The Clock That Moved the Particle

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IWhat sixty nanoseconds means

CERN's Super Proton Synchrotron accelerated protons to 400 GeV/c and kicked them onto a graphite target in two extractions, each lasting 10.5 µs. Charged mesons from the target decayed into muon neutrinos, which crossed about 730 km of rock to the OPERA detector under the Gran Sasso massif in Italy. Light takes a little under two and a half thousandths of a second to go that far. The claim is that the neutrinos took 60.7 billionths of a second less.

With that beam no single neutrino could be timed. OPERA said why:

The time of flight of CNGS neutrinos (TOFν) cannot be precisely measured at the single interaction level since any proton in the 10.5 µs extraction time may produce the neutrino detected by OPERA.

So OPERA compared shapes. A waveform digitiser recorded the proton pulse of every extraction at CERN. Under Gran Sasso, 16111 neutrino events were time-stamped. Slide the distribution of event times against the summed proton pulse by a trial offset δt, ask how well they line up, and the offset that lines them up best is the answer. That question is a likelihood, and its peak is the measurement.

The analysis was blind: it was first run with an old set of calibrations, and gave δt(blind) = 1048.5 ns. Six calibration terms in the paper's Table 1, together −987.8 ns, then brought it to 60.7 ns.

Their likelihood, redrawn

The paper does not release the event times or the waveforms. It does print Figure 8: each extraction's log likelihood near its peak, fitted with a parabolic shape for the determination of the central value and of its uncertainty. That figure is the reproducible claimant input, and this is it, rebuilt.

The page fits each curve as a parabola in z = x − 1050, reads the peak and the curvature, and adds the two log likelihoods, because the two extractions are independent measurements of one shared delay. The first extraction alone peaks at 59.3 ± 11.0 ns and the second at 65.1 ± 10.7 ns, after the corrections. Together: 62.3 ± 7.7 ns.

The six corrections

Table 1 of the preprint prints each term twice, once as used in the blind analysis and once as used in the final one, and then the correction between them. The page sums the correction column, and also checks that every correction really is the final value minus the blind value.

Sum of the printed corrections: computing ns; computing.

They sum to −987.8 ns, which is the printed total. These are version 1's blind-to-final calibration terms. They are not the later repair of the instrument, which section V comes to.

The gap, printed rather than hidden

So the claim at full strength, as far as its published summary allows anyone to rebuild it, is 62.3 ± 7.7 ns (stat., digitised likelihood summary) beside 60.7 ± 6.9 ns (stat., paper), with the paper's 7.4 ns systematic uncertainty. The rebuilt claim is slightly larger than the printed one and slightly less precise. The page keeps the printed values as the claim and prints its own beside them.

The page counts its reconstruction as agreeing with the paper under a documented approximation allowance of 2.0 ns in the centre and 1.0 ns in the width. That allowance was accepted for this specific reconstruction when the page was commissioned. It was set after the gap had been measured, to cover it, so agreement within it guards against a later regression; it is not independent evidence that the reconstruction is right. It is not a measured digitisation error, and it is not an extra experimental uncertainty.

How much of the gap could be pixels? Rerunning the digitisation with three darkness thresholds and three crop trims keeps the centre within 62.29 to 62.31 ns and the width within 7.667 to 7.669 ns. Moving each axis's end ticks by ±2 native pixels, in every combination, spreads them over 62.08 to 62.47 ns and 7.62 to 7.72 ns. Those are sensitivity envelopes for those perturbations, not confidence intervals.

The quadrature comparison, 62.31 / √(7.67² + 7.4²) = 5.85, sits beside the authors' 6.0 σ. That ratio is the page's arithmetic, not a newly calibrated tail probability.

What this is not: fitting a published likelihood summary is not a rerun of OPERA's event selection or of its waveform likelihood, and the searches behind this page did not locate those records in any public archive. OPERA did test its own procedure, and said so:

The average of the central values from this ensemble of simulated OPERA experiments reproduces well the time shift applied to the simulation (at the 0.3 ns level).

