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83-432: Located approximately 294  light-years from Earth, it is classified as a subgiant with a spectral type of F0 IV. Sigma Octantis has an apparent magnitude of 5.5, but is slightly variable and is classified as a Delta Scuti variable . σ Octantis ( Latinised to Sigma Octantis ) is the star's Bayer designation . As the southern hemisphere's pole star it bore the name Polaris Australis , first applied in

166-407: A star system tend to be small fractions of a light-year, and are usually expressed in astronomical units . However, smaller units of length can similarly be formed usefully by multiplying units of time by the speed of light. For example, the light-second , useful in astronomy, telecommunications and relativistic physics, is exactly 299 792 458 metres or ⁠ 1 / 31 557 600 ⁠ of

249-473: A unit of time . The light-year is most often used when expressing distances to stars and other distances on a galactic scale, especially in non-specialist contexts and popular science publications. The unit most commonly used in professional astronomy is the parsec (symbol: pc, about 3.26 light-years). As defined by the International Astronomical Union (IAU), the light-year

332-404: 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

415-495: 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 × 10 ) 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

498-461: 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

581-412: A light-year. Units such as the light-minute, light-hour and light-day are sometimes used in popular science publications. The light-month, roughly one-twelfth of a light-year, is also used occasionally for approximate measures. The Hayden Planetarium specifies the light month more precisely as 30 days of light travel time. Light travels approximately one foot in a nanosecond ; the term "light-foot"

664-617: 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

747-584: 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

830-416: 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 186 282 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

913-412: 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

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996-459: A time interval of 1 ⁄ 299 792 458 of a second", fixing the value of the speed of light at 299 792 458  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 . Outer space is a convenient setting for measuring the speed of light because of its large scale and nearly perfect vacuum . Typically, one measures

1079-548: Is "ly", International standards like ISO 80000:2006 (now superseded) have used "l.y." and localized abbreviations are frequent, such as "al" in French, Spanish, and Italian (from année-lumière , año luz and anno luce , respectively), "Lj" in German (from Lichtjahr ), etc. Before 1984, the tropical year (not the Julian year) and a measured (not defined) speed of light were included in

1162-402: Is a unit of length used to express astronomical distances and is equal to exactly 9 460 730 472 580 .8 km , which is approximately 5.88 trillion mi. As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in vacuum in one Julian year (365.25 days). Despite its inclusion of the word "year", the term should not be misinterpreted as

1245-528: Is an odd name. In 1868 an English journal labelled the light-year as a unit used by the Germans. Eddington called the light-year an inconvenient and irrelevant unit, which had sometimes crept from popular use into technical investigations. Although modern astronomers often prefer to use the parsec , light-years are also popularly used to gauge the expanses of interstellar and intergalactic space. Distances expressed in light-years include those between stars in

1328-424: 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

1411-421: 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

1494-427: 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

1577-511: 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

1660-459: 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 than   1 for some frequencies; in some exotic materials it is even possible for the index of refraction to become negative. The requirement that causality

1743-505: Is important in determining how a light wave travels through a material or from one material to another. It is often represented in terms of a refractive index . The refractive index of a material is defined as the ratio of c to the phase velocity  v p in the material: larger indices of refraction indicate lower speeds. The refractive index of a material may depend on the light's frequency, intensity, polarization , or direction of propagation; in many cases, though, it can be treated as

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1826-486: 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

1909-422: 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

1992-495: Is known as the Lorentz factor and is given by γ = (1 − v / c ) , where v is the speed of the object. The difference of γ from   1 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,

2075-491: 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

2158-554: 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

2241-473: 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. 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

2324-401: 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

2407-410: Is sometimes used as an informal measure of time. Speed of light 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

2490-560: Is the product of the Julian year (365.25 days, as opposed to the 365.2425-day Gregorian year or the 365.24219-day Tropical year that both approximate) and the speed of light ( 299 792 458  m/s ). Both of these values are included in the IAU (1976) System of Astronomical Constants , used since 1984. From this, the following conversions can be derived: The abbreviation used by the IAU for light-year

2573-545: Is the product of the J1900.0 mean tropical year and the defined speed of light. Abbreviations used for light-years and multiples of light-years are: The light-year unit appeared a few years after the first successful measurement of the distance to a star other than the Sun, by Friedrich Bessel in 1838. The star was 61 Cygni , and he used a 160-millimetre (6.2 in) heliometre designed by Joseph von Fraunhofer . The largest unit for expressing distances across space at that time

