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11,000 | Benzodiazepines are commonly used recreationally by poly-drug users. Mortality is higher among poly-drug users that also use benzodiazepines. Heavy alcohol use also increases mortality among poly-drug users. Dependence and tolerance, often coupled with dosage escalation, to benzodiazepines can develop rapidly among drug misusers; withdrawal syndrome may appear after as little as three weeks of continuous use. Long-term use has the potential to cause both physical and psychological dependence and severe withdrawal symptoms such as depression, anxiety (often to the point of panic attacks), and agoraphobia. Benzodiazepines and, in particular, temazepam are sometimes used intravenously, which, if done incorrectly or in an unsterile manner, can lead to medical complications including abscesses, cellulitis, thrombophlebitis, arterial puncture, deep vein thrombosis, and gangrene. Sharing syringes and needles for this purpose also brings up the possibility of transmission of hepatitis, HIV, and other diseases. Benzodiazepines are also misused intranasally, which may have additional health consequences. Once benzodiazepine dependence has been established, a clinician usually converts the patient to an equivalent dose of diazepam before beginning a gradual reduction program. | https://en.wikipedia.org/wiki?curid=4781 |
11,001 | A 1999–2005 Australian police survey of detainees reported preliminary findings that self-reported users of benzodiazepines were less likely than non-user detainees to work full-time and more likely to receive government benefits, use methamphetamine or heroin, and be arrested or imprisoned. Benzodiazepines are sometimes used for criminal purposes; they serve to incapacitate a victim in cases of drug assisted rape or robbery. | https://en.wikipedia.org/wiki?curid=4781 |
11,002 | Overall, anecdotal evidence suggests that temazepam may be the most psychologically habit-forming (addictive) benzodiazepine. Non-medical temazepam use reached epidemic proportions in some parts of the world, in particular, in Europe and Australia, and is a major addictive substance in many Southeast Asian countries. This led authorities of various countries to place temazepam under a more restrictive legal status. Some countries, such as Sweden, banned the drug outright. Temazepam also has certain pharmacokinetic properties of absorption, distribution, elimination, and clearance that make it more apt to non-medical use compared to many other benzodiazepines. | https://en.wikipedia.org/wiki?curid=4781 |
11,003 | Benzodiazepines are used in veterinary practice in the treatment of various disorders and conditions. As in humans, they are used in the first-line management of seizures, status epilepticus, and tetanus, and as maintenance therapy in epilepsy (in particular, in cats). They are widely used in small and large animals (including horses, swine, cattle and exotic and wild animals) for their anxiolytic and sedative effects, as pre-medication before surgery, for induction of anesthesia and as adjuncts to anesthesia. | https://en.wikipedia.org/wiki?curid=4781 |
11,004 | K2, at above sea level, is the second-highest mountain on Earth, after Mount Everest (at ). It lies in the Karakoram range, partially in the Gilgit-Baltistan region of Pakistan-administered Kashmir and partially in a China-administered territory of the Kashmir region included in the Taxkorgan Tajik Autonomous County of Xinjiang. | https://en.wikipedia.org/wiki?curid=17359 |
11,005 | K2 also became popularly known as the "Savage Mountain" after George Bell—a climber on the 1953 American expedition—told reporters, "It's a savage mountain that tries to kill you." Of the five highest mountains in the world, K2 is the deadliest; approximately one person dies on the mountain for every four who reach the summit. Also occasionally known as "Mount Godwin-Austen", other nicknames for K2 are "The King of Mountains" and "The Mountaineers' Mountain", as well as "The Mountain of Mountains" after prominent Italian climber Reinhold Messner titled his book about K2 the same. | https://en.wikipedia.org/wiki?curid=17359 |
11,006 | The summit was reached for the first time by the Italian climbers Lino Lacedelli and Achille Compagnoni, on the 1954 Italian expedition led by Ardito Desio. In January 2021, K2 became the final eight-thousander to be summited in the winter; the mountaineering feat was accomplished by a team of Nepalese climbers, led by Nirmal Purja and Mingma Gyalje Sherpa. | https://en.wikipedia.org/wiki?curid=17359 |
11,007 | K2 is the only 8,000+ metre peak that has never been climbed from its eastern face. Ascents have almost always been made in July and August, which are typically the warmest times of the year; K2's more northern location makes it more susceptible to inclement and colder weather. The peak has now been climbed by almost all of its ridges. Although the summit of Everest is at a higher altitude, K2 is a more difficult and dangerous climb, due in part to its more inclement weather. , only 377 people have completed the ascent to its summit. There have been 91 deaths during attempted climbs, according to the list maintained on the list of deaths on eight-thousanders. | https://en.wikipedia.org/wiki?curid=17359 |
