A number of terms are used in Islam to refer to the claims of events happening that are not explicable by natural or scientific laws, subjects where people sometimes invoke the supernatural. In the Quran the term āyah (/ˈɑːjə/; Arabic: آية; plural: آياتāyāt, literally "sign") refers to signs in the context of miracles of God's creation and of the prophets and messengers (such as Ibrahim/Abraham and Isa/Jesus). In later Islamic sources miracles of the prophets were referred to by Muʿjiza (مُعْجِزَة), literally meaning "that by means of which [the Prophet] confounds, overwhelms, his opponents"), while miracles of saints are referred to as karamat (charismata).
Anonymous painting, taken from a 16th-century falnama, a book of prophecy. Muhammad points out the splitting of the Moon,
depicted with his face hidden. Historians, such as A. J. Wensinck and
Denis Gril, reject the historicity of it, arguing that the Quran itself
denies miracles, in the traditional sense.
I'jaz al-Quran –
literally the inimitability of the Quran – refers to the Quranic
claim that no one can hope to imitate its (the Quran's) perfection, this quality being considered the primary miracle of the Quran and proof of Muhammad's prophethood. In recent decades, the term I'jaz has also come to refer to the belief that the Quran contains "scientific miracles", i.e. prophecies of scientific discoveries. Kharq al'adad –
"a break in God's customary order of things" – was a term used in
"theological or philosophical discussions" to refer to miraculous
events. Karamat – "gifts or graces" – was usually used for miraculous performances of Sufi
saints often used to convert unbelievers to Islam (considered a work of
"divine generosity" rather than "divine power" employed in the miracles
of prophets).
Definition
A systematic definition of miracles performed by apostles can be found in the work of the Muslim scholar al-Īd̲j̲ī Mawāḳif, historian A.J. Wensinck states. The main purpose of miracle is to prove the sincerity of the apostle and has to satisfy the following conditions:
It must be performed by God
"It must be contrary to the usual course of things"
It should be impossible to contradict it
"It must happen at the hands of him who claims to be an apostle
"It must be in conformity with his announcement of it, and the miracle itself must not be a disavowal of his claim"
"It must follow on his claim"
Theology
Belief in that which is transmitted by mutawatir is obligatory to believe in for Sunni Muslims. Rejection of that which is mutawatir is cause for leaving Islam according to consensus of Sunni scholars. The Qur'an is transmitted by mutawatir
and therefore every verse must be believed in, including every
reference to a miracle of any prophet. Additionally, there are several hadith reports which convey miracles of the Islamic prophetMuhammad which are also transmitted by mutawatir. Such hadiths and miracles must also be fully believed in for one to be a Muslim. However, rejecting an ahad, or solitary, narration is only sinful (fisq) and not disbelief.
Miracles are split up into Karamat and Mu'jizat; the former are given by God to saints and the latter are given by God exclusively to prophets. In Al-Aqidah al-Tahawiyyah, upon which there is consensus,
there are two points on this: "We do not prefer any of the saints of
this nation over any of the prophets, upon them be peace. We say that a
single prophet is better than all the saints put together. We have faith
in what has come of their miracles (karamat) and what has been authenticated in their narrations from trustworthy narrators."
Warding off of approaching calamity and protection from enemies
Islam and natural law
In order to defend the possibility of miracles and God'somnipotence against the encroachment of the independent secondary causes, medieval Muslim theologians rejected the idea of cause and effect
in essence, but accepted it as something that facilitates humankind's
investigation and comprehension of natural processes. They argued that
the nature was composed of uniform atoms that were "re-created" at every
instant by God. Thus if the soil was to fall, God would have to create
and re-create the accident of heaviness for as long as the soil was to fall. For Muslim theologians, the laws of nature were only the customary sequence of apparent causes: customs of God.
Quran
According
to Denis Gril, Islam teaches that miracles – i.e. a supernatural
interventions in the life of human beings – are present in the Quran "in
a threefold sense: in sacred history, in connection with Muhammad himself and in relation to revelation." By contrast, Ali Dashti (d. 1982) writes that "there has been much debate[...]
on the question whether the Qur'an is miraculous in respect of its
eloquence or of its subject-matter, or of both. In general the Muslim
scholars consider it to be miraculous in both respects."
In the Qur'an, the term ayah is used to refer to miracles—cosmic phenomena for example are ayat takwiniyyah—particularly miracles of creation. But it is also used to mean "evidence," "sign", "Quranic verse", (religious obligations are ayat taklifiyyah). In Islam in general ayah is often used to a mean Quranic verse, but there is overlap in meaning: ayat/verses are believed to be the divine speech in human language presented by Muhammad as his chief miracle, and miracles are a "sign" (ayah) of God and of Muhammad's prophethood.
