The speed of light in
vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often di ...
, commonly denoted , is a universal
physical constant that is important in many areas of
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
. The speed of light is exactly equal to ). According to the
special theory of relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
, is the upper limit for the speed at which conventional
matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic part ...
or
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...
(and thus any
signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...
carrying
information
Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
) can travel through
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually cons ...
.
All forms of
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) li ...
, including
visible light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 te ...
, travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects.
Starlight viewed on
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
left the
stars many years ago, allowing humans to study the history of the universe by viewing distant objects. When
communicating
Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inquir ...
with distant
space probe
A space probe is an artificial satellite that travels through space to collect scientific data. A space probe may orbit Earth; approach the Moon; travel through interplanetary space; flyby, orbit, or land or fly on other planetary bodies; or ...
s, it can take minutes to hours for signals to travel from Earth to the spacecraft and vice versa. In
computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, ...
, the speed of light fixes the ultimate minimum communication
delay
Delay (from Latin: dilatio) may refer to:
Arts, entertainment, and media
* ''Delay 1968'', a 1981 album by German experimental rock band Can
* ''The Delay'', a 2012 Uruguayan film
People
* B. H. DeLay (1891–1923), American aviator and acto ...
between computers, to
computer memory
In computing, memory is a device or system that is used to store information for immediate use in a computer or related computer hardware and digital electronic devices. The term ''memory'' is often synonymous with the term '' primary storag ...
, and within a
CPU. The speed of light can be used in
time of flight
Time of flight (ToF) is the measurement of the time taken by an object, particle or wave (be it acoustic, electromagnetic, etc.) to travel a distance through a medium. This information can then be used to measure velocity or path length, or as a w ...
measurements to measure large distances to extremely high precision.
Ole Rømer first
demonstrated in 1676 that light travels at a finite speed (non-instantaneously) by studying the apparent motion of
Jupiter
Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandth t ...
's moon
Io. Progressively more accurate measurements of its speed came over the following centuries. In a
paper
Paper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, rags, grasses or other vegetable sources in water, draining the water through fine mesh leaving the fibre evenly distrib ...
published in 1865,
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and li ...
proposed that light was an
electromagnetic wave
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
and, therefore, travelled at speed . In 1905,
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
postulated that the speed of light with respect to any
inertial frame of reference
In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. ...
is a constant and is independent of the motion of the light source.
He explored the consequences of that postulate by deriving the theory of relativity and, in doing so, showed that the parameter had relevance outside of the context of light and electromagnetism.
Massless particle
In particle physics, a massless particle is an elementary particle whose invariant mass is zero. There are two known gauge boson massless particles: the photon (carrier of electromagnetism) and the gluon (carrier of the strong force). However, g ...
s and
field
Field may refer to:
Expanses of open ground
* Field (agriculture), an area of land used for agricultural purposes
* Airfield, an aerodrome that lacks the infrastructure of an airport
* Battlefield
* Lawn, an area of mowed grass
* Meadow, a grass ...
perturbations, such as
gravitational waves, also travel at speed in a vacuum. Such particles and waves travel at regardless of the motion of the source or the inertial reference frame of the
observer
An observer is one who engages in observation or in watching an experiment.
Observer may also refer to:
Computer science and information theory
* In information theory, any system which receives information from an object
* State observer in co ...
. Particles with nonzero
rest mass
The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, i ...
can be accelerated to approach but can never reach it, regardless of the frame of reference in which their speed is measured. In the
special and general theories of relativity, interrelates
space and time Space and Time or Time and Space, or ''variation'', may refer to:
* '' Space and time'' or ''time and space'' or ''spacetime'', any mathematical model that combines space and time into a single interwoven continuum
* Philosophy of space and time
S ...
and also appears in the famous equation of
mass–energy equivalence
In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. The principle is described by the physici ...
, .
In some cases, objects or waves may appear to travel
faster than light
Faster-than-light (also FTL, superluminal or supercausal) travel and communication are the conjectural propagation of matter or information faster than the speed of light (). The special theory of relativity implies that only particles with zero ...
(e.g.,
phase velocities
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...
of waves,
the appearance of certain high-speed astronomical objects, and particular
quantum effects
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
). The
expansion of the universe is understood to exceed the speed of light beyond
a certain boundary.
The speed at which light propagates through
transparent materials
In the field of optics, transparency (also called pellucidity or diaphaneity) is the physical property of allowing light to pass through the material without appreciable scattering of light. On a macroscopic scale (one in which the dimensions ...
, such as glass or air, is less than ; similarly, the speed of
electromagnetic waves in wire cables is slower than . The ratio between and the speed at which light travels in a material is called the
refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
of the material (). For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at ; the
refractive index of air
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...
for visible light is about 1.0003, so the speed of light in air is about slower than .
Numerical value, notation, and units
The speed of light in vacuum is usually denoted by a lowercase , for "constant" or the Latin (meaning 'swiftness, celerity'). In 1856,
Wilhelm Eduard Weber
Wilhelm Eduard Weber (; ; 24 October 1804 – 23 June 1891) was a German physicist and, together with Carl Friedrich Gauss, inventor of the first electromagnetic telegraph.
Biography of Wilhelm
Early years
Weber was born in Schlossstrasse i ...
and
Rudolf Kohlrausch
Rudolf Hermann Arndt Kohlrausch (November 6, 1809 in Göttingen – March 8, 1858 in Erlangen) was a German physicist.
Biography
He was a native of Göttingen, the son of the Royal Hanovarian director general of schools Friedrich Kohlrausch. He ...
had used for a different constant that was later shown to equal times the speed of light in vacuum. Historically, the symbol ''V'' was used as an alternative symbol for the speed of light, introduced by
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and li ...
in 1865. In 1894,
Paul Drude
Paul Karl Ludwig Drude (; 12 July 1863 – 5 July 1906) was a German physicist specializing in optics. He wrote a fundamental textbook integrating optics with Maxwell's theories of electromagnetism.
Education
Born into an ethnic German family, D ...
redefined with its modern meaning.
Einstein used ''V'' in his
original German-language papers on special relativity in 1905, but in 1907 he switched to , which by then had become the standard symbol for the speed of light.
[
"The origins of the letter c being used for the speed of light can be traced back to a paper of 1856 by Weber and Kohlrausch ..Weber apparently meant c to stand for 'constant' in his force law, but there is evidence that physicists such as Lorentz and Einstein were accustomed to a common convention that c could be used as a variable for velocity. This usage can be traced back to the classic Latin texts in which c stood for 'celeritas', meaning 'speed'."
]
Sometimes is used for the speed of waves in any material medium, and
0 for the speed of light in vacuum.
[See for example:
*
*
*
* ] This subscripted notation, which is endorsed in official SI literature,
has the same form as related electromagnetic constants: namely, ''μ''
0 for the
vacuum permeability
The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum''), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, ...
or magnetic constant, ''ε''
0 for the
vacuum permittivity or electric constant, and ''Z''
0 for the
impedance of free space The impedance of free space, , is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is, , where is the electric field strength and is the magnetic fie ...
. This article uses exclusively for the speed of light in vacuum.
Use in unit systems
Since 1983, the constant has been defined in the
International System of Units (SI) as ''exactly'' ; this relationship is used to define the metre as exactly the distance that light travels in a vacuum in of a
second. By using the value of , as well as an accurate measurement of the
second, one can thus establish a standard for the metre.