11,008 | The name "K2" is derived from notation used by the Great Trigonometrical Survey of British India. Thomas Montgomerie made the first survey of the Karakoram from Mount Haramukh, some to the south, and sketched the two most prominent peaks, labelling them "K1" and "K2", where the "K" stands for "Karakoram". | https://en.wikipedia.org/wiki?curid=17359 |
11,009 | The policy of the Great Trigonometrical Survey was to use local names for mountains wherever possible and K1 was found to be known locally as Masherbrum. K2, however, appeared not to have acquired a local name, possibly due to its remoteness. The mountain is not visible from Askole, the last village to the south, or from the nearest habitation to the north, and is only fleetingly glimpsed from the end of the Baltoro Glacier, beyond which few local people would have ventured. The name "Chogori", derived from two Balti words, "chhogo ཆོ་གྷའོ་ (""big") and "ri རི "' ("mountain") (چھوغوری) has been suggested as a local name, but evidence for its widespread use is scant. It may have been a compound name invented by Western explorers or simply a bemused reply to the question "What's that called?" It does, however, form the basis for the name "Qogir" () by which Chinese authorities officially refer to the peak. Other local names have been suggested including "Lamba Pahar" ("Tall Mountain" in Urdu) and "Dapsang", but are not widely used. | https://en.wikipedia.org/wiki?curid=17359 |
11,010 | With the mountain lacking a local name, the name "Mount Godwin-Austen" was suggested, in honour of Henry Godwin-Austen, an early explorer of the area. While the name was rejected by the Royal Geographical Society, it was used on several maps and continues to be used occasionally. | https://en.wikipedia.org/wiki?curid=17359 |
11,011 | The surveyor's mark, K2, therefore continues to be the name by which the mountain is commonly known. It is now also used in the Balti language, rendered as "Kechu" or "Ketu" ( ). The Italian climber Fosco Maraini argued in his account of the ascent of Gasherbrum IV that while the name of K2 owes its origin to chance, its clipped, impersonal nature is highly appropriate for so remote and challenging a mountain. He concluded that it was: | https://en.wikipedia.org/wiki?curid=17359 |
11,012 | K2 lies in the northwestern Karakoram Range. It is located in the Baltistan region of Gilgit–Baltistan, Pakistan, and the Taxkorgan Tajik Autonomous County of Xinjiang, China. The Tarim sedimentary basin borders the range on the north and the Lesser Himalayas on the south. Melt waters from glaciers, such as those south and east of K2, feed agriculture in the valleys and contribute significantly to the regional fresh-water supply. | https://en.wikipedia.org/wiki?curid=17359 |
11,013 | K2 is ranked 22nd by topographic prominence, a measure of a mountain's independent stature. It is a part of the same extended area of uplift (including the Karakoram, the Tibetan Plateau, and the Himalaya) as Mount Everest, and it is possible to follow a path from K2 to Everest that goes no lower than , at the Kora La on the Nepal/China border in the Mustang Lo. Many other peaks far lower than K2 are more independent in this sense. It is, however, the most prominent peak within the Karakoram range. | https://en.wikipedia.org/wiki?curid=17359 |
11,014 | K2 is notable for its local relief as well as its total height. It stands over above much of the glacial valley bottoms at its base. It is a consistently steep pyramid, dropping quickly in almost all directions. The north side is the steepest: there it rises over above the K2 (Qogir) Glacier in only of horizontal distance. In most directions, it achieves over of vertical relief in less than . | https://en.wikipedia.org/wiki?curid=17359 |
11,015 | A 1986 expedition led by George Wallerstein made an inaccurate measurement showing that K2 was taller than Mount Everest, and therefore the tallest mountain in the world. A corrected measurement was made in 1987, but by then the claim that K2 was the tallest mountain in the world had already made it into many news reports and reference works. | https://en.wikipedia.org/wiki?curid=17359 |
11,016 | K2's height given on maps and encyclopedias is . In the summer of 2014, a Pakistani-Italian expedition to K2, named "K2 60 Years Later", was organized to commemorate the 60th anniversary of the first ascent of K2. One of the goals of the expedition was to accurately measure the height of the mountain using satellite navigation. The height of K2 measured during this expedition was . | https://en.wikipedia.org/wiki?curid=17359 |
11,017 | The mountains of K2 and Broad Peak, and the area westward to the lower reaches of Sarpo Laggo glacier, consist of metamorphic rocks, known as the "K2 Gneiss," and part of the Karakoram Metamorphic Complex. The K2 Gneiss consists of a mixture of orthogneiss and biotite-rich paragneiss. On the south and southeast face of K2, the orthogneiss consists of a mixture of a strongly foliated plagioclase-hornblende gneiss and a biotite-hornblende-K-feldspar orthogneiss, which has been intruded by garnet-mica leucogranitic dikes. In places, the paragneisses include clinopyroxene-hornblende-bearing psammites, garnet (grossular)-diopside marbles, and biotite-graphite phyllites. Near the memorial to the climbers who have died on K2, above Base Camp on the south spur, thin impure marbles with quartzites and mica schists, called the "Gilkey-Puchoz sequence", are interbanded within the orthogneisses. On the west face of Broad Peak and south spur of K2, lamprophyre dikes, which consist of clinopyroxene and biotite-porphyritic vogesites and minettes, have intruded the K2 gneiss. The K2 Gneiss is separated from the surrounding sedimentary and metasedimentary rocks of the surrounding Karakoram Metamorphic Complex by normal faults. For example, a fault separates the K2 gneiss of the east face of K2 from limestones and slates comprising nearby Skyang Kangri. | https://en.wikipedia.org/wiki?curid=17359 |
