Saturday, July 9, 2011
Sunday, March 27, 2011
Japan ( Japanese: 日本 Nihon or Nippon, officially 日本国 Nippon-koku or Nihon-koku) is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south. The characters that make up Japan's name mean "sun-origin", which is why Japan is sometimes referred to as the "Land of the Rising Sun".
Japan is an archipelago of 6,852 islands. The four largest islands are Honshu, Hokkaido, Kyushu and Shikoku, together accounting for ninety-seven percent of Japan's land area. Japan has the world's tenth-largest population, with over 127 million people. The Greater Tokyo Area, which includes the de facto capital city of Tokyo and several surrounding prefectures, is the largest metropolitan area in the world, with over 30 million residents.
Archaeological research indicates that people lived in Japan as early as the Upper Paleolithic period. The first written mention of Japan is in Chinese history texts from the 1st century AD. Influence from other nations followed by long periods of isolation has characterized Japan's history. Since adopting its revised constitution in 1947, Japan has maintained a unitary constitutional monarchy with an emperor and an elected parliament called the Diet.
A major economic power, Japan has the world's third-largest economy by nominal GDP and by purchasing power parity. It is also the world's fourth largest exporter and fourth largest importer. Although Japan has officially renounced its right to declare war, it maintains an extensive modern military force in self-defense and peacekeeping roles. After Singapore, Japan has the lowest homicide (including attempted homicide) rate in the world. According to both UN and WHO estimates, Japan has the longest life expectancy of any country in the world. According to the UN, it has the third lowest infant mortality rate.
The English word Japan is an exonym. The Japanese names for Japan are Nippon listen (help·info) and Nihon listen (help·info); both names are written using the kanji 日本. The Japanese name Nippon is used for most official purposes, including on Japanese yen, postage stamps, and for many international sporting events. Nihon is a more casual term and is used in contemporary speech. Japanese people refer to themselves as Nihonjin and to their language as Nihongo . Both Nippon and Nihonmean "sun-origin" and are often translated as Land of the Rising Sun. This nomenclature comes from Japanese missions to Imperial China and refers to Japan's eastward position relative to China. Before Nihon came into official use, Japan was known as Wa or Wakoku .
The English word for Japan came to the West via early trade routes. The early Mandarin or possibly Wu Chinese (吳語) word for Japan was recorded by Marco Polo as Cipangu. In modern Shanghainese, a Wu dialect, the pronunciation of characters 日本 'Japan' is Zeppen [zəʔpən]. The old Malay word for Japan, Jepang, was borrowed from a Chinese language, and this Malay word was encountered by Portuguese traders in Malacca in the 16th century. It is thought the Portuguese traders were the first to bring the word to Europe. It was first recorded in English in a 1565 letter, spelled Giapan.
Prehistory and ancient history
An example of Jōmon pottery, 3000-2000 BC
A Paleolithic culture around 30,000 BC constitutes the first known habitation of Japan. This was followed from around 14,000 BC (the start of the Jōmon period) by a Mesolithic to Neolithic semi-sedentary hunter-gatherer culture, who include ancestors of both the contemporary Ainu people and Yamato people, characterized by pit dwelling and rudimentary agriculture. Decorated clay vessels from this period are some of the oldest surviving examples of pottery in the world. Around 300 BC, the Yayoi people began to enter the Japanese islands, intermingling with the Jōmon. The Yayoi period, starting around 500 BC, saw the introduction of practices like wet-rice farming, a new style of pottery, and metallurgy, introduced from China and Korea.
The Japanese first appear in written history in the Chinese Book of Han. According to the Records of Three Kingdoms, the most powerful kingdom on the archipelago during the 3rd century was called Yamataikoku. Buddhism was first introduced to Japan from Baekje, one of the Three Kingdoms of Korea, but the subsequent development of Japanese Buddhism was primarily influenced by China. Despite early resistance, Buddhism was promoted by the ruling class and gained widespread acceptance beginning in the Asuka period.
The Nara period of the 8th century marked the emergence of a strong Japanese state, centered on an imperial court in Heijō-kyō (modern Nara). In addition to the continuing adoption of Chinese administrative practices, the Nara period is characterized by the appearance of a nascent literature with the completion of the Kojiki (712) and Nihon Shoki (720). The smallpox epidemic of 735–737 is believed to have killed as much as one-third of Japan's population. In 784, Emperor Kammu moved the capital from Nara to Nagaoka-kyō before relocating it to Heian-kyō (modern Kyoto) in 794. This marked the beginning of the Heian period, during which a distinctly indigenous Japanese culture emerged, noted for its art, poetry and literature. Lady Murasaki's The Tale of Genji and the lyrics of Japan's national anthem Kimigayo were written during this time.
The Mongol invasions in 1274 and 1281 were successfully repelled
Japan's feudal era was characterized by the emergence and dominance of a ruling class of warriors, the samurai. In 1185, following the defeat of the Taira clan, samurai Minamoto no Yoritomo was appointed shogun and established a base of power in Kamakura. After Yoritomo's death, the Hōjō clan came to power as regents for the shoguns. The Zen school of Buddhism was introduced from China in the Kamakura period(1185–1333) and became popular among the samurai class. The Kamakura shogunate repelled Mongol invasions in 1274 and 1281, but was eventually overthrown by Emperor Go-Daigo. Go-Daigo was himself defeated by Ashikaga Takauji in 1336. The succeeding Ashikaga shogunate failed to control the feudal warlords (daimyo), and a civil war (the Ōnin War) began in 1467, opening the century-long Sengoku period("Warring States").
During the 16th century, traders and Jesuit missionaries from Portugal reached Japan for the first time, initiating direct commercial and cultural exchange between Japan and the West (Nanban trade). Oda Nobunaga conquered many other daimyo using European technology and firearms; after he was assassinated in 1582, his successor Toyotomi Hideyoshi unified the nation in 1590. Hideyoshi invaded Korea twice, but following defeats by Korean and Ming Chinese forces and Hideyoshi's death, Japanese troops were withdrawn in 1598.
Tokugawa Ieyasu served as regent for Hideyoshi's son Toyotomi Hideyori, using his position to gain political and military support. When open war broke out, he defeated rival clans in theBattle of Sekigahara in 1600. Ieyasu was appointed shogun in 1603 and established the Tokugawa shogunate at Edo (modern Tokyo). The Tokugawa shogunate enacted measures like buke shohatto as a code of conduct to control the autonomous daimyo. In 1639, the shogunate began the isolationist sakoku ("closed country") policy that spanned the two and a half centuries of tenuous political unity known as the Edo period. The study of Western sciences, known as rangaku, continued during this period through contact with the Dutch enclave at Dejima in Nagasaki. The Edo period also gave rise to kokugaku ("national studies"), the study of Japan by the Japanese.