[See, for example:
*
*
*] As a
dimensional physical constant, the numerical value of is different for different unit systems. For example, in
imperial units
The imperial system of units, imperial system or imperial units (also known as British Imperial or Exchequer Standards of 1826) is the system of units first defined in the British Weights and Measures Act 1824 and continued to be developed th ...
, the speed of light is approximately miles per second, or roughly 1
foot per nanosecond.
In branches of physics in which appears often, such as in relativity, it is common to use systems of
natural units
In physics, natural units are physical units of measurement in which only universal physical constants are used as defining constants, such that each of these constants acts as a coherent unit of a quantity. For example, the elementary charge ma ...
of measurement or the
geometrized unit system
A geometrized unit system, geometric unit system or geometrodynamic unit system is a system of natural units in which the base physical units are chosen so that the speed of light in vacuum, ''c'', and the gravitational constant, ''G'', are set eq ...
where .
[
][
] Using these units, does not appear explicitly because multiplication or division by1 does not affect the result. Its unit of
light-second
The light-second is a unit of length useful in astronomy, telecommunications and relativistic physics. It is defined as the distance that light travels in free space in one second, and is equal to exactly .
Just as the second forms the basis for ...
per second is still relevant, even if omitted.
Fundamental role in physics
The speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the
inertial frame of reference
In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. ...
of the observer.
[However, the ]frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
of light can depend on the motion of the source relative to the observer, due to the Doppler effect. This invariance of the speed of light was postulated by Einstein in 1905,
after being motivated by
Maxwell's theory of electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions o ...
and the lack of evidence for the
luminiferous aether
Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), so ...
; it has since been consistently confirmed by many experiments.
[See ]Michelson–Morley experiment
The Michelson–Morley experiment was an attempt to detect the existence of the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves. The experiment was performed between April and July 188 ...
and Kennedy–Thorndike experiment
The Kennedy–Thorndike experiment, first conducted in 1932 by Roy J. Kennedy and Edward M. Thorndike, is a modified form of the Michelson–Morley experimental procedure, testing special relativity.
The modification is to make one arm of the class ...
, for example. It is only possible to verify experimentally that the two-way speed of light (for example, from a source to a mirror and back again) is frame-independent, because it is impossible to measure the
one-way speed of light
When using the term ' the speed of light' it is sometimes necessary to make the distinction between its one-way speed and its two-way speed. The "one-way" speed of light, from a source to a detector, cannot be measured independently of a conventio ...
(for example, from a source to a distant detector) without some convention as to how clocks at the source and at the detector should be synchronized. However, by adopting
Einstein synchronization
Einstein synchronisation (or Poincaré–Einstein synchronisation) is a convention for synchronising clocks at different places by means of signal exchanges. This synchronisation method was used by telegraphers in the middle 19th century, but ...
for the clocks, the one-way speed of light becomes equal to the two-way speed of light by definition.
[
] The
special theory of relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
explores the consequences of this invariance of ''c'' with the assumption that the laws of physics are the same in all inertial frames of reference. One consequence is that ''c'' is the speed at which all
massless particle
In particle physics, a massless particle is an elementary particle whose invariant mass is zero. There are two known gauge boson massless particles: the photon (carrier of electromagnetism) and the gluon (carrier of the strong force). However, g ...
s and waves, including light, must travel in vacuum.
![Lorentz factor](https://upload.wikimedia.org/wikipedia/commons/0/00/Lorentz_factor.svg)
Special relativity has many counterintuitive and experimentally verified implications. These include the
equivalence of mass and energy
Equivalence or Equivalent may refer to:
Arts and entertainment
*Album-equivalent unit, a measurement unit in the music industry
*Equivalence class (music)
*''Equivalent VIII'', or ''The Bricks'', a minimalist sculpture by Carl Andre
*''Equivale ...
,
length contraction
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald ...
(moving objects shorten), and
time dilation
In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
(moving clocks run more slowly). The factor ''γ'' by which lengths contract and times dilate is known as the
Lorentz factor
The Lorentz factor or Lorentz term is a quantity expressing how much the measurements of time, length, and other physical properties change for an object while that object is moving. The expression appears in several equations in special relativit ...
and is given by , where ''v'' is the speed of the object. The difference of ''γ'' from1 is negligible for speeds much slower than ''c'', such as most everyday speedsin which case special relativity is closely approximated by
Galilean relativity
Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames of reference. Galileo Galilei first described this principle in 1632 in his '' Dialogue Concerning the Two Chief World Systems'' using t ...
but it increases at relativistic speeds and diverges to infinity as ''v'' approaches ''c''. For example, a time dilation factor of ''γ'' = 2 occurs at a relative velocity of 86.6% of the speed of light (''v'' = 0.866 ''c''). Similarly, a time dilation factor of ''γ'' = 10 occurs at 99.5% the speed of light (''v'' = 0.995 ''c'').
The results of special relativity can be summarized by treating space and time as a unified structure known as
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
(with ''c'' relating the units of space and time), and requiring that physical theories satisfy a special
symmetry called
Lorentz invariance
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of ...
, whose mathematical formulation contains the parameter ''c''. Lorentz invariance is an almost universal assumption for modern physical theories, such as
quantum electrodynamics
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
,
quantum chromodynamics, the
Standard Model of
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, and
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
. As such, the parameter ''c'' is ubiquitous in modern physics, appearing in many contexts that are unrelated to light. For example, general relativity predicts that ''c'' is also the
speed of gravity
In classical theories of gravitation, the changes in a gravitational field propagate. A change in the distribution of energy and momentum of matter results in subsequent alteration, at a distance, of the gravitational field which it produces. In ...
and of
gravitational waves
Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1 ...
,
[
] and observations of gravitational waves have been consistent with this prediction. In
non-inertial frame
A non-inertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration. While the laws of motion ar ...
s of reference (gravitationally curved spacetime or
accelerated reference frame
A non-inertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration. While the laws of motion ar ...
s), the ''local'' speed of light is constant and equal to ''c'', but the
speed of light along a trajectory of finite length can differ from ''c'', depending on how distances and times are defined.
It is generally assumed that fundamental constants such as ''c'' have the same value throughout spacetime, meaning that they do not depend on location and do not vary with time. However, it has been suggested in various theories that the
speed of light may have changed over time.
[
] No conclusive evidence for such changes has been found, but they remain the subject of ongoing research.
[
][
]
It also is generally assumed that the speed of light is
isotropic, meaning that it has the same value regardless of the direction in which it is measured. Observations of the emissions from nuclear
energy level
A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The t ...
s as a function of the orientation of the emitting
nuclei in a magnetic field (see
Hughes–Drever experiment
Hughes–Drever experiments (also clock comparison-, clock anisotropy-, mass isotropy-, or energy isotropy experiments) are spectroscopic tests of the isotropy of mass and space. Although originally conceived of as a test of Mach's principle, they ...
), and of rotating
optical resonator An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors or other optical elements that forms a cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and provi ...
s (see
Resonator experiments) have put stringent limits on the possible two-way
anisotropy
Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
.
Upper limit on speeds
According to special relativity, the energy of an object with
rest mass
The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, i ...
