{"id":"3c313d77-356e-4d14-bc1f-9102efefe6e3","arxiv_id":"2501.10416","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":1,"one_line_summary":"The authors claim all three criticisms of their time-of-arrival proposal are without merit, but the non-arrival probability rebuttal mislabels a standard tail integral.","lead":"This paper is a reply to three criticisms of a quantum time-of-arrival proposal, arguing that all are based on misunderstandings. It offers classical analogies and a numerical comparison, but contains at least one logical mischaracterization of the critics' quantities.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The rebuttal of the third criticism mischaracterizes the tail integral as a joint probability; in standard TOA theories, ∫_T^∞ Π(t)dt is the non-arrival probability, so the central claim that all three criticisms are without merit is not established.","rationale":"The central claim requires all three criticisms to be without merit. The first reply (different predictions are a feature) is a defensible epistemological position: disagreement with other proposals is not a proof of error. The second reply is internally coherent under the authors' definition 'arrived iff at D', though it sidesteps whether that definition is the physically relevant TOA. The third reply, however, is the decisive one: the authors need to show that Cavendish et al.'s non-arrival quantity is not a non-arrival probability. They do not do so. In every standard TOA formalism, Π(t) is the probability density of the arrival time, and ∫_T^∞ Π(t)dt is the probability that arrival occurs after T. Calling this a 'joint probability of finding the particle at the detector at times greater than T' mistakes a single-condition tail probability for a multi-time joint measurement. The classical time-fraction example is irrelevant to this distinction because it concerns the fraction of time spent at D, not the distribution of the time of first arrival. The renormalization chosen for Fig. 1 reinforces the concern: normalizing Π_QC over a large period makes the tail match by construction, but does not establish that the unrenormalized quantity in Cavendish et al. was a different kind of object. Therefore the paper's central claim is not established, and the reader's REJECT verdict is appropriate.","tokens_in":4046,"tokens_out":3111,"duration_ms":28512,"concrete_test":"Take the Kijowski distribution Π_K(τ) for the same Gaussian wave packet parameters as Cavendish et al. Fig. 2 and sample N=10^6 arrival times; compute the empirical fraction with τ>T and compare to ∫_T^∞ Π_K(τ)dτ. If they agree within sampling error, the tail integral is indeed the non-arrival probability, disproving the paper's claim that it is a 'joint probability of finding the particle at the detector at times greater than T'. Repeat for the quantum flux and semiclassical distributions.","verdict_should_be":"REJECT","load_bearing_attack":"The load-bearing flaw is in the reply to criticism 3. The authors assert that P^{K/F/SC}(na|ψ)=∫_T^∞ dt Π^{K/F/SC}(t) 'is the joint probability of finding the particle at the detector at times greater than T', and hence is incomparable to P^{QC}(na|ψ). But for any normalized arrival-time density Π(t), the integral ∫_T^∞ Π(t)dt is by definition the probability that the arrival time is greater than T, i.e., the probability that the particle does not arrive during [0,T]. It is not a joint probability over repeated detections; it is a tail probability. The authors' classical counterexample (1 sec at D among T=10,30 sec) computes the time fraction of presence, a different quantity from the survival probability of an arrival-time distribution. Thus their conclusion that Cavendish et al.'s comparison is 'meaningless' rests on the very confusion they attribute to the critics. The ad hoc renormalization of Π_QC over a period much larger than T in their Fig. 1 changes the object being compared and does not repair the mischaracterization. Since the central claim is that all three criticisms lack merit and the third reply fails, the central claim is unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript is a reply by Maccone, Roncallo, and Sacha to three criticisms raised by Cavendish et al. against their Page-Wootters-based time-of-arrival proposal. The paper argues that (i) the \"dramatically different\" predictions are a feature, not a flaw; (ii) the dependence on the total duration T is an expected consequence of the paper's stipulated definition that \"a particle has arrived at the detector iff it is at the detector's position D\"; and (iii) Cavendish et al. commit a logical mistake by equating the probability of not finding the particle at the detector with the probability of non-arrival. The reply also presents Fig. 1, which compares the tail integral of the quantum-clock distribution, normalized over a period much larger than T, with the tail integrals of Kijowski, quantum-flux, and semiclassical proposals.","tokens_in":4209,"tokens_out":5093,"duration_ms":50965,"significance":"If the reply were correct, it would rehabilitate a contested nonstandard time-of-arrival proposal and remove all three objections raised in the criticized paper. The defense of T-dependence is internally coherent given the authors' explicit arrival-at-D definition, and the authors are transparent about their commitments. However, the