The Meiji Emperor
On March 31, 1854, Commodore Matthew Perry and the "Black Ships" of the United States Navy forced the opening of Japan to the outside world with the Convention of Kanagawa. Subsequent similar treaties with Western countries in the Bakumatsu period brought economic and political crises. The resignation of the shogun led to the Boshin War and the establishment of a centralized state nominally unified under the Emperor (the Meiji Restoration). Adopting Western political, judicial and military institutions, the Cabinet organized the Privy Council, introduced the Meiji Constitution, and assembled the Imperial Diet. The Meiji Restoration transformed the Empire of Japan into an industrialized world power that pursued military conflict to expand its sphere of influence. After victories in the First Sino-Japanese War (1894–1895) and the Russo-Japanese War (1904–1905), Japan gained control of Taiwan, Korea, and the southern half of Sakhalin. Japan's population grew from 35 million in 1873 to 70 million in 1935.
The early 20th century saw a brief period of "Taishō democracy" overshadowed by increasing expansionism and militarization. World War I enabled Japan, which joined the side of the victorious Allies, to widen its influence and territorial holdings. It continued its expansionist policy by occupying Manchuria in 1931; as a result of international condemnation of this occupation, Japan resigned from the League of Nations two years later. In 1936, Japan signed the Anti-Comintern Pact with Nazi Germany, and the 1940 Tripartite Pact made it one of the Axis Powers. In 1941, Japan negotiated the Soviet–Japanese Neutrality Pact.
The Empire of Japan invaded other parts of China in 1937, precipitating the Second Sino-Japanese War (1937–1945). In 1940, the Empire then invaded French Indochina, after which the United States placed an oil embargo on Japan. On December 7, 1941, Japan attacked the US naval base at Pearl Harbor and declared war on the United States, the United Kingdom and the Netherlands. This act brought the US into World War II and, on December 8, those three countries declared war on Japan. After the Soviet invasion of Manchuria and the atomic bombings of Hiroshima and Nagasaki in 1945, Japan agreed to an unconditional surrender on August 15. The war cost Japan and the rest of the Greater East Asia Co-Prosperity Sphere millions of lives and left much of the nation's industry and infrastructure destroyed. The Allies (led by the US) repatriated millions of ethnic Japanese from colonies and military camps throughout Asia, largely eliminating the Japanese empire and restoring the independence of its conquered territories. The Allies also convened the International Military Tribunal for the Far East on May 3, 1946 to prosecute some Japanese leaders for war crimes. However, the bacteriological research units and members of the imperial family involved in the war were exonerated from criminal prosecutions by the Supreme Allied Commander despite calls for trials for both groups.
In 1947, Japan adopted a new constitution emphasizing liberal democratic practices. The Allied occupation ended with the Treaty of San Francisco in 1952 and Japan was granted membership in the United Nations in 1956. Japan later achieved rapid growth to become the second-largest economy in the world. This ended in the mid-1990s when Japan suffered a major recession. In the beginning of the 21st century, positive growth has signaled a gradual economic recovery.
On March 11, 2011, Japan suffered the strongest earthquake in its recorded history. It had a magnitude of 9.0 and was aggravated by a tsunami, affecting the northeast area of Honshu, including Tokyo.
Japan has a total of 6,852 islands extending along the Pacific coast of Asia. The country, including all of the islands it controls, lies between latitudes 24° and 46°N, and longitudes 122° and 146°E. The main islands, from north to south, are Hokkaido, Honshū, Shikoku and Kyūshū. The Ryukyu Islands, including Okinawa, are a chain of islands south of Kyushū. Together they are often known as the Japanese Archipelago. About 73 percent of Japan is forested, mountainous, and unsuitable for agricultural, industrial, or residential use. As a result, the habitable zones, mainly located in coastal areas, have extremely high population densities. Japan is one of the most densely populated countries in the world.
The islands of Japan are located in a volcanic zone on the Pacific Ring of Fire. They are primarily the result of large oceanic movements occurring over hundreds of millions of years from the mid-Silurian to the Pleistocene as a result of the subduction of the Philippine Sea Plate beneath the continental Amurian Plate and Okinawa Plate to the south, and subduction of the Pacific Plate under the Okhotsk Plate to the north. Japan was originally attached to the eastern coast of the Eurasian continent. The subducting plates pulled Japan eastward, opening the Sea of Japan around 15 million years ago. Japan has 108 active volcanoes. Destructive earthquakes, often resulting in tsunamis, occur several times each century. The 1923 Tokyo earthquake killed over 140,000 people. The most recent major quakes are the 2004 Chūetsu earthquake and the 2011 Tōhoku earthquake, a 9.0-magnitude quake which hit Japan on March 11, 2011, and triggered a tsunami.
The climate of Japan is predominantly temperate, but varies greatly from north to south. Japan's geographical features divide it into six principal climatic zones: Hokkaido, Sea of Japan,Central Highland, Seto Inland Sea, Pacific Ocean, and Ryukyu Islands. The northernmost zone, Hokkaido, has a temperate climate with long, cold winters and cool summers.Precipitation is not heavy, but the islands usually develop deep snowbanks in the winter. In the Sea of Japan zone on Honshū's west coast, northwest winter winds bring heavy snowfall. In the summer, the region is cooler than the Pacific area, though it sometimes experiences extremely hot temperatures because of the foehn wind. The Central Highland has a typical inland climate, with large temperature differences between summer and winter, and between day and night; precipitation is light. The mountains of the Chūgoku and Shikoku regions shelter the Seto Inland Sea from seasonal winds, bringing mild weather year-round. The Pacific coast experiences cold winters with little snowfall and hot, humid summers because of the southeast seasonal wind. The Ryukyu Islands have a subtropical climate, with warm winters and hot summers. Precipitation is very heavy, especially during the rainy season.
The average winter temperature in Japan is 5.1 °C (41.2 °F) and the average summer temperature is 25.2 °C (77.4 °F). The highest temperature ever measured in Japan—40.9 °C (105.6 °F)—was recorded on August 16, 2007. The main rainy season begins in early May in Okinawa, and the rain front gradually moves north until reaching Hokkaido in late July. In most of Honshū, the rainy season begins before the middle of June and lasts about six weeks. In late summer and early autumn, typhoons often bring heavy rain.
Sakura (Cherry blossom)
Japan has nine forest ecoregions which reflect the climate and geography of the islands. They range from subtropical moist broadleaf forests in the Ryūkyū and Bonin islands, to temperate broadleaf and mixed forests in the mild climate regions of the main islands, to temperate coniferous forests in the cold, winter portions of the northern islands. Japan has over 90,000 species of wildlife, including the brown bear, the Japanese macaque, the raccoon dog, and the Japanese giant salamander.
