The Clock That Feels a Centimetre: Optical Atomic Clocks and Measuring Time at the Quantum Limit

The Hook: A clock that notices when you lift it

Put one clock on the floor and another on the table. According to Einstein's general theory of relativity, the upper one runs faster, because it sits farther from the centre of the Earth and the gravitational potential there is slightly higher. The relative rate difference is quickly computed:

$$\frac{\Delta f}{f} = \frac{g\,h}{c^2}$$

With \(g \approx 9.81\ \mathrm{m/s^2}\) and \(c^2 \approx 8.99\cdot10^{16}\ \mathrm{m^2/s^2}\), a height difference of one centimetre yields a relative frequency difference of roughly \(1.1\cdot10^{-18}\). That is 1.1 parts in a billion billion — a number that for decades counted among the beautiful but practically inaccessible consequences of relativity.

It is no longer inaccessible. In February 2022, Jun Ye's group at JILA in Boulder published a measurement in which the gravitational redshift was resolved within a single cloud of ultracold strontium atoms — across a height difference of less than one millimetre. The relative measurement uncertainty of the frequency comparisons was \(7.6\cdot10^{-21}\), more than ten times better than anything before it. The atoms at the top of the cloud aged measurably faster than those at the bottom. Inside that cloud, time is no longer a shared coordinate but a local property that changes measurably over the thickness of a grain of rice.

Two years later the same group reached a systematic uncertainty of \(8\cdot10^{-19}\) with a strontium lattice clock, and in July 2025 NIST and JILA jointly reported a single-ion clock based on \(^{27}\mathrm{Al}^+\) at \(5.5\cdot10^{-19}\) — the nineteenth decimal place of a physical quantity, under control. For comparison: such a clock, running for the entire age of the universe, 13.8 billion years, would be off by less than a quarter of a second.

This article answers three questions. First: how do you build such a device — what is the physical trick that turns an atom into a clock? Second: how can anyone claim an uncertainty of \(5\cdot10^{-19}\) when there is no better clock to compare against? Third: what is it good for — beyond the trophy in the record table?

The third answer is the most surprising. Optical clocks long ago stopped being timekeepers. They are the most sensitive instrument physics possesses for potentials, fields and fundamental constants, and metrology is in the process of redefining the second on their basis.

Part 1: What a clock actually is

Oscillator and counter

Every clock in the world — pendulum clock, quartz wristwatch, atomic clock — consists of exactly two components. An oscillator that does something periodically, and a counter that adds up the periods. The pendulum swings, the gear train counts. The quartz crystal oscillates at 32,768 Hz; a divider halves it fourteen times and gets a one-second tick out of it.

The quality of the clock depends almost entirely on the oscillator, and specifically on two separate properties:

• Stability: does the frequency stay the same over time? A stable clock always runs the same way — even if it runs uniformly wrong.
• Accuracy (in metrological terms: trueness, the flip side of the systematic uncertainty): does the frequency agree with what it is supposed to be by definition?

This distinction is the thread running through the whole subject, and it is why the phrase "the most accurate clock in the world" is so often used incorrectly. A mechanical chronometer can be extremely stable and still be seconds per day off. An atomic clock is accurate precisely because its oscillator is a property of nature that you do not have to adjust and cannot misadjust.

Why atoms

A pendulum depends on the length of its rod, which expands with temperature. A quartz crystal depends on the shape into which it was cut, which ages. Every macroscopic component carries its manufacturing history inside its frequency.

An atom does not. The energy gap between two states of a \(^{133}\mathrm{Cs}\) atom is the same for every caesium atom in the universe, yesterday and today, in Braunschweig and in Boulder. Atoms have no manufacturing tolerance. And when an atom moves between two states separated by \(\Delta E\), the frequency of the associated radiation is fixed by \(f = \Delta E / h\) — an oscillator supplied by nature, not open to negotiation.

That is the core idea, proposed publicly by Isidor Rabi in 1945 and first realized at Britain's National Physical Laboratory in the 1950s.

The caesium second of 1967

In 1967 the 13th General Conference on Weights and Measures drew the consequence and cut the second loose from the rotation of the Earth. Since then:

The second is 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the \(^{133}\mathrm{Cs}\) nuclide.

