What Happened
Physics · Metrology · Particle Physics · Standard Model · History of Science · Explainerstate of the record to 31 August 2026 · CODATA 2022 is the standing set
Measured to 0.13 parts per trillion · and unable to sharpen the test it was made for
The Electron, to Thirteen Digits
No property of any elementary particle is known as precisely as the electron’s magnetic moment: thirteen digits, measured at Northwestern in 2023 and published as a test of the Standard Model to one part in a trillion. Its charge is not measured at all — since 20 May 2019 it is a defined constant of the SI, fixed by convention. And yet the sharpest test physics has cannot be sharpened further, because two experiments measuring a different constant disagree with each other by more than five standard deviations, and nobody can say which is wrong. This is what the electron is in 2026: specified to more decimal places than almost anything else, and, in matter, capable of behaving as though it had come apart into thirds.
The figures Each read from a published record that anyone can fetch: NIST’s constants table, BIPM, and the papers themselves
- 0.13 pptthe precision of the measured electron magnetic moment — the most precisely determined property of any elementary particle
- exactthe elementary charge since 20 May 2019. It is no longer measured; it is one of the seven constants that define the SI
- 5.5σbetween the two best measurements of the fine-structure constant, caesium against rubidium — the gap that stops the electron test from getting sharper
- 98Feynman diagrams, out of 389 parts, that carried an error in the theory’s most precise prediction from 2018 until February 2025
- 0times the word electron appears in J. J. Thomson’s 1897 paper. He wrote corpuscle, seventeen times
What is established, and how firmly Sorted by standing, not by importance. The first column is the grade
| Standing | What | How it was checked |
|---|---|---|
| Confirmed | Since 20 May 2019 the elementary charge is fixed at exactly 1.602176634×10⁻¹⁹ C, one of seven constants defining the SI. The vacuum magnetic permeability, formerly exact, now carries an uncertainty | BIPM’s own list of the defining constants; the CODATA 2022 table published by NIST |
| Confirmed | The electron magnetic moment is g/2 = 1.00115965218059(13), a precision of 0.13 parts per trillion — 2.2 times better than the value that had stood for 14 years, and a test of the Standard Model to one part in 10¹² | Fan, Myers, Sukra and Gabrielse, Physical Review Letters 130, 071801 (2023), read at arXiv |
| Confirmed | Two atom-recoil measurements of the fine-structure constant disagree: 137.035999046(27) from caesium, 137.035999206(11) from rubidium. The rubidium paper says plainly that its value differs by more than five standard deviations from the caesium result | Parker and others, Science 360, 191 (2018); Morel and others, Nature 588, 61 (2020). Both abstracts read |
| Confirmed | A five-loop coefficient in the theory was wrong from 2018 until February 2025. A second group computing the same integrals a different way disagreed by 4.8 standard deviations; the difference was traced to 98 diagrams out of 389 parts, and the revised value is 6.800(128) | Volkov, Physical Review D 100, 096004 and 110, 036001; Aoyama, Hayakawa, Hirayama and Nio, Physical Review D 111, L031902 (2025) |
| Confirmed | No substructure has been found. Excited-electron masses below 4.8 TeV are excluded where the compositeness scale equals that mass, and the scale is bounded above 11 TeV for masses under 0.5 TeV | ATLAS Collaboration, European Physical Journal C 79, 803 (2019), 36.1 fb⁻¹ at 13 TeV |
| Confirmed | The coupling that gives the electron its mass has never been measured. The best limit on the Higgs boson decaying to an electron pair is 3.0×10⁻⁴, which allows a coupling up to 240 times the Standard Model value | CMS Collaboration, Physics Letters B 846, 137783 (2023), 138 fb⁻¹; the paper’s own bound on the coupling modifier |
| Confirmed | The electron is stable. For decay into a neutrino and a single photon the lower limit on its lifetime is 6.6×10²⁸ years, two orders of magnitude better than the previous bound | Borexino Collaboration, Physical Review Letters 115, 231802 (2015), at 90% confidence |