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2656-547: The Deep Space Network determine distances to the Moon, planets and spacecraft, respectively, by measuring round-trip transit times. 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

2739-453: The fundamental mode . Sigma Octantis is the current southern pole star , whose counterpart is Polaris , the current North Star. To an observer in the southern hemisphere, Sigma Octantis appears almost motionless and all the other stars in the Southern sky appear to rotate around it. It is part of a small "half hexagon" shape. It is slightly more than a degree away from the true south pole, and

2822-400: The geometrized unit system where c = 1 . Using these units, c does not appear explicitly because multiplication or division by   1 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

2905-459: 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

2988-430: 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 . Given that

3071-400: 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

3154-414: 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

3237-513: The 1700s. In 2016, the IAU organized a Working Group on Star Names (WGSN) to catalog and standardize proper names for stars. The WGSN approved the name Polaris Australis for this star on 5 September 2017 and it is now so included in the List of IAU-approved Star Names. It is the southernmost named star. With a spectral class of F0IV, Sigma Octantis appears to be a subgiant , although it has also been classified as F0III. Evolutionary models place it at

3320-543: 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 classical physics , light

3403-496: The IAU (1964) System of Astronomical Constants, used from 1968 to 1983. The product of Simon Newcomb 's J1900.0 mean tropical year of 31 556 925 .9747 ephemeris seconds and a speed of light of 299 792 .5 km/s produced a light-year of 9.460 530 × 10  m (rounded to the seven significant digits in the speed of light) found in several modern sources was probably derived from an old source such as C. W. Allen 's 1973 Astrophysical Quantities reference work, which

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3486-434: The advantage which radio waves travelling at near to the speed of light through air have over comparatively slower fibre optic signals. 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

3569-413: 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

3652-418: The appearance of certain high-speed astronomical objects , and particular quantum effects ). The expansion of the universe is understood to exceed the speed of light beyond a certain boundary . The speed at which light propagates through transparent materials , 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

3735-587: 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. Special relativity has many counterintuitive and experimentally verified implications. These include the equivalence of mass and energy ( E = mc ) , length contraction (moving objects shorten), and time dilation (moving clocks run more slowly). The factor  γ by which lengths contract and times dilate

3818-451: 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

3901-474: 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 . According to special relativity, the energy of an object with rest mass m and speed v is given by γmc , where γ is the Lorentz factor defined above. When v is zero, γ is equal to one, giving rise to

3984-418: The equation 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

4067-512: The equatorial circumference of the Earth is about 40 075  km and that c is about 300 000  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

4150-495: The famous E = mc 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 . More generally, it

4233-556: 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

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4316-416: 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

4399-429: The individual crests and troughs of a plane wave (a wave filling the whole space, with only one frequency ) propagate is called the phase velocity   v p . A physical signal with a finite extent (a pulse of light) travels at a different speed. The overall envelope of the pulse travels at the group velocity   v g , and its earliest part travels at the front velocity   v f . The phase velocity

4482-576: The major stars in Octans or using the Southern Cross (Crux) method, it can be positively verified using an asterism : Sigma, Chi , Tau , and Upsilon Octantis are all stars of around magnitude 5.6, and form the distinctive shape of a trapezoid . Sigma Octantis was used as a reference to measure the magnitudes of stars in the southern hemisphere for the 1908 Revised Harvard Photometry catalogue. The Pole Star and Lambda Ursae Minoris were used for

4565-502: The massive photon is described by Proca theory , the experimental upper bound for its mass is about 10 grams ; if photon mass is generated by a Higgs mechanism , the experimental upper limit is less sharp, m ≤ 10   eV/ c   (roughly 2 × 10  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,

4648-438: The mental picture of the approximate transit time for light, but he refrained from using the light-year as a unit. He may have resisted expressing distances in light-years because it would reduce the accuracy of his parallax data due to multiplying with the uncertain parameter of the speed of light. The speed of light was not yet precisely known in 1838; the estimate of its value changed in 1849 ( Fizeau ) and 1862 ( Foucault ). It

4731-484: 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 = mc . In some cases, objects or waves may appear to travel faster than light (e.g., phase velocities of waves,

4814-531: The northern hemisphere. It was then noted that "Neither of these stars appears to vary perceptibly" but that, due to the procedures used "if they did, the variation would have no effect on the final measures." Sigma Octantis is the dimmest star to be represented on a national flag. It appears on the flag of Brazil , symbolising the Brazilian Federal District . Light-years A light-year , alternatively spelled light year ( ly or lyr ),