11,018 | Ar/Ar ages of 115 to 120 million years ago obtained from and geochemical analyses of the K2 Gneiss demonstrate that it is a metamorphosed, older, Cretaceous, pre-collisional granite. The granitic precursor (protolith) to the K2 Gneiss originated as the result of the production of large bodies of magma by a northward-dipping subduction zone along what was the continental margin of Asia at that time and their intrusion as batholiths into its lower continental crust. During the initial collision of the Asia and Indian plates, this granitic batholith was buried to depths of about or more, highly metamorphosed, highly deformed, and partially remelted during the Eocene Period to form gneiss. Later, the K2 Gneiss was then intruded by leucogranite dikes and finally exhumed and uplifted along major breakback thrust faults during post-Miocene time. The K2 Gneiss was exposed as the entire K2-Broad Peak-Gasherbrum range experienced rapid uplift with which erosion rates have been unable to keep pace. | https://en.wikipedia.org/wiki?curid=17359 |
11,019 | The mountain was first surveyed by a British team in 1856. Team member Thomas Montgomerie designated the mountain "K2" for being the second peak of the Karakoram range. The other peaks were originally named K1, K3, K4, and K5, but were eventually renamed Masherbrum, Gasherbrum IV, Gasherbrum II, and Gasherbrum I, respectively. In 1892, Martin Conway led a British expedition that reached "Concordia" on the Baltoro Glacier. | https://en.wikipedia.org/wiki?curid=17359 |
11,020 | The first serious attempt to climb K2 was undertaken in 1902 by Oscar Eckenstein, Aleister Crowley, Jules Jacot-Guillarmod, Heinrich Pfannl, Victor Wessely, and Guy Knowles via the Northeast Ridge. In the early 1900s, modern transportation did not exist in the region: it took "fourteen days just to reach the foot of the mountain". | https://en.wikipedia.org/wiki?curid=17359 |
11,021 | After five serious and costly attempts, the team reached —although considering the difficulty of the challenge, and the lack of modern climbing equipment or weatherproof fabrics, Crowley's statement that "neither man nor beast was injured" highlights the relative skill of the ascent. The failures were also attributed to sickness (Crowley was suffering the residual effects of malaria), a combination of questionable physical training, personality conflicts, and poor weather conditions—of 68 days spent on K2 (at the time, the record for the longest time spent at such an altitude) only eight provided clear weather. | https://en.wikipedia.org/wiki?curid=17359 |
11,022 | The next expedition to K2, in 1909, led by Prince Luigi Amedeo, Duke of the Abruzzi, reached an elevation of around on the South East Spur, now known as the "Abruzzi Spur" (or Abruzzi Ridge). This would eventually become part of the standard route, but was abandoned at the time due to its steepness and difficulty. After trying and failing to find a feasible alternative route on the West Ridge or the North East Ridge, the Duke declared that K2 would never be climbed, and the team switched its attention to Chogolisa, where the Duke came within of the summit before being driven back by a storm. | https://en.wikipedia.org/wiki?curid=17359 |
11,023 | The next attempt on K2 was not made until 1938, when the First American Karakoram expedition led by Charles Houston made a reconnaissance of the mountain. They concluded that the Abruzzi Spur was the most practical route and reached a height of around before turning back due to diminishing supplies and the threat of bad weather. | https://en.wikipedia.org/wiki?curid=17359 |
11,024 | The following year, the 1939 American expedition led by Fritz Wiessner came within of the summit but ended in disaster when Dudley Wolfe, Pasang Kikuli, Pasang Kitar, and Pintso disappeared high on the mountain. | https://en.wikipedia.org/wiki?curid=17359 |
11,025 | Charles Houston returned to K2 to lead the 1953 American expedition. The attempt failed after a storm pinned down the team for 10 days at , during which time climber Art Gilkey became critically ill. A desperate retreat followed, during which Pete Schoening saved almost the entire team during a mass fall (known simply as The Belay), and Gilkey was killed, either in an avalanche or in a deliberate attempt to avoid burdening his companions. Despite the retreat and tragic end, the expedition has been given iconic status in mountaineering history. The Gilkey Memorial was built in his memory at the mountain's foot. | https://en.wikipedia.org/wiki?curid=17359 |