IISeven neutrinos, timed one at a time

At the end of the 2011 run CERN changed the beam. Instead of a 10.5 µs pulse it sent four narrow bunches, each about 3 ns wide and 524 ns apart. ICARUS dates that running from 21 October to 4 November 2011 (its page 2); OPERA's second version gives 22 October to 6 November. With bunches that short a neutrino can be matched to the bunch that made it and timed on its own: no pulse shape, no likelihood, one subtraction per event.

OPERA reported on it first. Its second version, posted on 17 November 2011, revised the main result to 57.8 ± 7.8 (stat.) +8.3/−5.9 (sys.) ns and added 20 events from the bunched beam, 6 inside the detector and 14 in the rock around it, each timed on its own. Their average early arrival was 62.1 ± 3.7 ns, with an RMS of 16.4 ns. The collaboration put it in the abstract:

The above result, obtained by comparing the time distributions of neutrino interactions and of protons hitting the CNGS target in 10.5 µs long extractions, was confirmed by a test performed using a beam with a short-bunch time-structure allowing to measure the neutrino time of flight at the single interaction level.

CERN's update of the next day: This test confirms the accuracy of OPERA's timing measurement, ruling out one potential source of systematic error. The new measurements do not change the initial conclusion. So by late November 2011 the claim no longer rested on a pulse-shape likelihood alone. Its strongest printed evidence was twenty neutrinos, each timed on its own, arriving about 62.1 ns early.

ICARUS, a liquid-argon detector in another hall of the same laboratory, caught seven of them between 31 October and 4 November 2011: three neutrino interactions inside the detector and four muons made by neutrinos in the rock upstream. Its Table 1 prints the timing of every event term by term, which is why this page can run the control rather than quote it.

Based on the seven recorded neutrino events, the result δt = +0.3 ± 4.9(stat.) ± 9.0(syst.) ns is compatible with a neutrino propagation velocity in agreement with the speed of light and incompatible with the result reported by the OPERA Collaboration.

Same beam, same weeks, same mountain: OPERA's twenty bunch-timed neutrinos averaged 62.1 ns early and ICARUS's seven +0.3 ns. They could not both be right about the neutrinos. The OPERA result the ICARUS paper sets itself against is version 2's 57.8 ns (its page 2). This page plants version 1's 60.7 ns, the claim as first printed.

Matching each neutrino to its bunch

For each event the page subtracts the proton's start time at CERN from the neutrino's stop time in ICARUS, finds the bunch that puts the neutrino closest to a light-speed arrival, takes off that bunch's delay, and compares what is left with the light-speed flight time ICARUS printed, 2439098 ± 1.7 ns. From the printed timestamps the seven residuals are −2, 0, −5, −19, +7, +3, +18 ns, with a mean of +0.29 ns and an RMS of 10.50 ns: the printed +0.3 and 10.5, to the place they were printed. Every bunch the page assigns, 2, 2, 3, 1, 3, 4, 2, matches the printed bunch column.

The seven events through the chosen route. A bunch the route assigns differently from the printed column would be marked.

The paper's 4.9 and 9.0 ns remain what they are: published inputs. The 4.9 ns statistical error was estimated from a Student distribution with 6 degrees of freedom and the 9.0 ns combines the authors' timing uncertainties; a mean and an RMS rebuild neither, and the page does not pretend to.

IIICould ICARUS have seen it?

A control that could not have seen the claim cannot count against it. So before the seven residuals are allowed to say anything about OPERA, the page asks whether they could have said yes. It plants the claim, at the size OPERA printed, into the control's own data, and runs the control again without changing a line of it.

• Copy the frozen table.
• Subtract 60.7 ns from each copied T_STOP, the neutrino's arrival. Nothing else changes: not T_START, not the light-speed flight time, not the error budget, not the bunch spacing.
• Run the same function that produced the real result: bunches are assigned again from scratch, flight times formed again, the mean taken again.
• Compare the two runs.

