Measuring the speed of light

Rømer and the moons of Jupiter (1676)

Ole Rømer was timing eclipses of Io, Jupiter's innermost moon, which orbits every 42.5 hours. He found the eclipses came progressively later than predicted as Earth moved away from Jupiter in its orbit, and earlier as Earth came closer. The extra delay, up to about 22 minutes by the measurements of the time, was the time light took to cross the extra distance: the diameter of Earth's orbit.

Rømer showed that light has a finite speed. He didn't publish a value himself; Christiaan Huygens combined his delay with the size of Earth's orbit to get about $2.2 \times 10^8$ m/s. The modern value of the delay is about 16.6 minutes, and the main errors came from the poorly known orbit size and from timing a slow, gradual eclipse by eye.

Fizeau's toothed wheel (1849)

Hippolyte Fizeau made the first measurement on Earth. Light from a lamp was reflected through a gap between the teeth of a rotating wheel, travelled 8633 m from Suresnes to a mirror on Montmartre in Paris, and came back to the wheel.

• With the wheel still or slow, the returning light passes back through the same gap and the observer sees it.
• At a certain speed, the wheel turns by half a tooth spacing during the round trip, the light hits a tooth, and the observer sees darkness.

For a wheel with $N$ teeth (and $N$ gaps) spinning at $f$ revolutions per second, a tooth replaces a gap in $\dfrac{1}{2Nf}$ seconds. At the first dark point this equals the round trip time $\dfrac{2d}{c}$, so

$$c = 4Ndf$$

Foucault's rotating mirror (1850–62)

Léon Foucault replaced the wheel with a rapidly rotating mirror. Light reflected from the spinning mirror to a fixed mirror and back; in the meantime the rotating mirror had turned through a small angle, so the returning beam was deflected. Measuring that tiny deflection gave the travel time. In 1862 he got $2.98 \times 10^8$ m/s, within 1% of today's value. His method needed only a short light path, so he could put a tube of water in it, and in 1850 he showed light travels slower in water than in air, a result that was decisive against Newton's particle model (7E).

Albert Michelson refined the rotating-mirror method for fifty years. In 1926 he sent light 35 km between Mount Wilson and Mount San Antonio in California and measured 299 796 km/s.

Modern methods

• Cavity resonators (1950). Louis Essen set up standing microwaves in a metal cavity of accurately known size. The cavity only resonates when a whole number of half-wavelengths fit, giving $\lambda$; the frequency was measured electronically; $c = f\lambda$ gave 299 792.5 km/s.
• Lasers (1972). Kenneth Evenson's team at the US National Bureau of Standards measured both the frequency and the wavelength of a stabilised laser, getting 299 792 456.2 ± 1.1 m/s. The uncertainty was now limited by how well the metre itself was defined.
• Lunar laser ranging. Apollo astronauts left reflectors on the Moon. Timing laser pulses there and back measures the Earth–Moon distance to a few millimetres, using the known value of $c$.

The speed of light now defines the metre

By the late 1970s, $c$ could be measured more precisely than the metre could be realised. So in 1983 the definition was turned around: the speed of light was fixed at exactly 299 792 458 m/s, and the metre was defined as the distance light travels in a vacuum in $\dfrac{1}{299\,792\,458}$ of a second.

The second is defined by atomic clocks: the radiation from a caesium-133 transition has exactly 9 192 631 770 oscillations per second. So length is now measured through time. You can't "measure" the speed of light in m/s any more; an experiment that seems to do so is really measuring the length of the metre. In Australia, the National Measurement Institute keeps the national time scale with caesium clocks and links it to world time, and GPS, radar and laser rangefinders all turn timing into distance with $d = ct$.