''m'' and speed ''v'' is given by , where ''γ'' is the Lorentz factor defined above. When ''v'' is zero, ''γ'' is equal to one, giving rise to the famous formula for mass–energy equivalence. The ''γ'' factor approaches infinity as ''v'' approaches ''c'', and it would take an infinite amount of energy to accelerate an object with mass to the speed of light. The speed of light is the upper limit for the speeds of objects with positive rest mass, and individual photons cannot travel faster than the speed of light. This is experimentally established in many
tests of relativistic energy and momentum
Tests of relativistic energy and momentum are aimed at measuring the relativistic expressions for energy, momentum, and mass. According to special relativity, the properties of particles moving approximately at the speed of light significantly de ...
.
![Relativity of Simultaneity](https://upload.wikimedia.org/wikipedia/commons/b/b1/Relativity_of_Simultaneity.svg)
More generally, it is impossible for signals or energy to travel faster than ''c''. One argument for this follows from the counter-intuitive implication of special relativity known as the
relativity of simultaneity. If the spatial distance between two events A and B is greater than the time interval between them multiplied by ''c'' then there are frames of reference in which A precedes B, others in which B precedes A, and others in which they are simultaneous. As a result, if something were travelling faster than ''c'' relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame, and
causality would be violated.
[
] In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded,
[ and would lead to ]paradox
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...
es such as the tachyonic antitelephone
A tachyonic antitelephone is a hypothetical device in theoretical physics that could be used to send signals into one's own past. Albert Einstein in 1907
presented a thought experiment of how faster-than-light signals can lead to a paradox of caus ...
.
Faster-than-light observations and experiments
There are situations in which it may seem that matter, energy, or information-carrying signal travels at speeds greater than ''c'', but they do not. For example, as is discussed in the propagation of light in a medium section below, many wave velocities can exceed ''c''. The phase velocity of X-ray
An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30&nb ...
s through most glasses can routinely exceed ''c'', but phase velocity does not determine the velocity at which waves convey information.
If a laser beam is swept quickly across a distant object, the spot of light can move faster than ''c'', although the initial movement of the spot is delayed because of the time it takes light to get to the distant object at the speed ''c''. However, the only physical entities that are moving are the laser and its emitted light, which travels at the speed ''c'' from the laser to the various positions of the spot. Similarly, a shadow projected onto a distant object can be made to move faster than ''c'', after a delay in time. In neither case does any matter, energy, or information travel faster than light.[
]
The rate of change in the distance between two objects in a frame of reference with respect to which both are moving (their closing speed) may have a value in excess of ''c''. However, this does not represent the speed of any single object as measured in a single inertial frame.
Certain quantum effects appear to be transmitted instantaneously and therefore faster than ''c'', as in the EPR paradox
EPR may refer to:
Science and technology
* EPR (nuclear reactor), European Pressurised-Water Reactor
* EPR paradox (Einstein–Podolsky–Rosen paradox), in physics
* Earth potential rise, in electrical engineering
* East Pacific Rise, a mid-oc ...
. An example involves the quantum state
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution i ...
s of two particles that can be entangled. Until either of the particles is observed, they exist in a superposition of two quantum states. If the particles are separated and one particle's quantum state is observed, the other particle's quantum state is determined instantaneously. However, it is impossible to control which quantum state the first particle will take on when it is observed, so information cannot be transmitted in this manner.
Another quantum effect that predicts the occurrence of faster-than-light speeds is called the Hartman effect The Hartman effect describes how the delay time for a quantum tunneling particle is independent of the thickness of the opaque barrier. It is named after Thomas Hartman, who discovered it in 1962.
Overview
The Hartman effect is the tunneling eff ...
: under certain conditions the time needed for a virtual particle
A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in the perturba ...
to tunnel
A tunnel is an underground passageway, dug through surrounding soil, earth or rock, and enclosed except for the entrance and exit, commonly at each end. A pipeline is not a tunnel, though some recent tunnels have used immersed tube cons ...
through a barrier is constant, regardless of the thickness of the barrier.[
][
] This could result in a virtual particle crossing a large gap faster than light. However, no information can be sent using this effect.
archive
/ref>
So-called superluminal motion is seen in certain astronomical objects, such as the relativistic jets of radio galaxies
A radio galaxy is a galaxy with giant regions of radio emission extending well beyond its visible structure. These energetic radio lobes are powered by jets from its active galactic nucleus. They have luminosities up to 1039 W at radio wav ...
and quasars. However, these jets are not moving at speeds in excess of the speed of light: the apparent superluminal motion is a projection
Projection, projections or projective may refer to:
Physics
* Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction
* The display of images by a projector
Optics, graphic ...
effect caused by objects moving near the speed of light and approaching Earth at a small angle to the line of sight: since the light which was emitted when the jet was farther away took longer to reach the Earth, the time between two successive observations corresponds to a longer time between the instants at which the light rays were emitted.
A 2011 experiment where neutrinos were observed to travel faster than light turned out to be due to experimental error.
In models of the expanding universe, the farther galaxies are from each other, the faster they drift apart. This receding is not due to motion through space, but rather to the expansion of space
The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not exp ...
itself. For example, galaxies far away from Earth appear to be moving away from the Earth with a speed proportional to their distances. Beyond a boundary called the Hubble sphere
In cosmology, a Hubble volume (named for the astronomer Edwin Hubble) or Hubble sphere, subluminal sphere, causal sphere and sphere of causality is a spherical region of the observable universe surrounding an observer beyond which objects recede ...
, the rate at which their distance from Earth increases becomes greater than the speed of light.[
]
Propagation of light
In classical physics, light is described as a type of electromagnetic wave
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
. The classical behaviour of the electromagnetic field is described by Maxwell's equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
...
, which predict that the speed ''c'' with which electromagnetic waves (such as light) propagate in vacuum is related to the distributed capacitance and inductance of vacuum, otherwise respectively known as the electric constant
Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric const ...
''ε''0 and the magnetic constant ''μ''0, by the equation
:
In modern quantum physics, the electromagnetic field is described by the theory of quantum electrodynamics
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
(QED). In this theory, light is described by the fundamental excitations (or quanta) of the electromagnetic field, called photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...
s. In QED, photons are massless particle
In particle physics, a massless particle is an elementary particle whose invariant mass is zero. There are two known gauge boson massless particles: the photon (carrier of electromagnetism) and the gluon (carrier of the strong force). However, g ...
s and thus, according to special relativity, they travel at the speed of light in vacuum.
Extensions of QED in which the photon has a mass have been considered. In such a theory, its speed would depend on its frequency, and the invariant speed ''c'' of special relativity would then be the upper limit of the speed of light in vacuum.[
] No variation of the speed of light with frequency has been observed in rigorous testing, putting stringent limits on the mass of the photon. The limit obtained depends on the model used: if the massive photon is described by Proca theory, the experimental upper bound for its mass is about 10−57 gram
The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram.
Originally defined as of 1795 as "the absolute weight of a volume of pure water equal to th ...
s;[
] if photon mass is generated by a Higgs mechanism
In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other be ...
, the experimental upper limit is less sharp, (roughly 2 × 10−47 g).
Another reason for the speed of light to vary with its frequency would be the failure of special relativity to apply to arbitrarily small scales, as predicted by some proposed theories of quantum gravity. In 2009, the observation of gamma-ray burst
In gamma-ray astronomy, gamma-ray bursts (GRBs) are immensely energetic explosions that have been observed in distant galaxies. They are the most energetic and luminous electromagnetic events since the Big Bang. Bursts can last from ten millise ...