That number is not a law of nature but a convention: it was chosen so the new second would match the old astronomical one as closely as possible. Since the SI revision of 2019 it is the defining constant of time, from which the metre (via \(c\)) and many other units are derived.

Modern caesium fountain clocks — in which a cloud of atoms is tossed vertically upwards and crosses a microwave cavity twice, on the way up and on the way down — reach relative systematic uncertainties around \(1\cdot10^{-16}\). That is excellent, and it is the end of the road. The limit is not a matter of craftsmanship; it is a matter of principle.

The jump into the optical: the quality factor

How precisely you can measure a frequency depends on the quality factor:

$$Q = \frac{f_0}{\Delta f}$$

that is, on the ratio of the carrier frequency to the width of the resonance line. The sharper the line at a given frequency, the more finely you can locate its centre. Intuitively: you read a ruler with millimetre markings more precisely than one with centimetre markings — not because millimetres are "better", but because there are more ticks per unit length.

This is where the entire leverage sits. The caesium resonance lies at 9.19 GHz, i.e. \(9.19\cdot10^9\) Hz. An optical transition lies at hundreds of terahertz:

That is four to five orders of magnitude more oscillations per second — four to five orders of magnitude more ticks on the ruler. At the same time, the optical transitions in use are extremely "forbidden": their natural linewidth sits in the millihertz range or below, because the excited state lives for seconds to years. In practice the linewidth is not limited by the atom but by the interrogation time (the Fourier limit) and by the purity of the interrogation laser.

That puts \(Q\) values beyond \(10^{15}\) within reach. This factor alone is why optical clocks beat the caesium fountain by two to three orders of magnitude.

And this factor was useless until 1999 — because nobody could count \(10^{14}\) oscillations per second.

Part 2: How you build an optical clock

An optical clock has four subsystems: an ensemble of cold atoms (or a single ion), an extremely pure interrogation laser, a servo loop that locks the laser to the atom, and a frequency comb that translates the optical frequency into a countable tick. Each of these was a Nobel-worthy development in its own right.

Holding the atoms still — and the problem with the trap

An atom flying freely through the apparatus produces Doppler shifts, and the recoil of individual photons smears the resonance further. So you cool it: first to microkelvin in a magneto-optical trap, then you hold it.

For neutral atoms such as strontium you use an optical lattice: two counter-propagating laser beams form a standing wave whose intensity maxima attract the atoms via the electric dipole interaction. The result is a chain of micro-traps, each holding one or a few atoms, frozen in place.

The catch: light strong enough to hold atoms shifts exactly the energy levels you want to measure. At typical trap depths the AC Stark effect (light shift) amounts to many kilohertz — which, relative to a line in the millihertz range, is a catastrophe.

The decisive trick came in 2003 from Hidetoshi Katori and colleagues: the magic wavelength. Ground and excited states have different polarizability spectra, and there exists a wavelength at which the lattice light shifts both states by exactly the same amount. Each level still moves, but their separation — the clock frequency — remains unchanged to first order. For \(^{87}\mathrm{Sr}\) that wavelength is around 813 nm. What remains are higher-order effects (hyperpolarizability, multipole terms), and a substantial part of today's progress hangs on modelling them: the \(8\cdot10^{-19}\) of Aeppli and colleagues in 2024 rests largely on a new, more precise treatment of the lattice light shift.

This is a recurring pattern in metrology: you eliminate a perturbation not by making it small, but by finding an operating point at which its derivative vanishes.

The interrogation laser: quieter than the atom

The atom can only serve as a reference as well as the laser used to interrogate it is pure. An off-the-shelf diode laser has a linewidth of megahertz — probing a millihertz line with it is like trying to hit the centre of a hair with a sledgehammer.

So you stabilize the laser to an optical cavity, a space between two mirrors whose length pins the frequency. The limit here is the thermal noise of the mirrors and the spacer: the atoms of the material jitter, the cavity length fluctuates, and the frequency with it. The way out is colder, stiffer material. Thomas Legero, Uwe Sterr and colleagues at PTB Braunschweig went to single-crystal silicon at cryogenic temperatures and in 2017 achieved lasers with a linewidth below 10 millihertz at 1.5 µm. Newer cavities of this design reach instabilities in the low \(10^{-17}\) range.

