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The speed of light in
vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Gree ...

vacuum
, commonly denoted , is a universal
physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity A physical quantity is a physical property of a material or system that can be Quantification (science), quantified by measurement. A physi ...
that is important in many areas of
physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of eve ...

physics
. Its exact value is defined as (approximately ). It is exact because, by international agreement, a
metre The metre ( Commonwealth spelling) or meter (American spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English o ...
is defined as the length of the path travelled by
light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that can be visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 ...

light
in vacuum during a time interval of
second The second (symbol: s, also abbreviated: sec) is the of in the (SI) (french: Système International d’unités), commonly understood and historically defined as of a – this factor derived from the division of the day first into 24 s, th ...
. According to
special relativity In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
, 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 particl ...
, energy or any
signal In signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images, and scientific measurements. Sig ...

signal
carrying information can travel through
space Space is the boundless extent in which and events have relative and . In , physical space is often conceived in three s, although modern s usually consider it, with , to be part of a boundless known as . The concept of space is considere ...

space
. A
light-year A light-year, alternatively spelt lightyear, is a unit of length A unit of length refers to any arbitrarily chosen and accepted reference standard for measurement of length. The most common units in modern use are the metric system, metric un ...
is a distance unit, defined as the distance travelled by light in one Julian year. The speed of light is sometimes referred to as lightspeed, especially in
science fiction Science fiction (sometimes shortened to sci-fi or SF) is a of which typically deals with and futuristic concepts such as advanced and , , , , and . It has been called the " of ", and it often explores the potential consequences of . Scien ...

science fiction
. All forms of
electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...

electromagnetic radiation
travel at the speed of light, not just
visible light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nano ...
.
Massless particle In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the n ...
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 grassl ...
perturbations such as
gravitational wave Gravitational waves are disturbances in the curvature of spacetime In , spacetime is any which fuses the and the one of into a single . can be used to visualize effects, such as why different observers perceive differently where and wh ...
s also travel at this speed in vacuum. Such particles and waves travel at regardless of the motion of the source or the
inertial reference frame In classical physics Classical physics is a group of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies mat ...
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 Information theory is the scientific study of the quantification, storage ...
. 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 Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** ...
can approach , but can never actually 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 In physics, spacetime is any mathematical model which fuses the three-dimensional space, three dimensions of space and the one dimension of time into a single four-dimensional manifold. The fabric of space-time is a conceptual model combining the ...
, and also appears in the famous equation of
mass–energy equivalence In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
, . In some cases objects or waves may appear to travel
faster than light Faster-than-light (also superluminal, FTL or supercausal) communications and travel are the conjectural propagation of information or matter faster than the speed of light. The special theory of relativity implies that only particles with zero mas ...
(e.g.
phase velocities in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the       green circles propagate with the group velocity. In this deep-water case, ''the phase velocity is twice th ...
of waves, the appearance of certain high-speed astronomical objects, and particular
quantum effects Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with s ...
). The
expansion of the universe 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 n ...
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 Optics is the branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its ...
, such as glass or air, is less than ; similarly, the speed of
electromagnetic waves In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through ...

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 , the refractive index (also known as refraction index or index of refraction) of a is a that describes how fast travels through the material. It is defined as :n = \frac, where ''c'' is the in and ''v'' is the of light in the medium. F ...

refractive index
of the material (). For example, for
visible light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nano ...
, the refractive index of glass is typically around 1.5, meaning that light in glass travels at ; the refractive index of air for visible light is about 1.0003, so the speed of light in air is about slower than . 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. In communicating with distant
space probe A space probe or a spaceprobe is a robotic spacecraft that doesn't Earth orbit, orbit the Earth (planet), Earth, but instead explores farther into outer space. A space probe may approach the Moon; travel through interplanetary space; planetary ...
s, it can take minutes to hours for a message to get from Earth to the spacecraft, or vice versa. The light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light also ultimately limits the data transfer between the CPU and memory chips in
computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations automatically. Modern computers can perform generic sets of operations known as Computer program, programs. These programs enable compu ...

computer
s. The speed of light can be used with
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 establish a time standard (such as an atomic ...

time of flight
measurements to measure large distances to high precision. 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 A gas giant is a giant planet composed mainly of hydrogen Hydrogen is the chemical element with the Symbol (chemistry), symbol H and at ...