The seven planted residuals are +58.7, +60.7, +55.7, +41.7, +67.7, +63.7, +78.7 ns, with mean +60.99 ns. The RMS stays 10.50 ns, every bunch assignment stays 2, 2, 3, 1, 3, 4, 2, and the displacement recovered against the real mean is 60.700 ns, the size that was planted. That exact figure is not the finding. The control is a mean of subtractions, so any planted shift that leaves every bunch in place comes back at exactly its own size, and no bunch can move without a refusal: to change bunch a residual would have to pass half the 524 ns spacing, and the ±200 ns window refuses it first. What the test shows is that the planted record stays inside that window, so the plant is measured rather than refused, and that its mean crosses a line the real one does not.

To say whether a mean counts, the page needs a yardstick, and it borrows the authors' own: u = √(4.9² + 9.0²) = 10.25 ns. It flags a positive displacement when the mean exceeds 3u = 30.74 ns. Call that the page's three-error sensitivity rule; it is not a discovery threshold, and the ICARUS paper states none. The real record sits at 0.028 u and does not cross it. The planted claim sits at 5.95 u and does. The rule is the same before and after. The common 9.0 ns systematic is not divided by √7, because it is shared by all seven events, and the 1.7 ns light-flight uncertainty, already inside the 9.0, is not added again.

A borrowed yardstick has a blind spot: it cannot notice a record noisier than the paper's. So the rule has a second condition. The mean must also exceed three times a scale built from the seven residuals' own scatter. Their RMS over √7, widened by √(6/4) for six degrees of freedom, is 4.86 ns; with the same 9.0 ns systematic that gives √(4.86² + 9.0²) = 10.23 ns and a line at 30.68 ns. On this record the two scales nearly agree, 4.86 ns from the scatter beside the printed 4.9 ns, and the published one is the stricter. The page does not claim this is how ICARUS computed its error. The second condition is there so that the verdict can fail: the button below hands the control a copy of the table with every residual 7 times as far from the mean, plants the claim, and lets the same unmodified test say what it can still see.

Running the same test at ever smaller plants finds where it stops seeing them. In this record the smallest planted early arrival the rule flags is 30.46 ns, and OPERA's claim, 60.7 ns, is 1.99 times that. OPERA's corrected 6.5 ns sits well under it: by this rule, these seven events could not have told the corrected value from no effect at all. They could exclude the claim as printed; they could not confirm the correction.

The control could have confirmed the claim. It did not find it.

These ratios are not p-values, and this is not a detection probability estimated over imagined repeats of the experiment. It is a deterministic recovery test in the seven events that exist, on the authors' own uncertainty scale. Grade A here means injection and recovery in published event times. ICARUS's detector reconstruction and its own sensitivity analysis were not rerun.

The same test through every route the table supports, each on its own line. On the printed flight-time route the bunches are read from the printed column, so there is nothing to reassign and the table says so. The official assertion uses the timestamps; the conclusion does not depend on the choice.

The claimants' method on nothing

Not applicable here, and the page will not fake it. OPERA's offset was not established by showing that its likelihood manufactures signals out of empty data, and Figure 8's curves keep none of the event sampling or proton-waveform noise that an honest null through their procedure would need. Gaussian timestamps generated by this page would not be OPERA's null, so none are generated.

Where the instrument refuses

An instrument that answers every question is not measuring anything. These three buttons hand the engine an input outside what its record supports. Each is refused, with the reason, and nothing is quietly dropped or relabelled.

The full domain: the seven-event 2011 record and no other (the 25-event 2012 ICARUS sample is a separate record and is never mixed in); finite times in every field a route uses; unique bunch associations within ±200 ns; planted amplitudes of zero or the printed claim only; likelihood fits with at least three distinct points inside the Figure 8 axes and downward curvature; muon recombinations that keep both classes, positive counts and at most one omitted period.

IVWhich timing row?

Table 1 prints event 1's timing in more ways than agree with one another. From the printed timestamps:

2578030 − 138406 = 2439624 ns, not the printed elapsed 2439632 ns
2439624 − 524 = 2439100 ns, not the printed flight time 2439104 ns
2439098 − 2439100 = −2 ns, not the final row's −6 ns

No other event has a disagreement between its timestamps and its elapsed time. The timestamps are this page's default because they reproduce the numbers the authors printed in their abstract, text and conclusion.