| Confirmed | No electric dipole moment has been detected. The bound is 4.1×10⁻³⁰ e·cm — or 4.5×10⁻³⁰ under the statistical prescription the previous experiment used. The paper states both | Roussy and others, Science 381, 46 (2023), full text read |
| Confirmed | Thomson’s 1897 paper never uses the word electron, and says outright that the experiment cannot tell whether the mass is small or the charge large. What it establishes is a ratio a thousand times smaller than any known | The Philosophical Magazine paper read in full, in transcription; word counts taken by script over that text |
| Confirmed | Inside matter, charge fractionalises with no magnetic field at all. Pentalayer graphene shows quantised plateaux at seven filling factors: 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 | Lu, Han, Yao and others, Nature 626, 759 (21 February 2024) |
| Confirmed, not verifiable here | CODATA 2022 is the standing recommended set and was published on 30 April 2025. The next adjustment closes to new data on 31 December 2026 | The citation resolves and the deadline notice is on NIST’s own page. The 2025 review article’s text was not read; its values were taken from NIST’s published table instead |
| Confirmed, not verifiable here | In heavy-fermion metals the conduction electrons behave as though their mass were far larger than the free value | The 1975 paper on CeAl₃ resolves as cited (Physical Review Letters 35, 1779), but its text was not read, so no multiple is quoted here |
| Unconfirmed | When the word electron entered use, who coined it, and what it first meant. It was in circulation before Thomson’s corpuscle and denoted something else | No record reachable in this work establishes the date, the person or the publication. It is left as a gap rather than filled |
The electron, as specified The recommended values, CODATA 2022, with the relative uncertainty each one carries.
| Quantity | Value | Relative uncertainty |
|---|---|---|
| Electric charge | −1.602176634×10⁻¹⁹ C | exact, by definition |
| Spin | ½ | exact, by definition |
| g-factor | −2.00231930436092(36) | 1.8×10⁻¹³ |
| Magnetic moment anomaly | 1.15965218046(18)×10⁻³ | 1.6×10⁻¹⁰ |
| Mass in the unified atomic mass unit | 5.485799090441(97)×10⁻⁴ u | 1.8×10⁻¹¹ |
| Mass relative to the proton | 5.446170214889(94)×10⁻⁴ | 1.7×10⁻¹¹ |
| Mass | 9.1093837139(28)×10⁻³¹ kg | 3.1×10⁻¹⁰ |
| Mass energy equivalent | 0.51099895069(16) MeV | 3.1×10⁻¹⁰ |
| Compton wavelength | 2.42631023538(76)×10⁻¹² m | 3.1×10⁻¹⁰ |
| Charge-to-mass quotient | −1.75882000838(55)×10¹¹ C/kg | 3.1×10⁻¹⁰ |
And the same electron, where the record runs out Six properties with no measured value. Each has a bound instead, and a bound is a number plus a convention.
| Property | Where it stands | The bound, and who set it |
|---|---|---|
| Whether it ever decays | Never observed. The limit is about 4.8×10¹⁸ times the present age of the universe, which is not the same statement as “it is stable”. | Mean life > 6.6×10²⁸ years at 90% confidence, for the channel to a neutrino and a photon — Borexino, 2015. |
| Electric dipole moment | Consistent with zero. A value above the bound would be physics the Standard Model does not contain. | Less than 4.1×10⁻³⁰ e·cm at 90% confidence — Roussy and colleagues, 2023; 4.5×10⁻³⁰ under the prescription the earlier ACME measurement used. |
| Whether it is made of anything | No evidence of substructure. The searches look for an excited state, and none has appeared. | Compositeness scale above 11 TeV for an excited electron lighter than 0.5 TeV — ATLAS, 2019, from 36.1 fb⁻¹ at 13 TeV. |
| Its size | No radius has ever been measured. It is point-like to the limit of every search above, and that is a ceiling on its extent rather than a value for it. | None. The classical electron radius, 2.8179403205(13)×10⁻¹⁵ m, is a combination of other constants that CODATA lists as derived — it is not an extent, and nothing has been measured at that scale. |
| The coupling that gives it its mass | Never measured. The only direct probe is a Higgs decay the Standard Model expects to be dominated by diagrams that do not contain the coupling at all. | Branching fraction to an electron pair below 3.0×10⁻⁴ at 95% confidence, which allows the coupling to be up to 240 times its Standard Model size — CMS, 2023. |