Verses of the Qur'an stating that the Qu'ran itself is a miracle –
i.e. so amazing it could not have been a natural occurrence – include:
Q11:13
"Will they say, he hath forged the Quran? Answer, bring therefore ten
chapters like unto it, forged by yourselves; and call on whomsoever ye
may to assist you, except God, if ye speak truth", was revealed in response to polytheists accusation that Muhammad's revelation was invented by Muhammad or came from other men.
Q17:88 "Say: 'If the mankind and the jinns
were together to produce the like of this Qur'an, they could not
produce the like thereof, even if they helped one another.'" was issued
in reply to an accusation found in 8:31: "We have already heard (such things). If we wished, we could say (things) like this. These are only fables of the ancients"
Sacred history
The Qur'an does not mention any miracle for Adam (Adem) who though an Islamic prophet was not supposed to convince anybody of God's message. Sura (verse) 11 (Hūd) and 23 (Al-Mu’minoon) mention miracles of Noah (Nuh), "The oven (tannur) out of which the water burst and announced the flood". Hud, prophet for the ancient tribe of ʿĀd and the first of five Arabian prophets of the Qur'an, does not have any particular miracle (thus according to historian Denis Gril prefiguring Muhammad). (See Q.7:69 for his response when he was rebuked for not producing a miracle.)
The term Quran code
(also known as Code 19) refers to the claim that the Quranic text
contains a hidden mathematically complex code. Advocates think that the
code represents a mathematical proof of the divine authorship of the Quran and they also think that it can be used to identify orthographic errors within the Quranic text. Proponents of the Quran code claim that the Quran code is based on statistical procedures.
In the United States, at the end of the 20th century, the Egyptian Quranist Muslim biochemist Rashad Khalifa
developed a theological doctrine that influenced Quranists in many
other countries. With the help of computers, he carried out a numerical
analysis of the Quran, which according to him clearly proved that it is
of divine origin.
The number 19, which is mentioned in chapter 74 of the Quran as being
"one of the greatest miracles" played the fundamental role,
which according to Khalifa can be found everywhere in the structure of
the Quran, and the fact that a Quranist discovered such a big miracle
proved the Quranist approach. Khalifa also cited Quran's chapter 74, verse 30: "Over it is nineteen".The movement popularized the phrase: "The Quran, the whole Quran, and nothing but the Quran." Some objected to these beliefs and, in 1990, Khalifa was assassinated by someone associated with the Sunni group Jamaat ul-Fuqra.
Ijaz movement
Starting the 1970s and 1980s, a genre of popular literature known as ijaz,
and often called "scientific miracles in the Quran", argued that the
Quran abounds with "scientific facts" centuries before their discovery
by science and thus demonstrating that the Quran must be of divine
origin.
Among these miracles found in the Quran are "everything, from
relativity, quantum mechanics, Big Bang theory, black holes and pulsars,
genetics, embryology, modern geology, thermodynamics, even the laser
and hydrogen fuel cells". "Widespread and well-funded" with "millions" from Saudi Arabia, the literature can be found in Muslim bookstores and on websites and television programs of Islamic preachers. According to author Ziauddin Sardar, the movement has created a "global craze in Muslim societies".
However, the ijaz movement has been criticized by scholars. Ziauddin Sardar argues that it requires "considerable mental gymnastics
and distortions to find scientific facts or theories in these verses."
According to Zafar Ishaq Ansari, the Quran is the source of guidance in right faith (iman) and righteous action (alladhina amanu wa amilu l-salihat),
but the idea that it contained "all knowledge, including scientific"
knowledge has not been a mainstream view among Muslim scholarship.
Unlettered prophet
The Quran describes Muhammad as ummi (Q7:157), which is traditionally interpreted as "unlettered," and the ability of such a person to produce the Quran is taken as miraculous and as a sign of the genuineness of his prophethood. For example, according to Fakhr al-Din al-Razi,
if Muhammad had mastered writing and reading he possibly would have
been suspected of having studied the books of the ancestors. Some
scholars such as Watt prefer the second meaning.
However, some scholars argue that the word did not mean "illiterate" but non-Jewish and non-Christian Arabs, pagan Arabs.