GRB 090510 found no evidence for a dependence of photon speed on energy, supporting tight constraints in specific models of spacetime quantization on how this speed is affected by photon energy for energies approaching the Planck scale.
In a medium
In a medium, light usually does not propagate at a speed equal to ''c''; further, different types of light wave will travel at different speeds. The speed at which the individual crests and troughs of a plane wave
In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space.
For any position \vec x in space and any time t, ...
(a wave filling the whole space, with only one frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
) propagate is called the phase velocity ''v''p. A physical signal with a finite extent (a pulse of light) travels at a different speed. The overall envelope
An envelope is a common packaging item, usually made of thin, flat material. It is designed to contain a flat object, such as a letter or card.
Traditional envelopes are made from sheets of paper cut to one of three shapes: a rhombus, a sh ...
of the pulse travels at the group velocity ''v''g, and its earliest part travels at the front velocity ''v''f.
The phase velocity is important in determining how a light wave travels through a material or from one material to another. It is often represented in terms of a ''refractive index''. The refractive index of a material is defined as the ratio of ''c'' to the phase velocity ''v''p in the material: larger indices of refraction indicate lower speeds. The refractive index of a material may depend on the light's frequency, intensity, polarization, or direction of propagation; in many cases, though, it can be treated as a material-dependent constant. The refractive index of air
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...
is approximately 1.0003. Denser media, such as water
Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...
, glass
Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling ( quenching ...
, and diamond
Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure, ...
, have refractive indexes of around 1.3, 1.5 and 2.4, respectively, for visible light. In exotic materials like Bose–Einstein condensate
In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.6 ...
s near absolute zero, the effective speed of light may be only a few metres per second. However, this represents absorption and re-radiation delay between atoms, as do all slower-than-''c'' speeds in material substances. As an extreme example of light "slowing" in matter, two independent teams of physicists claimed to bring light to a "complete standstill" by passing it through a Bose–Einstein condensate of the element rubidium. However, the popular description of light being "stopped" in these experiments refers only to light being stored in the excited states of atoms, then re-emitted at an arbitrarily later time, as stimulated by a second laser pulse. During the time it had "stopped", it had ceased to be light. This type of behaviour is generally microscopically true of all transparent media which "slow" the speed of light.
In transparent materials, the refractive index generally is greater than 1, meaning that the phase velocity is less than ''c''. In other materials, it is possible for the refractive index to become smaller than1 for some frequencies; in some exotic materials it is even possible for the index of refraction to become negative. The requirement that causality is not violated implies that the real and imaginary parts
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a ...
of the dielectric constant of any material, corresponding respectively to the index of refraction and to the attenuation coefficient
The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient valu ...
, are linked by the Kramers–Kronig relations. In practical terms, this means that in a material with refractive index less than 1, the wave will be absorbed quickly.
A pulse with different group and phase velocities (which occurs if the phase velocity is not the same for all the frequencies of the pulse) smears out over time, a process known as dispersion
Dispersion may refer to:
Economics and finance
* Dispersion (finance), a measure for the statistical distribution of portfolio returns
* Price dispersion, a variation in prices across sellers of the same item
*Wage dispersion, the amount of variat ...
. Certain materials have an exceptionally low (or even zero) group velocity for light waves, a phenomenon called slow light
Slow light is the propagation of an optical pulse or other modulation of an optical carrier at a very low group velocity. Slow light occurs when a propagating pulse is substantially slowed by the interaction with the medium in which the propagatio ...
.
The opposite, group velocities exceeding ''c'', was proposed theoretically in 1993 and achieved experimentally in 2000. It should even be possible for the group velocity to become infinite or negative, with pulses travelling instantaneously or backwards in time.
None of these options, however, allow information to be transmitted faster than ''c''. It is impossible to transmit information with a light pulse any faster than the speed of the earliest part of the pulse (the front velocity). It can be shown that this is (under certain assumptions) always equal to ''c''.
It is possible for a particle to travel through a medium faster than the phase velocity of light in that medium (but still slower than ''c''). When a charged particle
In physics, a charged particle is a particle with an electric charge. It may be an ion, such as a molecule or atom with a surplus or deficit of electrons relative to protons. It can also be an electron or a proton, or another elementary pa ...
does that in a dielectric
In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
material, the electromagnetic equivalent of a shock wave
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
, known as Cherenkov radiation, is emitted.
Practical effects of finiteness
The speed of light is of relevance to communications
Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inquir ...
: the one-way and round-trip delay time
In telecommunications, round-trip delay (RTD) or round-trip time (RTT) is the amount of time it takes for a signal to be sent ''plus'' the amount of time it takes for acknowledgement of that signal having been received. This time delay includes pr ...
are greater than zero. This applies from small to astronomical scales. On the other hand, some techniques depend on the finite speed of light, for example in distance measurements.
Small scales
In computers, the speed of light imposes a limit on how quickly data can be sent between processors
A central processing unit (CPU), also called a central processor, main processor or just processor, is the electronic circuitry that executes instructions comprising a computer program. The CPU performs basic arithmetic, logic, controlling, ...
. If a processor operates at 1gigahertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one he ...
, a signal can travel only a maximum of about in a single clock cycle — in practice, this distance is even shorter since the printed circuit board itself has a refractive index and slows down signals. Processors must therefore be placed close to each other, as well as memory
Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembered ...
chips, to minimize communication latencies, and care must be exercised when routing wires between them to ensure signal integrity. If clock frequencies continue to increase, the speed of light may eventually become a limiting factor for the internal design of single chips
''CHiPs'' is an American crime drama television series created by Rick Rosner and originally aired on NBC from September 15, 1977, to May 1, 1983. It follows the lives of two motorcycle officers of the California Highway Patrol (CHP). The seri ...
.
Large distances on Earth
Given that the equatorial circumference of the Earth is about and that ''c'' is about , the theoretical shortest time for a piece of information to travel half the globe along the surface is about 67 milliseconds. When light is traveling in optical fibre (a transparent material
In the field of optics, transparency (also called pellucidity or diaphaneity) is the physical property of allowing light to pass through the material without appreciable light scattering by particles, scattering of light. On a macroscopic scale ...
) the actual transit time is longer, in part because the speed of light is slower by about 35% in optical fibre, depending on its refractive index ''n''. Furthermore, straight lines are rare in global communications and the travel time increases when signals pass through electronic switches or signal regenerators.
Although this distance is largely irrelevant for most applications, latency becomes important in fields such as high-frequency trading, where traders seek to gain minute advantages by delivering their trades to exchanges fractions of a second ahead of other traders. For example, traders have been switching to microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ra ...
communications between trading hubs, because of the advantage which radio waves travelling at near to the speed of light through air have over comparatively slower fibre optic signals.
Spaceflight and astronomy
Similarly, communications between the Earth and spacecraft are not instantaneous. There is a brief delay from the source to the receiver, which becomes more noticeable as distances increase. This delay was significant for communications between ground control and Apollo 8 when it became the first crewed spacecraft to orbit the Moon: for every question, the ground control station had to wait at least three seconds for the answer to arrive. The communications delay between Earth and Mars
Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin at ...
can vary between five and twenty minutes depending upon the relative positions of the two planets. As a consequence of this, if a robot on the surface of Mars were to encounter a problem, its human controllers would not be aware of it until later. It would then take a further for commands to travel from Earth to Mars.