central claim that all three criticisms are without merit is not established: the reply to the third criticism mischaracterizes the standard tail integral of an arrival-time distribution, and the numerical matching in Fig. 1 relies on an unspecified normalization period. The paper therefore does not achieve its stated goal.","major_comments":[{"comment":"The statement that P^{K/F/SC}(na|ψ) = ∫_T^∞ Π^{K/F/SC}(t)dt is \"the joint probability of finding the particle at the detector at times greater than T\" is mathematically incorrect. For a normalized arrival-time density, the tail integral is the probability that the arrival time is larger than T, which is exactly the probability that no arrival occurred during [0,T]. It is a survival probability, not a joint probability over repeated detections. This error is load-bearing because the paper's conclusion that Cavendish et al. made a \"logical mistake\" rests entirely on this misinterpretation.","section":"NON-ARRIVAL PROBABILITY CRITICISM"},{"comment":"The classical counterexample of one second spent at the detector out of total durations T = 10 or 30 seconds computes the fraction of the observation interval during which the particle occupies D. This is not the tail of an arrival-time distribution: for a classical particle with a deterministic arrival time t0 < T, the arrival-time density is δ(t - t0) and ∫_T^∞ dt δ(t - t0) = 0, not 1/T. The example therefore does not support the claim that the K/F/SC tail integral should be interpreted as a time-fraction probability.","section":"EMPIRICALLY IMPLAUSIBLE CRITICISM"},{"comment":"Figure 1 normalizes Π_QC \"over a period much larger than T\" without specifying that period. The value of ∫_T^∞ Π_QC(t)dt depends on the chosen normalization interval, so the displayed agreement with the K/F/SC proposals is not a parameter-free prediction. The text itself concedes that the match is \"unwarranted\", which further weakens the evidentiary value of the figure as a response to the criticism.","section":"Figure 1 and normalization discussion"}],"minor_comments":[{"comment":"The reply to the \"dramatically different\" criticism is fair but could be strengthened by identifying a concrete experimental signature that would discriminate the proposals; the current response only notes the absence of evidence.","section":"Reply to first criticism"},{"comment":"The phrase \"we could not think of a reasonable one where this dependence is not present\" is too broad, since standard arrival-time distributions normalized over all times do not depend on the total duration T.","section":"EMPIRICALLY IMPLAUSIBLE CRITICISM"},{"comment":"The caption should state the exact normalization period and the detector width; \"much larger than T\" and \"negligible width\" are not quantitative.","section":"Figure 1"},{"comment":"There are typographical inconsistencies such as the irregular spacing in \"PK/F /SC\" and the references to un-numbered equations; these should be standardized throughout.","section":"General presentation"}],"recommendation":"reject","confidential_remarks":"The paper is a direct reply to criticisms, and the central claim fails because the third rebuttal mischaracterizes the standard tail integral of an arrival-time distribution. This is not a presentation issue that can be fixed locally; it is a load-bearing mathematical error in the core argument. I would not recommend major revision because the conclusion that all three criticisms are without merit cannot survive the corrected interpretation of the non-arrival probability."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper mounts a spirited defense, but the central claim that all three criticisms are without merit is not established. The replies to the first two criticisms are defensible under the authors' stipulated definition of arrival; the reply to the third rests on a clear misreading of the critics' quantity.\n\nWhat's genuinely useful here: the classical counterexample (a particle spending one second at the detector in an experiment of duration T) is a clean way to show that any \"probability of finding at D\" is a time fraction and necessarily depends on T. The response to the \"dramatically different\" criticism is fair: disagreement with untested TOA proposals is not evidence against a new one. And the response to the T-dependence criticism is internally consistent: if \"arrived iff at D\", then of course the probability of finding it there shrinks as T grows. The writing is clear and the authors are explicit about their definition.\n\nThe soft spot is load-bearing. For any normalized arrival-time density Π(t), the tail integral ∫_T^∞ Π(t)dt is the probability that arrival occurs after T—the survival, or non-arrival, probability. It is not the \"joint probability of finding the particle at the detector at times greater than T,\" as the authors claim. That is a different object. So when they dismiss the critics' comparison as \"meaningless\" because P_QC(na|ψ) and P^{K/F/SC}(na|ψ) are \"completely different quantities,\" the distinction is valid only if you first accept the authors' redefinition of non-arrival probability as a time fraction. They do not earn that redefinition; they just assert it. Figure 1 then compounds the problem by normalizing Π_QC over a period much larger than T, which alters the quantity being integrated and makes the apparent agreement with K/F/SC look like an artifact of the normalization choice.