Velocity of light
2024-4-21
Definition:
The speed of a particle is a very simple and clear concept, but the speed of light (and other wave phenomena) is a very complex issue. There are several different concepts of speed (especially when light travels through a medium), and they have different numerical values:
Phase velocity is the speed at which the phase wavefront propagates.
The group velocity is the speed at which the maximum intensity of light travels (for example, the peak of a pulse).
The phase velocity and group velocity of information propagation are different, see the entry Causality.
Figure 1 gives the different speeds. In this example, the phase velocities of different frequency components vary linearly with frequency: high-frequency component wavefronts propagate more slowly. The pulse maximum overlaps the wavefront and propagates at group velocity. More details are given in the entry on group velocity.
Figure 1: Propagation of light pulses in dispersive media. Phase wavefronts with different frequency components propagate at different velocities, and the pulses propagate at group velocity, which is smaller than the phase velocity.
The situation is more complicated when light propagates in non-isotropic media, especially in waveguides.
The phase velocity in vacuum is equal to the group velocity (plane wave) is c = 299 792 458 m/s. In the International System of Units (SI), the definition of the speed of light in vacuum corresponds exactly to the actual value. And combined with the definition of the second (defined by the hyperfine transition of the cesium atom), the length of the meter can be determined.
In some cases, usually in the presence of absorption or gain resonance, the phase velocity or even the group velocity can be greater than the speed of light in a vacuum (see superluminal transmission, "fast light"), but this does not violate the causal relationship. In other cases, the speed of light slows down in a very narrow region of the spectrum (slow light). A large reduction in velocity can be observed at narrow-band resonances, as occurs, for example, in ultracold gases.
A more exotic effect is the presence of negative group velocities and negative dn/dω in some cases.
In fundamental physics, the speed of light in vacuum is very important. A cornerstone of Einstein's theory of relativity is that the speed of light in vacuum is constant, that is, it is equal in all inertial systems and has nothing to do with the direction of propagation. There is no light ether in which light has a default speed. Einstein derived far-reaching conclusions about time and space based on this assumption. For example, the experimentally confirmed time delay effect, the length contraction of moving objects, and the inability of any object to reach or exceed the speed of light. The central role of light in the theory suggests that electromagnetic fields are directly related to space and time, although this relationship is not yet fully understood.
The speed of a particle is a very simple and clear concept, but the speed of light (and other wave phenomena) is a very complex issue. There are several different concepts of speed (especially when light travels through a medium), and they have different numerical values:
Phase velocity is the speed at which the phase wavefront propagates.
The group velocity is the speed at which the maximum intensity of light travels (for example, the peak of a pulse).
The phase velocity and group velocity of information propagation are different, see the entry Causality.
Figure 1 gives the different speeds. In this example, the phase velocities of different frequency components vary linearly with frequency: high-frequency component wavefronts propagate more slowly. The pulse maximum overlaps the wavefront and propagates at group velocity. More details are given in the entry on group velocity.
Figure 1: Propagation of light pulses in dispersive media. Phase wavefronts with different frequency components propagate at different velocities, and the pulses propagate at group velocity, which is smaller than the phase velocity.
The situation is more complicated when light propagates in non-isotropic media, especially in waveguides.
The phase velocity in vacuum is equal to the group velocity (plane wave) is c = 299 792 458 m/s. In the International System of Units (SI), the definition of the speed of light in vacuum corresponds exactly to the actual value. And combined with the definition of the second (defined by the hyperfine transition of the cesium atom), the length of the meter can be determined.
In some cases, usually in the presence of absorption or gain resonance, the phase velocity or even the group velocity can be greater than the speed of light in a vacuum (see superluminal transmission, "fast light"), but this does not violate the causal relationship. In other cases, the speed of light slows down in a very narrow region of the spectrum (slow light). A large reduction in velocity can be observed at narrow-band resonances, as occurs, for example, in ultracold gases.
A more exotic effect is the presence of negative group velocities and negative dn/dω in some cases.
In fundamental physics, the speed of light in vacuum is very important. A cornerstone of Einstein's theory of relativity is that the speed of light in vacuum is constant, that is, it is equal in all inertial systems and has nothing to do with the direction of propagation. There is no light ether in which light has a default speed. Einstein derived far-reaching conclusions about time and space based on this assumption. For example, the experimentally confirmed time delay effect, the length contraction of moving objects, and the inability of any object to reach or exceed the speed of light. The central role of light in the theory suggests that electromagnetic fields are directly related to space and time, although this relationship is not yet fully understood.