Scientific miracles
The
theory of the scientific miracle of the Qur'an claims that the Qur'an
has a miracle in expressing some scientific material (some modern
scientific discoveries that were unknown at the time of writing the
Qur'an). The history of writing in connection with the science and
religion of Islam dates back to the works of Ibn Sina, Fakhr al-Razi, and Abu Hamid al-Ghazali,
but has increased significantly in recent times. Authors in this field
include Naeem Al-Mohassi, Maurice Bukay, Rafiei Mohammadi, Mostarhameh,
Makarem Shirazi, and Rezaei Isfahani. These interpretations claim that
some verses of the Qur'an reflect prophetic statements about the nature
and structure of the universe, physics,
fetal biological growth, geology, mountain structure, and other
phenomena that have been later confirmed by scientific research. This
group of Quran commentators presents this as proof of the divinity of
the Qur'an.
The Qur'an does not overtly describe Muhammad performing miracles,
according to historian Denis Gril, and the supreme miracle of Muhammad
is finally identified with the Qur'an itself.
At least one scholar (Sunni scholar Muhammad Asad) states that Muhammad
performed no miracles other than to bring the Quran to humanity, and other scholars, such as Cyril Glasse and Marcia Hermansen, downplay the miracles of Muhammad, stating "they play no role in Islamic theology", or "play less of an evidentiary role than in some other religions".
However, Muslim tradition (hadith) credits Muhammad with several supernatural events. For example, many Muslim commentators and some western scholars have interpreted the sura 54 (Al-Qamar) to refer to Muhammad splitting the Moon in view of the Quraysh when they had begun to persecute his followers. This tradition has inspired many Muslim poets.
The speed of light in vacuum, commonly denoted c, is a universal physical constant
that is exactly equal to 299,792,458 metres per second (approximately
300,000 kilometres per second; 186,000 miles per second; 671 million
miles per hour). According to the special theory of relativity, c is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space.
All forms of electromagnetic radiation, including visible light,
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. Much starlight viewed on Earth is from the distant past, allowing humans to study the history of the universe by viewing distant objects. When communicating with distant space probes, it can take minutes to hours for signals to travel. In computing, the speed of light fixes the ultimate minimum communication delay. The speed of light can be used in time of flight measurements to measure large distances to extremely high precision.
Ole Rømer first demonstrated in 1676 that light does not travel instantaneously by studying the apparent motion of Jupiter's moon Io. Progressively more accurate measurements of its speed came over the following centuries. In a paper published in 1865, James Clerk Maxwell proposed that light was an electromagnetic wave and, therefore, travelled at speed c. In 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame of reference 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 c had relevance outside of the context of light and electromagnetism.
Massless particles and field perturbations, such as gravitational waves, also travel at speed c in vacuum. Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. Particles with nonzero rest mass can be accelerated to approach c but can never reach it, regardless of the frame of reference in which their speed is measured. In the theory of relativity, c interrelates space and time and appears in the famous mass–energy equivalence, E = mc2.
The speed at which light propagates through transparent materials, such as glass or air, is less than c; similarly, the speed of electromagnetic waves in wire cables is slower than c. The ratio between c and the speed v at which light travels in a material is called the refractive indexn of the material (n = c/v).
For example, for visible light, the refractive index of glass is
typically around 1.5, meaning that light in glass travels at c/1.5 ≈ 200000 km/s (124000 mi/s); the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 90 km/s (56 mi/s) slower than c.
Numerical value, notation, and units
The speed of light in vacuum is usually denoted by a lowercase c, for "constant" or the Latin celeritas (meaning 'swiftness, celerity'). In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant that was later shown to equal √2 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 in 1865. In 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, which by then had become the standard symbol for the speed of light.
Sometimes c is used for the speed of waves in any material medium, and c0 for the speed of light in vacuum. This subscripted notation, which is endorsed in official SI literature, has the same form as related electromagnetic constants: namely, μ0 for the vacuum permeability or magnetic constant, ε0 for the vacuum permittivity or electric constant, and Z0 for the impedance of free space. This article uses c exclusively for the speed of light in vacuum.
Since 1983, the constant c has been defined in the International System of Units (SI) as exactly299792458 m/s; this relationship is used to define the metre as exactly the distance that light travels in vacuum in 1⁄299792458 of a second. By using the value of c, as well as an accurate measurement of the second, one can thus establish a standard for the metre. As a dimensional physical constant, the numerical value of c is different for different unit systems. For example, in imperial units, the speed of light is approximately 186282 miles per second, or roughly 1 foot per nanosecond.
In branches of physics in which c appears often, such as in relativity, it is common to use systems of natural units of measurement or the geometrized unit system where c = 1. Using these units, c does not appear explicitly because multiplication or division by1 does not affect the result. Its unit of light-second per second is still relevant, even if omitted.
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 of the observer. 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 motion against the luminiferous aether. It has since been consistently confirmed by many experiments.
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.
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 particles and waves, including light, must travel in vacuum.
