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String theory

String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles) that are the basis of the Standard Model of particle physics. For this reason, string theories are able to avoid problems associated with the presence of pointlike particles in a physical theory. Study of string theories has revealed that they require not just strings but other objects, variously including points, membranes, and higher-dimensional objects.

Interest in string theory is driven largely by the hope that it will prove to be a theory of everything. It is a possible solution of the quantum gravity problem, and in addition to gravity it can naturally describe interactions similar to electromagnetism and the other forces of nature. Superstring theories include fermions, the building blocks of matter, and incorporate supersymmetry. It is not yet known whether string theory is able to describe a universe with the precise collection of forces and matter that is observed, nor how much freedom to choose those details the theory will allow. String theory as a whole has not yet made falsifiable predictions that would allow it to be experimentally tested, though various special corners of the theory are accessible to planned observations and experiments.

Work on string theory has led to advances in mathematics, mainly in algebraic geometry. String theory has also led to insight into supersymmetric gauge theories, which will be tested at the new Large Hadron Collider experiment.

History

String theory was originally invented to explain peculiarities of hadron (subatomic particle which experiences the strong nuclear force) behavior. In particle-accelerator experiments, physicists observed that the spin of a hadron is never larger than a certain multiple of the square of its energy. No simple model of the hadron, such as picturing it as a set of smaller particles held together by spring-like forces, was able to explain these relationships. In 1968, theoretical physicist Gabriele Veneziano was trying to understand the strong nuclear force when he made a startling discovery. Veneziano found that a 200-year-old formula created by Swiss mathematician Leonhard Euler (the Euler beta function) perfectly matched modern data on the strong force. Veneziano applied the Euler beta function to the strong force, but no one could explain why it worked.

In 1970, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind unveiled the physics beneath Euler’s strictly theoretical formula. By representing nuclear forces as vibrating, one-dimensional strings, these physicists showed how Euler’s function accurately described those forces. But even after physicists understood the physical explanation for Veneziano’s insight, the string description of the strong force made many predictions that directly contradicted experimental findings. The scientific community soon lost interest in string theory, and the standard model, with its particles and fields, remained unthreatened.

Then, in 1974, John Schwarz and Joel Scherk studied the messenger-like patterns of string vibration and found that their properties exactly matched those of the gravitational force’s hypothetical messenger particle -- graviton. Schwarz and Scherk argued that string theory had failed to catch on because physicists had underestimated its scope.

This led to the development of bosonic string theory, which is still the version first taught to many students. (The original need for a viable theory of hadrons has been fulfilled by quantum chromodynamics, the theory of quarks and their interactions. It is now hoped that string theory or some descendant of it will provide a fundamental understanding of the quarks themselves.)

Bosonic string theory is formulated in terms of the Polyakov action, a mathematical quantity which can be used to predict how strings move through space and time. By applying the ideas of quantum mechanics to the Polyakov action—a procedure known as quantization—one can deduce that each string can vibrate in many different ways, and that each vibrational state appears to be a different particle. The mass the particle has, and the fashion with which it can interact, are determined by the way the string vibrates—in essence, by the "note" which the string sounds. The scale of notes, each corresponding to a different kind of particle, is termed the "spectrum" of the theory.

These early models included both open strings, which have two distinct endpoints, and closed strings, where the endpoints are joined to make a complete loop. The two types of string behave in slightly different ways, yielding two spectra. Not all modern string theories use both types; some incorporate only the closed variety.

However, the bosonic theory has problems. Most importantly, the theory has a fundamental instability, believed to result in the decay of space-time itself. Additionally, as the name implies, the spectrum of particles contains only bosons, particles like the photon which obey particular rules of behavior. While bosons are a critical ingredient of the Universe, they are not its only constituents. Investigating how a string theory may include fermions in its spectrum led to supersymmetry, a mathematical relation between bosons and fermions which is now an independent area of study. String theories which include fermionic vibrations are now known as superstring theories; several different kinds have been described.

Roughly between 1984 and 1986, physicists realized that string theory could describe all elementary particles and interactions between them, and hundreds of them started to work on string theory as the most promising idea to unify theories of physics. This first superstring revolution was started by a discovery of anomaly cancellation in type I string theory by Michael Green and John Schwarz in 1984. The anomaly is cancelled due to the Green-Schwarz mechanism. Several other ground-breaking discoveries, such as the heterotic string, were made in 1985.