This point matters so much in practice that the record aluminium clock of 2025 does not even own its interrogation laser: the stability is piped in from another laboratory, from a cryogenic silicon cavity over a 3.6 km optical fibre. Only that makes a Rabi interrogation time of a full second possible — and one second of interrogation means, by the Fourier limit, a linewidth of about one hertz at 1.121 PHz, i.e. \(Q \approx 10^{15}\).

The gearbox: the frequency comb

Here lies the problem that delayed the optical clock by half a century. Electronics can count gigahertz. Nobody can count \(4\cdot10^{14}\) zero crossings per second. Without a translation from the optical to the electronic domain, an optical resonance is a very sharp line out of which you cannot make a second.

The solution is the optical frequency comb, developed around 1999/2000 by John Hall at NIST/JILA and Theodor Hänsch at MPQ Garching, and honoured with the 2005 Nobel Prize in Physics. A mode-locked femtosecond laser produces a pulse train; its spectrum is not a single line but a comb of hundreds of thousands of equally spaced lines, whose frequencies obey a remarkably simple formula:

$$f_n = n\, f_{\text{rep}} + f_{\text{ceo}}$$

\(f_{\text{rep}}\) is the laser's repetition rate (a few hundred megahertz — countable electronically), \(f_{\text{ceo}}\) the carrier-envelope offset (likewise measurable and stabilizable), and \(n\) a large integer. Know \(f_{\text{rep}}\) and \(f_{\text{ceo}}\), and you know every comb line exactly.

The comb is therefore a gearbox with an exactly integer gear ratio. It transfers precision from the optical into the radio-frequency domain without loss — and back again. It is also the instrument with which you can measure ratios of two optical clocks without declaring either one the reference; that detail becomes important in Part 5.

The single-ion variant

Alongside lattice clocks with tens of thousands of neutral atoms there are single-ion clocks. A charged ion can be held essentially indefinitely in one place in a Paul trap using oscillating electric fields, isolated from everything.

\(^{27}\mathrm{Al}^+\) is physically the most beautiful candidate: its clock transition responds unusually weakly to electric fields and to blackbody radiation, which makes two of the largest budget items of other clocks nearly disappear. The drawback: the ion has no convenient transition with which to cool it or read it out — metrologically speaking, it is an excellent witness who does not speak.

The solution is quantum logic spectroscopy, developed by David Wineland and colleagues (Nobel Prize in Physics 2012, shared with Serge Haroche): you put a second ion, at NIST \(^{25}\mathrm{Mg}^+\), into the same trap. Through the shared motional mode of the pair — they sit as a coupled unit in the same potential well — the magnesium ion cools the aluminium ion along with itself, and the aluminium's state is transferred to the magnesium and read out there. The logic ion works as an interpreter. Exactly this architecture sits inside the clock with \(5.5\cdot10^{-19}\).

Part 3: The uncertainty budget — where the nineteenth digit comes from

The question you have to ask first

When someone claims their clock is accurate to \(5.5\cdot10^{-19}\), the obvious follow-up is: compared to what? There is no better clock. You cannot substantiate the claim by measuring against a reference, because the reference would itself be the question.

Metrology's answer is radically different from what one is used to in software. Accuracy is not measured; it is itemized. You enumerate exhaustively which physical effects can shift the atom's frequency away from the ideal, unperturbed, stationary atom, determine each individual effect as well as you can, correct it out, and record the residual uncertainty of that correction. The sum of these residuals — added in quadrature — is the clock's systematic uncertainty. The document that results is called the uncertainty budget, and it is the actual scientific product. A clock without a budget is an oscillator, not a clock.

The line items

Two things stand out in this list.

First: several items are relativistic. The clock is so sensitive that the laboratory's height above sea level is a serious correction term — \(1.1\cdot10^{-16}\) per metre of height, i.e. more than a hundred times the entire uncertainty of the best clocks. Comparing two clocks at different locations necessarily means knowing the gravitational potential at both. That is not merely a nuisance; it is one of the eight mandatory items on the road to the new second (see Part 5).

Second: the biggest advances come not from better components but from understanding an item that had previously been bounded by a blanket estimate. In 2025 the central step for the aluminium clock was to measure, direction-resolved, the oscillating magnetic field produced by the trap drive — turning a conservatively estimated upper bound into a concrete correction with a small residual uncertainty. That is not a hardware upgrade. That is insight, converted directly into a digit.