There is more in the table than that. Section 4 of the paper prints how each timestamp is assembled from the delays in the columns above it. Applied to the printed delays, the T_START formula reproduces all seven printed T_START values to the nanosecond. The T_STOP formula lands 5 ns after the printed T_STOP for six of the events and 9 ns after it for event 1. The page cannot say what the common 5 ns is: the paper notes that the table shows only variable corrections, and the fixed fibre delay is quoted as 42037 ns in the formula and as 42036.6 ns two pages earlier. But set the common part aside, and the delay columns reproduce the final row exactly, for all seven events, event 1 included.

So the table holds two self-consistent readings that part company only at event 1, by 4 ns. The printed timestamps give the prose's +0.3 and 10.5. The delay columns and the final row give a mean of −0.29 ns and an RMS of 10.71 ns, or −5.29 ns if the unexplained 5 ns is left in. The printed elapsed time for event 1 agrees with neither, and on its own would give −10 ns. The page does not decide which printed entry is the odd one out, does not edit −6 to −2 in a file that transcribes the final row, and infers nothing about the unreleased original record. The table's own footnote says event 1's PMT time carries about twice the uncertainty of the others, roughly 4 ns, because its pulse was smaller. That is context from the same table, not an explanation of the arithmetic.

A source audit is only worth trusting if it catches a slip it was not told about. Plant one: move a single event's T_STOP 30 ns later, in a copy, and the table below is rebuilt from the copy.

Showing computing. Timestamp mean computing, moved by computing; bunches computing; the audit flags computing.

Any one slip moves the timestamp mean by −4.29 ns, which is −30/7, leaves every bunch where it was, and puts that event on the audit's list. Event 1 is on the list already; the slip takes its elapsed-time gap from −8 to +22 ns.

Every route through Table 1, event by event, in ns, for the table as printed or for the copy with the planted slip. Gaps are recomputed minus printed. The highlighted row is event 1, or the event given the slip.

Does any of this matter for the question this page asks? No: through all three routes the planted claim comes back at exactly 60.700 ns and crosses the rule, and the real record never does. It is shown because a page that picked a row silently would be doing the one thing this page exists to refuse.

VWhat decided it

ICARUS did not decide it. Its seven events rule out an early arrival as large as 60.7 ns in its own sample, and the section above shows they could have seen one. They say nothing about what had gone wrong at OPERA. That came from OPERA.

From December 2011 OPERA remeasured the delay of the 8.3 km optical fibre that carries the GPS time signal underground to its master clock, and found it 73.2 ns longer than in 2006 and 2007, with more jitter. By mid-February 2012 the difference had been traced to an optical cable not properly connected, which cut the light reaching the clock's optical-to-electrical converter; with proper connections restored, the old delay came back. A second effect ran the other way. The master clock's oscillator ran 0.124 ppm fast, so an event's timestamp was overestimated by an amount that depended on where in its 0.6 s acquisition cycle the event fell, up to 74 ns. CERN's update of 23 February 2012, when both were still being tested, put it plainly:

If confirmed, one would increase the size of the measured effect, the other would diminish it.

Three weeks later CERN's update of 16 March 2012 reported the ICARUS result, and its Research Director said: The evidence is beginning to point towards the OPERA result being an artefact of the measurement.

With the fibre and the oscillator both corrected, OPERA's final paper gives 6.5 ± 7.4 (stat.) +8.3/−8.0 (sys.) ns from the main data, now 15223 events, and from the short bunches −1.9 ± 3.7 ns with 20 Target Tracker events and −0.8 ± 3.5 ns with 16 RPC events. Those Target Tracker events come from the same bunched-beam run and the same selection, 6 inside the detector and 14 outside it, that version 2 had timed at 62.1 ns early. The page does not subtract 73.2 from 60.7 and call it the correction. The oscillator term depends on where each event fell in its acquisition cycle, the corrected main analysis selected its events differently, and that per-event record is not public.