In the 1990s, Edward Witten and others found strong evidence that the different superstring theories were different limits of an unknown 11-dimensional theory called M-theory. These discoveries sparked the second superstring revolution. (Several meanings of the "M" have been proposed; physicists joke that the true meaning will only be chosen when the theory is finally understood.)

Many recent developments in the field relate to D-branes, objects which physicists discovered must also be included in any theory which includes open strings of the super string theory.

Basic properties

The term 'string theory' properly refers to both the 26-dimensional bosonic string theories and to the 10-dimensional superstring theories discovered by adding supersymmetry. Nowadays, 'string theory' usually refers to the supersymmetric variant while the earlier is given its full name, 'bosonic string theory'.

While understanding the details of string and superstring theories requires considerable mathematical sophistication, some qualitative properties of quantum strings can be understood in a fairly intuitive fashion. For example, quantum strings have tension, much like regular strings made of twine; this tension is considered a fundamental parameter of the theory. The tension of a quantum string is closely related to its size. Consider a closed loop of string, left to move through space without external forces. Its tension will tend to contract it into a smaller and smaller loop. Classical intuition suggests that it might shrink to a single point, but this would violate Heisenberg's uncertainty principle. The characteristic size of the string loop will be a balance between the tension force, acting to make it small, and the uncertainty effect, which keeps it "stretched". Consequently, the minimum size of a string must be related to the string tension.

Unsolved problems in physics: Is string theory, superstring theory, or M-theory, or some other variant on this theme, a step on the road to a "theory of everything," or just a blind alley?

Extra dimensions

One intriguing feature of string theory is that it predicts the number of dimensions which the universe should possess. Nothing in Maxwell's theory of electromagnetism or Einstein's theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions "by hand". The first person to add a fifth dimension to Einstein's four was the German mathematician Theodor Kaluza in 1919. The reason for the unobservability of the fifth dimension (its compactness) was suggested by the Swedish physicist Oskar Klein in 1926.

Instead, string theory allows one to compute the number of spacetime dimensions from first principles. Technically, this happens because Lorentz invariance can only be satisfied in a certain number of dimensions. This is roughly like saying that if an observer measures the distance between two points, then rotates by some angle and measures again, the observed distance only stays the same if the universe has a particular number of dimensions.

The only problem is that when the calculation is done, the universe's dimensionality is not four as one may expect (three axes of space and one of time), but twenty-six. More precisely, bosonic string theories are 26-dimensional, while superstring and M-theories turn out to involve 10 or 11 dimensions. In bosonic string theories, the 26 dimensions come from the Polyakov equation

(see technical details in the CERN preprint "Quantum Geometry of Bosonic Strings - Revisited").

However, these models appear to contradict observed phenomena. Physicists usually solve this problem in one of two different ways. The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable in our phenomenal experience. The 6-dimensional model's resolution is achieved with Calabi-Yau spaces. In 7 dimensions, they are termed G2 manifolds. Essentially these extra dimensions are compactified by causing them to loop back upon themselves.

A standard analogy for this is to consider multidimensional space as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. This is akin to the 4 macroscopic dimensions we are accustomed to dealing with every day. If, however, one approaches the hose, one discovers that it contains a second dimension, its circumference. This "extra dimension" is only visible within a relatively close range to the hose, just as the extra dimensions of the Calabi-Yau space are only visible at extremely small distances, and thus are not easily detected.

(Of course, everyday garden hoses exist in three spatial dimensions, but for the purpose of the analogy, its thickness is neglected and only motion on the surface of the hose is considered. A point on the hose's surface can be specified by two numbers, a distance along the hose and a distance along the circumference, just as points on the Earth's surface can be uniquely specified by latitude and longitude. In either case, the object has two spatial dimensions. Like the Earth, garden hoses have an interior, a region that requires an extra dimension; however, unlike the Earth, a Calabi-Yau space has no interior.)

Another possibility is that we are stuck in a 3+1 dimensional subspace of the full universe, where the "3+1" reminds us that time is a different kind of dimension than space. Because it involves mathematical objects called D-branes, this is known as a braneworld theory.

