The speed of light, conventionally denoted (c), is the speed at which light and other electromagnetic radiation propagate through vacuum. Its value is exactly 299,792,458 metres per second, approximately 300,000 kilometres per second. A fundamental constant of physics, it connects measurements of distance and time and occupies a central position in the theory of relativity. The vacuum value must be distinguished from the propagation speeds of light in materials, which depend on the medium and the type of wave motion being measured. (nist.gov)
Exact value and measurement units
In the International System of Units (SI), the numerical value of (c) is fixed by definition rather than assigned an experimental uncertainty. The metre is defined through this fixed value and the second: light travelling through vacuum covers one metre in (1/299,792,458) of a second. This reverses the older procedure of independently establishing a length standard and then measuring how quickly light traverses it. (nist.gov)
The international decision to define the metre this way was adopted in 1983. It followed increasingly precise measurements using stable lasers and measurements of optical frequency and wavelength. Fixing (c) did not eliminate uncertainty from practical length measurements; instead, uncertainty resides in the instruments and procedures used to realize the metre. The exact number expresses a choice of units, while the physical significance of (c) comes from its role in natural laws. (bipm.org)
Electromagnetic foundations
In classical electromagnetism, Maxwell’s equations describe coupled electric and magnetic fields that can propagate as waves through empty space. Their propagation speed is
[ c=\frac{1}{\sqrt{\varepsilon_0\mu_0}}, ]
where (\varepsilon_0) is vacuum permittivity and (\mu_0) is vacuum permeability. The identification of this electromagnetic wave speed with the measured speed of light established light as an electromagnetic phenomenon. (feynmanlectures.caltech.edu)
For a monochromatic wave in vacuum,
[ c=f\lambda, ]
where (f) is frequency and (\lambda) is wavelength. Consequently, radiation at different frequencies has different wavelengths but the same vacuum propagation speed. This relationship also provides an experimental route to determining light speed from independently measured frequency and wavelength, and, with (c) fixed, to determining wavelength from frequency. (nvlpubs.nist.gov)
Relativity and the speed limit
Albert Einstein made the invariance of vacuum light speed a postulate of special relativity in 1905. Every inertial observer measures the same value of (c), regardless of the motion of the source or observer. Unlike ordinary velocities in classical mechanics, this speed is not obtained by simply adding the source’s velocity to the light’s velocity. Relativistic changes in measured distances and elapsed times preserve the invariant result. (feynmanlectures.caltech.edu)
The constant also links space and time in spacetime. It sets the local limiting speed for the transmission of matter, energy, and information. For a particle with nonzero rest mass, its total energy is
[ E=\gamma mc^2,\qquad \gamma=\frac{1}{\sqrt{1-v^2/c^2}}. ]
As its speed (v) approaches (c), the required energy increases without bound, preventing acceleration to light speed with finite energy. At rest, the expression becomes (E_0=mc^2), the relation of mass–energy equivalence. (feynmanlectures.caltech.edu)
In general relativity, this statement is local: measurements in a sufficiently small freely falling laboratory recover the special-relativistic result. Gravity can bend light paths, and coordinate descriptions over extended regions need not assign light a constant coordinate speed. These effects do not imply a change in the locally measured vacuum constant. (einstein-online.info)
Propagation through matter
In optics, the refractive index (n) relates vacuum light speed to the phase velocity in a transparent medium:
[ v_{\mathrm{phase}}=\frac{c}{n}. ]
Light generally travels more slowly through ordinary transparent materials than through vacuum. Its effective propagation results from the electromagnetic field interacting with charged constituents of matter, rather than from a change in the fundamental constant. Changes in wave speed across an interface help explain refraction. (feynmanlectures.caltech.edu)
A medium’s refractive index commonly varies with frequency, a phenomenon called dispersion. It is therefore necessary to distinguish phase velocity, the motion of a wave’s crests, from group velocity, the motion of a wave packet’s envelope. A phase velocity greater than (c) does not itself transmit information faster than light: an unmodulated crest is not an independently controllable signal. The propagation of a newly introduced disturbance must be considered separately. (feynmanlectures.caltech.edu)
Historical determination
In 1676, Ole Rømer established that light has a finite travel time by examining variations in the observed timing of eclipses of Jupiter’s moon Io. The timing changed as Earth moved closer to or farther from Jupiter, altering the distance the light travelled. This astronomical method revealed a delay too small to detect easily across everyday terrestrial distances. (pwg.gsfc.nasa.gov)
Later measurements increasingly used laboratory techniques. By the twentieth century, frequency and wavelength measurements of microwave and laser radiation provided highly precise values. These developments ultimately supported the transition from measuring (c) against a separate metre standard to using (c) to define that standard. (nvlpubs.nist.gov)
Astronomical distances and observation
Finite light speed means that astronomical observations show objects as they were when their light departed. Light from the Sun takes approximately eight minutes and twenty seconds to reach Earth. A light-year is a distance, not a duration: it is the distance light travels through vacuum in one year, approximately 9.46 trillion kilometres. Thus, observing a distant object also involves observing an earlier stage of its history. (spaceplace.nasa.gov)