In the period of rapid economic growth after World War II, environmental policies were downplayed by the government and industrial corporations; as a result, environmental pollution was widespread in the 1950s and 1960s. Responding to rising concern about the problem, the government introduced several environmental protection laws in 1970. The oil crisis in 1973 also encouraged the efficient use of energy due to Japan's lack of natural resources. Current environmental issues include urban air pollution (NOx, suspended particulate matter, and toxics), waste management, water eutrophication, nature conservation, climate change, chemical management and international co-operation for conservation.
Japan is one of the world's leaders in the development of new environment-friendly technologies, and is ranked 20th best in the world in the 2010 Environmental Performance Index. As a signatory of the Kyoto Protocol, and host of the 1997 conference which created it, Japan is under treaty obligation to reduce its carbon dioxide emissions and to take other steps to curb climate change.
Emperor Akihito and Empress Michiko
Japan is a constitutional monarchy where the power of the Emperor is very limited. As a ceremonial figurehead, he is defined by the constitution as "the symbol of the state and of the unity of the people". Power is held chiefly by the Prime Minister of Japan and other elected members of the Diet, while sovereignty is vested in the Japanese people. Akihito is the current Emperor of Japan; Naruhito, Crown Prince of Japan, stands as next in line to the throne.
Japan's legislative organ is the National Diet, a bicameral parliament. The Diet consists of a House of Representatives with 480 seats, elected by popular vote every four years or when dissolved, and a House of Councillors of 242 seats, whose popularly-elected members serve six-year terms. There is universal suffrage for adults over 20 years of age, with a secret ballot for all elected offices. In 2009, the social liberal Democratic Party of Japan took power after 54 years of the liberal conservative Liberal Democratic Party's rule.
The Prime Minister of Japan is the head of government. The Prime Minister is appointed by the Emperor after being designated by the Diet from among its members, and must maintain the confidence of the House of Representatives to remain in office. The Prime Minister is the head of the Cabinet and appoints and dismisses the Ministers of State, a majority of whom must be Diet members. Naoto Kan was designated by the Diet to replace Yukio Hatoyama as the Prime Minister of Japan on June 2, 2010. Although the Prime Minister is formally appointed by the Emperor, the Constitution of Japan explicitly requires the Emperor to appoint whoever is designated by the Diet. Emperor Akihito formally appointed Kan as the country's 94th Prime Minister on June 8.
Historically influenced by Chinese law, the Japanese legal system developed independently during the Edo period through texts such as Kujikata Osadamegaki. However, since the late 19th century the judicial system has been largely based on the civil law of Europe, notably Germany. For example, in 1896, the Japanese government established a civil code based on a draft of the German Bürgerliches Gesetzbuch; with post–World War II modifications, the code remains in effect. Statutory law originates in Japan's legislature and has the rubber stamp of the Emperor. The Constitution requires that the Emperor promulgate legislation passed by the Diet, without specifically giving him the power to oppose legislation. Japan's court system is divided into four basic tiers: the Supreme Court and three levels of lower courts. The main body of Japanese statutory law is called the Six Codes.
The Tokyo Stock Exchange
From 1868, the Meiji period launched economic expansion in Japan as Meiji rulers embraced the market economy. Many of today's enterprises were founded at the time, and Japan emerged as the most developed nation in Asia. The period of overall real economic growth from the 1960s to the 1980s has been called a "Japanese miracle": it averaged 7.5 percent in the 1960s and 1970s, and 3.2 percent in the 1980s and early 1990s. Growth slowed markedly in the 1990s during what the Japanese call the Lost Decade, largely because of the after-effects of the Japanese asset price bubble and domestic policies intended to wring speculative excesses from the stock and real estate markets. Government efforts to revive economic growth met with little success and were further hampered by the global slowdown in 2000. The economy showed strong signs of recovery after 2005; GDP growth for that year was 2.8 percent, surpassing the growth rates of the US and European Union during the same period.
As of 2010, Japan is the third largest national economy in the world, after the United States and China, in terms of both nominal GDP and purchasing power parity. As of January 2011, Japan's public debt was more than 200 percent of its annual gross domestic product, the largest of any nation in the world. The service sector accounts for three quarters of the gross domestic product. Japan has a large industrial capacity, and is home to some of the largest and most technologically advanced producers of motor vehicles, electronics, machine tools, steel and nonferrous metals, ships, chemical substances, textiles, and processed foods. Agricultural businesses in Japan often utilize a system of terrace farming, and crop yields are high; 13 percent of Japan's land is cultivated. Japan accounts for nearly 15 percent of the global fish catch, second only to China.
As of 2010, Japan's labor force consisted of some 65.9 million workers. Japan has a low unemployment rate of around four percent. Almost one in six Japanese, or 20 million people, lived in poverty in 2007. Housing in Japan is characterized by limited land supply in urban areas; more than half of all Japanese live in suburbs or more rural areas, where detached houses are the dominant housing type.
Toyota, one of the world's largest automakers. Japan is the second-largest producer of automobiles in the world.
Japan's exports amounted to US$4,210 per capita in 2005. Japan's main export markets are China (18.88 percent), the United States (16.42 percent), South Korea (8.13 percent), Taiwan (6.27 percent) and Hong Kong (5.49 percent) as of 2009. Its main exports are transportation equipment, motor vehicles, electronics, electrical machinery and chemicals. Japan's main import markets as of 2009 are China (22.2 percent), the US (10.96 percent), Australia (6.29 percent), Saudi Arabia (5.29 percent), United Arab Emirates (4.12 percent), South Korea (3.98 percent) and Indonesia (3.95 percent). Its main imports are machinery and equipment, fossil fuels, foodstuffs (in particular beef), chemicals, textiles and raw materials for its industries. By market share measures, domestic markets are the least open of any OECD country. Junichiro Koizumi's administration began some pro-competition reforms, and foreign investment in Japan has soared.
Japan ranks 12th of 178 countries in the 2008 Ease of Doing Business Index and has one of the smallest tax revenues of the developed world. The Japanese variant of capitalism has many distinct features: keiretsu enterprises are influential, and lifetime employment and seniority-based career advancement are relatively common in the Japanese work environment. Japanese companies are known for management methods like "The Toyota Way", and shareholder activism is rare. Some of the largest enterprises in Japan include Toyota, Nintendo, NTT DoCoMo, Canon, Honda,Takeda Pharmaceutical, Sony, Panasonic, Toshiba, Sharp, Nippon Steel, Nippon Oil, and Seven & I Holdings Co. It has some of the world's largest banks, and the Tokyo Stock Exchange (known for its Nikkei 225 and Topix indices) stands as the second largest in the world by market capitalization. Japan is home to 326 companies from the Forbes Global 2000 or 16.3 percent (as of 2006).