Receiving light and other signals from distant astronomical sources takes much longer. For example, it takes 13 billion (13) years for light to travel to Earth from the faraway galaxies viewed in the Hubble Ultra Deep Field images. Those photographs, taken today, capture images of the galaxies as they appeared 13 billion years ago, when the universe was less than a billion years old.[ The fact that more distant objects appear to be younger, due to the finite speed of light, allows astronomers to infer the ]evolution of stars
Stellar evolution is the process by which a star changes over the course of time. Depending on the mass of the star, its lifetime can range from a few million years for the most massive to trillions of years for the least massive, which is cons ...
, of galaxies, and of the universe itself.
Astronomical distances are sometimes expressed in light-years, especially in popular science publications and media. A light-year is the distance light travels in one Julian year, around 9461 billion kilometres, 5879 billion miles, or 0.3066 parsec
The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, an ...
s. In round figures, a light year is nearly 10 trillion kilometres or nearly 6 trillion miles. Proxima Centauri, the closest star to Earth after the Sun, is around 4.2 light-years away.[Further discussion can be found at ]
Distance measurement
Radar
Radar is a detection system that uses radio waves to determine the distance ('' ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, we ...
systems measure the distance to a target by the time it takes a radio-wave pulse to return to the radar antenna after being reflected by the target: the distance to the target is half the round-trip transit time multiplied by the speed of light. A Global Positioning System
The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...
(GPS) receiver measures its distance to GPS satellites
GPS satellite blocks are the various production generations of the Global Positioning System (GPS) used for satellite navigation. The first satellite in the system, Navstar 1, was launched on 22 February 1978. The GPS satellite constellatio ...
based on how long it takes for a radio signal to arrive from each satellite, and from these distances calculates the receiver's position. Because light travels about () in one second, these measurements of small fractions of a second must be very precise. The Lunar Laser Ranging Experiment, radar astronomy
Radar astronomy is a technique of observing nearby astronomical objects by reflecting radio waves or microwaves off target objects and analyzing their reflections. Radar astronomy differs from '' radio astronomy'' in that the latter is a passiv ...
and the Deep Space Network
The NASA Deep Space Network (DSN) is a worldwide network of American spacecraft communication ground segment facilities, located in the United States (California), Spain (Madrid), and Australia (Canberra), that supports NASA's interplanetary ...
determine distances to the Moon, planets and spacecraft, respectively, by measuring round-trip transit times.
Measurement
There are different ways to determine the value of ''c''. One way is to measure the actual speed at which light waves propagate, which can be done in various astronomical and Earth-based setups. However, it is also possible to determine ''c'' from other physical laws where it appears, for example, by determining the values of the electromagnetic constants ''ε''0 and ''μ''0 and using their relation to ''c''. Historically, the most accurate results have been obtained by separately determining the frequency and wavelength of a light beam, with their product equalling ''c''. This is described in more detail in the "Interferometry" section below.
In 1983 the metre was defined as "the length of the path travelled by light in vacuum during a time interval of of a second",[ fixing the value of the speed of light at by definition, as described below. Consequently, accurate measurements of the speed of light yield an accurate realization of the metre rather than an accurate value of ''c''.
]
Astronomical measurements
Outer space
Outer space, commonly shortened to space, is the expanse that exists beyond Earth and its atmosphere and between celestial bodies. Outer space is not completely empty—it is a near-perfect vacuum containing a low density of particles, pred ...
is a convenient setting for measuring the speed of light because of its large scale and nearly perfect vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often di ...
. Typically, one measures the time needed for light to traverse some reference distance in the Solar System
The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
, such as the radius
In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...
of the Earth's orbit. Historically, such measurements could be made fairly accurately, compared to how accurately the length of the reference distance is known in Earth-based units.
Ole Christensen Rømer used an astronomical measurement to make the first quantitative estimate of the speed of light in the year 1676.[
]
Translated in
Reproduced in
The account published in ''Journal des sçavans'' was based on a report that Rømer read to the French Academy of Sciences in November 1676 (Cohen, 1940, p. 346). When measured from Earth, the periods of moons orbiting a distant planet are shorter when the Earth is approaching the planet than when the Earth is receding from it. The distance travelled by light from the planet (or its moon) to Earth is shorter when the Earth is at the point in its orbit that is closest to its planet than when the Earth is at the farthest point in its orbit, the difference in distance being the diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid fo ...
of the Earth's orbit around the Sun. The observed change in the moon's orbital period is caused by the difference in the time it takes light to traverse the shorter or longer distance. Rømer observed this effect for Jupiter
Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandth t ...
's innermost major moon Io and deduced that light takes 22 minutes to cross the diameter of the Earth's orbit.
Another method is to use the aberration of light
In astronomy, aberration (also referred to as astronomical aberration, stellar aberration, or velocity aberration) is a phenomenon which produces an apparent motion of celestial objects about their true positions, dependent on the velocity of t ...
, discovered and explained by James Bradley
James Bradley (1692–1762) was an English astronomer and priest who served as the third Astronomer Royal from 1742. He is best known for two fundamental discoveries in astronomy, the aberration of light (1725–1728), and the nutation of th ...
in the 18th century. This effect results from the vector addition
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors a ...
of the velocity of light arriving from a distant source (such as a star) and the velocity of its observer (see diagram on the right). A moving observer thus sees the light coming from a slightly different direction and consequently sees the source at a position shifted from its original position. Since the direction of the Earth's velocity changes continuously as the Earth orbits the Sun, this effect causes the apparent position of stars to move around. From the angular difference in the position of stars (maximally 20.5 arcseconds) it is possible to express the speed of light in terms of the Earth's velocity around the Sun, which with the known length of a year can be converted to the time needed to travel from the Sun to the Earth. In 1729, Bradley used this method to derive that light travelled times faster than the Earth in its orbit (the modern figure is times faster) or, equivalently, that it would take light 8 minutes 12 seconds to travel from the Sun to the Earth.
Astronomical unit
An astronomical unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits ...
(AU) is approximately the average distance between the Earth and Sun. It was redefined in 2012 as exactly . Previously the AU was not based on the International System of Units but in terms of the gravitational force exerted by the Sun in the framework of classical mechanics. The current definition uses the recommended value in metres for the previous definition of the astronomical unit, which was determined by measurement. This redefinition is analogous to that of the metre and likewise has the effect of fixing the speed of light to an exact value in astronomical units per second (via the exact speed of light in metres per second).
Previously, the inverse of expressed in seconds per astronomical unit was measured by comparing the time for radio signals to reach different spacecraft in the Solar System, with their position calculated from the gravitational effects of the Sun and various planets. By combining many such measurements, a best fit
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is ...
value for the light time per unit distance could be obtained. For example, in 2009, the best estimate, as approved by the International Astronomical Union
The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreac ...
(IAU), was:[
]
:light time for unit distance: ''t''au =
:''c'' = =
The relative uncertainty in these measurements is 0.02 parts per billion (), equivalent to the uncertainty in Earth-based measurements of length by interferometry. Since the metre is defined to be the length travelled by light in a certain time interval, the measurement of the light time in terms of the previous definition of the astronomical unit can also be interpreted as measuring the length of an AU (old definition) in metres.