OPERA's reply to the control was not a rebuttal. Of those twenty events, now at −1.9 ns, the corrected paper says it is also in agreement with the ICARUS result reported in [47], reference 47 being the ICARUS paper of section II (Section 9.1, PDF page 29). And it ends:

After several months of additional studies, with the new results reported in this paper, the OPERA Collaboration has completed the scrutiny of the originally reported neutrino velocity anomaly by identifying its instrumental sources and coming to a coherent interpretation scheme.

And CERN, on 8 June 2012, reporting four experiments at once:

The four, Borexino, ICARUS, LVD and OPERA all measure a neutrino time of flight consistent with the speed of light. This is at odds with a measurement that the OPERA collaboration put up for scrutiny last September, indicating that the original OPERA measurement can be attributed to a faulty element of the experiment’s fibre optic timing system.

OPERA then measured again, with a dedicated short-bunch beam in spring 2012 and an upgraded set-up, and found δt = 0.6 ± 0.4 (stat.) ± 3.0 (syst.) ns for muon neutrinos:

This new measurement confirms with higher accuracy the revised OPERA result.

The original preprint had not claimed to overturn anything. It ended:

Despite the large significance of the measurement reported here and the stability of the analysis, the potentially great impact of the result motivates the continuation of our studies in order to investigate possible still unknown systematic effects that could explain the observed anomaly. We deliberately do not attempt any theoretical or phenomenological interpretation of the results.

The latest authoritative statement the searches for this page located is context, not a reanalysis. KM3NeT, constraining superluminal neutrinos at far higher energies in 2025, lists OPERA among searches without a positive result:

Several experimental searches for superluminal neutrino propagation have been performed, for instance, at OPERA and MINOS; while conclusive evidences of superluminal propagation, and therefore LIV, has not been observed, limits have been set.

What would change the verdict: authenticated timing and calibration records that overturn the instrumental diagnosis, together with independent flight-time measurements that reproduce the claimed displacement after calibrated timing corrections. A better digitisation that moved this page's anchor would change the page's reproduction status; it would not by itself reverse the historical verdict.

VIThe same muons keep time across two detectors

Everything so far leans on the CERN to Gran Sasso link: its GPS clocks, its fibres, its 730 km. There is a way to test OPERA's clock that uses none of it.

Part of the Gran Sasso massif is unusually thin when seen sideways, and cosmic-ray muons coming in almost horizontally can pass through OPERA and then through LVD, a large detector in another hall. The flight between them is fixed by geometry, and so the difference between the two detectors' timestamps for the same muon should be the same year after year, whatever the neutrinos are doing. LVD and OPERA went back through their records together and found 306 such muons from 2007 to March 2012. Their Table 2 prints the mean time difference in eight calendar periods.

The observable is t_LVD − t*_OPERA, a local difference between two detectors' clocks, where the asterisk means the authors had already corrected OPERA's times for its oscillator drift. It is not a neutrino's δt. Recombining the table with count weights gives class A, 64 muons, at 595.45 ns and class B, 242 muons, at 668.38 ns: a change of −72.92 ns. The paper prints 595 ± 8, 668 ± 4 and −73 ± 9 ns. The recomputed centres agree to the integer. Each printed mean is rounded to the nanosecond, so each class mean carries at most ±0.5 ns from rounding and their difference at most ±1 ns.

Could one odd calendar period be carrying the whole change? Leave each out in turn:

Every one of the eight deletions keeps the sign, which this table guarantees: every class A period mean (at most 628 ns) lies below every class B period mean (at least 667 ns), so no deletion, and no set of deletions, could flip it. The informative result is the size. The change runs from −91.18 ns, leaving out 2008-2, to −65.70 ns, leaving out 2007; leaving out the last period, early 2012, gives −68.27 ns. Even at the far edge of the rounding bound no deletion shrinks the change below 64.70 ns. This is a deterministic deletion result, not a confidence statement.

Recombining the eight published period means gives a local timing change of −72.9 ns. Removing any one period leaves a change between −91.2 and −65.7 ns.

The deletion analysis is this page's. The discovery, and the reading of it as an instrumental change, belong to LVD and OPERA. The page does not compute a new pooled significance from the period errors: done naively, that would not reproduce the printed ±9 ns, which the authors took from the grouped distributions in their Figure 18.