In either case, gravity acting in the hidden dimensions produces other non-gravitational forces such as electromagnetism. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility.

Problems

String theory remains to be verified. No version of string theory has yet made a prediction which differs from those made by other theories—at least, not in a way that could be checked by a currently feasible experiment. In this sense, string theory is still in a "larval stage": it possesses many features of mathematical interest, and it may yet become supremely important in our understanding of the Universe, but it requires further developments before it is accepted or falsified. Since string theory may not be tested in the foreseeable future, some scientists[1] have asked if it even deserves to be called a scientific theory: it is not yet falsifiable in the sense of Popper.

It is by no means the only theory currently being developed which suffers from this difficulty; any new development can pass through a stage of uncertainty before it becomes conclusively accepted or rejected. As Richard Feynman noted in The Character of Physical Law, the key test of a scientific theory is whether its consequences agree with the measurements taken in experiments. It does not matter who invented the theory, "what his name is", or even how aesthetically appealing the theory may be—"if it disagrees with experiment, it's wrong." (Of course, there are subsidiary issues: something may have gone wrong with the experiment, or perhaps the person computing the consequences of the theory made a mistake. All these possibilities must be checked, which may take a considerable time.) These developments may be in the theory itself, such as new methods of performing calculations and deriving predictions, or they may be advances in experimental science, which make formerly ungraspable quantities measurable.

Since the influence of quantum effects upon gravity only become significant at distances many orders of magnitude smaller than human beings have the technology to observe (or at roughly the Planck length, about 10-35 meters), string theory, or any other candidate theory of quantum gravity, will be very difficult to test experimentally. Eventually, scientists may be able to test string theory by observing cosmological phenomena which may be sensitive to string physics.

In the early 2000s, string theorists revived interest in an older concept, the cosmic string. Originally discussed in the 1980s, cosmic strings are a different type of object than the entities of superstring theories. For several years, cosmic strings were a popular model for explaining various cosmological phenomena, such as the way galaxies formed in the early Universe. However, further experiments — and in particular the detailed measurements of the cosmic microwave background — failed to support the cosmic-string model's predictions, and the cosmic string fell out of vogue. If such objects did exist, they must be few and far between. Several years later, it was pointed out that the expanding Universe could have stretched a "fundamental" string (the sort which superstring theory considers) until it was of intergalactic size. Such a stretched string would exhibit many of the properties of the old "cosmic" string variety, making the older calculations useful again. Furthermore, modern superstring theories offer other objects which could feasibly resemble cosmic strings, such as highly elongated one-dimensional D-branes (known as "D-strings"). As theorist Tom Kibble remarks, "string theory cosmologists have discovered cosmic strings lurking everywhere in the undergrowth". Older proposals for detecting cosmic strings could now be used to investigate superstring theory. For example, astronomers have also detected a few cases of what might be string-induced gravitational lensing.

Superstrings, D-strings or other stringy objects stretched to intergalactic scales would radiate gravitational waves, which could presumably be detected using experiments like LIGO. They might also cause slight irregularities in the cosmic microwave background, too subtle to have been detected yet but possibly within the realm of future observability.

While intriguing, these cosmological proposals fall short in one respect: testing a theory requires that the test be capable, at least in principle, of falsifying the theory. For example, if observing the Sun during a solar eclipse had not shown that the Sun's gravity deflected light, Einstein's general relativity theory would have been proven wrong. Not finding cosmic strings would not demonstrate that string theory is fundamentally wrong — merely that the particular idea of highly stretched strings acting "cosmic" is in error. While many measurements could in principle be made that would suggest that string theory is on the right track, scientists have not at present devised a stringent "test".

On a more mathematical level, another problem is that, like quantum field theory, much of string theory is still only formulated perturbatively (i.e., as a series of approximations rather than as an exact solution). Although nonperturbative techniques have progressed considerably — including conjectured complete definitions in space-times satisfying certain asymptotics — a full nonperturbative definition of the theory is still lacking.