Time of flight techniques
A method of measuring the speed of light is to measure the time needed for light to travel to a mirror at a known distance and back. This is the working principle behind the Fizeau–Foucault apparatus
The Fizeau–Foucault apparatus is either of two types of instrument historically used to measure the speed of light. The conflation of the two instrument types arises in part because Hippolyte Fizeau and Léon Foucault had originally been friends ...
developed by Hippolyte Fizeau
Armand Hippolyte Louis Fizeau FRS FRSE MIF (; 23 September 181918 September 1896) was a French physicist, best known for measuring the speed of light in the namesake Fizeau experiment.
Biography
Fizeau was born in Paris to Louis and Beatrice Fi ...
and Léon Foucault
Jean Bernard Léon Foucault (, ; ; 18 September 1819 – 11 February 1868) was a French physicist best known for his demonstration of the Foucault pendulum, a device demonstrating the effect of Earth's rotation. He also made an early measurement ...
, based on a suggestion by François Arago.
The setup as used by Fizeau consists of a beam of light directed at a mirror away. On the way from the source to the mirror, the beam passes through a rotating cogwheel. At a certain rate of rotation, the beam passes through one gap on the way out and another on the way back, but at slightly higher or lower rates, the beam strikes a tooth and does not pass through the wheel. Knowing the distance between the wheel and the mirror, the number of teeth on the wheel, and the rate of rotation, the speed of light can be calculated.
The method of Foucault replaces the cogwheel with a rotating mirror. Because the mirror keeps rotating while the light travels to the distant mirror and back, the light is reflected from the rotating mirror at a different angle on its way out than it is on its way back. From this difference in angle, the known speed of rotation and the distance to the distant mirror the speed of light may be calculated.
Today, using oscilloscopes
An oscilloscope (informally a scope) is a type of electronic test instrument that graphically displays varying electrical voltages as a two-dimensional plot of one or more signals as a function of time. The main purposes are to display repetiti ...
with time resolutions of less than one nanosecond, the speed of light can be directly measured by timing the delay of a light pulse from a laser or an LED reflected from a mirror. This method is less precise (with errors of the order of 1%) than other modern techniques, but it is sometimes used as a laboratory experiment in college physics classes.
Electromagnetic constants
An option for deriving ''c'' that does not directly depend on a measurement of the propagation of electromagnetic waves is to use the relation between ''c'' and the vacuum permittivity ''ε''0 and vacuum permeability
The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum''), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, ...
''μ''0 established by Maxwell's theory: ''c''2 = 1/(''ε''0''μ''0). The vacuum permittivity may be determined by measuring the capacitance
Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized ar ...
and dimensions of a capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
, whereas the value of the vacuum permeability was historically fixed at exactly through the definition of the ampere. Rosa
Rosa or De Rosa may refer to:
People
*Rosa (given name)
* Rosa (surname)
* Santa Rosa (female given name from Latin-a latinized variant of Rose)
Places
* 223 Rosa, an asteroid
*Rosa, Alabama, a town, United States
* Rosa, Germany, in Thuringia, ...
and Dorsey used this method in 1907 to find a value of . Their method depended upon having a standard unit of electrical resistance, the "international ohm
Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm.
Ohm or OHM may also refer to:
People
* Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm''
* Germán Ohm (born 1936), Mexican boxer
* Jörg Ohm (b ...
", and so its accuracy was limited by how this standard was defined.
Cavity resonance
Another way to measure the speed of light is to independently measure the frequency ''f'' and wavelength ''λ'' of an electromagnetic wave in vacuum. The value of ''c'' can then be found by using the relation ''c'' = ''fλ''. One option is to measure the resonance frequency of a cavity resonator
A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator ...
. If the dimensions of the resonance cavity are also known, these can be used to determine the wavelength of the wave. In 1946, Louis Essen
Louis Essen FRS O.B.E. (6 September 1908 – 24 August 1997) was an English physicist whose most notable achievements were in the precise measurement of time and the determination of the speed of light. He was a critic of Albert Einstein' ...
and A.C. Gordon-Smith established the frequency for a variety of normal modes of microwaves of a microwave cavity
A microwave cavity or ''radio frequency (RF) cavity'' is a special type of resonator, consisting of a closed (or largely closed) metal structure that confines electromagnetic fields in the microwave region of the spectrum. The structure is eithe ...
of precisely known dimensions. The dimensions were established to an accuracy of about ±0.8 μm using gauges calibrated by interferometry. As the wavelength of the modes was known from the geometry of the cavity and from electromagnetic theory
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
, knowledge of the associated frequencies enabled a calculation of the speed of light.
The Essen–Gordon-Smith result, , was substantially more precise than those found by optical techniques. By 1950, repeated measurements by Essen established a result of .[
]
A household demonstration of this technique is possible, using a microwave oven
A microwave oven (commonly referred to as a microwave) is an electric oven that heats and cooks food by exposing it to electromagnetic radiation in the microwave frequency range. This induces polar molecules in the food to rotate and produce ...
and food such as marshmallows or margarine: if the turntable is removed so that the food does not move, it will cook the fastest at the antinode
A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effect ...
s (the points at which the wave amplitude is the greatest), where it will begin to melt. The distance between two such spots is half the wavelength of the microwaves; by measuring this distance and multiplying the wavelength by the microwave frequency (usually displayed on the back of the oven, typically 2450 MHz), the value of ''c'' can be calculated, "often with less than 5% error".
Interferometry
Interferometry is another method to find the wavelength of electromagnetic radiation for determining the speed of light. A coherent
Coherence, coherency, or coherent may refer to the following:
Physics
* Coherence (physics), an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference
* Coherence (units of measurement), a deri ...
beam of light (e.g. from a laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fi ...
), with a known frequency (''f''), is split to follow two paths and then recombined. By adjusting the path length while observing the interference pattern
In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
and carefully measuring the change in path length, the wavelength of the light (''λ'') can be determined. The speed of light is then calculated using the equation ''c'' = ''λf''.
Before the advent of laser technology, coherent radio
Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmi ...
sources were used for interferometry measurements of the speed of light.[
] However interferometric determination of wavelength becomes less precise with wavelength and the experiments were thus limited in precision by the long wavelength (~) of the radiowaves. The precision can be improved by using light with a shorter wavelength, but then it becomes difficult to directly measure the frequency of the light. One way around this problem is to start with a low frequency signal of which the frequency can be precisely measured, and from this signal progressively synthesize higher frequency signals whose frequency can then be linked to the original signal. A laser can then be locked to the frequency, and its wavelength can be determined using interferometry.[
] This technique was due to a group at the National Bureau of Standards (which later became the National Institute of Standards and Technology
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical s ...
). They used it in 1972 to measure the speed of light in vacuum with a fractional uncertainty of .[
]
History
Until the early modern period, it was not known whether light travelled instantaneously or at a very fast finite speed. The first extant recorded examination of this subject was in ancient Greece
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean Sea, Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of Classical Antiquity, classical antiquity ( AD 600), th ...
. The ancient Greeks, Arabic scholars, and classical European scientists long debated this until Rømer provided the first calculation of the speed of light. Einstein's Theory of Special Relativity concluded that the speed of light is constant regardless of one's frame of reference. Since then, scientists have provided increasingly accurate measurements.
Early history
Empedocles
Empedocles (; grc-gre, Ἐμπεδοκλῆς; , 444–443 BC) was a Greek pre-Socratic philosopher and a native citizen of Akragas, a Greek city in Sicily. Empedocles' philosophy is best known for originating the cosmogonic theory of the ...