Jupiter
's moon Io. In 1865,
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of interest. In classica ...

James Clerk Maxwell
proposed that light was an electromagnetic wave, and therefore travelled at the speed appearing in his theory of electromagnetism. In 1905,
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born , widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the , but he also made important contributions to the develo ...

Albert Einstein
postulated that the speed of light with respect to any inertial frame 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 The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
and in doing so showed that the parameter had relevance outside of the context of light and electromagnetism. After centuries of increasingly precise measurements, in 1975 the speed of light was known to be with a
measurement uncertainty In metrology 290px, alt=Man in white standing in front of a large machine, A scientist stands in front of the Microarcsecond Metrology (MAM) testbed. Metrology is the scientific study of measurement ' Measurement is the number, numerical qua ...
of 4
parts per billion In science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantity, dimensionless quantities, e.g. mole fraction or mass fraction (chemistry), mass fraction. Since these fr ...
. In 1983, the
metre The metre ( Commonwealth spelling) or meter (American spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English o ...
was redefined in the
International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' (Kevin Michael album), 2011 * International (New Order album), '' ...
(SI) as the distance travelled by light in vacuum in 1 /  of a
second The second (symbol: s, also abbreviated: sec) is the of in the (SI) (french: Système International d’unités), commonly understood and historically defined as of a – this factor derived from the division of the day first into 24 s, th ...
.


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 A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area ...

Wilhelm Eduard Weber
and
Rudolf Kohlrausch Rudolf Hermann Arndt Kohlrausch (November 6, 1809 in Göttingen Göttingen (, also , ; nds, Chöttingen) is a college town, university city in Lower Saxony, Germany, the Capital (political), capital of Göttingen (district), the eponymous dist ...

Rudolf Kohlrausch
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 scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of interest. In classica ...

James Clerk Maxwell
in 1865. In 1894,
Paul Drude Paul Karl Ludwig Drude (; 12 July 1863 – 5 July 1906) was a German physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of in ...

Paul Drude
redefined with its modern meaning.
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theory ...

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 other related constants: namely, ''μ''0 for the
vacuum permeability Vacuum permeability is the magnetic permeability in a classical vacuum. ''Vacuum permeability'' is derived from production of a magnetic field by an electric current or by a moving electric charge and in all other formulas for magnetic-field prod ...
or magnetic constant, ''ε''0 for the
vacuum permittivity Vacuum permittivity, commonly denoted (pronounced as "epsilon nought" or "epsilon zero") is the value of the absolute dielectric permittivity of classical vacuum. Alternatively may be referred to as the permittivity of free space, the electr ...
or electric constant, and ''Z''0 for the
impedance of free spaceThe impedance of free space, , is a physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant (mathematic ...
. This article uses exclusively for the speed of light in vacuum. Since 1983, the metre has been defined in the
International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' (Kevin Michael album), 2011 * International (New Order album), '' ...
(SI) as the distance light travels in vacuum in of a second. This definition fixes the speed of light in vacuum at exactly . As a dimensional physical constant, the numerical value of is different for different unit systems. In branches of physics in which appears often, such as in relativity, it is common to use systems of
natural units In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Phy ...
of measurement or the
geometrized unit system A geometrized unit system or geometric unit system is a system of natural units In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural sc ...
where . Using these units, does not appear explicitly because multiplication or division by1 does not affect the result. Its unit of lightsecond/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 is a frame of reference that is not undergoing acceleration. In an inertial frame of reference, a physical object with zero net force acting on it moves with a const ...
of the observer.However, the
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

frequency
of light can depend on the motion of the source relative to the observer, due to the
Doppler effect The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is 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 and the lack of evidence for the
luminiferous aether Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium Medium may refer to: Science and technology Aviation *Medium bomber, a class of war plane *Tecma Medium, a French hang glider design Communic ...
; 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 upright=1.25, The luminiferous aether: it was hypothesised that the Earth moves through a "medium" of aether that carries light Luminiferous aet ...
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 experiment The Michelson–Morley experiment was an attempt to detect the existence of the lumini ...
, 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 (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 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 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 Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of ...
s and waves, including light, must travel in vacuum. Special relativity has many counterintuitive and experimentally verified implications. These include the equivalence of mass and energy ,
length contraction Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length Proper length or rest length is the length of an object in the object's rest frame. The measurement of lengths is more compl ...
(moving objects shorten), and
time dilation In physics and Theory of relativity, relativity, time dilation is the difference in the elapsed Time in physics, time as measured by two clocks. It is either due to a relative velocity between them (special relativity, special relativistic "kine ...

time dilation
(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 Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assi ...