4897-495: 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, 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

4980-421: 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)

5063-408: The other hand, some techniques depend on the finite speed of light, for example in distance measurements. In computers , the speed of light imposes a limit on how quickly data can be sent between processors . If a processor operates at 1   gigahertz , 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

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5146-420: 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 ),

5229-403: 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

5312-412: 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

5395-485: The same general area, such as those belonging to the same spiral arm or globular cluster . Galaxies themselves span from a few thousand to a few hundred thousand light-years in diameter, and are separated from neighbouring galaxies and galaxy clusters by millions of light-years. Distances to objects such as quasars and the Sloan Great Wall run up into the billions of light-years. Distances between objects within

5478-539: The south celestial pole is moving away from it due to precession of the equinoxes . At magnitude +5.42, Sigma Octantis is barely visible to the naked eye, making it unusable for navigation, especially by comparison with the much brighter and more easily visible Polaris . Because of this, the constellation Crux is often preferred for determining the position of the South Celestial Pole . Once Sigma Octantis' approximate position has been determined, either by

5561-417: The speed v at which light travels in a material is called the refractive index n 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 ⁠ ≈ 200 000  km/s ( 124 000  mi/s) ; the refractive index of air for visible light is about 1.0003, so

5644-473: 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

5727-466: The speed of light in air is about 90 km/s (56 mi/s) slower than c . 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,

5810-470: The speed of light in vacuum. Since 1983, the constant c has been defined in the International System of Units (SI) as exactly 299 792 458  m/s ; this relationship is used to define the metre as exactly the distance that light travels in vacuum in 1 ⁄ 299 792 458 of a second. By using the value of c , as well as an accurate measurement of the second, one can thus establish

5893-470: 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 300 000  kilometres ( 186 000  miles ) in one second, these measurements of small fractions of a second must be very precise. The Lunar Laser Ranging experiment , radar astronomy and

5976-439: The speed of waves in any material medium, and c 0 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, μ 0 for the vacuum permeability or magnetic constant, ε 0 for the vacuum permittivity or electric constant, and Z 0 for the impedance of free space . This article uses c exclusively for

6059-509: 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

6142-407: 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

6225-471: 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

6308-468: 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,

6391-529: 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,

6474-436: The values of the electromagnetic constants ε 0 and μ 0 and using their relation to c . Historically, the most accurate results have been obtained by separately determining the frequency and wavelength of a light beam, with their product equalling c . This is described in more detail in the "Interferometry" section below. In 1983 the metre was defined as "the length of the path travelled by light in vacuum during

6557-408: The very end of its main sequence life with an age of about 900 million years. It has expanded somewhat to a size 4.4 that of the Sun and emits 44 times as much electromagnetic radiation from its photosphere at an effective temperature of 7,415  K . Sigma Octantis is a Delta Scuti variable , varying by about 0.03 magnitudes every 2.33 hours. It is thought to pulsate only in

6640-498: Was farther away took longer to reach the Earth, the time between two successive observations corresponds to a longer time between the instants at which the light rays were emitted. A 2011 experiment where neutrinos were observed to travel faster than light turned out to be due to experimental error. In models of the expanding universe , the farther galaxies are from each other, the faster they drift apart. For example, galaxies far away from Earth are inferred to be moving away from

6723-432: Was not yet considered to be a fundamental constant of nature, and the propagation of light through the aether or space was still enigmatic. The light-year unit appeared in 1851 in a German popular astronomical article by Otto Ule . Ule explained the oddity of a distance unit name ending in "year" by comparing it to a walking hour ( Wegstunde ). A contemporary German popular astronomical book also noticed that light-year

6806-440: Was the astronomical unit , equal to the radius of the Earth's orbit at 150 million kilometres (93 million miles). In those terms, trigonometric calculations based on 61 Cygni's parallax of 0.314 arcseconds, showed the distance to the star to be 660 000 astronomical units (9.9 × 10  km; 6.1 × 10  mi). Bessel added that light takes 10.3 years to traverse this distance. He recognized that his readers would enjoy

6889-438: Was updated in 2000, including the IAU (1976) value cited above (truncated to 10 significant digits). Other high-precision values are not derived from a coherent IAU system. A value of 9.460 536 207 × 10  m found in some modern sources is the product of a mean Gregorian year (365.2425 days or 31 556 952  s ) and the defined speed of light ( 299 792 458  m/s ). Another value, 9.460 528 405 × 10  m ,

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