The kilogram was the last SI base unit tied to a physical object — a platinum-iridium cylinder locked in a vault outside Paris — until 2019. The current definition breaks that dependency and anchors the kilogram to Planck's constant (\( h \)). This section closes the long march of the SI toward constants of nature.
A short history
1795. The kilogram was defined as the mass of one liter of pure water at the melting point of ice. Elegant in principle, hard in practice: you had to build a container of exactly 1 liter, fill it with exactly one liter of water, and weigh it. Errors in measuring water density, temperature, and dissolved air quickly ate into the precision.
1799. To sidestep this problem, an Archive Kilogram (Kilogramme des Archives) was cast from platinum — a cylinder whose mass was declared exactly equal to one liter of water at 4°C. From here on, the standard shifted from "1 liter of water" to "this cylinder." The water-density problem was gone.
1889 — International Prototype Kilogram (IPK). The kilogram was officially redefined as the mass of a platinum-iridium cylinder (90% Pt, 10% Ir), 39 mm high and 39 mm wide, cast in 1879 and kept under three nested bell jars in a vault at the BIPM in Sèvres, France. This cylinder was nicknamed "Le Grand K."
\[ 1\ \text{kg} \;\equiv\; \text{mass of the IPK} \]
The IPK carried a huge risk: every mass measurement in the world was tied to this single cylinder. If one morning a dust speck settled on it, or a microgram oxidized off, the actual mass of every object in the universe would change — because by definition, the kilogram was the mass of that particular object.
Periodic verifications (1889, 1946, 1989). The IPK was compared occasionally to six "witness" copies (témoins) and about forty "national copies" (distributed to different countries, including NIST for the US). The uncomfortable finding: the IPK had drifted about 50 μg lighter than the mean of the copies over a century — or the copies had gained 50 μg (depending on your reference frame). Either way, one conclusion: the standard was not reliable.
2019 (current). With the SI redefinition, the kilogram was tied to Planck's constant:
\[ h \;=\; 6.626\,070\,15 \times 10^{-34}\ \mathrm{J{\cdot}s} \quad \text{(exact, by definition)} \]
If we fix \( h \) to an exact value, and the second (from Cs-133) and the meter (from \( c \)) are also fixed, then mass is unambiguously defined because:
\[ [h] \;=\; \mathrm{J{\cdot}s} \;=\; \mathrm{kg{\cdot}m^2{\cdot}s^{-1}} \]
So \( \mathrm{kg} = h \cdot m^{-2} \cdot s \). The kilogram is no longer an object — it's a relation.
What is Planck's constant, and why does it matter?
\( h \) is a fundamental number that governs the quantum-mechanical behavior of energy. The famous relation:
\[ E \;=\; h\nu \]
says the energy of a photon of frequency \( \nu \) is exactly \( h\nu \). This constant appears in every equation of quantum mechanics, quantum electrodynamics, and statistical thermodynamics.
Fixing \( h \) to a constant value means our physical world accepts this number as a natural input and derives units from it.
The Kibble balance — realizing the kilogram in the lab
Fine, so 1 kg is defined by a mathematical relation involving \( h \). But that's very abstract. In a real lab, how do you actually measure a mass?
The answer is the Kibble balance (originally called a watt balance; renamed in honor of Bryan Kibble, who invented it in 1975). A Kibble balance links mass to electromagnetic measurements — and electrical measurements come from voltage (Josephson junction) and resistance (quantum Hall) that are both tied directly to \( h \).
The two-mode method
Weighing mode. A coil is suspended in a horizontal magnetic field \( B \). Place the mass to be measured on the coil, and pass a current \( I \) through the coil so that the magnetic force cancels the weight:
\[ BIL \;=\; mg \]
where \( L \) is the effective length of the coil in the field and \( g \) is the local gravitational acceleration.
Velocity mode. Remove the mass. Move the coil horizontally through the same field at velocity \( v \), and measure the induced voltage \( U \):
\[ U \;=\; BLv \]
Dividing the two equations, \( B \) and \( L \) cancel (they are the same in both modes):
\[ UI \;=\; mgv \]
\( m \) becomes:
\[ \boxed{m \;=\; \dfrac{UI}{gv}} \]
Every term on the right can be measured independently to very high precision:
- \( U \) via the Josephson effect (itself tied to \( h \))
- \( I \) via a combination of Josephson + quantum Hall (again tied to \( h \))
- \( g \) with an absolute gravimeter
- \( v \) with an optical interferometer (tied to the meter and second)
Result: mass is realized via electromagnetic and quantum measurements — no reference object required.
Current precision
Modern Kibble balances (NIST-4, LNE, NRC, NPL) reach relative accuracies of about \( 10^{-8} \) — so for a 1 kg reference mass, the uncertainty is about 10 μg. That's still orders of magnitude behind atomic clocks, but better than the IPK (which had a ~50 μg per century drift) because Kibble-balance errors are not systematic and don't drift in time.
The pattern — end of an era
| Era | Anchor |
|---|---|
| 1795 | Volume of water |
| 1799 | The Archive platinum cylinder |
| 1889 | IPK (Pt-Ir cylinder) |
| 2019 | Planck's constant (\( h \)) |
With the 2019 redefinition, all seven SI base units are now tied to constants of nature — no longer to reference objects. This transformation took roughly 230 years, from the French Revolution to today. The IPK still physically exists in Sèvres, but it is no longer the definition of the kilogram — it's become a museum piece.
What you should be able to do
After this section you should be able to:
- Explain why anchoring the definition to the IPK was neither safe nor stable
- Write the current definition of the kilogram based on \( h \) and show how \( \mathrm{kg} = h \cdot m^{-2} \cdot s \) follows
- Describe the Kibble balance in its two modes (weighing / velocity) and explain why \( B \) and \( L \) cancel in the final equation
- Distinguish the "formal definition" (\( h \) is fixed) from the "lab realization" (Kibble balance)
- Explain why the 2019 SI redefinition marks the end of an era in metrology
📚 See also: Halliday Vol 1, Ch 1 §1-6 (mass standard). 🎓 Watch: Veritasium — "The Kilogram Has Died. Long Live the Kilogram." 📖 Free reading: NIST — Kibble Balance (nist.gov/kibble-balance). 📖 SI Brochure (9th ed.), BIPM — appendix on constant-based definitions (bipm.org).
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