The speed of light

Q: What is the value of the speed of light?

299,792,458 m/s. Since 1983 the value has no error bar at all, because it is a definition. Any better experiment now makes the metre more accurate, not c. Caesium clocks set the second, and the metre follows from c.

How fast is light, and how did anyone time something that quick?

c = 299\,792\,458\ \text{m/s}

Exact, by definition, since 1983 12 min read, with an experiment to run

Light crosses a room in about ten billionths of a second. The speed of light, $c$ , is about 300,000 km every second: seven and a half times round the Earth before you can say "one".

It is also the speed limit of the universe. Nothing with mass can reach it, and it ties space to time and mass to energy in $E = mc^2$ . Today it is so well known that the metre itself is defined by it.

1 · Play first

Time light with a spinning wheel

In 1849 Hippolyte Fizeau shone a lamp through the gaps of a toothed wheel, off a mirror 8.6 km away, and back through the same gaps. Spin the wheel slowly and the light comes back through a gap. Spin it just fast enough and a tooth has moved into the way: the light goes dark.

Speed the wheel up until the returning light first disappears, then let the wheel work out $c$ for you.

What to notice

The light goes dark when the wheel turns by half a gap in the time light takes to go there and back.
Spin faster still and it comes back bright, then dark again: each dark spot gives the same $c$ .
A longer path or more teeth means the first dark comes at a slower spin.

2 · The equation, piece by piece

Light makes a round trip of $2L$ while the wheel turns from a gap to the next tooth, which is half of one tooth spacing. Setting the two times equal gives Fizeau's formula. Tap any piece.

\htmlClass{t0}{c} = \htmlClass{t1}{4}\,\htmlClass{t2}{N}\,\htmlClass{t3}{L}\,\htmlClass{t4}{f}

c

The speed of light

What we want, in metres per second.

Fizeau got about 313,000 km/s, about 5% high, because judging the exact moment of darkness by eye is hard. Still, it was the first time light was timed on Earth rather than with planets and moons.

3 · How we found it

1Is light instant?

Galileo tried timing lanterns between two hilltops and found nothing: light was far too fast for human reflexes. Many thought it simply arrived everywhere at once.

In 1676 Ole Rømer noticed that Jupiter's moon Io came out of Jupiter's shadow late when Earth was far from Jupiter and early when it was near. The delay, about 22 minutes across Earth's orbit, was the time light took to cross it. Light had a speed.

2Timing it on the ground

Fizeau's toothed wheel (1849) and then Léon Foucault's spinning mirror (1862) brought the measurement down to Earth. Foucault got 298,000 km/s, within 1% of today's value, and showed light is slower in water.

Albert Michelson spent fifty years refining spinning mirrors, and in 1926 timed light over 35 km between two California mountains to about 299,796 km/s.

3From measuring to defining

Lasers in the 1970s measured $c$ so precisely that the weak point became the metre itself, then defined by a wavelength of krypton light.

So in 1983 the world flipped it round: $c$ was fixed at exactly 299,792,458 m/s, and the metre became the distance light goes in 1/299,792,458 of a second.

1638
Galileo's lantern test finds light too fast to time.
1676
Rømer times light across Earth's orbit using Io's eclipses.
1849
Fizeau's toothed wheel gives about 313,000 km/s.
1862
Foucault's rotating mirror gets within 1%.
1905
Einstein makes $c$ the same for every observer in special relativity.
1926
Michelson's mountain-to-mountain run gives 299,796 km/s.
1983
$c$ is fixed at exactly 299,792,458 m/s and the metre is defined from it.

4 · How the value is pinned down

Since 1983 the value has no error bar at all, because it is a definition. Any better experiment now makes the metre more accurate, not $c$ . Caesium clocks set the second, and the metre follows from $c$ .

That is why lasers and atomic clocks, not rulers, are the world's length standard. GPS uses the same idea: it turns travel times of radio signals into distances using $c$ .

5 · What if it were different?

If light were much slower

If $c$ were walking pace, you would see a car's past as it drove by, and relativity's stretched time would show up on a bicycle ride.

If light were instant

There would be no fixed link between space and time, $E = mc^2$ would break, and GPS would have nothing to time.

Why it matters to you

Every web page crosses an ocean in fibre at about two-thirds of $c$ . That delay is why far-away servers feel slow.

6 · Try it at home

Measure light with a microwave and chocolate

A microwave oven fills with a standing wave. Hot spots sit half a wavelength apart, and the frequency is printed on the back, so you can find $c$ with a ruler.

You need

A microwave oven (with the turntable taken out)
A large flat bar of chocolate, or a plate of grated cheese
A ruler

Do this

Take the turntable out so the food sits still. Put the chocolate on an upside-down plate.
Heat on full power for about 15 to 20 seconds, until two or three soft spots begin to melt.
Measure the distance between the centres of two melted spots next to each other.
Read the frequency on the oven's label, usually 2,450 MHz.

The maths

The spots are half a wavelength apart, so the wavelength is twice your gap: about 12 cm. Then $c = f\lambda$ , so $2.45\times10^9 \times 0.12 \approx 2.9\times10^8$ m/s.

Stay safe: Never run the microwave empty, keep heating short, and let the chocolate cool before you touch it. Ask an adult first.

7 · Common mix-ups

MythLight always goes at 299,792,458 m/s.

ActuallyThat is its speed in empty space. In glass it is about a third slower, which is why lenses bend light.

MythScientists still measure $c$ more and more accurately.

ActuallySince 1983 it is exact by definition. Better measurements improve the metre instead.

MythNothing can go faster than light.

ActuallyNothing can beat $c$ in a vacuum, but in water fast particles can beat light's slower local speed and glow blue.

8 · References

CODATA value: speed of light in vacuum, NIST, 2018
The International System of Units (SI Brochure, 9th edition), BIPM, 2019
Measurement of the velocity of light between Mount Wilson and Mount San Antonio, A. A. Michelson, Astrophysical Journal 65, 1927
Resolution 1 of the 17th CGPM (definition of the metre), BIPM, 1983

Next constantThe gravitational constant: How hard does gravity pull, and how do you weigh the Earth?