Science and technology
Japan is a leading nation in scientific research, particularly technology, machinery and biomedical research. Nearly 700,000 researchers share a US$130 billion research and development budget, the third largest in the world. Japan is a world leader in fundamental scientific research, having produced fifteen Nobel laureates in either physics, chemistry or medicine, three Fields medalists, and one Gauss Prize laureate. Some of Japan's more prominent technological contributions are in the fields of electronics, automobiles, machinery, earthquake engineering, industrial robotics, optics, chemicals, semiconductors and metals. Japan leads the world in robotics production and use, possessing more than half (402,200 of 742,500) of the world's industrial robots.
The Japan Aerospace Exploration Agency (JAXA) is Japan's space agency; it conducts space, planetary, and aviation research, and leads development of rockets and satellites. It is a participant in the International Space Station: the Japanese Experiment Module (Kibo) was added to the station during Space Shuttle assembly flights in 2008. Japan's plans in space exploration include: launching a space probe to Venus, Akatsuki; developing the Mercury Magnetospheric Orbiter to be launched in 2013; and building a moon base by 2030. On September 14, 2007, it launched lunar explorer "SELENE" (Selenological and Engineering Explorer) on an H-IIA (Model H2A2022) carrier rocket from Tanegashima Space Center. SELENE is also known as Kaguya, after the lunar princess of The Tale of the Bamboo Cutter. Kaguya is the largest lunar mission since the Apollo program. Its purpose is to gather data on the moon's origin and evolution. It entered a lunar orbit on October 4, flying at an altitude of about 100 km (62 mi). The probe's mission was ended when it was deliberately crashed by JAXA into the Moon on 11 June 2009.
Shinkansen or Bullet trains are a popular form of transport in Japan.
As of 2008, 46.4 percent of energy in Japan is produced from petroleum, 21.4 percent from coal, 16.7 percent from natural gas, 9.7 percent from nuclear power, and 2.9 percent from hydro power. Nuclear power produces 22.5 percent of Japan's electricity. Given its heavy dependence on imported energy, Japan has aimed to diversify its sources and maintain high levels of energy efficiency.
Japan's road spending has been extensive. Its 1.2 million kilometers of paved road are the main means of transportation. A single network of high-speed, divided, limited-access toll roads connects major cities and is operated by toll-collecting enterprises. New and used cars are inexpensive; car ownership fees and fuel levies are used to promote energy efficiency. However, at just 50 percent of all distance traveled, car usage is the lowest of all G8 countries.
Dozens of Japanese railway companies compete in regional and local passenger transportation markets; major companies include seven JR enterprises, Kintetsu Corporation, Seibu Railway and Keio Corporation. Some 250 high-speed Shinkansen trains connect major cities. Japanese trains are known for their punctuality. There are 173 airports in Japan; the largest domestic airport, Haneda Airport, is Asia's second-busiest airport. The largest international gateways are Narita International Airport, Kansai International Airport and Chūbu Centrair International Airport. Nagoya Port is the country's largest and busiest port, accounting for 10 percent of Japan's trade value.
Friday, March 4, 2011
In physics, a wormhole is a hypothetical topological feature of spacetime that would be, fundamentally, a "shortcut" through spacetime. For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional (2D) surface. If this surface is folded along a third dimension, it allows one to picture a wormhole "bridge". (Please note, though, that this is merely a visualization displayed to convey an essentially unvisualisable structure existing in 4 or more dimensions. The parts of the wormhole could be higher-dimensional analogues for the parts of the curved 2D surface; for example, instead of mouths which are circular holes in a 2D plane, a real wormhole's mouths could be spheres in 3D space.) A wormhole is, in theory, much like a tunnel with two ends each in separate points in spacetime.
There is no observational evidence for wormholes, but on a theoretical level there are valid solutions to the equations of the theory of general relativity which contain wormholes. The first type of wormhole solution discovered was the Schwarzschild wormhole which would be present in the Schwarzschild metric describing an eternal black hole, but it was found that this type of wormhole would collapse too quickly for anything to cross from one end to the other. Wormholes which could actually be crossed, known as traversable wormholes, would only be possible if exotic matter with negative energy density could be used to stabilize them. (Many physicists such as Stephen Hawking, Kip Thorne, and others believe that the Casimir effect is evidence that negative energy densities are possible in nature). Physicists have also not found any natural process which would be predicted to form a wormhole naturally in the context of general relativity, although the quantum foam hypothesis is sometimes used to suggest that tiny wormholes might appear and disappear spontaneously at the Planck scale, and stable versions of such wormholes have been suggested as dark matter candidates. It has also been proposed that if a tiny wormhole held open by a negative-mass cosmic string had appeared around the time of the Big Bang, it could have been inflated to macroscopic size by cosmic inflation.
The American theoretical physicist John Archibald Wheeler coined the term wormhole in 1957; however, in 1921, the German mathematician Hermann Weyl already had proposed the wormhole theory, in connection with mass analysis of electromagnetic field energy.
This analysis forces one to consider situations...where there is a net flux of lines of force, through what topologists would call "a handle" of the multiply-connected space, and what physicists might perhaps be excused for more vividly terming a "wormhole".
—John Wheeler in Annals of Physics
The basic notion of an intra-universe wormhole is that it is a compact region of spacetime whose boundary is topologically trivial but whose interior is not simply connected. Formalizing this idea leads to definitions such as the following, taken from Matt Visser's Lorentzian Wormholes.
If a Minkowski spacetime contains a compact region Ω, and if the topology of Ω is of the form Ω ~ R x Σ, where Σ is a three-manifold of the nontrivial topology, whose boundary has topology of the form dΣ ~ S2, and if, furthermore, the hypersurfaces Σ are all spacelike, then the region Ω contains a quasipermanent intra-universe wormhole.
Characterizing inter-universe wormholes is more difficult. For example, one can imagine a 'baby' universe connected to its 'parent' by a narrow 'umbilicus'. One might like to regard the umbilicus as the throat of a wormhole, but the spacetime is simply connected. For this reason wormholes have been defined geometrically, as opposed to topologically, as regions of spacetime that constrain the incremental deformation of closed surfaces. For example, in Enrico Rodrigo’s The Physics of Stargates a wormhole is defined informally as
a region of spacetime containing a "world tube" (the time evolution of a closed surface) that cannot be continuously deformed (shrunk) to a world line [(the time evolution of a point)].