11,026 | The 1954 Italian expedition finally succeeded in ascending to the summit of K2 via the Abruzzi Spur on 31 July 1954. The expedition was led by Ardito Desio, and the two climbers who reached the summit were Lino Lacedelli and Achille Compagnoni. The team included a Pakistani member, Colonel Muhammad Ata-ullah, who had been a part of the 1953 American expedition. Also on the expedition were Walter Bonatti and Pakistani Hunza porter Amir Mehdi, who both proved vital to the expedition's success in that they carried oxygen tanks to for Lacedelli and Compagnoni. The ascent is controversial because Lacedelli and Compagnoni established their camp at a higher elevation than originally agreed with Mehdi and Bonatti. It being too dark to ascend or descend, Mehdi and Bonatti were forced to overnight without shelter above 8,000 metres leaving the oxygen tanks behind as requested when they descended. Bonatti and Mehdi survived, but Mehdi was hospitalised for months and had to have his toes amputated because of frostbite. Efforts in the 1950s to suppress these facts to protect Lacedelli and Compagnoni's reputations as Italian national heroes were later brought to light. It was also revealed that the moving of the camp was deliberate, a move apparently made because Compagnoni feared being outshone by the younger Bonatti. Bonatti was given the blame for Mehdi's hospitalisation. | https://en.wikipedia.org/wiki?curid=17359 |
11,027 | On 9 August 1977, 23 years after the Italian expedition, Ichiro Yoshizawa led the second successful ascent, with Ashraf Aman as the first native Pakistani climber. The Japanese expedition took the Abruzzi Spur and used more than 1,500 porters. | https://en.wikipedia.org/wiki?curid=17359 |
11,028 | The third ascent of K2 was in 1978, via a new route, the long and corniced Northeast Ridge. The top of the route traversed left across the East Face to avoid a vertical headwall and joined the uppermost part of the Abruzzi route. This ascent was made by an American team, led by James Whittaker; the summit party was Louis Reichardt, Jim Wickwire, John Roskelley, and Rick Ridgeway. Wickwire endured an overnight bivouac about below the summit, one of the highest bivouacs in history. This ascent was emotional for the American team, as they saw themselves as completing a task that had been begun by the 1938 team forty years earlier. | https://en.wikipedia.org/wiki?curid=17359 |
11,029 | Another notable Japanese ascent was that of the difficult North Ridge on the Chinese side of the peak in 1982. A team from the led by Isao Shinkai and put three members, Naoe Sakashita, Hiroshi Yoshino, and Yukihiro Yanagisawa, on the summit on 14 August. However Yanagisawa fell and died on the descent. Four other members of the team achieved the summit the next day. | https://en.wikipedia.org/wiki?curid=17359 |
11,030 | The first climber to reach the summit of K2 twice was Czech climber Josef Rakoncaj. Rakoncaj was a member of the 1983 Italian expedition led by Francesco Santon, which made the second successful ascent of the North Ridge (31 July 1983). Three years later, on 5 July 1986, he reached the summit via the Abruzzi Spur (double with Broad Peak West Face solo) as a member of Agostino da Polenza's international expedition. | https://en.wikipedia.org/wiki?curid=17359 |
11,031 | The first woman to summit K2 was Polish climber Wanda Rutkiewicz on 23 June 1986. Liliane and Maurice Barrard who had summitted later that day, fell during the descent; Liliane Barrard's body was found on 19 July 1986 at the foot of the south face. | https://en.wikipedia.org/wiki?curid=17359 |
11,032 | In 1986, two Polish expeditions summitted via two new routes, the Magic Line and the Polish Line (Jerzy Kukuczka and Tadeusz Piotrowski). Piotrowski fell to his death as the two were descending. This latter route has never been repeated. | https://en.wikipedia.org/wiki?curid=17359 |
11,033 | Thirteen climbers from several expeditions died in the 1986 K2 disaster. Another six mountaineers died in the 1995 K2 disaster, while eleven climbers died in the 2008 K2 disaster. | https://en.wikipedia.org/wiki?curid=17359 |
11,034 | There are a number of routes on K2, of somewhat different character, but they all share some key difficulties, the first being the extremely high altitude and resulting lack of oxygen: there is only one-third as much oxygen available to a climber on the summit of K2 as there is at sea level. | https://en.wikipedia.org/wiki?curid=17359 |
11,035 | The second is the propensity of the mountain to experience extreme storms of several days duration, which have resulted in many of the deaths on the peak. The third is the steep, exposed, and committing nature of all routes on the mountain, which makes retreat more difficult, especially during a storm. Despite many attempts the first successful winter ascents occurred only in 2021. All major climbing routes lie on the Pakistani side. The base camp is also located on the Pakistani side. | https://en.wikipedia.org/wiki?curid=17359 |
