[Relativity FAQ] - [Copyright]

Original by Philip Gibbs 23 December 1997

The speed of light in vacuum *c* is not measured.
It has an exact fixed value when given in standard
units. Since 1983 the metre has been defined
by international agreement as the length of the
path travelled by light in vacuum during a time
interval of 1/299792458 of a second. This makes
the speed of light exactly 299,792.458 km/s. Since
the inch is defined as 2.54 centimetres, the speed
of light also has an exact value in non-metric units.
This definition only makes sense because the
speed of light in vacuum is constant; a fact
which is subject to experimental verification
(see relativity FAQ article Is the speed of light constant?). Experiments
are still needed to measure the speed of light in
media such as air and water.

Before the seventeenth century it was generally
thought that light is transmitted instantaneously.
This was supported by the observation that there is
no noticeable lag in the position of the Earth's
shadow on the moon during a lunar eclipse as would be
expected if *c* is finite. Now we know
that light is just too fast for the lag to be noticeable.
Galileo doubted that light speed is infinite and described
an experiment to measure its speed by covering and uncovering
lanterns observed at a distance of a few miles. We don't know
if he really attempted the experiment, but again
*c* is too high for such a method to work.

The first successful measurement of *c* was
made by Olaus Roemer in 1676. He noticed that the time
between the eclipses of the moons of Jupiter was less
as the distance away from Earth is decreasing than when it
is increasing. He correctly surmised that
this is due to the varying length of time it takes for
light to travel from Jupiter to Earth as the distance
changes. He obtained a value equivalent to 214,000 km/s which was
very approximate because planetary distances were not
accurately known at that time.

In 1728 James Bradley made another estimate by observing stellar aberration: The apparent displacement of stars due to the motion of the Earth around the Sun. He observed the star Draconis and found that its apparent position changed during the year. All stellar positions are affected equally in this way. This distinguishes the effect from parallax which affects nearby stars more noticeably. A useful analogy to help understand aberration is to imagine the effect of motion on the angle at which rain falls. If you stand still in the rain when there is no wind it comes down vertically on your head. If you run through the rain it appears to come at you from an angle and hit you on the front. Bradley measured this angle for starlight. Knowing the speed of the Earth around the Sun he found a value for the speed of light of 301,000 km/s.

The first measurement of *c* on Earth was by
Armand Fizeau in 1849. He used a beam of light reflected
from a mirror 8km away. The beam passed through the
gaps between teeth of a rapidly rotating wheel. The speed
of the wheel was increased until the returning light
passed through the next gap and could be seen. Then *c*
was calculated to be 315,000 km/s. Leon Foucault improved on
this a year later by using rotating mirrors and got the much more
accurate answer of 298,000 km/s. His technique was good enough to
confirm that light travels slower in water than in air.

After Maxwell published his theory of electromagnetism it became possible to calculate the speed of light indirectly from the magnetic permeability and electric permitivity of free space. This was first done by Weber and Kohlrausch in 1857. In 1907 Rosa and Dorsey obtained 299,788 km/s in this way. It was the most accurate value at that time.

Many other methods were employed to improve accuracy further.
It soon became necessary to correct for the refractive index of air.
In 1958 Froome had the value of 299,792.5 km/s using a microwave
interferometer and a Kerr cell shutter.
After 1970 the development of lasers with very high spectral
stability and accurate caesium clocks made even better
measurements possible. Up until then the changing definition
of the metre had always kept ahead of the accuracy in
measurements of the speed of light. Then the point was
reached where the speed of light
was known to within an error of plus or minus 1 m/s. It
became more practical to fix the value of *c*
in the definition of the metre and use atomic clocks and
lasers to measure accurate distances instead.

This table gives some of the best measurements according to Froome and Essen:

Date | Author | Method | Result (km/s) | Error |
---|---|---|---|---|

1676 | Olaus Roemer | Jupiter's satellites | 214,000 | |

1726 | James Bradley | Stellar Aberration | 301,000 | |

1849 | Armand Fizeau | Toothed Wheel | 315,000 | |

1862 | Leon Foucault | Rotating Mirror | 298,000 | +-500 |

1879 | Albert Michelson | Rotating Mirror | 299,910 | +-50 |

1907 | Rosa, Dorsay | Electromagnetic constants | 299,788 | +-30 |

1926 | Albert Michelson | Rotating Mirror | 299,796 | +-4 |

1947 | Essen, Gorden-Smith | Cavity Resonator | 299,792 | +-3 |

1958 | K. D. Froome | Radio Interferometer | 299,792.5 | +-0.1 |

1973 | Evanson et al | Lasers | 299,792.4574 | +-0.001 |

1983 | Adopted Value | 299,792.458 |

"Twentieth Century Physics", Vol 2, IOP/AIP press

Hutchinson Science Library

"The Velocity of Light and Radio Waves" Froome and Essen