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Although nonperturbative techniques have progressed considerably — including conjectured complete definitions in space-times satisfying certain asymptotics — a full nonperturbative definition of the theory is still lacking. David Beckham's left foot." - From the film Love Actually, said by Hugh Grant, posed as Britain's Prime Minister. On a more mathematical level, another problem is that, like quantum field theory, much of string theory is still only formulated perturbatively (i.e., as a series of approximations rather than as an exact solution). David Beckham's right foot. While many measurements could in principle be made that would suggest that string theory is on the right track, scientists have not at present devised a stringent "test". The country of Shakespeare, Churchill, the Beatles, Sean Connery, Harry Potter. Not finding cosmic strings would not demonstrate that string theory is fundamentally wrong — merely that the particular idea of highly stretched strings acting "cosmic" is in error. "We may be a small country but we're a great one, too.

For example, if observing the Sun during a solar eclipse had not shown that the Sun's gravity deflected light, Einstein's general relativity theory would have been proven wrong. "David Beckham must never go near a penalty kick again! — The Sun. While intriguing, these cosmological proposals fall short in one respect: testing a theory requires that the test be capable, at least in principle, of falsifying the theory. "Without being too harsh on David Beckham, he cost us the match." - Ian Wright, former England striker. They might also cause slight irregularities in the cosmic microwave background, too subtle to have been detected yet but possibly within the realm of future observability. Apart from that he's alright." — George Best. Superstrings, D-strings or other stringy objects stretched to intergalactic scales would radiate gravitational waves, which could presumably be detected using experiments like LIGO. "He cannot kick with his left foot, he cannot head a ball, he cannot tackle, and he doesn't score many goals.

For example, astronomers have also detected a few cases of what might be string-induced gravitational lensing. "David Beckham is Britain's finest striker of a football not because of God-given talent but because he practises with a relentless application that the vast majority of less gifted players wouldn't contemplate" — Sir Alex Ferguson (1999)[20]. Older proposals for detecting cosmic strings could now be used to investigate superstring theory. "10 heroic lions, one stupid boy" — Daily Mirror headline after Beckham's sending off against Argentina. As theorist Tom Kibble remarks, "string theory cosmologists have discovered cosmic strings lurking everywhere in the undergrowth". Some regarded Beckham as instrumental in the success of the Olympic bid for London 2012. Furthermore, modern superstring theories offer other objects which could feasibly resemble cosmic strings, such as highly elongated one-dimensional D-branes (known as "D-strings"). He has bought a multi-million dollar home in The Palm, Jumeirah, in Dubai, United Arab Emirates.

Such a stretched string would exhibit many of the properties of the old "cosmic" string variety, making the older calculations useful again. Beckham is viewed by some as the most famous example of metrosexuality, a type of personality which combines feminine and masculine characteristics. Several years later, it was pointed out that the expanding Universe could have stretched a "fundamental" string (the sort which superstring theory considers) until it was of intergalactic size. It has been speculated that he believed it to be too effeminate. If such objects did exist, they must be few and far between. Allegedly, in May 2003 Manchester United manager Sir Alex Ferguson ordered Beckham not to wear his hair band during matches. However, further experiments — and in particular the detailed measurements of the cosmic microwave background — failed to support the cosmic-string model's predictions, and the cosmic string fell out of vogue. It is about a British Sikh girl who idolises David Beckham and harbours ambitions of being a football player.

For several years, cosmic strings were a popular model for explaining various cosmological phenomena, such as the way galaxies formed in the early Universe. He has become more well known in North America since the success of the British film Bend It Like Beckham. Originally discussed in the 1980s, cosmic strings are a different type of object than the entities of superstring theories. For the first time, the Beckham 'brand' had been tainted. In the early 2000s, string theorists revived interest in an older concept, the cosmic string. Following his move to Real Madrid and the disappointment of Euro 2004, British media interest in the Beckham's has faded despite an alleged affair with Rebecca Loos, his former personal assistant. Eventually, scientists may be able to test string theory by observing cosmological phenomena which may be sensitive to string physics. Despite the USA's uneven acceptance of soccer, Beckham's recognition in the USA is strong enough to enable him to appear in print and television advertising for various sponsors, including Gillette razors.

