Fundamentals of Time and Relativity

Light Velocity

  • The speed of light that is actually measured is the round-trip speed (or ‘two-way’ speed) of light, i.e., from the source to a mirror and back again.
  • Henry Poincaré concluded in 1898 that determining the speed of light is partly a matter of convention.

To measure the speed of light, or any speed for that matter, from one spatial point to another at some distance, two clocks, one at each point, are needed in general. The distance, say Δx , must be known. But also, the two clocks must have been synchronized before they can be used to formally calculate the (one-way) speed v:=Δx/Δt , where Δt is the measured time interval.

However, with light there is a fundamental problem that Henri Poincaré (1854-1912) seems to have been the first one to recognize. Distances between points in space far apart can only be determined if it is possible to determine which events are simultaneous. In practice this is always done by light-signalling. But if the spatial frame of reference is determined by light-signals, and is then to be used to measure the speed of light, the reasoning would appear to be going in a circle.

In the year 1898 Poincaré published a philosophical paper titled: “The Measure of Time”. In this paper, Poincaré points out how astronomers often assume that the (one-way) speed of light is both constant and the same in every direction, without which no measurement of distance and velocity could be attempted. For this reason, Poincaré concluded that determining the speed of light is partly a matter of convention. In a number of papers, he discussed this issue in detail and analyzed synchronization with the help of optical and other (even gravitational) signals.

What can be experimentally measured is the round-trip speed (or ‘two-way’ speed) of light, i.e., from the source to a mirror (or other method of reflection) and back again. Then only one clock is involved. In this manner Hippolyte Fizeau determined, in 1849, the speed of light between an intense light source and a mirror about 8 km distant. His result was only about 4 km/s higher than the current accepted value. Improved measurements by Albert Michelson in the period 1877-79 were accurate to within about 0.05%.

  • In 1983 the speed of light in vacuum has been defined in the International System of Units (S.I.) to have exactly the value 299.792.458 m/s.
  • The value of the speed of light defines the meter as exactly the distance that light travels in vacuum in the fraction 1/299.792.458 of one second. Since 1984 this is the S.I. definition of the unit of length.