| The constant its magnetic moment is tested against | Two independent measurements of the fine-structure constant disagree with each other by far more than either one's stated uncertainty. It is this, and not the precision of the electron measurement, that limits the most exacting test in physics. | No bound — a disagreement. The caesium and rubidium values are set side by side in section three. |
Timeline
Nearly a hundred and thirty years of the same object Every entry is a dated publication, and every citation below resolves to the volume and pages given
- 1897J. J. Thomson measures the mass-to-charge ratio of cathode rays and finds 10⁻⁷ against 10⁻⁴ for the hydrogen ion. He calls the carrier a corpuscle and states that the result cannot say whether the mass is small or the charge large
- Aug 1913R. A. Millikan publishes the first direct measurement of the elementary charge, in Physical Review 2, 109
- Dec 1926Schrödinger’s wave mechanics reaches Physical Review. The electron becomes a wavefunction, and orbits become orbitals
- Dec 1927Davisson and Germer diffract electrons off a nickel crystal. The particle behaves as a wave in the laboratory
- 1 Feb 1928Dirac publishes the relativistic equation. Spin one-half and g = 2 fall out of the mathematics rather than being put in
- Aug 1947Lamb and Retherford find a splitting between two hydrogen levels that Dirac theory says should coincide
- Aug 1948Kusch and Foley measure a magnetic moment that is not exactly g = 2. The gap between 2 and what is measured becomes the most computed number in physics
- 31 May 1982Tsui, Störmer and Gossard observe the fractional quantum Hall effect; Laughlin explains it a year later with fractionally charged excitations
- 6 Jul 1987Van Dyck, Schwinberg and Dehmelt compare the g-factors of the electron and the positron in a Penning trap — the benchmark test of CPT symmetry in the lepton sector
- 20 May 2019The SI is redefined. The elementary charge stops being a measured quantity and becomes a defined one; the uncertainty moves elsewhere
- 17 Sep 2019Sergey Volkov posts an independent five-loop calculation. It disagrees with the standing value by 4.8 standard deviations, and the disagreement will stand for five years
- 2023Fan, Myers, Sukra and Gabrielse measure g/2 to 0.13 parts per trillion, 2.2 times better than the value that had stood since 2008
- Jun–Aug 2023Fractional quantum anomalous Hall states are observed in twisted molybdenum ditelluride — fractional charge with no external magnetic field at all
- 7 Jul 2023A JILA group tightens the bound on the electron’s electric dipole moment by a factor of about 2.4, using electrons held inside molecular ions for up to three seconds
- Oct 2023The Nobel Prize in Physics goes to Agostini, Krausz and L’Huillier “for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter”
- 21 Feb 2024The same effect appears in rhombohedral pentalayer graphene, at seven different filling factors and still at zero field
- 2 Aug 2024Volkov publishes the complete five-loop contribution. The disagreement is now stated at five standard deviations and still unexplained
- 25 Feb 2025Aoyama, Hayakawa, Hirayama and Nio split the contribution into 389 parts, find the differences of 98 diagrams are not randomly distributed, recompute those with more statistics, and the discrepancy closes
- 30 Apr 2025CODATA 2022 is published in Reviews of Modern Physics. It is the standing recommended set for the electron’s properties
- 31 Dec 2026The data-closing date for the next CODATA adjustment. Anything not published or posted as a preprint by then waits for the one after
What will not go on a timeline Three things a chronology cannot hold, for three different reasons
The oldest thing here is among the best evidenced, and that is an accident. Thomson’s 1897 paper can be read end to end and counted; Millikan’s 1913 paper, sixteen years newer, could not be opened at all for this piece, so nothing is quoted from it and no figure of his is repeated. What decides is not age but whether somebody put the text where a reader can reach it.