An artist's impression of a wormhole from an observer's perspective, crossing the event horizon of a Schwarzschild wormhole which bridges two different universes. The observer originates from the right, and another universe becomes visible in the center of the wormhole’s shadow once the horizon is crossed, the observer seeing light that has fallen into the black hole interior region from the other universe; however, this other universe is unreachable in the case of a Schwarzschild wormhole, as the bridge always collapses before the observer has time to cross it, and everything that has fallen through the event horizon of either universe is inevitably crushed in the black hole singularity. See White Holes and Wormholes for a technical discussion and animation of what an observer sees when falling into a Schwarzschild wormhole (also see Approaching the Black Hole from the same site for background, and perhaps also the more detailed renderings at Journey into a Schwarzschild black hole)
Lorentzian wormholes known as Schwarzschild wormholes or Einstein-Rosen bridges are bridges between areas of space that can be modeled as vacuum solutions to the Einstein field equations, and which are now understood to be intrinsic parts of the maximally extended version of the Schwarzschild metric describing an eternal black hole with no charge and no rotation. Here, "maximally extended" refers to the idea that the spacetime should not have any "edges": for any possible trajectory of a free-falling particle (following a geodesic) in the spacetime, it should be possible to continue this path arbitrarily far into the particle's future or past, unless the trajectory hits a gravitational singularity like the one at the center of the black hole's interior. In order to satisfy this requirement, it turns out that in addition to the black hole interior region which particles enter when they fall through the event horizon from the outside, there must be a separate white hole interior region which allows us to extrapolate the trajectories of particles which an outside observer sees rising up away from the event horizon. And just as there are two separate interior regions of the maximally extended spacetime, there are also two separate exterior regions, sometimes called two different "universes", with the second universe allowing us to extrapolate some possible particle trajectories in the two interior regions. This means that the interior black hole region can contain a mix of particles that fell in from either universe (and thus an observer who fell in from one universe might be able to see light that fell in from the other one), and likewise particles from the interior white hole region can escape into either universe. All four regions can be seen in a spacetime diagram which uses Kruskal–Szekeres coordinates, as discussed and illustrated on the page White Holes and Wormholes.
In this spacetime, it is possible to come up with coordinate systems such that if you pick a hypersurface of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a space-like separation, giving what is called a 'space-like surface') and draw an "embedding diagram" depicting the curvature of space at that time (see the discussion of embedding diagrams on this page), the embedding diagram will look like a tube connecting the two exterior regions, known as an "Einstein-Rosen bridge". For example, see the diagrams on this page which show the maximally extended Schwarzschild solution in Kruskal–Szekeres coordinates along with white hypersurfaces of constant time drawn on (time in some other coordinate system besides Kruskal–Szekeres coordinates, since a hypersurface of constant Kruskal–Szekeres time would just look like a horizontal line when drawn in a Kruskal–Szekeres diagram), and the corresponding embedding diagram for that hypersurface. Note that the Schwarzschild metric describes an idealized black hole that exists eternally from the perspective of external observers; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric. When the infalling stellar matter is added to a diagram of a black hole's history, it removes the part of the diagram corresponding to the white hole interior region, along with the part of the diagram corresponding to the other universe.
The Einstein-Rosen bridge was discovered by Albert Einstein and his colleague Nathan Rosen, who first published the result in 1935. However, in 1962 John A. Wheeler and Robert W. Fuller published a paper showing that this type of wormhole is unstable, and that it will pinch off too quickly for light (or any particle moving slower than light) that falls in from one exterior region to make it to the other exterior region.
Before the stability problems of Schwarzschild wormholes were apparent, it was proposed that quasars were white holes forming the ends of wormholes of this type.
While Schwarzschild wormholes are not traversable, their existence inspired Kip Thorne to imagine traversable wormholes created by holding the 'throat' of a Schwarzschild wormhole open with exotic matter (material that has negative mass/energy).
Image of a traversable wormhole which connects the place in front of the physical institutes of Tübingen university with the sand dunes near Boulogne sur Mer in the north of France. The image is calculated with 4D raytracing in a Morris-Thorne wormhole metric, but the gravitational effects on the wavelength of light have not been simulated.
Lorentzian traversable wormholes would allow travel from one part of the universe to another part of that same universe very quickly or would allow travel from one universe to another. The possibility of traversable wormholes in general relativity was first demonstrated by Kip Thorne and his graduate student Mike Morris in a 1988 paper for this reason the type of traversable wormhole they proposed held open by a spherical shell of exotic matter is referred to as a Morris-Thorne wormhole. Later, other types of traversable wormholes were discovered as allowable solutions to the equations of general relativity, including a variety analyzed in a 1989 paper by Matt Visser, in which a path through the wormhole can be made in which the traversing path does not pass through a region of exotic matter. However in the pure Gauss-Bonnet theory(a modification to general relativity involving extra spatial dimensions which is sometimes studied in the context of brane cosmology) exotic matter is not needed in order for wormholes to exist- they can exist even with no matter. A type held open by negative mass cosmic strings was put forth by Visser in collaboration with Cramer et al., in which it was proposed that such wormholes could have been naturally created in the early universe.
Wormholes connect two points in spacetime, which means that they would in principle allow travel in time, as well as in space. In 1988, Morris, Thorne and Yurtsever worked out explicitly how to convert a wormhole traversing space into one traversing time. However, according to general relativity it would not be possible to use a wormhole to travel back to a time earlier than when the wormhole was first converted into a time machine by accelerating one of its two mouths.
Raychaudhuri's theorem and exotic matter
To see why exotic matter is required, consider an incoming light front traveling along geodesics, which then crosses the wormhole and re-expands on the other side. The expansion goes from negative to positive. As the wormhole neck is of finite size, we would not expect caustics to develop, at least within the vicinity of the neck. According to the optical Raychaudhuri's theorem, this requires a violation of the averaged null energy condition. Quantum effects such as the Casimir effect cannot violate the averaged null energy condition in any neighborhood of space with zero curvature, but calculations in semiclassical gravity suggest that quantum effects may be able to violate this condition in curved spacetime. Although it was hoped recently that quantum effects could not violate an achronal version of the averaged null energy condition, violations have nevertheless been found, thus eliminating a basis on which traversable wormholes could be rendered unphysical.
The impossibility of faster-than-light relative speed only applies locally. Wormholes allow superluminal (faster-than-light) travel by ensuring that the speed of light is not exceeded locally at any time. While traveling through a wormhole, subluminal (slower-than-light) speeds are used. If two points are connected by a wormhole, the time taken to traverse it would be less than the time it would take a light beam to make the journey if it took a path through the space outside the wormhole. However, a light beam traveling through the wormhole would always beat the traveler. As an analogy, running around to the opposite side of a mountain at maximum speed may take longer than walking through a tunnel crossing it.