11,036 | The standard route of ascent, used by 75% of all climbers, is the Abruzzi Spur, located on the Pakistani side, first attempted by Prince Luigi Amedeo, Duke of the Abruzzi in 1909. This is the peak's southeast ridge, rising above the Godwin-Austen Glacier. The spur proper begins at an altitude of , where Advanced Base Camp is usually placed. The route follows an alternating series of rock ribs, snow/ice fields, and some technical rock climbing on two famous features, "House's Chimney" and the "Black Pyramid." Above the Black Pyramid, dangerously exposed and difficult to navigate slopes lead to the easily visible "Shoulder", and thence to the summit. The last major obstacle is a narrow couloir known as the "Bottleneck", which places climbers dangerously close to a wall of seracs that form an ice cliff to the east of the summit. It was partly due to the collapse of one of these seracs around 2001 that no climbers reached the summit in 2002 and 2003. | https://en.wikipedia.org/wiki?curid=17359 |
11,037 | On 1 August 2008, 11 climbers from several expeditions died during a series of accidents, including several ice falls in the Bottleneck. | https://en.wikipedia.org/wiki?curid=17359 |
11,038 | Almost opposite from the Abruzzi Spur is the North Ridge, which ascends the Chinese side of the peak. It is rarely climbed, partly due to very difficult access, involving crossing the Shaksgam River, which is a hazardous undertaking. In contrast to the crowds of climbers and trekkers at the Abruzzi basecamp, usually at most two teams are encamped below the North Ridge. This route, more technically difficult than the Abruzzi, ascends a long, steep, primarily rock ridge to high on the mountain—Camp IV, the "Eagle's Nest" at —and then crosses a dangerously slide-prone hanging glacier by a leftward climbing traverse, to reach a snow couloir which accesses the summit. | https://en.wikipedia.org/wiki?curid=17359 |
11,039 | Besides the original Japanese ascent, a notable ascent of the North Ridge was the one in 1990 by Greg Child, Greg Mortimer, and Steve Swenson, which was done alpine style above Camp 2, though using some fixed ropes already put in place by a Japanese team. | https://en.wikipedia.org/wiki?curid=17359 |
11,040 | Because 75% of people who climb K2 use the Abruzzi Spur, these listed routes are rarely climbed. No one has climbed the East Face of the mountain due to the instability of the snow and ice formations on that side. Besides the East Face, the North Face has not yet been climbed either. In 2007 Denis Urubko and Serguey Samoilov intended to climb the K2's North Face but they were stymied by increasingly deteriorating conditions. After finding their intended route menaced by growing avalanche danger, they traversed onto the normal North Ridge route and summited on 2 October 2007, making the latest summer season ascent of the peak in history. | https://en.wikipedia.org/wiki?curid=17359 |
11,041 | For most of its climbing history, K2 was not usually climbed with supplemental oxygen, and small, relatively lightweight teams were the norm. However, the 2004 season saw a great increase in the use of oxygen: 28 of 47 summitteers used oxygen in that year. | https://en.wikipedia.org/wiki?curid=17359 |
11,042 | K2's summit is well above the altitude at which high altitude pulmonary edema (HAPE), or high altitude cerebral edema (HACE) can occur. In mountaineering, when ascending above an altitude of , the climber enters what is known as the "death zone". | https://en.wikipedia.org/wiki?curid=17359 |
11,043 | The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space. | https://en.wikipedia.org/wiki?curid=28736 |
11,044 | 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. Starlight viewed on Earth left the stars many years ago, 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 from Earth to the spacecraft and vice versa. In computing, the speed of light fixes the ultimate minimum communication delay between computers, to computer memory, and within a CPU. The speed of light can be used in time of flight measurements to measure large distances to extremely high precision. | https://en.wikipedia.org/wiki?curid=28736 |
11,045 | Ole Rømer first demonstrated in 1676 that light travels at a finite speed (non-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 . In 1905, Albert Einstein postulated that the speed of light 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 had relevance outside of the context of light and electromagnetism. | https://en.wikipedia.org/wiki?curid=28736 |
11,046 | Massless particles and field perturbations, such as gravitational waves, also travel at speed in a vacuum. Such particles and waves travel at regardless of the motion of the source or the inertial reference frame of the observer. Particles with nonzero rest mass can be accelerated to approach but can never reach it, regardless of the frame of reference in which their speed is measured. In the special and general theories of relativity, interrelates space and time and also appears in the famous equation of mass–energy equivalence, . | https://en.wikipedia.org/wiki?curid=28736 |
11,047 | In some cases, objects or waves may appear to travel faster than light (e.g., phase velocities of waves, 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,048 | The speed at which light propagates through transparent materials, such as glass or air, is less than ; similarly, the speed of electromagnetic waves in wire cables is slower than . The ratio between and the speed at which light travels in a material is called the refractive index of the material (). For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at ; the refractive index of air for visible light is about 1.0003, so the speed of light in air is about slower than . | https://en.wikipedia.org/wiki?curid=28736 |