(c. 490–430 BCE) was the first to propose a theory of light and claimed that light has a finite speed. He maintained that light was something in motion, and therefore must take some time to travel. Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ph ...
argued, to the contrary, that "light is due to the presence of something, but it is not a movement".[
(click on "Historical background" in the table of contents)] Euclid
Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...
and Ptolemy
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importance ...
advanced Empedocles' emission theory
Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson–Morley experiment of 1887. Emission theories obey the principle of rel ...
of vision, where light is emitted from the eye, thus enabling sight. Based on that theory, Heron of Alexandria
Hero of Alexandria (; grc-gre, Ἥρων ὁ Ἀλεξανδρεύς, ''Heron ho Alexandreus'', also known as Heron of Alexandria ; 60 AD) was a Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. He i ...
argued that the speed of light must be infinite
Infinite may refer to:
Mathematics
* Infinite set, a set that is not a finite set
*Infinity, an abstract concept describing something without any limit
Music
*Infinite (group), a South Korean boy band
*''Infinite'' (EP), debut EP of American m ...
because distant objects such as stars appear immediately upon opening the eyes.
Early Islamic philosophers initially agreed with the Aristotelian view that light had no speed of travel. In 1021, Alhazen (Ibn al-Haytham) published the '' Book of Optics'', in which he presented a series of arguments dismissing the emission theory of vision
Vision, Visions, or The Vision may refer to:
Perception Optical perception
* Visual perception, the sense of sight
* Visual system, the physical mechanism of eyesight
* Computer vision, a field dealing with how computers can be made to gain und ...
in favour of the now accepted intromission theory, in which light moves from an object into the eye. This led Alhazen to propose that light must have a finite speed,[
][
] and that the speed of light is variable, decreasing in denser bodies.[ He argued that light is substantial matter, the propagation of which requires time, even if this is hidden from the senses. Also in the 11th century, ]Abū Rayhān al-Bīrūnī
Abu Rayhan Muhammad ibn Ahmad al-Biruni (973 – after 1050) commonly known as al-Biruni, was a Khwarazmian Iranian in scholar and polymath during the Islamic Golden Age. He has been called variously the "founder of Indology", "Father of Co ...
agreed that light has a finite speed, and observed that the speed of light is much faster than the speed of sound.
In the 13th century, Roger Bacon argued that the speed of light in air was not infinite, using philosophical arguments backed by the writing of Alhazen and Aristotle.[
] In the 1270s, Witelo
Vitello ( pl, Witelon; german: Witelo; – 1280/1314) was a friar, theologian, natural philosopher and an important figure in the history of philosophy in Poland.
Name
Vitello's name varies with some sources. In earlier publications he was quo ...
considered the possibility of light travelling at infinite speed in vacuum, but slowing down in denser bodies.[
]
In the early 17th century, Johannes Kepler believed that the speed of light was infinite since empty space presents no obstacle to it. René Descartes
René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Ma ...
argued that if the speed of light were to be finite, the Sun, Earth, and Moon would be noticeably out of alignment during a lunar eclipse. (Although this argument fails when aberration of light
In astronomy, aberration (also referred to as astronomical aberration, stellar aberration, or velocity aberration) is a phenomenon which produces an apparent motion of celestial objects about their true positions, dependent on the velocity of t ...
is taken into account, the latter was not recognized until the following century.) Since such misalignment had not been observed, Descartes concluded the speed of light was infinite. Descartes speculated that if the speed of light were found to be finite, his whole system of philosophy might be demolished. Despite this, in his derivation of Snell's law, Descartes assumed that some kind of motion associated with light was faster in denser media. Pierre de Fermat
Pierre de Fermat (; between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he ...
derived Snell's law using the opposing assumption, the denser the medium the slower light travelled. Fermat also argued in support of a finite speed of light.
First measurement attempts
In 1629, Isaac Beeckman
Isaac Beeckman (10 December 1588van Berkel, p10 – 19 May 1637) was a Dutch philosopher and scientist, who, through his studies and contact with leading natural philosophers, may have "virtually given birth to modern atomism".Harold J. Cook, in ...
proposed an experiment in which a person observes the flash of a cannon reflecting off a mirror about one mile (1.6 km) away. In 1638, Galileo Galilei
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He wa ...
proposed an experiment, with an apparent claim to having performed it some years earlier, to measure the speed of light by observing the delay between uncovering a lantern and its perception some distance away. He was unable to distinguish whether light travel was instantaneous or not, but concluded that if it were not, it must nevertheless be extraordinarily rapid.[
][
] In 1667, the Accademia del Cimento of Florence reported that it had performed Galileo's experiment, with the lanterns separated by about one mile, but no delay was observed. The actual delay in this experiment would have been about 11 microsecond
A microsecond is a unit of time in the International System of Units (SI) equal to one millionth (0.000001 or 10−6 or ) of a second. Its symbol is μs, sometimes simplified to us when Unicode is not available.
A microsecond is equal to 1000 ...
s.
The first quantitative estimate of the speed of light was made in 1676 by Ole Rømer. From the observation that the periods of Jupiter's innermost moon Io appeared to be shorter when the Earth was approaching Jupiter than when receding from it, he concluded that light travels at a finite speed, and estimated that it takes light 22 minutes to cross the diameter of Earth's orbit. Christiaan Huygens combined this estimate with an estimate for the diameter of the Earth's orbit to obtain an estimate of speed of light of , which is 27% lower than the actual value.
In his 1704 book ''Opticks
''Opticks: or, A Treatise of the Reflexions, Refractions, Inflexions and Colours of Light'' is a book by English natural philosopher Isaac Newton that was published in English in 1704 (a scholarly Latin translation appeared in 1706). (''Opti ...
'', Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a " natural philosopher"), widely recognised as one of the grea ...
reported Rømer's calculations of the finite speed of light and gave a value of "seven or eight minutes" for the time taken for light to travel from the Sun to the Earth (the modern value is 8 minutes 19 seconds). Newton queried whether Rømer's eclipse shadows were coloured; hearing that they were not, he concluded the different colours travelled at the same speed. In 1729, James Bradley
James Bradley (1692–1762) was an English astronomer and priest who served as the third Astronomer Royal from 1742. He is best known for two fundamental discoveries in astronomy, the aberration of light (1725–1728), and the nutation of th ...
discovered stellar aberration. From this effect he determined that light must travel 10,210 times faster than the Earth in its orbit (the modern figure is 10,066 times faster) or, equivalently, that it would take light 8 minutes 12 seconds to travel from the Sun to the Earth.
Connections with electromagnetism
In the 19th century Hippolyte Fizeau
Armand Hippolyte Louis Fizeau FRS FRSE MIF (; 23 September 181918 September 1896) was a French physicist, best known for measuring the speed of light in the namesake Fizeau experiment.
Biography
Fizeau was born in Paris to Louis and Beatrice Fi ...
developed a method to determine the speed of light based on time-of-flight measurements on Earth and reported a value of . His method was improved upon by Léon Foucault
Jean Bernard Léon Foucault (, ; ; 18 September 1819 – 11 February 1868) was a French physicist best known for his demonstration of the Foucault pendulum, a device demonstrating the effect of Earth's rotation. He also made an early measurement ...
who obtained a value of in 1862. In the year 1856, Wilhelm Eduard Weber
Wilhelm Eduard Weber (; ; 24 October 1804 – 23 June 1891) was a German physicist and, together with Carl Friedrich Gauss, inventor of the first electromagnetic telegraph.