The theory of general relativity predicts that if traversable wormholes exist, they could allow time travel. This would be accomplished by accelerating one end of the wormhole to a high velocity relative to the other, and then sometime later bringing it back; relativistic time dilation would result in the accelerated wormhole mouth aging less than the stationary one as seen by an external observer, similar to what is seen in the twin paradox. However, time connects differently through the wormhole than outside it, so that synchronized clocks at each mouth will remain synchronized to someone traveling through the wormhole itself, no matter how the mouths move around. This means that anything which entered the accelerated wormhole mouth would exit the stationary one at a point in time prior to its entry.
For example, consider two clocks at both mouths both showing the date as 2000. After being taken on a trip at relativistic velocities, the accelerated mouth is brought back to the same region as the stationary mouth with the accelerated mouth's clock reading 2005 while the stationary mouth's clock read 2010. A traveler who entered the accelerated mouth at this moment would exit the stationary mouth when its clock also read 2005, in the same region but now five years in the past. Such a configuration of wormholes would allow for a particle's world line to form a closed loop in spacetime, known as a closed timelike curve.
It is thought that it may not be possible to convert a wormhole into a time machine in this manner; the predictions are made in the context of general relativity, but general relativity does not include quantum effects. Some analyses using the semiclassical approach to incorporating quantum effects into general relativity indicate that a feedback loop of virtual particles would circulate through the wormhole with ever-increasing intensity, destroying it before any information could be passed through it, in keeping with the chronology protection conjecture. This has been called into question by the suggestion that radiation would disperse after traveling through the wormhole, therefore preventing infinite accumulation. The debate on this matter is described by Kip S. Thorne in the book Black Holes and Time Warps, and a more technical discussion can be found in The quantum physics of chronology protection by Matt Visser. There is also the Roman ring, which is a configuration of more than one wormhole. This ring seems to allow a closed time loop with stable wormholes when analyzed using semiclassical gravity, although without a full theory of quantum gravity it is uncertain whether the semiclassical approach is reliable in this case.
A possible resolution to the paradoxes resulting from wormhole-enabled time travel rests on the Many Worlds Interpretation of quantum mechanics. In 1991 David Deutsch showed that quantum theory is fully consistent (in the sense that the so-called density matrix can be made free of discontinuities) in spacetimes with closed timelike curves. Accordingly, the destructive positive feedback loop of virtual particles circulating through a wormhole time machine, a result indicated by semi-classical calculations, is averted. A particle returning from the future does not return to its universe of origination but to a parallel universe. This suggests that a wormhole time machine with an exceedingly short time jump is a theoretical bridge between contemporaneous parallel universes. Because a wormhole time-machine introduces a type of nonlinearity into quantum theory, this sort of communication between parallel universes is consistent with Joseph Polchinski’s discovery of an “Everett phone” in Steven Weinberg’s formulation of nonlinear quantum mechanics.
Embedded diagram of a Schwarzschild wormhole
Theories of wormhole metrics describe the spacetime geometry of a wormhole and serve as theoretical models for time travel. An example of a (traversable) wormhole metric is the following:
One type of non-traversable wormhole metric is the Schwarzschild solution:
A supermassive black hole sits inside the galaxy Centaurus A, as seen in a composite picture.
Like part of a cosmic Russian doll, our universe may be nested inside a black hole that is itself part of a larger universe.
In turn, all the black holes found so far in our universe—from the microscopic to the supermassive—may be doorways into alternate realities.
According to a mind-bending new theory, a black hole is actually a tunnel between universes—a type of wormhole. The matter the black hole attracts doesn't collapse into a single point, as has been predicted, but rather gushes out a "white hole" at the other end of the black one, the theory goes.
In a recent paper published in the journal Physics Letters B, Indiana University physicist Nikodem Poplawski presents new mathematical models of the spiraling motion of matter falling into a black hole. His equations suggest such wormholes are viable alternatives to the "space-time singularities" that Albert Einstein predicted to be at the centers of black holes.
According to Einstein's equations for general relativity, singularities are created whenever matter in a given region gets too dense, as would happen at the ultradense heart of a black hole.
Einstein's theory suggests singularities take up no space, are infinitely dense, and are infinitely hot—a concept supported by numerous lines of indirect evidence but still so outlandish that many scientists find it hard to accept.
If Poplawski is correct, they may no longer have to.
According to the new equations, the matter black holes absorb and seemingly destroy is actually expelled and becomes the building blocks for galaxies, stars, and planets in another reality.
Wormholes Solve Big Bang Mystery?
The notion of black holes as wormholes could explain certain mysteries in modern cosmology, Poplawski said.
For example, the big bang theory says the universe started as a singularity. But scientists have no satisfying explanation for how such a singularity might have formed in the first place.
If our universe was birthed by a white hole instead of a singularity, Poplawski said, "it would solve this problem of black hole singularities and also the big bang singularity."
Wormholes might also explain gamma ray bursts, the second most powerful explosions in the universe after the big bang.
Gamma ray bursts occur at the fringes of the known universe. They appear to be associated with supernovae, or star explosions, in faraway galaxies, but their exact sources are a mystery.
Poplawski proposes that the bursts may be discharges of matter from alternate universes. The matter, he says, might be escaping into our universe through supermassive black holes—wormholes—at the hearts of those galaxies, though it's not clear how that would be possible.
"It's kind of a crazy idea, but who knows?" he said.
There is at least one way to test Poplawski's theory: Some of our universe's black holes rotate, and if our universe was born inside a similarly revolving black hole, then our universe should have inherited the parent object's rotation.
If future experiments reveal that our universe appears to rotate in a preferred direction, it would be indirect evidence supporting his wormhole theory, Poplawski said.
Wormholes Are "Exotic Matter" Makers?
The wormhole theory may also help explain why certain features of our universe deviate from what theory predicts, according to physicists.
Based on the standard model of physics, after the big bang the curvature of the universe should have increased over time so that now—13.7 billion years later—we should seem to be sitting on the surface of a closed, spherical universe.
But observations show the universe appears flat in all directions.
What's more, data on light from the very early universe show that everything just after the big bang was a fairly uniform temperature.
That would mean that the farthest objects we see on opposite horizons of the universe were once close enough to interact and come to equilibrium, like molecules of gas in a sealed chamber.
Again, observations don't match predictions, because the objects farthest from each other in the known universe are so far apart that the time it would take to travel between them at the speed of light exceeds the age of the universe.
To explain the discrepancies, astronomers devised the concept of inflation.
