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Velocity of Light

Author: the photonics expert

Definition: the velocity with which light propagates in a medium

More specific terms: phase velocity, group velocity, velocity of information transport

Units: m/s

Whereas the velocity of some particle is a quantity which is based on a fairly simple and unambiguous concept, the velocity of light (as of other wave phenomena) is a much more sophisticated matter. There are different kinds of velocities, which are different conceptually and can (particularly for light propagation in media) have substantially different values:

• The phase velocity is the velocity with which wavefronts propagate.
• The group velocity determines the speed with which intensity maxima propagate (e.g. the peaks of pulses).
• The velocity of information transport can differ from both phase and group velocity, see the article on causality.

Figure 1 illustrates the different velocities. In that example, the phase velocities of different frequency components vary linearly with frequency: the wavefronts of the higher-frequency components (drawn at higher positions) travel more slowly. The pulse maximum forms where the wavefronts coincide, and propagates with the (lower) group velocity. More details are given in the article on group velocity.

Further complications can arise from light propagation in inhomogeneous media, particularly in waveguides.

In vacuum, phase and group velocity (defined for plane waves) are identical at <$c$> = 299 792 458 m/s. Within the International System of Units (SI), the vacuum velocity of light has been defined to match this value exactly. Together with the definition of the second (via a hyperfine transition of cesium atoms), this determines the length of a meter.

In some situations, often associated with absorption or gain resonances, the phase velocity or even the group velocity of light can exceed the vacuum velocity of light (→ superluminal transmission, “fast light”), although this is not associated with a violation of causality. There are other situations where the group velocity of light at least within a narrow spectral region is reduced (slow light). Enormous velocity reductions can be observed for narrowband resonances, as occur e.g. in ultracold gases.

The perhaps most peculiar effect is the occurrence of negative group velocities in situations with strongly negative <$\partial n / \partial\omega$>.

Velocity of Light and Theory of Relativity

The vacuum velocity of light plays a very important role in fundamental physics. One of the cornerstones of Einstein's theory of relativity is that the vacuum velocity of light is constant, i.e., it is the same in all inertial systems and does never depend on the propagation direction. In other words, there is not such a thing as a light aether, defining a single system where light has its “default” velocity. This seemingly innocent assumption lead Einstein to very far-reaching conclusions concerning the nature of space and time. Examples are the experimentally well confirmed phenomena of time dilatation, length contraction of moving objects, and the impossibility for any massive objects to reach or exceed the vacuum velocity of light.

The central role of light in this theory indicates that electromagnetism is intimately related to the nature of spacetime, although that relation is still not entirely understood.

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