A relative record, opened
The Kilogram That Could Not Lose Weight
For years the standard kilogram was said to have lost 50 micrograms. The comparisons never established that. Shift every artifact together and every recorded difference stays fixed, then use the 2023 post-redefinition realization record to give the former defining object a measured value that was impossible while it defined the unit.
Before 20 May 2019
Move the thing that was not allowed to move
Choose any history for the International Prototype of the Kilogram. The ledger absorbs it. Every observed comparison stays exactly where it was.
This is a free common offset, not an estimate. Drag it from loss to gain.
IPK history 0 µg. All 21 recorded relative changes are unchanged. Maximum change: 0 ng.
shifted = [mᵢ(t) + c(t)] - [mIPK(t) + c(t)]
shifted = mᵢ(t) - mIPK(t)
The slider does not prove that the IPK was stable. It proves the narrower and more important thing: these comparisons cannot identify its absolute change. A falling IPK, a rising IPK, or a stationary IPK can each produce the same relative record if every compatible replica history shifts with it.
| prototype | role or country | recorded change relative to IPK, µg | compatible hidden change, µg |
|---|
Source transcription: Girard, Table III, columns 1889 and 1989/92. Each value is the later mass excess minus the 1889 mass excess, both relative to the IPK and after the report’s conditioning. The table does not supply an absolute IPK history.
The number inside the story
Which “about 50”?
NIST describes four long-record official copies as gaining around 50 micrograms relative to the IPK. From Table III their changes are K1 +8, K7 +49, K8(41) +61, and K32 +69 micrograms. Their live mean is +46.75 µg. That is one named population, not proof that the IPK lost the same amount.
Calculating from Girard’s Table III values for a later 18-object selection gives a mean of +23.5 micrograms and a sample standard deviation of 30.1 micrograms. Girard does not report those two statistics as a table summary or define that selection as a non-outlier set. He says damaged K2, K16, and K39 cannot be taken into account, and separately flags K23’s peculiar behavior. The later selection instead excludes K2, K23, and K39 while retaining K16. This page has not established who first selected those 18 objects or published the resulting summary.
Population rule
Calculated by this page from Girard Table III values, not reported by Girard as a table summary. Included: K1, K7, K8(41), K32, K5, K6, K12, K16, K18, K20, K21, K24, K34, K35, K36, K37, K38, K40. Excluded: K2, K23, K39.
After 20 May 2019
The definition lets go
Resolution 1 fixed the numerical value of the Planck constant and abrogated the artifact definition. It says the IPK’s value would in future be determined experimentally. The former defining artifact became a test object.
Two independent primary routes can realize the new definition: Kibble balances compare mechanical and electrical power, while XRCD experiments count atoms through the density of a silicon crystal. The 2023 dissemination basis combined three international realization records by an unweighted arithmetic mean. The source explicitly says the listed input uncertainties were not used in that mean.
(+12.4 - 18.8 - 15.2) / 3
Published 2023 basis, standard uncertainty 20 µg.
3 of 3 inputs selected. This reproduces the official unweighted 2023 calculation.
This does not reveal which artifact changed during the preceding century. It does something that the old definition made conceptually impossible: it assigns the former defining object a mass from an external realization record. On the 2023 basis the published raw mean is -7.2 micrograms, disseminated as 1 kg minus 7 micrograms with standard uncertainty 20 micrograms.
Scope: this is the BIPM’s 2023 consensus dissemination basis, effective 1 March 2023. It is not an eternal value of the IPK, a current calibration certificate, or a claim that the 2023 realization experiments perfectly agreed.
The check
- Common-offset sweep: 21/21 comparisons stay exact at every integer setting from -100 to +100 µg; maximum change 0 ng.
- Independent route: residual bisection gives -7.200 µg; the page’s direct integer mean gives -7.200 µg.
- Published anchor: all three source values reproduce -7.2 µg exactly and round to the published -7 µg dissemination adjustment.
- Control on the control: adding 30 µg to the Pilot Study input produces +2.8 µg, so the -7.2 µg anchor rejects it.
- Refusal path: 0-input and 1-input settings are both rejected, 2/2 refusal cases.
- Selection audit: 18 named rows sum to 423 µg, giving mean +23.5 µg and sample standard deviation 30.1 µg.
Uncertainties and free choices
Free gauge: the first slider is an arbitrary common time-dependent offset. It is deliberately not presented as evidence about the IPK’s real history.
Population: the +23.5 and 30.1 figures depend on the later 18-object selection. Girard’s prose flags a different combination. The page shows both choices and all 21 source rows.
Conditioning: cleaning, washing, use, surface contamination, wear, and comparison timing matter. This page transcribes Table III’s already-conditioned changes and does not splice unconditioned campaign points.
Consensus rule: the 2023 source uses an unweighted mean of +12.4, -18.8, and -15.2 µg. Their listed standard uncertainties, 11.4, 8.1, and 7.4 µg, are informational and were not used. The 20 µg consensus uncertainty was agreed by the task group, not computed here.
Reference: the BIPM table expresses the result relative to the BIPM as-maintained mass unit tied to the 2014 IPK. The -7 µg statement belongs to the 2023 dissemination basis.
Apparatus
What the record can say
The Girard transcription
The 21 first-batch changes come from Table III of G. Girard, The Third Periodic Verification of National Prototypes of the Kilogram (1988-1992), Metrologia 31 (1994), 317-336. They are differences of two reported mass excesses relative to the IPK. The PDF and exact row list are identified in the research README.
The legal hinge
CGPM Resolution 1 (2018) made the new definition effective on 20 May 2019, fixed h at 6.626 070 15 × 10-34 J s, abrogated the IPK definition, and stated that the IPK’s value would subsequently be determined experimentally.
The 2023 calculation
The CCM task group’s two-page calculation prints all three inputs, the unweighted rule, the -7.2 µg mean, the rounded -7 µg action, and the agreed 20 µg standard uncertainty. The toggle is a sensitivity instrument. Only all three checked reproduces that official basis.