11,049 | The speed of light in vacuum is usually denoted by a lowercase , for "constant" or the Latin (meaning 'swiftness, celerity'). In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used for a different constant that was later shown to equal times the speed of light in vacuum. Historically, the symbol "V" was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1894, Paul Drude redefined with its modern meaning. Einstein used "V" in his original German-language papers on special relativity in 1905, but in 1907 he switched to , which by then had become the standard symbol for the speed of light. | https://en.wikipedia.org/wiki?curid=28736 |
11,050 | Sometimes is used for the speed of waves in any material medium, and 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" for the vacuum permeability or magnetic constant, "ε" for the vacuum permittivity or electric constant, and "Z" for the impedance of free space. This article uses exclusively for the speed of light in vacuum. | https://en.wikipedia.org/wiki?curid=28736 |
11,051 | Since 1983, the constant has been defined in the International System of Units (SI) as "exactly" ; this relationship is used to define the metre as exactly the distance that light travels in a vacuum in of a second. By using the value of , as well as an accurate measurement of the second, one can thus establish a standard for the metre. As a dimensional physical constant, the numerical value of is different for different unit systems. For example, in imperial units, the speed of light is approximately miles per second, or roughly 1 foot per nanosecond. | https://en.wikipedia.org/wiki?curid=28736 |
11,052 | In branches of physics in which appears often, such as in relativity, it is common to use systems of natural units of measurement or the geometrized unit system where . Using these units, 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,053 | 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 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. However, by adopting Einstein synchronization for the clocks, the one-way speed of light becomes equal to the two-way speed of light by definition. The special theory of relativity explores the consequences of this invariance of "c" with the assumption that the laws of physics are the same in all inertial frames of reference. One consequence is that "c" is the speed at which all massless particles and waves, including light, must travel in vacuum. | https://en.wikipedia.org/wiki?curid=28736 |
11,054 | Special relativity has many counterintuitive and experimentally verified implications. These include the equivalence of mass and energy , 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 , where "v" is the speed of the object. The difference of "γ" from1 is negligible for speeds much slower than "c", such as most everyday speedsin which case special relativity is closely approximated by Galilean relativitybut 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"). | https://en.wikipedia.org/wiki?curid=28736 |
11,055 | 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 along a trajectory of finite length can differ from "c", depending on how distances and times are defined. | https://en.wikipedia.org/wiki?curid=28736 |
11,056 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,057 | It also is generally assumed that the speed of light is isotropic, meaning that it has the same value regardless of the direction in which it is measured. Observations of the emissions from nuclear energy 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,058 | According to special relativity, the energy of an object with rest mass "m" and speed "v" is given by , where "γ" is the Lorentz factor defined above. When "v" is zero, "γ" is equal to one, giving rise to the famous formula for mass–energy equivalence. The "γ" factor approaches infinity as "v" approaches "c", and it would take an infinite amount of energy to accelerate an object with mass to the speed of light. The speed of light is the upper limit for the speeds of objects with positive rest mass, and individual photons cannot travel faster than the speed of light. This is experimentally established in many tests of relativistic energy and momentum. | https://en.wikipedia.org/wiki?curid=28736 |
11,059 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,060 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,061 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,062 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,063 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,064 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,065 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,066 | A 2011 experiment where neutrinos were observed to travel faster than light turned out to be due to experimental error. | https://en.wikipedia.org/wiki?curid=28736 |
11,067 | In models of the expanding universe, the farther galaxies are from each other, the faster they drift apart. This receding is not due to motion through space, but rather to the expansion of space itself. For example, galaxies far away from Earth appear to be moving away from the Earth with a speed proportional to their distances. Beyond a boundary called the Hubble sphere, the rate at which their distance from Earth increases becomes greater than the speed of light. | https://en.wikipedia.org/wiki?curid=28736 |
