Speed of Light

In 1983 the 17th CGPM defined the metre as the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. This step abrogated the metre definition that had been in force since 1960 and based on the krypton-86 transition. The 1960 definition had used the krypton-86 isotope, chosen over mercury-198 partly because it was more widely available in Europe and gave higher precision in the laboratory at the time.

The 1983 metre definition was itself abrogated in 2018 by the 26th CGPM, and the change became effective in 2019 under the revised SI. The current SI metre is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458, with the second itself defined by the caesium frequency. In the revised SI the constant c helps to define the metre and the kilogram.

The CODATA recommended value of the speed of light in vacuum is 299 792 458 metres per second, and its standard uncertainty is listed as exact.

In special relativity, the speed of light in vacuum is an absolute upper speed limit: nothing — matter, information or energy — can travel faster than c, and no object can directly overtake or catch up with light. Einstein's 1905 paper rests on two principles: the principle of relativity, which states that the laws of physics are the same and can be stated in their simplest form in all inertial frames of reference, and the principle of the constancy of the velocity of light. Consequently, every inertial observer who measures the speed of light in vacuum obtains the same constant value, c = 299,792,458 metres per second.

The 1983 international agreement fixed the metre as the distance travelled by light in vacuum in 1/299,792,458 of a second, which implies the exact relation c = 299,792,458 m/s (299,792.458 km/s).

In 1728 James Bradley measured the aberration angle for starlight and, knowing the speed of the Earth around the Sun, found a value for the speed of light of 301,000 km/s. In 1849 Fizeau made the first terrestrial measurement of the speed of light, using a rotating toothed wheel to chop a light beam into pulses projected along a round trip from Suresnes to Montmartre, almost 9 km away.Foucault's rotating mirror produced a result of 298,000 km/s in 1862.

Michelson spent forty years investigating the speed of light, and the November 1926 result came from experiments with light beams shot from Mount Wilson to Mount San Antonio, a distance of 44 miles and back. Mount Wilson served as the launch site for a beam of light that crossed the San Gabriels, bounced from a return mirror on a ridge of Mount San Antonio, and re-traversed the 22 miles between the two mountains. The experiment, devised and carried out during 1924-26 by Albert A. Michelson, provided the first modern and truly accurate measurement of the speed of light, a fundamental physical constant. Five years later Michelson tried another measurement in an evacuated pipe a mile long, and died as he was writing up his results.

NIST physicists led by Ken Evenson, with future Nobel laureate Jan Hall and Don Jennings, measured the speed of light at 299,792,456. 1 metres per second — a hundredfold improvement in the accuracy of the accepted value.

• 1728
  James Bradley
  Measured the aberration angle for starlight and found a value of 301,000 km/s ^{14July 1849: Fizeau Publishes Results of Speed of Light Experiment · American Physical Society (APS News) ↗}.
• 1862
  Léon Foucault
  Used a rotating mirror to obtain a result of 298,000 km/s ^{9How is the speed of light measured? · DESY — Deutsches Elektronen-Synchrotron (Physics FAQ) ↗}.

The 15th CGPM recommended in 1975 the value c = 299 792 458 m/s, which the 17th CGPM noted in 1983 would take on an exact value under the new definition of the metre.

Before the seventeenth century, light was generally thought to be transmitted instantaneously, an idea supported by the absence of any noticeable lag in the Earth's shadow during a lunar eclipse. Most scientists of the period, including Johannes Kepler and Rene Descartes, considered the speed of light to be infinite. Galileo, attempting to time the interval between flashes of lamps, could conclude only that light was extraordinarily rapid and at least ten times faster than sound.

The first serious measurement of the speed of light came in 1676, when the Danish astronomer Ole Roemer observed the moons of Jupiter and noticed that their eclipses seemed to occur at different times — late when Earth was far away and early when Earth was closer to Jupiter. Roemer was not looking for the speed of light when he found it: he was compiling extensive observations of the orbit of Io, the innermost of the four big satellites of Jupiter discovered by Galileo. He noticed that the time interval between successive eclipses of Io became steadily shorter as the Earth moved toward Jupiter and steadily longer as the Earth moved away.

Roemer's 1676 measurement was the first successful measurement of c, made after he noticed differences of up to 1000 seconds between the predicted and observed times of eclipses of Jupiter's moons. He obtained a value equivalent to 214,000 km/s, very approximate because planetary distances were not accurately known at that time. Roemer measured the delay of the eclipses and, knowing approximately the diameter of the Earth's orbit, made the first good estimate of the speed of light.

By 1970 the speed of light was known to within an error of plus or minus 1 m/s, after which it became more practical to fix the value of c in the definition of the metre and measure distances with atomic clocks and lasers instead.

Each GPS satellite carries multiple atomic clocks whose very precise time data let receivers synchronize to within 100 billionths of a second. The system must account for the constancy of the speed of light, the equivalence principle, the Sagnac effect, time dilation, gravitational frequency shifts and relativity of synchronization. Because the signal travels at the speed of light, timing errors of one nanosecond lead to positioning errors of the order of 30 cm. The benefits of this timing extend beyond navigation, including precise synchronization of communications systems, power grids and financial networks, and traceable time tags for financial transactions and billing.

In the Kansas State University capstone project the light is sent through roughly 2 km of single-mode telecommunication-grade optical fiber and detected by a photodiode. The time difference between the two photodiode pulses was found by LabVIEW to be about 10.16 microseconds at the maximum sampling rate of 1.25 MS/s. The speed of light in the optical fiber was calculated to be about 2.054 x 10^8 metres per second, corresponding to a refractive index of about 1.4606 which is typical for the fiber.

Radar pulses are transmitted away from the radar at the speed of light, but they are very short in duration. Each transmitted pulse lasts only 1.57 millionths of a second and is repeated around 1300 times per second, while the radar listens for returns in between.

Light-time makes these vast distances legible: the Sun's light takes about 8.3 minutes to reach us. The next closest star to us is about 4.3 light-years away, so seeing it today means seeing it as it was 4.3 years ago. The nearest large galaxy, Andromeda, lies 2.5 million light-years away. On the scale of the Galaxy itself, the Milky Way is about 100,000 light-years across and probably contains 100 to 400 billion stars.

Within the solar system, the light time for 1 au is 499.004783836 s. In the IAU system the parsec is defined in terms of the astronomical unit of length, the appropriate unit for studies of the structure of the Galaxy. The IAU unit recommendations describe the light-year as appropriate to popular expositions on astronomy and sometimes used in scientific papers as an indicator of distance.

NASA defines a light-year as the distance light travels in one year: light zips through interstellar space at 186,000 miles (300,000 kilometers) per second and 5. 88 trillion miles (9. 46 trillion kilometers) per year. NASA Space Place gives the same unit as about 6 trillion miles (9 trillion km).