"The right-hand panel is described as a set of points with no ordinal structure, but as drawn it can be misread as a trajectory projected onto a two-dimensional plane; a caption note clarifying that no betweenness relation is intended would prevent confusion.","section":"Figure 1"},{"comment":"The parenthetical remark about the bound on the difference between ways of defining Venus-year durations is sensible, but the phrase 'bounded above by the time it takes for light to travel between Earth and Venus' should specify that this is a rough estimate, since the actual value depends on orbital configuration.","section":"Section 4, footnote 8"},{"comment":"Several references contain line breaks inserted into URLs (e.g., Rovelli 2002 and Thébault 2021); the final published version should ensure that all URLs are rendered as continuous strings.","section":"References"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Let me cut to the chase. This paper does something useful and long overdue: it names radical relationalism—the view that the physical content of classical GR is just correlations among partial observables, with no temporal order—and pushes back against it. The core observation, that chrono-ordinal structure is invariant under reparametrizations and diffeomorphisms and therefore cannot be dismissed as gauge, is correct and worth saying. On that basis the paper makes a fair case that the burden of proof sits with the eliminativist.\n\nThe new contribution is a careful conceptual characterization of the target and two toy examples (the solar-system model and the self-intersecting trajectory). The paper also connects the debate to spacetime functionalism in a helpful way: if you want to be a functionalist about time, you need to say how ordinal structure gets recovered, not just how it could be dropped.\n\nWhere it softens is the central ineliminability thesis. The whole argument leans on the claim that radical relationalism treats a model as an unordered set of measured pairs. But that characterization is exactly what Rovelli-style relationalists will contest. They don't need to say there is no order; they can say order is relative to a clock, and any clock variable defines an order within the set of correlations. The paper anticipates this reply in Section 3 and sets it aside as 'a bit strange' without argument. That is not a refutation, and it is the load-bearing point. If order can be encoded through correlations with a clock, then ordinal structure is not ineliminable; it is derivative.\n\nThe loop example also doesn't do the work assigned to it. The two trajectories are supposed to have identical correlations but different order. But in the setup, the planet's spin behaves differently in the two cases, so the set of pairs (x, α) actually differs. A relationalist who keeps the full set of correlations can tell them apart without invoking a primitive betweenness relation. The example needs to be redesigned or dropped.\n\nThe claim that ordinal structure is 'empirical content' is also stronger than what the argument shows. What the paper convincingly shows is that the order is an invariant, indispensable feature of the mathematical models, and that dropping it would cripple explanation and prediction. Whether it is 'in the world' in the metaphysically loaded sense—that is a further step the toy examples don't reach.\n\nNone of this sinks the paper. The core dialectical point stands: if classical GR has an invariant partial order, then a timeless quantum gravity needs a story about how that order emerges, and radical relationalism's story—just correlations, no order—is incomplete. The author should be asked to address the clock-variable reply directly, to test whether any ordering can be reconstructed from partial-observable correlations, and to qualify the ineliminability claim accordingly.\n\nWorth serious peer review? Yes. It is a genuine, clearly argued contribution to a live debate, and the soft spots are fixable.","headline":"A clear, useful challenge to eliminativist readings of time in classical GR, but the central 'ineliminable' claim overreaches: the clock-variable reply is waved off rather than refuted, and the loop example misfires.","tokens_in":15199,"tokens_out":5070,"would_cite":true,"duration_ms":48867,"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":"The paper argues that the ordinal structure of time is an ineliminable part of Newtonian mechanics and general relativity, against \"radical relationalist\" attempts to reduce physics to unordered correlations.","keywords":["philosophy of time","relationalism","general relativity","chrono-ordinal structure","quantum gravity","reparametrization invariance","causal structure","philosophy of physics"],"falsifier":"Find two diffeomorphism-related solutions of general relativity that reproduce the same correlations between partial observables yet disagree about whether one event lies in the future of another; no such pair exists if the paper's invariance claim is right.","tokens_in":14247,"feed_emoji":"🕰️","tokens_out":8663,"duration_ms":81543,"temperature":0.7,"pith_summary":"This paper argues that the ordinal structure of time—the fact that events form a before/after/in-between sequence—cannot be eliminated from classical physics. It targets the \"radical relationalist\" view, common in parts of the quantum gravity literature, that a model's physical content is just an unordered set of correlations between measurable quantities. Against this, the author claims that in Newtonian mechanics and general relativity the order of events is invariant under reparametrizations and diffeomorphisms, that it is needed to define relative durations, velocities, causation, and explanation, and that it belongs to the empirical content of the theories. If correct, the conceptual gap between timeless quantum gravity proposals and classical physics is larger than their defenders claim.","feed_headline":"Temporal order is ineliminable, even in general relativity","feed_subtitle":"Even in general relativity, the before/after order of events survives reparametrization and carries empirical weight.","key_machinery":"The central object is the chrono-ordinal structure, defined as the in-betweeness relation between instants or events (not necessarily directed). The argument's load-bearing mechanism is the comparison of two formalisms: the Newtonian action with absolute time and the Jacobi action with an arbitrary parameter $\\tau$, whose solutions form