1.3 — The meter: length standard

The meter has been redefined several times, each redefinition driven by the same motivation: anchor the unit to something more stable and more universally reproducible than the previous version.

A short history

1791 (French Revolution). Defined as 1 / 10,000,000 of the distance from the equator to the North Pole, along the meridian passing through Paris.

1 m = (1 / 10,000,000) × (equator-to-pole distance along the Paris meridian)

The French Academy commissioned a 7-year geodetic survey of that meridian. Beautiful in spirit (a unit "from the Earth itself"), but accuracy was limited by the surveyors — a small survey error was baked into every meter stick for the next century.

1889. Defined as the length between two fine scratches on a platinum-iridium bar (90% Pt, 10% Ir), at 0 °C, kept under controlled conditions at the BIPM in Sèvres, France.

Stable and durable, but vulnerable: if the bar warped, got damaged, or burned in a fire, the unit was gone. Worse, anyone needing high precision had to physically compare their meter sticks against that bar — a logistical nightmare for global science.

1960. Defined as 1,650,763.73 wavelengths, in vacuum, of the orange-red light emitted by Kr-86 atoms during a specific atomic transition (2p_{10} → 5d_5).

Now any lab on Earth — or, in principle, Mars — could build a krypton lamp and an interferometer and realize the meter from first principles. No more pilgrimage to Sèvres.

1983 (current). Defined as the distance light travels in vacuum during a time interval of 1 / 299,792,458 of a second.

\[ c \;=\; 299{,}792{,}458\ \mathrm{m/s} \quad\text{(exact, by definition)} \]

where c is the speed of light in vacuum.

This is a clever inversion: we fix c to an exact value (zero uncertainty), and the meter becomes a derived unit — defined in terms of the second. Because the second is realized far more precisely than any direct length measurement, this redefinition pulled length measurement up to the precision of atomic clocks (parts in 10^15 or better).

The pattern

Era	Anchor
1791	Earth's geometry
1889	A physical artifact
1960	An atomic transition
1983	A fundamental constant of nature

Physics keeps pushing standards toward things that do not change: from arbitrary objects, to atoms, to constants of nature. The kilogram took the same path in 2019 (see §1.5 — kilogram).

What you should be able to do

After this section you should be able to:

• Recite the four historical definitions of the meter in order and explain the motivation for each redefinition
• Explain why in the 1983 definition "the speed of light is an exact value, with no uncertainty"
• Estimate how many orders of magnitude better precision an atomic-frequency-anchored standard gives you over a physical bar

📚 See also: Halliday Vol 1, Ch 1 §1-4 (length standard). 🎓 Watch: MIT 8.01, Lecture 1 (Walter Lewin) — "Powers of Ten and Units". 📖 Free reading: OpenStax University Physics Vol 1, §1.2.

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