The naming cannot be placed anywhere. The word electron was in use before Thomson called his carrier a corpuscle, and it did not mean a particle. That much follows from his own paper, which never uses it. Who introduced it, in what year, and for what — none of that could be established from any record reachable here, so it is absent above rather than approximated. It is the most interesting hole in this account: the object acquired its name from a different idea, and the handover is undocumented on this page.
The interpretational question has no date because it has no resolution. Whether the wavefunction is knowledge, an objectively branching world, a pilot wave, or an agent’s belief is not settled by any measurement in the list above, and no source read for this article bears on it. The mathematics is agreed. What the mathematics is about is not, and has not been for a century.
- 1897readable in full today; the 1913 paper was not
- ?the year the word entered use, and for what
- 100years since wave mechanics, and the question is still open
The Argument
Precision is not the constraint What the 2023 measurement can and cannot do, in the words of the people who made it
The Northwestern group states the position themselves. Their measurement, they write, is “the most precisely determined property of an elementary particle” and it “tests the most precise prediction of the Standard Model to 1 part in 10¹²”. Then, in the same abstract: the test “would improve an order of magnitude if the uncertainty from discrepant measurements of the fine structure constant α is eliminated”.
That sentence is the whole of it. The Standard Model’s prediction for the electron’s magnetic moment is a function of α, so the comparison is only ever as good as the independent value of α put into it. Two atom-recoil experiments have measured α to better than a part in 10⁹, and they do not agree. The gap is in the tenth significant figure and it is larger than either team’s stated uncertainty. Neither group attributes it to caesium against rubidium; both treat it as an unidentified systematic somewhere.
The consequence is visible in the published constants and is easy to walk past. The recommended value of α carries a relative uncertainty of 1.6×10⁻¹⁰ — about twice the uncertainty of the single best measurement of it. The most carefully determined number in physics is quoted less precisely than it has been measured, because two measurements of it disagree and nobody can show which is wrong. That comparison is this article’s own arithmetic over the published figures, not a claim any of the sources makes.
- 1 in 10¹²how sharply the measurement tests the Standard Model today
- 10×how much sharper it would be if the two α values agreed
- 2×worse than the best single measurement, in the recommended value of α
The two measurements, side by side Both are recoil measurements on a cold atom; the difference is which atom
| Source | Inverse fine-structure constant | Relative uncertainty |
|---|---|---|
| Caesium recoil, 2018 | 137.035999046(27) | 2.0×10⁻¹⁰ |
| Rubidium recoil, 2020 | 137.035999206(11) | 81 ppt |
| Implied by the 2023 g/2 measurement plus theory | 137.035999166(15) | 0.11 ppb |
| CODATA 2022 recommended | 137.035999177(21) | 1.6×10⁻¹⁰ |
And the theory had an error in it for five years Found by a second person computing the same integrals a different way
The prediction the measurement is compared against runs to five loops. In 2019 Sergey Volkov computed the five-loop graphs without lepton loops and got 6.793(90), where the standing value was 7.668(159) — 4.8 standard deviations apart. In 2024 he completed the total and the gap was restated at five standard deviations. Neither result told anybody where the difference was.
The resolution came in February 2025, and the method is the interesting part. Aoyama, Hayakawa, Hirayama and Nio decomposed the contribution into 389 parts so the two calculations could be compared diagram by diagram. No individual diagram was significantly off. But the differences for 98 diagrams that share a common structure were not randomly distributed — they leaned one way, and it was their accumulation that made five standard deviations. Recomputing those 98 with more Monte Carlo statistics gave 6.800(128), which agrees with Volkov to within a twentieth of a standard deviation.
Two numbers that are not the same number. The revised 6.800 replaces 7.668 and is the sum over diagrams without fermion loops. Volkov’s 5.891 is the total five-loop contribution — a different sum. Set side by side as though they were one quantity, the resolution reads as an arithmetic mistake; kept apart, it reads as what it was, which is the field’s error-correcting machinery working exactly as intended, slowly, and in public.