\n\nThere is also a heavy reliance on the authors' own prior work [2,6] for key points, though [6] is a real comparison paper and the citation is not inappropriate.\n\nWho this is for: people following the time-of-arrival debate, and anyone interested in how rebuttals can conflate different notions of probability. As a referee I'd say the paper needs major revision: the third reply is wrong as written, but a corrected version—arguing that the two non-arrival quantities are simply incommensurable, without mislabeling the tail integral—might salvage it. Send it to referees; an editor should not desk-reject a substantive reply from the original authors to a published PRL critique.","headline":"Two of the three replies hold up, but the third misreads the tail integral as a joint probability, so the claim that all criticisms lack merit fails as written.","tokens_in":4815,"tokens_out":3263,"would_cite":false,"duration_ms":30304,"reading_group":"maybe","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 all three criticisms of its quantum time-of-arrival proposal are without merit, and that one misreads 'not found at the detector' as 'never arrived'.","keywords":["time of arrival","quantum clock","stationary-clock formalism","non-arrival probability","quantum time measurements","arrival-time distribution","conditional probability","harmonic trap"],"falsifier":"A concrete test would be a single-particle experiment in a harmonic trap with a narrow detector at $D$ and a wave packet known to traverse $D$ once: record, over many runs and several total times $T$, both the fraction of runs with no detection event and the normalized distribution of detection times. If the no-detection fraction tracks the time-fraction prediction while the normalized detection-time distribution stays independent of $T$, the paper's interpretation is supported; if a well-defined arrival event can be certified independently and the no-detection fraction still fails to vanish for large $T$ in a way inconsistent with the time-fraction model, the rebuttal would be falsified.","tokens_in":33,"feed_emoji":"⏱️","tokens_out":9956,"duration_ms":142275,"temperature":0.7,"pith_summary":"The paper defends a proposal for measuring time of arrival in quantum mechanics against three published criticisms. Its central move is to insist on its own definition: a particle has arrived when it is at the detector position, so the probability of finding it there is naturally the fraction of the total observation time it spends there. On that reading, the criticized dependence on total time $T$ is not a defect but a basic consequence, and the critics' 'non-arrival probability' is really the probability of not finding the particle at the detector, which can approach one even for a particle that definitely arrives. The reply also recasts the mismatch with other time-of-arrival proposals as a feature that makes the proposal experimentally distinguishable. If the paper is right, the published criticism rests on a logical conflation rather than on a physical failure.","feed_headline":"Reply defends time-of-arrival proposal against all three criticisms","feed_subtitle":"The 'non-arrival probability' is the chance of not finding the particle at the detector, not proof it never arrived.","key_machinery":"The load-bearing object is the stipulated definition of arrival: a particle has arrived at the detector iff it is at the detector's position $D$. This turns arrival probability into a time fraction -- time spent at $D$ divided by total observation time -- which immediately explains the $T$-dependence and the limiting behavior of the non-arrival quantity. The underlying physical mechanism is the clock-based extension of quantum mechanics, in which arrival-time probabilities are conditional distributions read from a stationary clock-system state rather than textbook observables; the paper uses that mechanism to define $\\Pi_{\\rm QC}(t)$, the quantum-clock arrival-time distribution, and to argue that comparisons with other proposals must use that conditional quantity normalized consistently.","core_discovery":"The paper's central claim, stated in its own terms, is that the three criticisms fail: being different from other proposals is what makes the scheme testable; the dependence on total duration $T$ follows from the stipulated arrival definition and is therefore expected; and the 'non-arrival probability' object singled out by the critics does not measure non-arrival at all. The key to the third rebuttal is a simple classical example: a particle that spends one second at the detector has arrival probability one, yet in a total experiment of duration $T$ the probability of finding it at the detector is $1$ second divided by $T$, so the probability of not finding it there tends to one as $T\\to\\infty$ even though the particle has arrived. What the critics' equation actually computes, the authors argue, is the probability that the particle is not found at the detector, not the probability that it was never there; the correct comparison for late times, $\\int_T^\\infty dt\\,\\Pi_{\\rm QC}(t)$ with the quantum-clock distribution normalized over a period much larger than $T$, matches the other proposals.","pith_inferences":["Beyond the paper, the dispute looks largely definitional: the