Biography of Wilhelm
Early years
Weber was born in Schlossstrasse i ...
and Rudolf Kohlrausch
Rudolf Hermann Arndt Kohlrausch (November 6, 1809 in Göttingen – March 8, 1858 in Erlangen) was a German physicist.
Biography
He was a native of Göttingen, the son of the Royal Hanovarian director general of schools Friedrich Kohlrausch. He ...
measured the ratio of the electromagnetic and electrostatic units of charge, 1/, by discharging a Leyden jar
A Leyden jar (or Leiden jar, or archaically, sometimes Kleistian jar) is an electrical component that stores a high-voltage electric charge (from an external source) between electrical conductors on the inside and outside of a glass jar. It typ ...
, and found that its numerical value was very close to the speed of light as measured directly by Fizeau. The following year Gustav Kirchhoff
Gustav Robert Kirchhoff (; 12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects.
He ...
calculated that an electric signal in a resistanceless wire travels along the wire at this speed. In the early 1860s, Maxwell showed that, according to the theory of electromagnetism he was working on, electromagnetic waves propagate in empty space at a speed equal to the above Weber/Kohlrausch ratio, and drawing attention to the numerical proximity of this value to the speed of light as measured by Fizeau, he proposed that light is in fact an electromagnetic wave.[
]
"Luminiferous aether"
It was thought at the time that empty space was filled with a background medium called the luminiferous aether
Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), so ...
in which the electromagnetic field existed. Some physicists thought that this aether acted as a preferred frame
In theoretical physics, a preferred frame or privileged frame is usually a special hypothetical frame of reference in which the laws of physics might appear to be identifiably different (simpler) from those in other frames.
In theories that apply ...
of reference for the propagation of light and therefore it should be possible to measure the motion of the Earth with respect to this medium, by measuring the isotropy
Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
of the speed of light. Beginning in the 1880s several experiments were performed to try to detect this motion, the most famous of which is Michelson–Morley experiment, the experiment performed by Albert A. Michelson and Edward W. Morley in 1887. The detected motion was always less than the observational error. Modern experiments indicate that the two-way speed of light is isotropic (the same in every direction) to within 6 nanometres per second.
Because of this experiment Hendrik Lorentz proposed that the motion of the apparatus through the aether may cause the apparatus to Lorentz contraction, contract along its length in the direction of motion, and he further assumed that the time variable for moving systems must also be changed accordingly ("local time"), which led to the formulation of the Lorentz transformation. Based on Lorentz ether theory, Lorentz's aether theory, Henri Poincaré (1900) showed that this local time (to first order in ''v''/''c'') is indicated by clocks moving in the aether, which are synchronized under the assumption of constant light speed. In 1904, he speculated that the speed of light could be a limiting velocity in dynamics, provided that the assumptions of Lorentz's theory are all confirmed. In 1905, Poincaré brought Lorentz's aether theory into full observational agreement with the principle of relativity.
Special relativity
In 1905 Einstein postulated from the outset that the speed of light in vacuum, measured by a non-accelerating observer, is independent of the motion of the source or observer. Using this and the principle of relativity as a basis he derived the special theory of relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
, in which the speed of light in vacuum ''c'' featured as a fundamental constant, also appearing in contexts unrelated to light. This made the concept of the stationary aether (to which Lorentz and Poincaré still adhered) useless and revolutionized the concepts of space and time.
Increased accuracy of ''c'' and redefinition of the metre and second
In the second half of the 20th century, much progress was made in increasing the accuracy of measurements of the speed of light, first by cavity resonance techniques and later by laser interferometer techniques. These were aided by new, more precise, definitions of the metre and second. In 1950, Louis Essen
Louis Essen FRS O.B.E. (6 September 1908 – 24 August 1997) was an English physicist whose most notable achievements were in the precise measurement of time and the determination of the speed of light. He was a critic of Albert Einstein' ...
determined the speed as , using cavity resonance. This value was adopted by the 12th General Assembly of the Radio-Scientific Union in 1957. In 1960, the history of the metre#Krypton standard, metre was redefined in terms of the wavelength of a particular spectral line of krypton-86, and, in 1967, the second was redefined in terms of the hyperfine transition frequency of the ground state of caesium-133.
In 1972, using the laser interferometer method and the new definitions, a group at the US National Institute of Standards and Technology, National Bureau of Standards in Boulder, Colorado determined the speed of light in vacuum to be ''c'' = . This was 100 times less uncertain than the previously accepted value. The remaining uncertainty was mainly related to the definition of the metre. As similar experiments found comparable results for ''c'', the 15th General Conference on Weights and Measures in 1975 recommended using the value for the speed of light.[
]
Defined as an explicit constant
In 1983 the 17th meeting of the General Conference on Weights and Measures (CGPM) found that wavelengths from frequency measurements and a given value for the speed of light are more reproducibility, reproducible than the previous standard. They kept the 1967 definition of second, so the caesium Hyperfine structure#Use in defining the SI second and meter, hyperfine frequency would now determine both the second and the metre. To do this, they redefined the metre as "the length of the path traveled by light in vacuum during a time interval of 1/ of a second."[
] As a result of this definition, the value of the speed of light in vacuum is exactly [
][
] and has become a defined constant in the SI system of units. Improved experimental techniques that, prior to 1983, would have measured the speed of light no longer affect the known value of the speed of light in SI units, but instead allow a more precise realization of the metre by more accurately measuring the wavelength of krypton-86 and other light sources.[
][
]
In 2011, the CGPM stated its intention to redefine all seven SI base units using what it calls "the explicit-constant formulation", where each "unit is defined indirectly by specifying explicitly an exact value for a well-recognized fundamental constant", as was done for the speed of light. It proposed a new, but completely equivalent, wording of the metre's definition: "The metre, symbol m, is the unit of length; its magnitude is set by fixing the numerical value of the speed of light in vacuum to be equal to exactly when it is expressed in the SI unit ." This was one of the changes that was incorporated in the 2019 redefinition of the SI base units, also termed the ''New SI''.[See, for example:
*
*
* ]
See also
* Light-second
* Speed of electricity
* Speed of gravity
* Speed of sound
* Velocity factor
* Warp drive, Warp factor (fictional)
Notes
References
Further reading
Historical references
*
** Translated as
*
*
*
*
*
*
*
Modern references
*
*
*
*
*
*
External links
"Test Light Speed in Mile Long Vacuum Tube."
''Popular Science Monthly'', September 1930, pp. 17–18.
(International Bureau of Weights and Measures, BIPM)
Speed of light in vacuum
(National Institute of Standards and Technology, NIST)
(download data gathered by Albert A. Michelson)
Subluminal
(Java applet by Greg Egan demonstrating group velocity information limits)
Light discussion on adding velocities
(Sixty Symbols, University of Nottingham Department of Physics [video])
Speed of Light
BBC Radio4 discussion (''In Our Time'', 30 November 2006)
Speed of Light
(Live-Counter – Illustrations)
Speed of Light – animated demonstrations
*
The Velocity of Light
, Albert A. Nicholson, Scientific American, 28 September 1878, p. 193
{{DEFAULTSORT:Speed Of Light
Fundamental constants
Physical quantities
Light
Special relativity, Light
Velocity