velocity of light (original) (raw)

Author: the photonics expert (RP)

Definition: the velocity with which light propagates in a medium

Alternative term: speed of light

Categories: article belongs to category general optics general optics, article belongs to category physical foundations physical foundations

Related: wavefrontsphase velocitygroup velocitycausalitysuperluminal transmission

Units: m/s

Page views in 12 months: 1055

DOI: 10.61835/smr Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

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Contents

Introduction

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:

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.

illustration of group velocity

Figure 1: Propagation of a light pulse in a dispersive medium. Note that the phase fronts of different frequency components (shown as straight lines) propagate with different velocities, and the pulse propagates with the group velocity, which is lower than all the phase velocities.

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 never depends 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 led Einstein to very far-reaching conclusions concerning the nature of space and time. Examples are the experimentally well confirmed phenomena of time dilation, 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.

Frequently Asked Questions

This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).

What is the difference between the phase and group velocity of light?

The phase velocity is the speed at which wavefronts propagate, whereas the group velocity is the speed of intensity maxima, such as the peak of a light pulse. These velocities can differ significantly when light propagates through a dispersive medium.

What is the speed of light in a vacuum?

The speed of light in a vacuum, denoted as ($c$), is a fundamental physical constant defined to be exactly 299,792,458 m/s in the International System of Units (SI).

Can light travel faster than the vacuum speed of light?

In some special situations, for example near an absorption or gain resonance in a medium, the phase or group velocity of light can exceed the vacuum velocity ($c$). This phenomenon is called superluminal transmission, but it does not allow for a violation of causality.

What is the role of the speed of light in the theory of relativity?

A cornerstone of Einstein's theory of relativity is that the vacuum velocity of light is the same for all observers in all inertial systems. This principle leads to far-reaching consequences concerning the nature of space and time, such as time dilation and length contraction.

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