11,068 | In classical physics, light is described as a type of electromagnetic wave. The classical behaviour of the electromagnetic field is described by Maxwell's equations, which predict that the speed "c" with which electromagnetic waves (such as light) propagate in vacuum is related to the distributed capacitance and inductance of vacuum, otherwise respectively known as the electric constant "ε" and the magnetic constant "μ", by the equation | https://en.wikipedia.org/wiki?curid=28736 |
11,069 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,070 | 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 grams; if photon mass is generated by a Higgs mechanism, the experimental upper limit is less sharp, (roughly 2 × 10 g). | https://en.wikipedia.org/wiki?curid=28736 |
11,071 | Another reason for the speed of light to vary with its frequency would be the failure of special relativity to apply to arbitrarily small scales, as predicted by some proposed theories of quantum gravity. In 2009, the observation of gamma-ray burst GRB 090510 found no evidence for a dependence of photon speed on energy, supporting tight constraints in specific models of spacetime quantization on how this speed is affected by photon energy for energies approaching the Planck scale. | https://en.wikipedia.org/wiki?curid=28736 |
11,072 | 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 velocity "v". 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", and its earliest part travels at the front velocity "v". | https://en.wikipedia.org/wiki?curid=28736 |
11,073 | The phase velocity is important in determining how a light wave travels through a material or from one material to another. It is often represented in terms of a "refractive index". The refractive index of a material is defined as the ratio of "c" to the phase velocity "v" 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. However, the popular description of light being "stopped" in these experiments refers only to light being stored in the excited states of atoms, then re-emitted at an arbitrarily later time, as stimulated by a second laser pulse. During the time it had "stopped", it had ceased to be light. This type of behaviour is generally microscopically true of all transparent media which "slow" the speed of light. | https://en.wikipedia.org/wiki?curid=28736 |
11,074 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,075 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,076 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,077 | None of these options, however, allow information to be transmitted faster than "c". It is impossible to transmit information with a light pulse any faster than the speed of the earliest part of the pulse (the front velocity). It can be shown that this is (under certain assumptions) always equal to "c". | https://en.wikipedia.org/wiki?curid=28736 |
11,078 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,079 | The speed of light is of relevance to communications: the one-way and round-trip delay time are greater than zero. This applies from small to astronomical scales. On the other hand, some techniques depend on the finite speed of light, for example in distance measurements. | https://en.wikipedia.org/wiki?curid=28736 |
11,080 | 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 in a single clock cycle — in practice, this distance is even shorter since the printed circuit board itself has a refractive index and slows down signals. Processors must therefore be placed close to each other, as well as memory 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,081 | Given that the equatorial circumference of the Earth is about and that "c" is about , the theoretical shortest time for a piece of information to travel half the globe along the surface is about 67 milliseconds. When light is traveling in optical fibre (a transparent material) the actual transit time is longer, in part because the speed of light is slower by about 35% in optical fibre, depending on its refractive index "n". Furthermore, straight lines are rare in global communications and the travel time increases when signals pass through electronic switches or signal regenerators. | https://en.wikipedia.org/wiki?curid=28736 |
11,082 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,083 | 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 later. It would then take a further for commands to travel from Earth to Mars. | https://en.wikipedia.org/wiki?curid=28736 |
11,084 | Receiving light and other signals from distant astronomical sources takes much longer. For example, it takes 13 billion (13) years for light to travel to Earth from the faraway galaxies viewed in the Hubble Ultra Deep Field images. Those photographs, taken today, capture images of the galaxies as they appeared 13 billion years ago, when the universe was less than a billion years old. The fact that more distant objects appear to be younger, due to the finite speed of light, allows astronomers to infer the evolution of stars, of galaxies, and of the universe itself. | https://en.wikipedia.org/wiki?curid=28736 |