Stability: the second budget

Alongside trueness stands stability, usually quoted as the Allan deviation \(\sigma_y(\tau)\) versus averaging time \(\tau\). For white frequency noise it falls as \(1/\sqrt{\tau}\): average a hundred times longer and the statistical uncertainty shrinks tenfold.

The 2025 aluminium clock achieves \(3.5\cdot10^{-16}/\sqrt{\tau/\mathrm{s}}\). Work that through and it needs roughly \(4\cdot10^5\) seconds — about five days — to average down statistically into the range of its own systematic uncertainty. That is why stability matters so much: it does not determine how good a clock can be, but how long you must measure to demonstrate it. Every factor of two in stability saves a factor of four in measurement time, and with apparatus that doctoral students realign daily, measurement time is the scarcest resource of all.

Part 4: The Standard Quantum Limit — and how to beat it

There is a limit to stability that depends not on technology but on quantum mechanics itself.

You interrogate \(N\) atoms simultaneously. Each atom is ultimately projected into one of two states — excited or not. Which atom comes out which way is, for a superposition, random. The outcome is therefore a binomial experiment, and as in any ensemble of coin flips, the fraction scatters by \(1/\sqrt{N}\). This quantum projection noise sets the Standard Quantum Limit (SQL):

$$\sigma_y \propto \frac{1}{Q\sqrt{N}}\cdot\frac{1}{\sqrt{\tau/T_c}}$$

It is the analogue of shot noise and holds for all clocks whose atoms are independent of one another. You can improve it with more atoms — but only as the square root, and more atoms mean more collisional shift, i.e. a worse budget on the other side of the ledger.

Quantum mechanics does, however, leave a back door open. If the atoms are entangled, the independence assumption no longer holds. For maximally entangled states the limit extends all the way to the Heisenberg limit \(\propto 1/N\) — a quadratic improvement. The practicable route there is spin squeezing: you take uncertainty away from the phase direction you want to measure and push it into the direction you do not need. This is typically generated by a quantum non-demolition (QND) measurement through an optical cavity: the light acquires a phase shift that depends on the total excitation, and measuring that phase correlates the atoms without revealing their individual states.

For a long time, squeezing was an effect demonstrated in experiments of moderate baseline precision — not in a clock that was already world-leading. That changed in 2025. Y. A. Yang and colleagues at JILA split about 30,000 strontium atoms into two spin-squeezed ensembles and compared them synchronously. The result: 2.0(2) dB below the Standard Quantum Limit — and, more important than the decibels, a precision of \(1.1\cdot10^{-18}\) for a single squeezed clock at 61 ms interrogation time. Entanglement has thereby become, for the first time, a tool inside precision metrology rather than beside it.

The caveat stands: 2 dB is a factor of 1.26 in amplitude. The decoherence of the squeezed state grows with interrogation time, and long interrogation time is precisely the strength of optical clocks. I am of the opinion that over the next few years squeezing will pay off mainly where short interrogation times are technically enforced — in transportable clocks, say, and in clocks searching for fast signals — and not as a general replacement for unentangled operation.

Part 5: What it is good for

The redefinition of the second

The second is currently defined via caesium, and the best caesium clocks are two to three orders of magnitude worse than the best optical clocks. That is an untenable situation: an optical clock cannot state its own frequency more accurately than the unit it is supposed to state it in. You are measuring a micrometre with a folding ruler.

The International Bureau of Weights and Measures (BIPM) therefore runs a roadmap towards redefinition, set up in 2017 by the Consultative Committee for Time and Frequency (CCTF), revised by a task force in 2020, and published in 2023 as a review article by Noël Dimarcq, Sébastien Bize and colleagues. The roadmap names eight mandatory criteria in three groups:

1. Frequency standards and their contribution to time scales — defensible uncertainty budgets; validation of those budgets through frequency ratios between independent clocks; demonstrated continuity with the caesium second; regular contributions of optical standards to International Atomic Time (TAI).
2. Comparison and dissemination techniques — sustainably available methods for comparing optical standards; knowledge of the local geopotential at adequately small uncertainty.
3. Acceptability of the new definition — a definition that permits more accurate realizations in the future; practical access to that realization for the national metrology institutes.

