History
| <1638 | Galileo, covered lanterns | inconclusive:1252Note | |
| <1667 | Accademia del Cimento, covered lanterns | inconclusive:1253 | |
| 1675 | Rømer and Huygens, moons of Jupiter | 220000 | ‒27% error |
| 1729 | James Bradley, aberration of light | 301000 | +0.40% error |
| 1849 | Hippolyte Fizeau, toothed wheel | 315000 | +5.1% error |
| 1862 | Léon Foucault, rotating mirror | 298000±500 | ‒0.60% error |
| 1907 | Rosa and Dorsey, EM constants | 299710±30 | ‒280 ppm error |
| 1926 | Albert A. Michelson, rotating mirror | 299796±4 | +12 ppm error |
| 1950 | Essen and Gordon-Smith, cavity resonator | 299792.5±3.0 | +0.14 ppm error |
| 1958 | K.D. Froome, radio interferometry | 299792.50±0.10 | +0.14 ppm error |
| 1972 | Evenson et al., laser interferometry | 299792.4562±0.0011 | ‒0.006 ppm error |
| 1983 | 17th CGPM, definition of the metre | 299792.458 (exact) | exact, as defined |
Until the early modern period, it was not known whether light travelled instantaneously or at a very fast finite speed. The first extant recorded examination of this subject was in ancient Greece. The ancient Greeks, Muslim scholars, and classical European scientists long debated this until Rømer provided the first calculation of the speed of light. Einstein's Theory of Special Relativity concluded that the speed of light is constant regardless of one's frame of reference. Since then, scientists have provided increasingly accurate measurements.
Early history
Empedocles (c. 490–430 BC) was the first to propose a theory of light and claimed that light has a finite speed. He maintained that light was something in motion, and therefore must take some time to travel. Aristotle argued, to the contrary, that "light is due to the presence of something, but it is not a movement". Euclid and Ptolemy advanced Empedocles' emission theory of vision, where light is emitted from the eye, thus enabling sight. Based on that theory, Heron of Alexandria argued that the speed of light must be infinite because distant objects such as stars appear immediately upon opening the eyes. Early Islamic philosophers initially agreed with the Aristotelian view that light had no speed of travel. In 1021, Alhazen (Ibn al-Haytham) published the Book of Optics, in which he presented a series of arguments dismissing the emission theory of vision in favour of the now accepted intromission theory, in which light moves from an object into the eye. This led Alhazen to propose that light must have a finite speed, and that the speed of light is variable, decreasing in denser bodies. He argued that light is substantial matter, the propagation of which requires time, even if this is hidden from our senses. Also in the 11th century, Abū Rayhān al-Bīrūnī agreed that light has a finite speed, and observed that the speed of light is much faster than the speed of sound.
In the 13th century, Roger Bacon argued that the speed of light in air was not infinite, using philosophical arguments backed by the writing of Alhazen and Aristotle. In the 1270s, Witelo considered the possibility of light travelling at infinite speed in vacuum, but slowing down in denser bodies.
In the early 17th century, Johannes Kepler believed that the speed of light was infinite, since empty space presents no obstacle to it. René Descartes argued that if the speed of light were to be finite, the Sun, Earth, and Moon would be noticeably out of alignment during a lunar eclipse. Since such misalignment had not been observed, Descartes concluded the speed of light was infinite. Descartes speculated that if the speed of light were found to be finite, his whole system of philosophy might be demolished. In Descartes' derivation of Snell's law, he assumed that even though the speed of light was instantaneous, the denser the medium, the faster was light's speed. Pierre de Fermat derived Snell's law using the opposing assumption, the denser the medium the slower light traveled. Fermat also argued in support of a finite speed of light.
First measurement attempts
In 1629, Isaac Beeckman proposed an experiment in which a person observes the flash of a cannon reflecting off a mirror about one mile (1.6 km) away. In 1638, Galileo Galilei proposed an experiment, with an apparent claim to having performed it some years earlier, to measure the speed of light by observing the delay between uncovering a lantern and its perception some distance away. He was unable to distinguish whether light travel was instantaneous or not, but concluded that if it were not, it must nevertheless be extraordinarily rapid. In 1667, the Accademia del Cimento of Florence reported that it had performed Galileo's experiment, with the lanterns separated by about one mile, but no delay was observed. The actual delay in this experiment would have been about 11 microseconds.
The first quantitative estimate of the speed of light was made in 1676 by Rømer. From the observation that the periods of Jupiter's innermost moon Io appeared to be shorter when the Earth was approaching Jupiter than when receding from it, he concluded that light travels at a finite speed, and estimated that it takes light 22 minutes to cross the diameter of Earth's orbit. Christiaan Huygens combined this estimate with an estimate for the diameter of the Earth's orbit to obtain an estimate of speed of light of 220000 km/s, 26% lower than the actual value.
In his 1704 book Opticks, Isaac Newton reported Rømer's calculations of the finite speed of light and gave a value of "seven or eight minutes" for the time taken for light to travel from the Sun to the Earth (the modern value is 8 minutes 19 seconds). Newton queried whether Rømer's eclipse shadows were coloured; hearing that they were not, he concluded the different colours travelled at the same speed. In 1729, James Bradley discovered stellar aberration. From this effect he determined that light must travel 10210 times faster than the Earth in its orbit (the modern figure is 10066 times faster) or, equivalently, that it would take light 8 minutes 12 seconds to travel from the Sun to the Earth.