an equivalence class under reparametrization. The author shows that all members of the class agree on the ordinal structure but not on metric durations, so the moderate relationalist can retain order; the radical relationalist's further step to an unordered set of pairs discards a shared, invariant feature. In general relativity the same mechanism is the diffeomorphism-invariance of the past/future relation defined by the metric and causal structure.","core_discovery":"The central claim is that chrono-ordinal structure—the one-dimensional \"in-between\" ordering of instants in Newtonian mechanics and the partial order of past/future in general relativity—is a genuine, ineliminable part of the physical content of our classical theories. The author argues that even after quotienting by arbitrary temporal reparametrizations (the Jacobi action) or by spacetime diffeomorphisms (general relativity), the equivalence classes still share a definite order structure: if an event lies between two others in one representative, it does so in all. Therefore the radical relationalist's proposal to discard the order and keep only correlations throws away predictive and explanatory content, such as the fact that one planet-year lasts a definite number of planet-days or that two black-hole mergers are an ordered sequence ending in detection.","pith_inferences":["If the argument is right, a full radical-relationalist model of the universe would have to encode temporal order through correlations with clock variables, and the paper's \"a bit strange\" reply leaves that route open rather than closed.","A testable extension is to try to reformulate a simple Newtonian system—say, the orbiting and spinning planet—without any in-betweenness relation and check whether all order-sensitive predictions survive.","The argument suggests that approaches to quantum gravity that retain a discrete or continuous causal order are closer to classical physics than fully timeless proposals.","The recovery criterion implied by the paper can be sharpened: a timeless theory should be required to reproduce not just correlations but specific ordinal facts, such as \"this event lies between those two,\" before being counted empirically adequate."],"forward_implications":["Radical relationalism cannot account for relative durations, since counting spins \"between\" the endpoints of a year presupposes an in-betweenness relation.","Velocities and rates of change are either abandoned or redefined in a way that smuggles in temporal derivatives, so the position is not a clean eliminativism.","The gauge-type arguments from reparametrization and diffeomorphism invariance do not support radical relationalism, because the order structure is common to all representatives of an equivalence class.","If the paper is right, timeless quantum gravity approaches face a larger explanatory burden: they must recover or approximate chrono-ordinal structure rather than deny its physical significance.","Spacetime functionalism, if it is to be viable, should aim to explain how ordinal structure could be recovered from a more fundamental theory."],"supporting_citations":[{"why":"Source of the \"Forget time\" thesis that physical content is correlations between partial observables rather than temporal order.","marker":"(Rovelli, 2011)"},{"why":"The two-variable toy model radical relationalists cite as showing that no time variable is needed.","marker":"(Colosi & Rovelli, 2003)"},{"why":"Supplies the Jacobi-action formalism that moderate relationalism uses and that the paper shows retains ordinal structure.","marker":"(Barbour, 1994, 2011)"},{"why":"The application of the gauge observability criterion to general relativity that radical relationalism relies on.","marker":"(Earman, 2002)"},{"why":"The hole argument, the pattern of relationalist reasoning the paper challenges when extended to temporal order.","marker":"(Earman & Norton, 1987)"},{"why":"Prior objection that time remains in canonical gravity; the paper's conceptual argument parallels it.","marker":"(Gryb & Thébault, 2016)"},{"why":"Claim that timeless quantum gravity can bridge the gap with classical physics, which the paper argues is too wide.","marker":"(Huggett & Wüthrich, 2013)"},{"why":"Spacetime functionalism proposal that the paper says should recover ordinal structure rather than deny it.","marker":"(Lam & Wüthrich, 2018)"}],"fun_headline_variants":["General relativity can't erase the order of events","Radical relationalism drops essential time structure","Time's ordinal structure isn't just a gauge choice","Defending the ineliminable order of time","The 'between' of instants is physically real"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that radical relationalism is genuinely committed to treating a model's physical content as an unordered set of measured pairs, with no physical meaning to the sequence in which they occur; the paper sets aside the rival reading in which order is recovered from correlations with an external clock as \"a bit strange\" rather than proving it impossible.","fun_headline_variants_meta":{"raw":{"variants":["General relativity can't erase the order of events","Radical relationalism drops essential time structure","Time's ordinal structure isn't just a gauge choice","Defending the ineliminable order of time","The 'between' of instants is physically real"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000731,"raw_usage":{"total_tokens":3202,"prompt_tokens":803,"completion_tokens":2399,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":419,"completion_tokens_details":{"reasoning_tokens":2326}},"tokens_in":419,"tokens_out":2399,"duration_ms":20784,"temperature":1.0,"reasoning_tokens":2326,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:57:43.049248+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Find two diffeomorphism-related solutions of general relativity that reproduce the same correlations between partial observables yet disagree about whether one event lies in the future of another; no such pair exists if the paper's invariance claim is right.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Jacobi-action formalism that moderate relationalism uses and that the paper shows retains ordinal structure."},{"cited_title":"Spacetime functionalism from a realist perspective","cited_arxiv_id":"2003.10172","evidence_quote":"Spacetime functionalism proposal that the paper says should recover ordinal structure rather than deny it."}],"review_version":1}