The timeline as of 2025: the 2026 General Conference reviews progress and may resolve to aim the work at a proposal for 2030; the CCTF assesses the criteria in 2028 and shortlists a proposal in 2029; the 2030 General Conference decides — but only given consensus and fulfilled mandatory criteria.

The interesting question is what gets defined. Two options are essentially on the table: a single optical transition as the new anchor, or a weighted geometric mean of several transitions. The first is conceptually clean, but it crowns one species as a monopolist and penalizes every institute that bet on another. The second is more robust — if one species drops out through a previously unknown systematic error, the unit does not break — but it turns the definition into a convention requiring continuous maintenance. Both options have a property any software architect will recognize instantly: it is the choice between a single source of truth and a quorum.

Frequency ratios: validation without a reference

Because there is no superior reference, the ratio of two clock frequencies is the field's real currency. A ratio is dimensionless; it does not need the second. And it has a property that makes it the whole system's self-check: ratios must be consistent around closed loops. Measure \(A/B\), \(B/C\) and \(C/A\), and the product of the three must be exactly one. Any deviation is an undiscovered systematic error in at least one of the three clocks.

In 2025 this principle became the largest coordinated experiment in time metrology so far: Thomas Lindvall, Marco Pizzocaro, Rachel Godun and some sixty further authors compared ten optical clocks in six countries simultaneously, connected by fibre links and by satellite links, and reported 38 optical frequency ratios, four of them measured directly for the first time. What matters is not only the number of ratios but the treatment of their correlations: when two ratios share a clock or share a link, their errors are not independent, and a naive combination would underestimate the uncertainty.

The fibre links are an achievement in their own right. With active noise cancellation, optical frequencies can now be transferred over roughly a thousand kilometres without the transfer dominating the uncertainty. Satellite links are worse, but they work across oceans — and without transatlantic comparisons there is no worldwide unit.

Chronometric levelling: clocks as altimeters

Turn the relativistic correction around and the perturbation becomes a measurement technique. If the rate difference of two clocks depends on the gravitational potential, and you know the clocks, then you are measuring the geopotential — which is exactly the quantity geodesists actually mean when they speak of "height above sea level".

Reading the calculation from the beginning of this article backwards: an uncertainty of \(1\cdot10^{-18}\) corresponds to about one centimetre of height uncertainty. Classical methods — geometric levelling over hundreds of kilometres — accumulate errors over long distances, and tying together the height systems of different continents across oceans is a notoriously hard problem. A transportable optical clock delivers the local potential point by point and absolutely, without a chain of intermediate benchmarks. The method is called chronometric levelling, and it is telling that the BIPM roadmap lists it not as an application but as a mandatory criterion: without sufficiently well-known geopotentials the clocks cannot be compared, and without clock comparisons there is no new second.

Fundamental physics: constants, dark matter, nuclear clocks

Different clock transitions depend to different degrees on the fine-structure constant \(\alpha\). Repeat a ratio measurement \(A/B\) over years, therefore, and any drift of \(\alpha\) shows up as a drift of the ratio — without your ever needing to know an absolute frequency. The same principle applies to models of ultralight dark matter: if a scalar field couples to the electron mass or to \(\alpha\), clock frequencies oscillate at a frequency set by that field's mass. A network of synchronized clocks is thereby a detector for something no particle detector sees.

The logical escalation is the nuclear clock. Almost all nuclear transitions lie between kiloelectronvolts and megaelectronvolts — unreachable for lasers. One known exception is the isomeric state of \(^{229}\mathrm{Th}\), which sits only about 8 eV above the ground state and is therefore accessible in the vacuum ultraviolet. In September 2024, Chuankun Zhang, Tian Ooi, Jun Ye and colleagues published in Nature the direct excitation of this nuclear transition with a VUV frequency comb in a calcium fluoride crystal and — decisively — the measurement of its frequency ratio to the \(^{87}\mathrm{Sr}\) atomic clock. A nuclear transition was thereby tied into the metrological infrastructure for the first time.