Lorentz factor
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 speeds—in 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. Galileo Galilei first described this principle in 1632 in his ''Dialogue Concerning the Two Chief World Systems'' using Galileo's ship, ...
—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 ''v'' = 99.5% ''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 any mathematical model which fuses the three-dimensional space, three dimensions of space and the one dimension of time into a single four-dimensional manifold. Minkowski diagram, Spacetime diagrams can be used to visuali ...
(with ''c'' relating the units of space and time), and requiring that physical theories satisfy a special
symmetry Symmetry (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appro ...
called
Lorentz invariance In relativistic physics, Lorentz symmetry, named after Hendrik Lorentz Lorentz' theory of electrons. Formulas for the Curl (mathematics), curl of the magnetic field (IV) and the electrical field E (V), ''La théorie electromagnétique de Ma ...
, 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 relativity theory, 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 m ...
,
quantum chromodynamics In theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, natural phenomena. This is in c ...
, the
Standard Model The Standard Model of particle physics Particle physics (also known as high energy physics) is a branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsi ...

Standard Model
of
particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which rel ...
, and
general relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
. 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 Changes may refer to: Books * Changes (The Dresden Files), ''Changes'', the 12th novel in Jim Butcher's ''The Dresden Files'' Series * ''Changes'', a novel by Danielle Steel * ''Changes'', a tril ...
and of
gravitational waves Gravitational waves are disturbances in the curvature of spacetime In , spacetime is any which fuses the and the one of into a single . can be used to visualize effects, such as why different observers perceive differently where and wh ...
. In
non-inertial frame A non-inertial reference frame is a frame of reference In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies ma ...
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 of reference, inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration. Whi ...
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 Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, "equal") and ''tropos'' (τρόπος, "way"). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by ...
, 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 Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking ...
s as a function of the orientation of the emitting
nuclei ''Nucleus'' (plural nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA ...
in a magnetic field (see
Hughes–Drever experiment Hughes–Drever experiments (also clock comparison-, clock anisotropy-, mass isotropy-, or energy isotropy experiments) are Spectroscopy, spectroscopic tests of the isotropy of mass and space. Although originally conceived of as a test of Mach's pri ...
), and of rotating
optical resonatorAn optical cavity, resonating cavity or optical resonator is an arrangement of mirror Grange, East Yorkshire, UK, from World War I. The mirror magnified the sound of approaching enemy Zeppelins for a microphone placed at the Focus (geometry), ...
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 Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** ...
''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 In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
. 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. 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 In physics, the relativity of simultaneity is the concept that ''distant simultaneity'' – whether two spatially separated events occur at the same Time in physics, time – is not absolute time and space, absolute, but depends on th ...

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 Causality (also referred to as causation, or cause and effect) is influence by which one Event (relativity), event, process, state or object (a ''cause'') contributes to the production of another event, process, state or object (an ''effect'') ...
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 ...

paradox
es such as the .


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''. For example, the
phase velocity The phase velocity of a wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...

phase velocity
of
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Moti ...

X-ray
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. An example involves the quantum states of two particles that can be quantum entanglement, entangled. Until either of the particles is observed, they exist in a quantum superposition, 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: under certain conditions the time needed for a virtual particle to quantum tunnelling, tunnel 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 galaxy, radio galaxies and quasars. However, these jets are not moving at speeds in excess of the speed of light: the apparent superluminal motion is a graphical projection, projection 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. 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 Metric expansion of space, expansion of space 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, 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. The classical behaviour of the electromagnetic field is described by Maxwell's equations, 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 ''ε''0 and the magnetic constant ''μ''0, by the equation : c =\frac \ . In modern quantum physics, the electromagnetic field is described by the theory of
quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativity theory, 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 m ...
(QED). In this theory, light is described by the fundamental excitations (or quanta) of the electromagnetic field, called photons. In QED, photons are
massless particle In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of ...
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 action, Proca theory, the experimental upper bound for its mass is about 10−57 grams; if photon mass is generated by a Higgs mechanism, 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 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 (a wave filling the whole space, with only one
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

frequency
) propagate is called the
phase velocity The phase velocity of a wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...