11,085 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,086 | 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 () 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,087 | There are different ways to determine the value of "c". One way is to measure the actual speed at which light waves propagate, which can be done in various astronomical and Earth-based setups. However, it is also possible to determine "c" from other physical laws where it appears, for example, by determining the values of the electromagnetic constants "ε" and "μ" 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,088 | In 1983 the metre was defined as "the length of the path travelled by light in vacuum during a time interval of of a second", fixing the value of the speed of light at by definition, as described below. Consequently, accurate measurements of the speed of light yield an accurate realization of the metre rather than an accurate value of "c". | https://en.wikipedia.org/wiki?curid=28736 |
11,089 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,090 | 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 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,091 | Another method is to use the aberration of light, discovered and explained by James Bradley in the 18th century. This effect results from the vector addition of the velocity of light arriving from a distant source (such as a star) and the velocity of its observer (see diagram on the right). A moving observer thus sees the light coming from a slightly different direction and consequently sees the source at a position shifted from its original position. Since the direction of the Earth's velocity changes continuously as the Earth orbits the Sun, this effect causes the apparent position of stars to move around. From the angular difference in the position of stars (maximally 20.5 arcseconds) it is possible to express the speed of light in terms of the Earth's velocity around the Sun, which with the known length of a year can be converted to the time needed to travel from the Sun to the Earth. In 1729, Bradley used this method to derive that light travelled times faster than the Earth in its orbit (the modern figure is times faster) or, equivalently, that it would take light 8 minutes 12 seconds to travel from the Sun to the Earth. | https://en.wikipedia.org/wiki?curid=28736 |
11,092 | An astronomical unit (AU) is approximately the average distance between the Earth and Sun. It was redefined in 2012 as exactly . Previously the AU was not based on the International System of Units 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). | https://en.wikipedia.org/wiki?curid=28736 |
11,093 | Previously, the inverse of expressed in seconds per astronomical unit was measured by comparing the time for radio signals to reach different spacecraft in the Solar System, with their position calculated from the gravitational effects of the Sun and various planets. By combining many such measurements, a best fit value for the light time per unit distance could be obtained. For example, in 2009, the best estimate, as approved by the International Astronomical Union (IAU), was: | https://en.wikipedia.org/wiki?curid=28736 |
11,094 | The relative uncertainty in these measurements is 0.02 parts per billion (), equivalent to the uncertainty in Earth-based measurements of length by interferometry. Since the metre is defined to be the length travelled by light in a certain time interval, the measurement of the light time in terms of the previous definition of the astronomical unit can also be interpreted as measuring the length of an AU (old definition) in metres. | https://en.wikipedia.org/wiki?curid=28736 |
11,095 | A method of measuring the speed of light is to measure the time needed for light to travel to a mirror at a known distance and back. This is the working principle behind the Fizeau–Foucault apparatus developed by Hippolyte Fizeau and Léon Foucault, based on a suggestion by François Arago. | https://en.wikipedia.org/wiki?curid=28736 |
11,096 | The setup as used by Fizeau consists of a beam of light directed at a mirror away. On the way from the source to the mirror, the beam passes through a rotating cogwheel. At a certain rate of rotation, the beam passes through one gap on the way out and another on the way back, but at slightly higher or lower rates, the beam strikes a tooth and does not pass through the wheel. Knowing the distance between the wheel and the mirror, the number of teeth on the wheel, and the rate of rotation, the speed of light can be calculated. | https://en.wikipedia.org/wiki?curid=28736 |
11,097 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,098 | 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. | https://en.wikipedia.org/wiki?curid=28736 |
11,099 | An option for deriving "c" that does not directly depend on a measurement of the propagation of electromagnetic waves is to use the relation between "c" and the vacuum permittivity "ε" and vacuum permeability "μ" established by Maxwell's theory: "c" = 1/("ε""μ"). 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 through the definition of the ampere. Rosa and Dorsey used this method in 1907 to find a value of . Their method depended upon having a standard unit of electrical resistance, the "international ohm", and so its accuracy was limited by how this standard was defined. | https://en.wikipedia.org/wiki?curid=28736 |
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