- 389parts the contribution was split into, so the two calculations could be compared
- 98of them leaned the same way; no single one was significantly wrong
- 5 yrbetween the first disagreement and its cause being found
What Others Add
Four other places the electron is being pressed None of them is about precision, and each one asks a different question about what the thing is
1982 → 2024 · condensed matter
Inside matter it comes apart
- The fractional quantum Hall effect was seen in 1982 and explained in 1983 with excitations carrying a fraction of the electron charge — the supposedly indivisible unit, behaving as though split
- Since 2023 the same fractionalisation happens with no external magnetic field at all: first in twisted molybdenum ditelluride, then in pentalayer graphene at seven filling factors
- The authors call it a platform for anyons and for topological quantum computing. None of this says a free electron in vacuum is divisible. These are collective excitations in a medium, and the distinction is the one popular accounts most often lose
2023 · the CMS limit
The parameter that gives it mass has never been measured
- The best limit on the Higgs boson decaying to an electron pair is 3.0×10⁻⁴, from 138 fb⁻¹ of CMS data. That permits an electron coupling up to 240 times the Standard Model value
- The predicted rate is about 5×10⁻⁹, about five orders of magnitude below what the LHC can reach. A future electron-positron Higgs factory is the usual proposal for closing that
- A detail from the CMS paper that sharpens the point: even that tiny predicted rate is expected to be dominated by diagrams that do not contain the electron Yukawa coupling at all. The only direct probe of the coupling is a decay the theory says is mostly something else
2015 → 2023 · null results
What has been looked for, and not found
- No substructure. Excited-electron masses below 4.8 TeV are excluded where the compositeness scale equals the mass; for masses under 0.5 TeV the scale is bounded above 11 TeV
- No electric dipole moment. Below 4.1×10⁻³⁰ e·cm, which constrains CP-violating extensions well above what any near-term collider reaches. The same paper gives 4.5×10⁻³⁰ under a different statistical convention, and says so
- No decay. The lifetime for decay into a neutrino and a photon exceeds 6.6×10²⁸ years — roughly 5×10¹⁸ times the age of the universe, and a test of charge conservation rather than of the electron as such
2023 · the Nobel
And now it can be watched moving
- The 2023 Nobel Prize in Physics was awarded to Pierre Agostini, Ferenc Krausz and Anne L’Huillier “for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter”
- An attosecond is 10⁻¹⁸ seconds. The award citation says what the tool is for in its own words: the study of electron dynamics — not the electron as an object, but the electron in motion
- It is a useful corrective to the rest of this page. Almost everything above is a number about the electron. This is the line of work that treats it as something that does things, on the timescale at which it does them
Conclusion
So what is an electron in 2026 What holds, what is holding it up, what to hold loosely, and when it next moves
What holds
The electron is elementary as far as anyone has been able to look: no substructure to 11 TeV, no dipole moment to 4.1×10⁻³⁰ e·cm, no decay in 6.6×10²⁸ years. Its magnetic moment is the most precisely known property of any elementary particle, and its charge is not a measurement at all but a defining constant of the SI. Those four facts sit on published records that anyone can fetch, and none of them is in dispute.
What is holding everything up
One disagreement, about a different constant. Until caesium and rubidium are reconciled, the sharpest test in physics stays where it is, and the people who made the measurement say so in their own abstract. A third independent determination of α would do more for the electron than another decimal place on its magnetic moment — which is an unusual position for a field to be in, and worth watching for exactly that reason.
What to hold loosely
Every bound above is a null result, which means a sensitivity rather than a value, and every one of them will move. The eEDM bound changes by a factor of 1.1 depending on which statistical convention is applied — the paper prints both. The theory that the measurements are compared against carried a wrong coefficient for five years and nothing outside the calculation revealed it. And what the mathematics is about is not decided by any of this: no measurement in the record above favours one interpretation of quantum mechanics over another.
When this page next changes
31 December 2026 is the data-closing date for the next CODATA adjustment, so every value in the table above is fixed until then and then moves at once. The rest is open-ended: a third measurement of α would change the argument of this article more than anything else on the horizon, and nobody has announced one.