Inflation states that shortly after the universe was created, it experienced a rapid growth spurt during which space itself expanded at faster-than-light speeds. The expansion stretched the universe from a size smaller than an atom to astronomical proportions in a fraction of a second.
The universe therefore appears flat, because the sphere we're sitting on is extremely large from our viewpoint—just as the sphere of Earth seems flat to someone standing in a field.
Inflation also explains how objects so far away from each other might have once been close enough to interact.
But—assuming inflation is real—astronomers have always been at pains to explain what caused it. That's where the new wormhole theory comes in.
According to Poplawski, some theories of inflation say the event was caused by "exotic matter," a theoretical substance that differs from normal matter, in part because it is repelled rather than attracted by gravity.
Based on his equations, Poplawski thinks such exotic matter might have been created when some of the first massive stars collapsed and became wormholes.
"There may be some relationship between the exotic matter that forms wormholes and the exotic matter that triggered inflation," he said.
Wormhole Equations an "Actual Solution"
The new model isn't the first to propose that other universes exist inside black holes. Damien Easson, a theoretical physicist at Arizona State University, has made the speculation in previous studies.
"What is new here is an actual wormhole solution in general relativity that acts as the passage from the exterior black hole to the new interior universe," said Easson, who was not involved in the new study.
"In our paper, we just speculated that such a solution could exist, but Poplawski has found an actual solution," said Easson, referring to Poplawski's equations.
Nevertheless, the idea is still very speculative, Easson said in an email.
"Is the idea possible? Yes. Is the scenario likely? I have no idea. But it is certainly an interesting possibility."
Future work in quantum gravity—the study of gravity at the subatomic level—could refine the equations and potentially support or disprove Poplawski's theory, Easson said.
Wormhole Theory No Breakthrough
Overall, the wormhole theory is interesting, but not a breakthrough in explaining the origins of our universe, said Andreas Albrecht, a physicist at the University of California, Davis, who was also not involved in the new study.
By saying our universe was created by a gush of matter from a parent universe, the theory simply shifts the original creation event into an alternate reality.
In other words, it doesn't explain how the parent universe came to be or why it has the properties it has—properties our universe presumably inherited.
"There're really some pressing problems we're trying to solve, and it's not clear that any of this is offering a way forward with that," he said.
Still, Albrecht doesn't find the idea of universe-bridging wormholes any stranger than the idea of black hole singularities, and he cautions against dismissing the new theory just because it sounds a little out there.
"Everything people ask in this business is pretty weird," he said. "You can't say the less weird [idea] is going to win, because that's not the way it's been, by any means."
Saturday, February 19, 2011
A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from traditional computers based on transistors. The basic principle behind quantum computation is that quantum properties can be used to represent data and perform operations on these data. A theoretical model is the quantum Turing machine, also known as the universal quantum computer.
Although quantum computing is still in its infancy, experiments have been carried out in which quantum computational operations were executed on a very small number of qubits (quantum bits). Both practical and theoretical research continues, and many national government and military funding agencies support quantum computing research to develop quantum computers for both civilian and national security purposes, such as cryptanalysis.
If large-scale quantum computers can be built, they will be able to solve certain problems much faster than any current classical computers (for example integer factorization using Shor's algorithm). All problems solvable with a quantum computer can also be solved using a traditional computer given enough time and resources.
classical computer has a memory made up of bits, where each bit represents either a one or a zero. A quantum computer maintains a sequence of qubits. A single qubit can represent a one, a zero, or, crucially, any quantum superposition of these; moreover, a pair of qubits can be in any quantum superposition of 4 states, and three qubits in any superposition of 8. In general a quantum computer with n qubits can be in an arbitrary superposition of up to 2n different states simultaneously (this compares to a normal computer that can only be in one of these 2n states at any one time). A quantum computer operates by manipulating those qubits with a fixed sequence of quantum logic gates. The sequence of gates to be applied is called a quantum algorithm.
An example of an implementation of qubits for a quantum computer could start with the use of particles with two spin states: "down" and "up" (typically written and , or and ). But in fact any system possessing an observable quantity A which is conserved under time evolution and such that A has at least two discrete and sufficiently spaced consecutiveeigenvalues, is a suitable candidate for implementing a qubit. This is true because any such system can be mapped onto an effective spin-1/2 system.
Bits vs. qubits:-
Consider first a classical computer that operates on a three-bit register. The state of the computer at any time is a probability distribution over the23 = 8 different three-bit strings 000, 001, 010, 011, 100, 101, 110, 111. If it is a deterministic computer, then it is in exactly one of these states with probability 1. However, if it is a probabilistic computer, then there is a possibility of it being in any one of a number of different states. We can describe this probabilistic state by eight nonnegative numbers a,b,c,d,e,f,g,h (where a = probability computer is in state 000, b = probability computer is in state 001, etc.). There is a restriction that these probabilities sum to 1.
The state of a three-qubit quantum computer is similarly described by an eight-dimensional vector (a,b,c,d,e,f,g,h), called a ket. However, instead of adding to one, the sum of the squares of the coefficient magnitudes, | a | 2 + | b | 2 + ... + | h | 2, must equal one. Moreover, the coefficients arecomplex numbers. Since states are represented by complex wavefunctions, two states being added together will undergo interference, which is a key difference between quantum computing and probabilistic classical computing.
If you measure the three qubits, you will observe a three-bit string. The probability of measuring a given string is the squared magnitude of that string's coefficient (i.e., the probability of measuring 000 = | a | 2, the probability of measuring 001 = | b | 2, etc..). Thus, measuring a quantum state described by complex coefficients (a,b,...,h) gives the classical probability distribution ( | a | 2, | b | 2,..., | h | 2) and we say that the quantum state "collapses" to a classical state as a result of making the measurement.
Note that an eight-dimensional vector can be specified in many different ways depending on what basis is chosen for the space. The basis of bit strings (e.g., 000, 001, ..., 111) is known as the computational basis. Other possible bases are unit-length, orthogonal vectors and the eigenvectors of the Pauli-x operator. Ket notation is often used to make the choice of basis explicit. For example, the state (a,b,c,d,e,f,g,h) in the computational basis can be written as:
- where, e.g.,
The computational basis for a single qubit (two dimensions) is and .
Using the eigenvectors of the Pauli-x operator, a single qubit is and .
A quantum computer with a given number of qubits is exponentially more complex than a classical computer with the same number of bits because describing the state of n qubits requires 2n complex coefficients. Measuring the qubits would produce a classical state of only n bits, but such an action would also destroy the quantum state. We can think of the system as being exactly one of the n-bit strings—we just don't know which one. For example, a 300-qubit quantum computer has a state described by 2300 (approximately 1090) complex numbers, more than the number of atoms in the observable universe.