reply refutes the critics under the 'arrival iff at $D$' definition, whereas a first-passage or crossing-time definition of arrival would make the criticized quantity a different object and the classical example would not settle it.","A testable extension suggested by the reply is to measure a quantum-clock arrival-time distribution for a single narrow wave packet in a harmonic trap over several observation windows $T$ and check whether the normalized conditional distribution is independent of $T$, as the reply's time-fraction reading implies.","If the logical-mistake claim is right, published comparisons of time-of-arrival proposals should separate the unconditional probability of ever finding the particle at the detector from the conditional distribution of arrival times; otherwise apparent disagreements may be artifacts."],"forward_implications":["If the rebuttal stands, the third criticism collapses: the quantity that tends to one for large $T$ is the probability of not finding the particle at the detector, which is compatible with the particle having arrived.","The $T$-dependence that the critics called empirically implausible becomes a predicted, controllable feature: experiments must specify the total observation window, and arrival-time distributions should be read as conditional probabilities given arrival.","The large differences between the quantum-clock predictions and other proposals are not evidence against the proposal; they identify regimes where a time-of-arrival experiment could discriminate between competing definitions.","When the quantum-clock distribution is normalized over a period much larger than $T$, the late-time tail integral $\\int_T^\\infty dt\\,\\Pi_{\\rm QC}(t)$ matches the corresponding tails of the other proposals, so the apparent disagreement in the critics' comparison is an artifact of comparing different quantities."],"supporting_citations":[{"why":"The target of the reply: it supplies the three criticisms and the un-numbered non-arrival equation under dispute.","marker":"[1]"},{"why":"The original time-of-arrival proposal whose defence is the paper's purpose.","marker":"[2]"},{"why":"Supplies the stationary-clock mechanism from which the proposal's arrival-time distribution is derived.","marker":"[4]"},{"why":"Extends and formalizes the clock-based time observable used by the proposal.","marker":"[5]"},{"why":"Earlier detailed comparison with other time-of-arrival proposals, including the normalization divergence of slow packets that answers the 'dramatically different' criticism.","marker":"[6]"}],"fun_headline_variants":["Reply refutes all three criticisms of time-of-arrival","Authors show critics' third objection rests on a logical mistake","Non-arrival probability is a misread, reply argues","Classical example clears time-of-arrival objection"],"cache_read_input_tokens":6912,"weakest_assumption_plain":"The whole rebuttal rests on the stipulated definition that a particle has arrived iff it is at the detector position; if a reader instead takes arrival to mean a first crossing or a separate event, the criticized quantities are no longer the same objects and the classical counterexample does not refute the critics.","fun_headline_variants_meta":{"raw":{"variants":["Reply refutes all three criticisms of time-of-arrival","Authors show critics' third objection rests on a logical mistake","Non-arrival probability is a misread, reply argues","Classical example clears time-of-arrival objection"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000621,"raw_usage":{"total_tokens":2816,"prompt_tokens":819,"completion_tokens":1997,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":435,"completion_tokens_details":{"reasoning_tokens":1929}},"tokens_in":435,"tokens_out":1997,"duration_ms":15663,"temperature":1.0,"reasoning_tokens":1929,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:29:28.225907+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete test would be a single-particle experiment in a harmonic trap with a narrow detector at $D$ and a wave packet known to traverse $D$ once: record, over many runs and several total times $T$, both the fraction of runs with no detection event and the normalized distribution of detection times. If the no-detection fraction tracks the time-fraction prediction while the normalized detection-time distribution stays independent of $T$, the paper's interpretation is supported; if a well-defined arrival event can be certified independently and the no-detection fraction still fails to vanish for large $T$ in a way inconsistent with the time-fraction model, the rebuttal would be falsified.","supporting_citations":[{"cited_title":"dramatically different","cited_arxiv_id":null,"evidence_quote":"The target of the reply: it supplies the three criticisms and the un-numbered non-arrival equation under dispute."},{"cited_title":"empirically implausible","cited_arxiv_id":null,"evidence_quote":"The original time-of-arrival proposal whose defence is the paper's purpose."},{"cited_title":"the dramatically different","cited_arxiv_id":null,"evidence_quote":"Supplies the stationary-clock mechanism from which the proposal's arrival-time distribution is derived."},{"cited_title":"empirically implausible","cited_arxiv_id":null,"evidence_quote":"Extends and formalizes the clock-based time observable used by the proposal."}],"review_version":1}