Speed of light

The speed of light in vacuum, commonly denoted c, is a universal physical constant exactly equal to 299,792,458 metres per second (approximately 1 billion kilometres per hour; 700 million miles per hour). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1⁄299792458 second. The speed of light is the same for all observers, no matter their relative velocity. It is the upper limit for the speed at which information, matter, or energy can travel through space.

All forms of electromagnetic radiation, including visible light, travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and sensitive measurements, their finite speed has noticeable effects. Much starlight viewed on Earth is from the distant past, allowing humans to study the history of the universe by viewing distant objects. When communicating with distant space probes, it can take hours for signals to travel. In computing, the speed of light fixes the ultimate minimum communication delay. The speed of light can be used in time of flight measurements to measure large distances to extremely high precision.

Ole Rømer first demonstrated that light does not travel instantaneously by studying the apparent motion of Jupiter's moon Io. In an 1865 paper, James Clerk Maxwell proposed that light was an electromagnetic wave and, therefore, travelled at speed c. Albert Einstein postulated that the speed of light c with respect to any inertial frame of reference is a constant and is independent of the motion of the light source. He explored the consequences of that postulate by deriving the theory of relativity, and so showed that the parameter c had relevance outside of the context of light and electromagnetism.

Massless particles and field perturbations, such as gravitational waves, also travel at speed c in vacuum. Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. Particles with nonzero rest mass can be accelerated to approach c but can never reach it, regardless of the frame of reference in which their speed is measured. In the theory of relativity, c interrelates space and time and appears in the famous mass–energy equivalence, E = mc².

In some cases, objects or waves may appear to travel faster than light. The expansion of the universe is understood to exceed the speed of light beyond a certain boundary. The speed at which light propagates through transparent materials, such as glass or air, is less than c; similarly, the speed of electromagnetic waves in wire cables is slower than c. The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material (n = ⁠c/v⁠). For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at ⁠c/1.5⁠ ≈ 200000 km/s (124000 mi/s); the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 90 km/s (56 mi/s) slower than c.

The speed of light in vacuum is usually denoted by a lowercase c. The origin of the letter choice is unclear, with guesses including "c" for "constant" or the Latin celeritas (meaning 'swiftness, celerity'). The "c" was used for "celerity" meaning a velocity in books by Leonhard Euler and others, but this velocity was not specifically for light; Isaac Asimov wrote a popular science article, "C for Celeritas", but did not explain the origin. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant that was later shown to equal √2 times the speed of light in vacuum. Historically, the symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1903, Max Abraham used c with its modern meaning in a widely read textbook on electromagnetism. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, which by then had become the standard symbol for the speed of light.

Sometimes c is used for the speed of waves in any material medium, and c₀ for the speed of light in vacuum. This subscripted notation, which is endorsed in official SI literature, has the same form as related electromagnetic constants: namely, μ₀ for the vacuum permeability or magnetic constant, ε₀ for the vacuum permittivity or electric constant, and Z₀ for the impedance of free space. This article uses c exclusively for the speed of light in vacuum.

Since 1983, the constant c has been defined in the International System of Units (SI) as exactly 299792458 m/s; this relationship is used to define the metre as exactly the distance that light travels in vacuum in 1⁄299792458 of a second. The second is, in turn, defined to be the length of time occupied by 9192631770 cycles of the radiation emitted by a caesium-133 atom in a transition between two specified energy states. By using the value of c, as well as an accurate measurement of the second, one can establish a standard for the metre.