Connections with electromagnetism
In the 19th century Hippolyte Fizeau developed a method to determine the speed of light based on time-of-flight measurements on Earth and reported a value of 315000 km/s. His method was improved upon by Léon Foucault who obtained a value of 298000 km/s in 1862. In the year 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch measured the ratio of the electromagnetic and electrostatic units of charge, 1/√ε0μ0, by discharging a Leyden jar, and found that its numerical value was very close to the speed of light as measured directly by Fizeau. The following year Gustav Kirchhoff calculated that an electric signal in a resistanceless wire travels along the wire at this speed. In the early 1860s, Maxwell showed that, according to the theory of electromagnetism he was working on, electromagnetic waves propagate in empty space at a speed equal to the above Weber/Kohlrausch ratio, and drawing attention to the numerical proximity of this value to the speed of light as measured by Fizeau, he proposed that light is in fact an electromagnetic wave.
"Luminiferous aether"
It was thought at the time that empty space was filled with a background medium called the luminiferous aether in which the electromagnetic field existed. Some physicists thought that this aether acted as a preferred frame of reference for the propagation of light and therefore it should be possible to measure the motion of the Earth with respect to this medium, by measuring the isotropy of the speed of light. Beginning in the 1880s several experiments were performed to try to detect this motion, the most famous of which is the experiment performed by Albert A. Michelson and Edward W. Morley in 1887. The detected motion was always less than the observational error. Modern experiments indicate that the two-way speed of light is isotropic (the same in every direction) to within 6 nanometres per second. Because of this experiment Hendrik Lorentz proposed that the motion of the apparatus through the aether may cause the apparatus to contract along its length in the direction of motion, and he further assumed, that the time variable for moving systems must also be changed accordingly ("local time"), which led to the formulation of the Lorentz transformation. Based on Lorentz's aether theory, Henri Poincaré (1900) showed that this local time (to first order in v/c) is indicated by clocks moving in the aether, which are synchronized under the assumption of constant light speed. In 1904, he speculated that the speed of light could be a limiting velocity in dynamics, provided that the assumptions of Lorentz's theory are all confirmed. In 1905, Poincaré brought Lorentz's aether theory into full observational agreement with the principle of relativity.
Special relativity
In 1905 Einstein postulated from the outset that the speed of light in vacuum, measured by a non-accelerating observer, is independent of the motion of the source or observer. Using this and the principle of relativity as a basis he derived the special theory of relativity, in which the speed of light in vacuum c featured as a fundamental constant, also appearing in contexts unrelated to light. This made the concept of the stationary aether (to which Lorentz and Poincaré still adhered) useless and revolutionized the concepts of space and time.
Increased accuracy of c and redefinition of the metre and second
In the second half of the 20th century much progress was made in increasing the accuracy of measurements of the speed of light, first by cavity resonance techniques and later by laser interferometer techniques. These were aided by new, more precise, definitions of the metre and second. In 1950, Louis Essen determined the speed as 299792.5±1 km/s, using cavity resonance. This value was adopted by the 12th General Assembly of the Radio-Scientific Union in 1957. In 1960, the metre was redefined in terms of the wavelength of a particular spectral line of krypton-86, and, in 1967, the second was redefined in terms of the hyperfine transition frequency of the ground state of caesium-133.
In 1972, using the laser interferometer method and the new definitions, a group at the US National Bureau of Standards in Boulder, Colorado determined the speed of light in vacuum to be c = 299792456.2±1.1 m/s. This was 100 times less uncertain than the previously accepted value. The remaining uncertainty was mainly related to the definition of the metre.Note As similar experiments found comparable results for c, the 15th General Conference on Weights and Measures in 1975 recommended using the value 299792458 m/s for the speed of light.
Defining the speed of light as an explicit constant
In 1983 the 17th CGPM found that wavelengths from frequency measurements and a given value for the speed of light are more reproducible than the previous standard. They kept the 1967 definition of second, so the caesium hyperfine frequency would now determine both the second and the metre. To do this, they redefined the metre as: "The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second." As a result of this definition, the value of the speed of light in vacuum is exactly 299792458 m/s and has become a defined constant in the SI system of units. Improved experimental techniques that, prior to 1983, would have measured the speed of light no longer affect the known value of the speed of light in SI units, but instead allow a more precise realization of the metre by more accurately measuring the wavelength of Krypton-86 and other light sources.
In 2011, the CGPM stated its intention to redefine all seven SI base units using what it calls "the explicit-constant formulation", where each "unit is defined indirectly by specifying explicitly an exact value for a well-recognized fundamental constant", as was done for the speed of light. It proposed a new, but completely equivalent, wording of the metre's definition: "The metre, symbol m, is the unit of length; its magnitude is set by fixing the numerical value of the speed of light in vacuum to be equal to exactly 299792458 when it is expressed in the SI unit m s−1." This was one of the changes that was incorporated in the 2019 redefinition of the SI base units, also termed the New SI.
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