Speed of Light - Numerical Value, Notation, and Units

Numerical Value, Notation, and Units

The speed of light in vacuum is denoted c. The symbol c is a "constant" in physical unit systems, and c also stands for "celeritas", Latin for "swiftness". (Capital C is the SI unit for Coulomb of electric charge.) Originally, the symbol V was used for the speed of light, introduced by James Clerk Maxwell in 1865. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant later shown to equal √2 times the speed of light in vacuum. In 1894, Paul Drude redefined c with its modern meaning. 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.

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 other related 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.

In the International System of Units (SI), the metre is defined as the distance light travels in vacuum in 1 ⁄ 299,792,458 of a second. This definition fixes the speed of light in vacuum at exactly 299,792,458 m/s. As a dimensional physical constant, the numerical value of c is different for different unit systems. In branches of physics in which c appears often, such as in relativity, it is common to use systems of natural units of measurement or the Geometrized unit system where c = 1. Using these units, c does not appear explicitly because multiplication or division by 1 does not affect the result.

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