OPERA's corrected paper reads the muon result as the same step seen from outside:

The extracted value of (73.2 ± 9) nsec [43] is compatible with the fibre recalibration described in Section 6.1.

we searched the Artificial Wasteland corpus, arXiv and web-indexed GitHub results on 2026-09-22 and did not find a browser interactive that combines the digitised OPERA likelihood summary, an injection into the seven ICARUS event timestamps and a leave-one-period-out reconstruction of the LVD-OPERA muon timing change.

That search was bounded and did not cover GitHub exhaustively. The muon paper itself already contains the historical result.

VIIThe check

The headline, as this page states it: ICARUS's seven published event times give a mean early arrival of 0.3 ns; plant OPERA's 60.7 ns into those same times and the unmodified control returns 61.0 ns, so the control could have seen the claim and did not.

Sources, and what was done with them

1. The OPERA Collaboration, T. Adam et al., Measurement of the neutrino velocity with the OPERA detector in the CNGS beam, arXiv:1109.4897v1, hep-ex, 22 September 2011. version record, PDF. The claim, the method, Table 1 (page 15) transcribed, Figure 8 (page 16) digitised. arXiv's non-exclusive distribution licence: the page ships only its own numerical transcription and digitisation, never the PDF or the figure.
2. The OPERA Collaboration, T. Adam et al., Measurement of the neutrino velocity with the OPERA detector in the CNGS beam, arXiv:1109.4897v2, hep-ex, 17 November 2011. PDF. The revised main result and the 20-event bunched-beam test (pages 24 to 27), quoted. arXiv's non-exclusive distribution licence.
3. OPERA Collaboration, T. Adam et al., Measurement of the neutrino velocity with the OPERA detector in the CNGS beam, Journal of High Energy Physics, JHEP 10 (2012) 093, published 12 October 2012, doi:10.1007/JHEP10(2012)093; arXiv:1109.4897v4, 12 July 2012, PDF. Section 6.1, Section 9.1 and the conclusions, quoted. The journal article is open access under CC BY 2.0; that licence belongs to the final article, not to the version 1 figure.
4. ICARUS Collaboration, M. Antonello et al., Measurement of the neutrino velocity with the ICARUS detector at the CNGS beam, Physics Letters B 713, 17-22 (2012), doi:10.1016/j.physletb.2012.05.033; arXiv:1203.3433v3, 29 March 2012, PDF. Table 1 (page 9) transcribed column by column; Section 4 formulas and constants (page 6). Numbers cited from the PDF.
5. LVD and OPERA Collaborations, N. Yu. Agafonova et al., Determination of a time-shift in the OPERA set-up using high energy horizontal muons in the LVD and OPERA detectors, arXiv:1206.2488v1, hep-ex, 12 June 2012. version record. Table 2 (page 18) transcribed; drift fit (page 16) and class results (pages 18 and 19) cited.
6. CERN, OPERA experiment reports anomaly in flight time of neutrinos from CERN to Gran Sasso, first dated 23 September 2011, updates of 18 November 2011, 23 February 2012, 16 March 2012 and 8 June 2012. CERN. Quoted.
7. The OPERA Collaboration, T. Adam et al., Measurement of the neutrino velocity with the OPERA detector in the CNGS beam using the 2012 dedicated data, JHEP 01 (2013) 153, doi:10.1007/JHEP01(2013)153; arXiv:1212.1276, 6 December 2012, version record. The result and one sentence of the abstract, quoted.
8. The KM3NeT Collaboration, KM3NeT constraint on Lorentz-violating superluminal neutrino velocity, Communications Physics 8, 457, 11 November 2025, doi:10.1038/s42005-025-02347-z. Quoted as context, CC BY 4.0.

Every source was read at the address given, on 2026-09-22; version 2, the 2012 remeasurement and CERN's updates of 18 November 2011 and 16 March 2012 were added and read on 2026-09-23. The transcriptions, their SHA-256 hashes and the code that made them are listed with the verifier's notes. The verdict ARTEFACT, as of 2026-09-22, rests on sources 3, 6 and 7, with source 5 as the independent clock evidence.