The physical appeal lies in the sensitivity. Nuclear levels arise from a near-complete cancellation between the electromagnetic and the strong interaction; a small relative change in the underlying constants shifts the gap disproportionately. A nuclear clock would therefore not be a substantially better timekeeper, but a detector for new physics that is orders of magnitude more sensitive. And because the nucleus is a thousand times smaller than the electron shell, it responds far more weakly to external fields — solid-state nuclear clocks may even become possible, with \(10^{14}\) nuclei at once instead of a single ion.

Everyday life: where the precision actually lands

One should be honest here: no application needs \(10^{-19}\). What applications need is for that precision to be inherited downwards. Satellite navigation is at heart a time measurement — a one-nanosecond error in a satellite clock is thirty centimetres of position error. The very-long-baseline interferometry of radio astronomy, which the Event Horizon Telescope relies on, demands clocks at every station that stay coherent over the observation. International Atomic Time (TAI), from which UTC and therefore every timestamp in the world is derived, is a weighted average over hundreds of clocks; regular contributions by optical standards are a mandatory criterion of the roadmap precisely because they improve world time directly.

And in distributed systems the difference between stability and trueness feeds straight into architecture: Google's Spanner turns the uncertainty of clock synchronization into an explicit interval and waits it out, instead of trusting timestamps that have not earned it.

Frameworks Worth Keeping

The Central Takeaway

The transferable lesson of optical clocks is not "precision is achievable". It is: a claim about accuracy is worthless without an itemized error budget — and the budget is the work.

Metrology had to earn this discipline because the comfortable route is closed to it. For the best clock in the world there is no better clock to hold it against. So all that remains is: name every effect, quantify every effect separately, record every correction with its residual uncertainty, and book nothing under "miscellaneous". And then — this is the second half of the discipline — make the claim externally checkable, through ratios and closed loops whose consistency nobody can fake.

Two concrete things follow for your own work.

First, separate stability from trueness. A system that reproducibly delivers the same result is not thereby correct. A pipeline that produces the same report every day, a latency measurement with a tight percentile band, a forecast with a narrow confidence interval — all of that is stability. Trueness lives in the systematic offsets: in the time zone that is consistently assumed wrong, in the filter that silently drops records, in the monitoring that cannot see the cases in which it itself has failed. Reproducibility conceals these errors; it does not cure them.

Second, keep a budget instead of a number. Anyone quoting a latency bound, a cost forecast or an availability commitment should be able to write down the line items individually — each with its own uncertainty and a note on how it was determined (measured, estimated, from the literature, conservative upper bound). The benefit is not the total, which you rarely need anyway. The benefit is that you see immediately which item dominates — and therefore where work pays off and where it is wasted. The aluminium clock did not improve in 2025 through better hardware; it improved because a single conservatively estimated item was replaced by a real measurement. A budget gives you that information; a single number never will.

The practical prompt: take the most important accuracy or performance commitment you currently stand behind, and write it out as a table of items, contribution, uncertainty and provenance. If one item contributes more than half of the total and its provenance reads "estimated", you have found your next task.

Cross-References in the Vault

This topic hangs on several articles already covered. The distinction between stability and trueness — and what it costs to take uncertainty seriously rather than ignore it — is exactly the architectural decision behind Clocks That Know Their Own Uncertainty: Google Spanner, TrueTime, and Mastering Time in the Cloud; how to do without synchronized clocks altogether and order only causality instead is shown in Order Without a Clock: Lamport Timestamps, Vector Clocks, and Causality in Distributed Systems. That a unit becomes dependable only once it follows from a law of nature rather than from an artefact can be read in the story of the resistance standard, The Most Exact Number in Physics: The Quantum Hall Effect and the Topology of Matter — and in its historical variant, when ships were still at stake, in The Clock That Measured the Ocean: John Harrison, the Longitude Problem, and How a Carpenter Saved Navigation. The entanglement that makes the spin squeezing of Part 4 possible is the subject of Spooky Action at a Distance: Quantum Entanglement from Einstein to the Quantum Internet and The Wager Against Reality: Bell's Theorem and the End of Local Realism; why entangled states decay so quickly and thereby limit the interrogation time is explained in Why the World Turns Classical: Decoherence, Einselection, and Quantum Darwinism. That entanglement can also be deployed against noise rather than only against projection noise is shown in Order from Noise: Quantum Error Correction and the Road to a Fault-Tolerant Quantum Computer. Astronomical clocks of an entirely different construction, which also survey spacetime, are the pulsars of The Clocks Made of Neutrons: Pulsars, Pulsar Timing Arrays, and the Hum of Spacetime. And that a discrepancy between two measurement methods for the same quantity can be physics' most productive problem is the story of The Cosmic Tension: Why the Universe Seems to Have Two Rates of Expansion.