While a classical three-bit state and a quantum three-qubit state are both eight-dimensional vectors, they are manipulated quite differently for classical or quantum computation. For computing in either case, the system must be initialized, for example into the all-zeros string, , corresponding to the vector (1,0,0,0,0,0,0,0). In classical randomized computation, the system evolves according to the application of stochastic matrices, which preserve that the probabilities add up to one (i.e., preserve the L1 norm). In quantum computation, on the other hand, allowed operations are unitary matrices, which are effectively rotations (they preserve that the sum of the squares add up to one, the Euclidean or L2 norm). (Exactly what unitaries can be applied depend on the physics of the quantum device.) Consequently, since rotations can be undone by rotating backward, quantum computations are reversible. (Technically, quantum operations can be probabilistic combinations of unitaries, so quantum computation really does generalize classical computation. See quantum circuit for a more precise formulation.)
Finally, upon termination of the algorithm, the result needs to be read off. In the case of a classical computer, we sample from the probability distribution on the three-bit register to obtain one definite three-bit string, say 000. Quantum mechanically, we measure the three-qubit state, which is equivalent to collapsing the quantum state down to a classical distribution (with the coefficients in the classical state being the squared magnitudes of the coefficients for the quantum state, as described above) followed by sampling from that distribution. Note that this destroys the original quantum state. Many algorithms will only give the correct answer with a certain probability, however by repeatedly initializing, running and measuring the quantum computer, the probability of getting the correct answer can be increased.
For more details on the sequences of operations used for various quantum algorithms, see universal quantum computer, Shor's algorithm, Grover's algorithm, Deutsch-Jozsa algorithm,amplitude amplification, quantum Fourier transform, quantum gate, quantum adiabatic algorithm and quantum error correction.
Integer factorization is believed to be computationally infeasible with an ordinary computer for large integers if they are the product of few prime numbers (e.g., products of two 300-digit primes). By comparison, a quantum computer could efficiently solve this problem using Shor's algorithm to find its factors. This ability would allow a quantum computer to decrypt many of the cryptographic systems in use today, in the sense that there would be a polynomial time (in the number of digits of the integer) algorithm for solving the problem. In particular, most of the popular public key ciphers are based on the difficulty of factoring integers (or the related discrete logarithm problem which can also be solved by Shor's algorithm), including forms of RSA. These are used to protect secure Web pages, encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic privacy and security.
However, other existing cryptographic algorithms don't appear to be broken by these algorithms. Some public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems to which Shor's algorithm applies, like the McEliece cryptosystem based on a problem in coding theory. Lattice based cryptosystemsare also not known to be broken by quantum computers, and finding a polynomial time algorithm for solving the dihedral hidden subgroup problem, which would break many lattice based cryptosystems, is a well-studied open problem. It has been proven that applying Grover's algorithm to break a symmetric (secret key) algorithm by brute force requires roughly 2n/2invocations of the underlying cryptographic algorithm, compared with roughly 2n in the classical case, meaning that symmetric key lengths are effectively halved: AES-256 would have the same security against an attack using Grover's algorithm that AES-128 has against classical brute-force search (see Key size). Quantum cryptography could potentially fulfill some of the functions of public key cryptography.
Besides factorization and discrete logarithms, quantum algorithms offering a more than polynomial speedup over the best known classical algorithm have been found for several problems, including the simulation of quantum physical processes from chemistry and solid state physics, the approximation of Jones polynomials, and solving Pell's equation. No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, although this is considered unlikely. For some problems, quantum computers offer a polynomial speedup. The most well-known example of this is quantum database search, which can be solved by Grover's algorithm using quadratically fewer queries to the database than are required by classical algorithms. In this case the advantage is provable. Several other examples of provable quantum speedups for query problems have subsequently been discovered, such as for finding collisions in two-to-one functions and evaluating NAND trees.
Consider a problem that has these four properties:
- The only way to solve it is to guess answers repeatedly and check them,
- The number of possible answers to check is the same as the number of inputs,
- Every possible answer takes the same amount of time to check, and
- There are no clues about which answers might be better: generating possibilities randomly is just as good as checking them in some special order.
For problems with all four properties, the time for a quantum computer to solve this will be proportional to the square root of the number of inputs. That can be a very large speedup, reducing some problems from years to seconds. It can be used to attack symmetric ciphers such as Triple DES and AES by attempting to guess the secret key.
Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible to simulate in an efficient manner classically, many believe quantum simulation will be one of the most important applications of quantum computing.
There are a number of practical difficulties in building a quantum computer, and thus far quantum computers have only solved trivial problems. David DiVincenzo, of IBM, listed the following requirements for a practical quantum computer:
- scalable physically to increase the number of qubits;
- qubits can be initialized to arbitrary values;
- quantum gates faster than decoherence time;
- universal gate set;
- qubits can be read easily.
One of the greatest challenges is controlling or removing quantum decoherence. This usually means isolating the system from its environment as the slightest interaction with the external world would cause the system to decohere. This effect is irreversible, as it is non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems, in particular the transverse relaxation time T2 (for NMR and MRI technology, also called the dephasing time), typically range between nanoseconds and seconds at low temperature.
These issues are more difficult for optical approaches as the timescales are orders of magnitude shorter and an often-cited approach to overcoming them is optical pulse shaping. Error rates are typically proportional to the ratio of operating time to decoherence time, hence any operation must be completed much more quickly than the decoherence time.
If the error rate is small enough, it is thought to be possible to use quantum error correction, which corrects errors due to decoherence, thereby allowing the total calculation time to be longer than the decoherence time. An often cited figure for required error rate in each gate is 10−4. This implies that each gate must be able to perform its task in one 10,000th of the decoherence time of the system.
Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction brings with it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's algorithm is still polynomial, and thought to be between L and L2, where L is the number of bits in the number to be factored; error correction algorithms would inflate this figure by an additional factor of L. For a 1000-bit number, this implies a need for about 104 qubits without error correction. With error correction, the figure would rise to about 107 qubits. Note that computation time is about L2 or about 107 steps and on 1 MHz, about 10 seconds.
A very different approach to the stability-decoherence problem is to create a topological quantum computer with anyons, quasi-particles used as threads and relying on braid theory to form stable logic gates.
Monday, January 24, 2011
Tim Leffel, author of The World's Cheapest Destinations: 21 Countries Where Your Money Is Worth a Fortune ($14.95, Booklocker.com Inc.), says when problems put a nation in the headlines, tourists often shun the whole region — even when it's perfectly safe. "You can get a deal of a lifetime," he says.Even if your budget is stretched, 2011 can still be a year of travel. It's just a matter of choosing the right place.