REVIEW 3 major objections 4 minor 12 references
Quantum Measurements of Time: A reply to criticisms
T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash
Pith's one-line read 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'.
desk verdict 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. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
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.
What would settle it
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.
Extended reading notes
Core claim
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.
Load-bearing premise
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.
Editorial extensions
If this is right
- 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.
Reading between the lines
- 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.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
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.
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 (3)
- [NON-ARRIVAL PROBABILITY CRITICISM] 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.
- [EMPIRICALLY IMPLAUSIBLE CRITICISM] 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.
- [Figure 1 and normalization discussion] 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.
minor comments (4)
- [Reply to first criticism] 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.
- [EMPIRICALLY IMPLAUSIBLE CRITICISM] 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.
- [Figure 1] The caption should state the exact normalization period and the detector width; "much larger than T" and "negligible width" are not quantitative.
- [General presentation] 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.
Circularity Check
Rebuttal partially circular: T-dependence is a restatement of the stipulated 'arrived iff at D' definition, and the criticized tail integral is renamed a 'joint probability' to dismiss the comparison.
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self definitional
[Introduction; section 'Empirically implausible' criticism]
"In the following and in our papers, we use a natural TOA definition: we say that "a particle has arrived at the detector" iff (by definition) "it is at the detector's position D". ... the dependence of the probability of arrival on the experiment duration time T is a trivial fact, that immediately follows from our TOA definition."
The reply does not independently test the critics' notion of time of arrival; it replaces it with the paper's own definition and then declares the criticized T-dependence expected. The 'prediction' that the probability of finding the particle at D is proportional to the time spent at D divided by T is a direct consequence of the stipulated definition 'arrived iff at D'. Thus the conclusion that the empirical-implausibility criticism is without merit is the definition restated, not an independent argument responding to the critics' quantity.
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renaming known result
[Section 'Non-arrival probability' criticism]
"(i) this quantity is not the probability of non-arrival even for the K/F/SC proposals: by direct inspection, one can immediately see that it is the "joint probability of finding the particle at the detector at times greater than T", which is , in general, a very different situation from "the particle not arriving during the observation time T"."
For any normalized arrival-time density Π(t), the tail integral ∫_T^∞ Π(t)dt is, by definition, the probability that the arrival time exceeds T, i.e. that no arrival occurs during [0,T]. Calling it a 'joint probability of finding the particle at the detector at times greater than T' renames the standard tail probability without changing the mathematics. This renaming is load-bearing: it is used to declare Cavendish et al.'s comparison 'meaningless' and to conclude that the non-arrival criticism rests on a logical mistake, so the rebuttal reduces to a relabeling of the very quantity criticized.
full rationale
The reply to the first criticism is not circular: it correctly points out that disagreement with previous untested proposals is not by itself evidence of error, and the citation of [6] is contextual rather than load-bearing. The circularity is in the replies to the second and third criticisms. The 'empirically implausible' reply rests on the paper's stipulated definition of arrival as presence at D; under that definition the T-dependence and 1/T scaling follow trivially. The critics' objection is precisely to the physical appropriateness of that definition, so restating the definition does not answer the objection. The 'non-arrival probability' reply then renames the tail integral ∫_T^∞ Π(t)dt — which for a normalized arrival-time density is by definition the non-arrival probability during [0,T] — as a 'joint probability of finding the particle at the detector at times greater than T'. This renaming is used to declare the critics' comparison meaningless and to support the claim that the third criticism involves a logical mistake. The Fig. 1 agreement is obtained with a normalization period chosen much larger than T, and the paper itself notes that the agreement is unwarranted, so it provides no independent support. Overall, the central rebuttal partially reduces to the paper's own definition and to a relabeling of the criticized quantity, while the first criticism is handled non-circularly and the self-citations are not the principal problem.
Assumptions & free parameters
free parameters (1)
- Normalization period for the quantum clock distribution Pi_QC =
unspecified, chosen much larger than T
assumptions (3)
- ad hoc to paper A particle has arrived at the detector iff it is at the detector's position D.
- domain assumption The Page-Wootters mechanism provides a valid extension of quantum mechanics for describing time observables.
- domain assumption The total duration T of the experiment legitimately enters the time-of-arrival statistics as a normalization factor.
Cite this review
Pith. "Pith review of Quantum Measurements of Time: A reply to criticisms." pith.science (2026). https://pith.science/paper/JJ4PDFPT
@misc{pith2026250110416,
author = {Pith},
title = {Pith review of: Quantum Measurements of Time: A reply to criticisms},
year = {2026},
howpublished = {\url{https://pith.science/paper/JJ4PDFPT}},
note = {Machine review of arXiv:2501.10416}
}
read the original abstract
In [arXiv:2409.00161v1 (2024)] Cavendish et al. raise three criticisms against our time of arrival proposal [L. Maccone and K. Sacha, Phys. Rev. Lett. 124, 110402 (2020)]. Here we show that all three criticisms are without merit. One of them is founded on a logical mistake.
Figures
Reference graph
Works this paper leans on
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[6]
With a simple counterexample, we show that the “non-arrival probability” criticism is incorrect: Cavendish et al. erroneously equate the “probabil- ity that the particle does not arrive” to the “prob- ability that the particle is not found at the detec- tor”, instead of looking at the “probability that the particle is not found at the detector AND that it...
arXiv 2025
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[1]
The “dramatically different” criticism: Cavendish et al. point out that our predictions are “dramati- cally different from those of other well known pro- posals in the literature”, and they show a regime where these differences are very evident
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[2]
The “empirically implausible” criticism: Cavendish et al. suggest that our proposal is empirically im- plausible because of its dependence on the total time of the experiment T , and they suggest that this is not to be expected in a TOA
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[3]
The “non-arrival probability” criticism: Cavendish et al. claim that our proposal would predict that the probability that a particle does not arrive tends to one for large total time T , which is not what one would expect if the particle has arrived at some point in time. In the following, we carefully reply to these criticisms:
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[4]
We point out that “the dramatically different” crit- icism is hardly a criticism per se: in the absence of experimental evidence, the argument that a rad- ical new proposal matches the previous ones (or not), cannot be used to support (or disprove) its validity. We also point out that Cavendish et al.’s analysis on these differences has already appeared i...
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[5]
Using very simple examples, we show that, far from being “empirically implausible”, the dependence of the TOA related quantities on T is to be expected. We suspect that Cavendish et al.’s claim to the con- trary might arise from a definition of TOA that does not match ours (Ours: “the particle has ar- rived iff it is at the detector’s position”)
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[7]
W. Cavendish, S. Das, M. N¨ oth, and A. A. Rafsanjani, (Un)physical consequences of “Quantum Measurements of Time” (2024), arXiv:2409.00161v1 [quant-ph]
arXiv 2024
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[8]
L. Maccone and K. Sacha, Quantum measurements of time, Phys. Rev. Lett. 124, 110402 (2020)
work page 2020
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Mielnik, The screen problem, Found
B. Mielnik, The screen problem, Found. Phys. 24, 1113 (1994)
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D. N. Page and W. K. Wootters, Evolution without evolu- tion: Dynamics described by stationary observables, Phys. Rev. D 27, 2885 (1983)
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Giovannetti, S
V. Giovannetti, S. Lloyd, and L. Maccone, Quantum time, Phys. Rev. D 92, 045033 (2015)
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[12]
Roncallo, K
S. Roncallo, K. Sacha, and L. Maccone, When does a par- ticle arrive?, Quantum 7, 968 (2023)
2023
Reviewed August 10, 2026 · model on record in the stance chip above.
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