phase velocity
 ''v''p. A physical signal with a finite extent (a pulse of light) travels at a different speed. The largest part 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 (waves), polarization, or direction of propagation; in many cases, though, it can be treated as a material-dependent constant. The refractive index of air is approximately 1.0003. Denser media, such as Optical properties of water and ice, water, glass, and Material properties of diamond#Optical properties, diamond, have refractive indexes of around 1.3, 1.5 and 2.4, respectively, for visible light. In exotic materials like Bose–Einstein condensates 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 of the dielectric constant of any material, corresponding respectively to the index of refraction and to the attenuation coefficient, are linked by the Kramers–Kronig relations. In practical terms, this means that in a material with refractive index less than 1, the absorption of the wave is so quick that no signal can be sent faster than ''c''. 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 (optics), dispersion. Certain materials have an exceptionally low (or even zero) group velocity for light waves, a phenomenon called slow light, which has been confirmed in various experiments. The opposite, group velocities exceeding ''c'', has also been shown in experiment. 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 does that in a dielectric material, the electromagnetic equivalent of a shock wave, known as Cherenkov radiation, is emitted.


Practical effects of finiteness

The speed of light is of relevance to telecommunication, communications: the one-way and round-trip delay time 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 supercomputers, the speed of light imposes a limit on how quickly data can be sent between central processing unit, processors. If a processor operates at 1gigahertz, a signal can travel only a maximum of about in a single cycle. Processors must therefore be placed close to each other to minimize communication latencies; this can cause difficulty with cooling. If clock frequencies continue to increase, the speed of light will eventually become a limiting factor for the internal design of single integrated circuit, chips.


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 travelling around the globe in an optical fibre, the actual transit time is longer, in part because the speed of light is slower by about 35% in an optical fibre, depending on its refractive index ''n''. Furthermore, straight lines rarely occur in global communications situations, and delays are created when the signal passes through an electronic switch or signal regenerator.


Spaceflights 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 Mission Control Center, ground control and Apollo 8 when it became the first manned 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 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 at least five minutes later, and possibly up to twenty minutes later; it would then take a further five to twenty minutes for instructions to travel from Earth to Mars. Receiving light and other signals from distant astronomical sources can even take much longer. For example, it has taken 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, Galaxy formation and evolution, of galaxies, and history of the universe, of the universe itself. Astronomical distances are sometimes expressed in
light-year A light-year, alternatively spelt lightyear, is a unit of length A unit of length refers to any arbitrarily chosen and accepted reference standard for measurement of length. The most common units in modern use are the metric system, metric un ...
s, especially in popular science publications and media. A light-year is the distance light travels in one year, around 9461 billion kilometres, 5879 billion miles, or 0.3066 parsecs. 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 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 Radar#Transit time, transit time multiplied by the speed of light. A Global Positioning System (GPS) receiver measures its distance to GPS satellites 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 and the Deep Space Network determine distances to the Moon, planets and spacecraft, respectively, by measuring round-trip transit times.


High-frequency trading

The speed of light has become important in 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 communications between trading hubs, because of the advantage which microwaves travelling at near to the speed of light in air have over fibre optic signals, which travel 30–40% slower.


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 relative permittivity, ''ε''0 and permeability (electromagnetism), ''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''. 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 #Increased accuracy of c and redefinition of the metre and second, 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 is a convenient setting for measuring the speed of light because of its large scale and nearly perfect
vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Gree ...

vacuum
. Typically, one measures the time needed for light to traverse some reference distance in the Solar System, such as the radius 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. It is customary to express the results in astronomical units (AU) per day. Ole Christensen Rømer used an astronomical measurement to make Rømer's determination of the speed of light, 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, (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 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 A gas giant is a giant planet composed mainly of hydrogen Hydrogen is the chemical element with the Symbol (chemistry), symbol H and at ...