The Lorentz factorγ as a function of velocity. It starts at1 and approaches infinity as v approaches c.
Special relativity has many counterintuitive and experimentally verified implications. These include the equivalence of mass and energy(E = mc2), length contraction (moving objects shorten), and time dilation (moving clocks run more slowly). The factor γ by which lengths contract and times dilate is known as the Lorentz factor and is given by γ = (1 − v2/c2)−1/2, 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 – 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 (with c relating the units of space and time), and requiring that physical theories satisfy a special symmetry called Lorentz invariance, whose mathematical formulation contains the parameter c. Lorentz invariance is an almost universal assumption for modern physical theories, such as quantum electrodynamics, quantum chromodynamics, the Standard Model of particle physics, and general relativity. 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 and of gravitational waves, and observations of gravitational waves have been consistent with this prediction. In non-inertial frames of reference (gravitationally curved spacetime or accelerated reference frames), the local speed of light is constant and equal to c, but the speed of light can differ from c when measured from a remote frame of reference, depending on how measurements are extrapolated to the region.
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 is generally assumed that the two-way 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 levels as a function of the orientation of the emitting nuclei in a magnetic field (see Hughes–Drever experiment), and of rotating optical resonators (see Resonator experiments) have put stringent limits on the possible two-way anisotropy.
Upper limit on speeds
According to special relativity, the energy of an object with rest massm and speed v is given by γmc2, where γ is the Lorentz factor defined above. When v is zero, γ is equal to one, giving rise to the famous E = mc2 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.
Event A precedes B in the red frame, is simultaneous with B in the green frame, and follows B in the blue frame.
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 paradoxes such as the tachyonic antitelephone.
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-rays 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 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: under certain conditions the time needed for a virtual particle to 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.
So-called superluminal motion is seen in certain astronomical objects, such as the relativistic jets of 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 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.
For example, galaxies far away from Earth are inferred to be moving away
from the Earth with speeds 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.
These recession rates, defined as the increase in proper distance per cosmological time, are not velocities in a relativistic sense. Faster-than-light cosmological recession speeds are only a coordinate artifact.
In modern quantum physics, the electromagnetic field is described by the theory of quantum electrodynamics (QED). In this theory, light is described by the fundamental excitations (or quanta) of the electromagnetic field, called photons. In QED, photons are massless particles 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 10−57grams; if photon mass is generated by a Higgs mechanism, the experimental upper limit is less sharp, m ≤ 10−14eV/c2 (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 burstGRB 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, 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) propagate is called the phase velocityvp. A physical signal with a finite extent (a pulse of light) travels at a different speed. The overall envelope of the pulse travels at the group velocityvg, and its earliest part travels at the front velocityvf.
The
blue dot moves at the speed of the ripples, the phase velocity; the
green dot moves with the speed of the envelope, the group velocity; and
the red dot moves with the speed of the foremost part of the pulse, the
front velocity.
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 vp
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 is approximately 1.0003. Denser media, such as water, glass, and 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.
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 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. Certain materials have an exceptionally low (or even zero) group velocity for light waves, a phenomenon called slow light.
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 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 telecommunications: 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 computers, the speed of light imposes a limit on how quickly data can be sent between processors. If a processor operates at 1gigahertz,
a signal can travel only a maximum of about 30 centimetres (1 ft) in a
single clock cycle – in practice, this distance is even shorter since
the printed circuit board refracts and slows down signals. Processors must therefore be placed close to each other, as well as memory 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.
Large distances on Earth
Duration: 4 seconds.0:04Acoustic representation of the speed of light, at every beep the light makes a full circle around the equator
Given that the equatorial circumference of the Earth is about 40075 km and that c is about 300000 km/s,
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)
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.
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
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
A
beam of light is depicted travelling between the Earth and the Moon in
the time it takes a light pulse to move between them: 1.255 seconds at
their mean orbital (surface-to-surface) distance. The relative sizes and
separation of the Earth–Moon system are shown to scale.
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
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 approximately 4–24 minutes later. It would then take a further 4–24 minutes 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 (13×109) 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, 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 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.
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 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 300000 kilometres (186000 mi) 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.
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. It is also
possible to determine c from other physical laws where it appears, for example, by determining the values of the electromagnetic constants ε0 and μ0 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 1⁄299792458 of a second", fixing the value of the speed of light at 299792458 m/s 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
Measurement
of the speed of light from the time it takes Io to orbit Jupiter, using
eclipses of Io by Jupiter's shadow to precisely measure its orbit.
Outer space is a convenient setting for measuring the speed of light because of its large scale and nearly perfect 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.