Something to Think About

Metrology claims an accuracy of \(5.5\cdot10^{-19}\) without possessing a superior reference — purely through a fully itemized error budget and through closed loops between instruments of equal rank, loops that cannot be consistent if one of them is wrong.

Which number in your own work do you currently quote with a confidence drawn only from reproducibility — and not from being able to name and justify every line item separately? And what "closed loop" could you build to refute yourself, without waiting for a reference that does not exist?

Sources

• A. Aeppli, K. Kim, W. Warfield, M. S. Safronova, J. Ye, "Clock with \(8\times10^{-19}\) Systematic Uncertainty", Physical Review Letters 133 (2024), 023401, DOI 10.1103/PhysRevLett.133.023401: https://www.nist.gov/publications/clock-8-x-10-19-systemic-uncertainty
• M. C. Marshall, D. A. Rodriguez Castillo, W. J. Arthur-Dworschack, A. Aeppli, K. Kim, D. Lee, W. Warfield, J. Hinrichs, N. V. Nardelli, T. M. Fortier, J. Ye, D. R. Leibrandt, D. B. Hume, "High-Stability Single-Ion Clock with \(5.5\times10^{-19}\) Systematic Uncertainty" (2025), DOI 10.1103/hb3c-dk28, arXiv:2504.13071: https://arxiv.org/abs/2504.13071
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• Y. A. Yang, M. Miklos, Y. M. Tso, S. Kraus, J. Hur, J. Ye, "Clock Precision beyond the Standard Quantum Limit at the \(10^{-18}\) Level" (2025), DOI 10.1103/6v93-whwq, arXiv:2505.04538: https://arxiv.org/abs/2505.04538
• T. Lindvall, M. Pizzocaro, R. M. Godun et al. (65 authors), "Coordinated international comparisons between optical clocks connected via fiber and satellite links", Optica (2025), DOI 10.1364/OPTICA.561754, arXiv:2505.06763: https://arxiv.org/abs/2505.06763
• C. Zhang, T. Ooi, … J. Ye, "Frequency ratio of the \(^{229m}\)Th nuclear isomeric transition and the \(^{87}\)Sr atomic clock", Nature 633 (2024), 63–70, DOI 10.1038/s41586-024-07839-6: https://www.nature.com/articles/s41586-024-07839-6
• N. Dimarcq, M. Gertsvolf, G. Mileti, S. Bize et al., "Roadmap towards the redefinition of the second", Metrologia (Review, Open Access), arXiv:2307.14141 — contains the eight mandatory criteria in Table 4: https://arxiv.org/pdf/2307.14141
• BIPM, "FAQ – Redefinition of the second" (as of version 2.2, October 2026): timeline with CGPM 2026, CCTF 2028/2029 and the 2030 decision, plus the definition options: https://www.bipm.org/en/faq-redefinition-second
• H. Katori, M. Takamoto, V. G. Pal'chikov, V. D. Ovsiannikov, "Ultrastable Optical Clock with Neutral Atoms in an Engineered Light Shift Trap", Physical Review Letters 91 (2003), 173005, arXiv:physics/0309043 — the magic wavelength: https://arxiv.org/abs/physics/0309043
• D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, U. Sterr, "1.5 µm Lasers with Sub-10 mHz Linewidth", Physical Review Letters 118 (2017), 263202, DOI 10.1103/PhysRevLett.118.263202: https://link.aps.org/accepted/10.1103/PhysRevLett.118.263202
• Nobel Prize in Physics 2005 (J. L. Hall, T. W. Hänsch, for laser-based precision spectroscopy including the optical frequency comb technique): https://www.nobelprize.org/prizes/physics/2005/summary/
• Nobel Prize in Physics 2012 (S. Haroche, D. J. Wineland, for methods to measure and manipulate individual quantum systems): https://www.nobelprize.org/prizes/physics/2012/summary/

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