Jupiter
's innermost 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, discovered and explained by James Bradley in the 18th century. This effect results from the vector addition 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 (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 International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' (Kevin Michael album), 2011 * International (New Order album), '' ...
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 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 (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 developed by Hippolyte Fizeau and Léon Foucault. 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. Nowadays, using oscilloscopes 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 Vacuum permittivity, commonly denoted (pronounced as "epsilon nought" or "epsilon zero") is the value of the absolute dielectric permittivity of classical vacuum. Alternatively may be referred to as the permittivity of free space, the electr ...
''ε''0 and
vacuum permeability Vacuum permeability is the magnetic permeability in a classical vacuum. ''Vacuum permeability'' is derived from production of a magnetic field by an electric current or by a moving electric charge and in all other formulas for magnetic-field prod ...
''μ''0 established by Maxwell's theory: ''c''2 = 1/(''ε''0''μ''0). The vacuum permittivity may be determined by measuring the capacitance and dimensions of a capacitor, whereas the value of the vacuum permeability is fixed at exactly through the definition of the ampere (unit), ampere. Rosa and Dorsey used this method in 1907 to find a value of .


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. 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 and A.C. Gordon-Smith established the frequency for a variety of normal modes of microwaves of a microwave cavity 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, 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 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 antinodes (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 Coherence (physics), coherent beam of light (e.g. from a laser), with a known frequency (''f''), is split to follow two paths and then recombined. By adjusting the path length while observing the interference (wave propagation), interference pattern 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 radiowave, radio 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 (NBS) (which later became National Institute of Standards and Technology, NIST). They used it in 1972 to measure the speed of light in vacuum with a Measurement uncertainty, 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. The ancient Greeks, Muslim 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 (c. 490–430 BC) 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 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 and Ptolemy advanced Empedocles' Emission theory (vision), emission theory of vision, where light is emitted from the eye, thus enabling sight. Based on that theory, Heron of Alexandria argued that the speed of light must be Infinity, infinite because distant objects such as stars appear immediately upon opening the eyes. Early Islamic philosophy, Early Islamic philosophers initially agreed with the Aristotelian physics, 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 Visual perception, vision 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 our senses. Also in the 11th century, Abū Rayhān al-Bīrūnī 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 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 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. 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. In Descartes' derivation of Snell's law, he assumed that even though the speed of light was instantaneous, the denser the medium, the faster was light's speed. Pierre de Fermat 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 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 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 microseconds. Rømer's determination of the speed of light, The first quantitative estimate of the speed of light was made in 1676 by 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 , 26% lower than the actual value. In his 1704 book ''Opticks'', Isaac Newton 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 discovered aberration of light, stellar aberration. From this effect he determined that light must travel 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.


Connections with electromagnetism

In the 19th century Hippolyte Fizeau 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 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 A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area ...

Wilhelm Eduard Weber
and
Rudolf Kohlrausch Rudolf Hermann Arndt Kohlrausch (November 6, 1809 in Göttingen Göttingen (, also , ; nds, Chöttingen) is a college town, university city in Lower Saxony, Germany, the Capital (political), capital of Göttingen (district), the eponymous dist ...

Rudolf Kohlrausch
measured the ratio of the electromagnetic and electrostatic units of charge, 1/, by discharging a Leyden jar, and found that its numerical value was very close to the speed of light as measured directly by Fizeau. The following year Gustav Kirchhoff calculated that an electric signal in a electrical resistance, 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 Medium may refer to: Science and technology Aviation *Medium bomber, a class of war plane *Tecma Medium, a French hang glider design Communic ...
in which the electromagnetic field existed. Some physicists thought that this aether acted as a preferred frame 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 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 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 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 The second (symbol: s, also abbreviated: sec) is the of in the (SI) (french: Système International d’unités), commonly understood and historically defined as of a – this factor derived from the division of the day first into 24 s, th ...
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 Measurement uncertainty, 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.


Defining the speed of light 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 The second (symbol: s, also abbreviated: sec) is the of in the (SI) (french: Système International d’unités), commonly understood and historically defined as of a – this factor derived from the division of the day first into 24 s, th ...
, 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 metre is 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 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 demonstrating group velocity information limits)
Usenet Physics FAQ


at MathPages



(University of Colorado Department of Physics)

(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 Units of velocity