Ole Christensen Rømer used an astronomical measurement to make the first quantitative estimate of the speed of light in the year 1676.
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 difference is small, but the
cumulative time becomes significant when measured over months. 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's innermost major moon Io and deduced that light takes 22 minutes to cross the diameter of the Earth's orbit.
Aberration
of light: light from a distant source appears to be from a different
location for a moving telescope due to the finite speed of light.
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 10210 times faster than the Earth in its orbit (the modern figure is 10066 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 149597870700 m. 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 c
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: tau = 499.004783836(10) s,
c = 0.00200398880410(4) AU/s = 173.144632674(3) AU/d.
The relative uncertainty in these measurements is 0.02 parts per billion (2×10−11), 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
One
of the last and most accurate time of flight measurements, Michelson,
Pease and Pearson's 1930–1935 experiment used a rotating mirror and a
one-mile (1.6 km) long vacuum chamber which the light beam traversed 10
times. It achieved accuracy of ±11 km/s.Diagram of the Fizeau apparatus:
Light source
Beam-splitting semi-transparent mirror
Toothed wheel-breaker of the light beam
Remote mirror
Telescopic tube
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 experiments by Hippolyte Fizeau and Léon Foucault.
The setup as used by Fizeau
consists of a beam of light directed at a mirror 8 kilometres (5 mi)
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. Foucault used this apparatus to measure the speed of light in air versus water, based on a suggestion by François Arago.
Today, 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 permittivityε0 and vacuum permeabilityμ0 established by Maxwell's theory: c2 = 1/(ε0μ0). The vacuum permittivity may be determined by measuring the capacitance and dimensions of a capacitor, whereas the value of the vacuum permeability was historically fixed at exactly 4π×10−7 H⋅m−1 through the definition of the ampere. Rosa and Dorsey used this method in 1907 to find a value of 299710±22 km/s. Their method depended upon having a standard unit of electrical resistance, the "international ohm", and so its accuracy was limited by how this standard was defined.
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, 299792±9 km/s, was substantially more precise than those found by optical techniques. By 1950, repeated measurements by Essen established a result of 299792.5±3.0 km/s.
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 is another method to find the wavelength of electromagnetic radiation for determining the speed of light. A 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 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 radio sources were used for interferometry measurements of the speed of light.
Interferometric determination of wavelength becomes less precise with
wavelength and the experiments were thus limited in precision by the
long wavelength (~4 mm (0.16 in)) 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). They used it in 1972 to measure the speed of light in vacuum with a fractional uncertainty of 3.5×10−9.
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, 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 postulates that
the speed of light is constant regardless of one's frame of reference.
Since then, scientists have provided increasingly accurate measurements.
Empedocles (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 argued, to the contrary, that "light is due to the presence of something, but it is not a movement". Euclid and Ptolemy advanced Empedocles' 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 infinite 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 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 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. Although this argument fails when aberration of light 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
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 observations of the occultations of Io from Earth
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 220000 km/s, which is 27% 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 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.
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 315000 km/s. His method was improved upon by Léon Foucault who obtained a value of 298000 km/s in 1862. In the year 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch measured the ratio of the electromagnetic and electrostatic units of charge, 1/√ε0μ0, 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 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.
Maxwell backed up his claim with his own experiment published in the
1868 Philosophical Transactions which determined the ratio of the
electrostatic and electromagnetic units of electricity.
The wave properties of light were well known since Thomas Young.
In the 19th century, physicists believed light was propagating in a
medium called aether (or ether). But for electric force, it looks more
like the gravitational force in Newton's law. A transmitting medium was
not required. After Maxwell theory unified light and electric and
magnetic waves, it was favored that both light and electric magnetic
waves propagate in the same aether medium (or called the luminiferous aether).
Hendrik Lorentz (right) with Albert Einstein (1921)
It was thought at the time that empty space was filled with a background medium called the luminiferous aether 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 the experiment performed by Albert A. Michelson and Edward W. Morley in 1887.
The detected motion was found to always be nil (within 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 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'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 299792.5±3.0 km/s, using cavity resonance. This value was adopted by the 12th General Assembly of the Radio-Scientific Union in 1957. In 1960, the 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 Bureau of Standards in Boulder, Colorado determined the speed of light in vacuum to be c = 299792456.2±1.1 m/s.
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 299792458 m/s 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 reproducible than the previous standard. They kept the 1967 definition of second, so the caesiumhyperfine 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 1/299792458 of a second".
As a result of this definition, the value of the speed of light in vacuum is exactly 299792458 m/s 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 299792458 when it is expressed in the SI unit m s−1." This was one of the changes that was incorporated in the 2019 revision of the SI, also termed the New SI.