Since the influence of quantum effects upon gravity only become significant at distances many orders of magnitude smaller than human beings have the technology to observe (or at roughly the Planck length, about 10-35 meters), string theory, or any other candidate theory of quantum gravity, will be very difficult to test experimentally. Early on in his career Beckham secured a number of lucrative sponsorship deals including Brylcreem, Adidas, Vodafone (which ended in July 2005) and Diesel. All these possibilities must be checked, which may take a considerable time.) These developments may be in the theory itself, such as new methods of performing calculations and deriving predictions, or they may be advances in experimental science, which make formerly ungraspable quantities measurable. Beckham is one of only four players to have appeared 100 times in the Champions League.[19]. It does not matter who invented the theory, "what his name is", or even how aesthetically appealing the theory may be—"if it disagrees with experiment, it's wrong." (Of course, there are subsidiary issues: something may have gone wrong with the experiment, or perhaps the person computing the consequences of the theory made a mistake. He captained his country for a landmark 50th time in the friendly international against Argentina in November 2005. As Richard Feynman noted in The Character of Physical Law, the key test of a scientific theory is whether its consequences agree with the measurements taken in experiments. Beckham is also a reasonable candidate to record 100 appearances for his country.

It is by no means the only theory currently being developed which suffers from this difficulty; any new development can pass through a stage of uncertainty before it becomes conclusively accepted or rejected. If so, he would become only the sixth England player to represent his country at three World Cup competitions (although Sol Campbell and Michael Owen are expected to achieve this feat at the same time), and the fourth (after Billy Wright, Bobby Moore and Bryan Robson) to captain the team at more than one World Cup. Since string theory may not be tested in the foreseeable future, some scientists[1] have asked if it even deserves to be called a scientific theory: it is not yet falsifiable in the sense of Popper. Beckham made his 85th appearance for England in 2005 and is expected to captain the team at the 2006 World Cup in Germany. In this sense, string theory is still in a "larval stage": it possesses many features of mathematical interest, and it may yet become supremely important in our understanding of the Universe, but it requires further developments before it is accepted or falsified. In January, Beckham was named a judge for the 2006 British Book Awards, while his wife Victoria Beckham announced plans to write a children's book. No version of string theory has yet made a prediction which differs from those made by other theories—at least, not in a way that could be checked by a currently feasible experiment. Currently (as of 30 December), the performance of Real Madrid is even more sluggish than last year with the team is 11 points behind their main rivals FC Barcelona, who are topping the table with 40 points.

String theory remains to be verified. The turnover of the company equates to David Beckham earning almost £47,500 every day, before expenses. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility. He owns a company called Footwork Productions Ltd. In either case, gravity acting in the hidden dimensions produces other non-gravitational forces such as electromagnetism. Beckham established two football academies bearing his name, one in Los Angeles and one in East London. Because it involves mathematical objects called D-branes, this is known as a braneworld theory. On December 3, 2005, in the Real Madrid v Getafe match in the Spanish league, Beckham was again sent off in the 58th minute for a rash tackle.

Another possibility is that we are stuck in a 3+1 dimensional subspace of the full universe, where the "3+1" reminds us that time is a different kind of dimension than space. Having received a yellow card, he appeared to sarcastically applaud the referee and was given a second yellow card, causing an automatic dismissal, athough the dismissal was cancelled on appeal two days later. Like the Earth, garden hoses have an interior, a region that requires an extra dimension; however, unlike the Earth, a Calabi-Yau space has no interior.). Shortly afterwards, Beckham was sent off while playing in a league match for Real Madrid against Valencia. In either case, the object has two spatial dimensions. Four days later they beat Poland 2-1 to top the qualifying group. A point on the hose's surface can be specified by two numbers, a distance along the hose and a distance along the circumference, just as points on the Earth's surface can be uniquely specified by latitude and longitude. Nonetheless, England held on to win the match 1-0 and later qualified for the 2006 tournament due to results elsewhere.

(Of course, everyday garden hoses exist in three spatial dimensions, but for the purpose of the analogy, its thickness is neglected and only motion on the surface of the hose is considered. In October 2005, while playing in the World Cup Qualifying match against Austria, Beckham became the first England captain to be sent off, and the first player to be sent off twice while playing for England. This "extra dimension" is only visible within a relatively close range to the hose, just as the extra dimensions of the Calabi-Yau space are only visible at extremely small distances, and thus are not easily detected. Real Madrid had another disappointing season, finishing second in the league to Barcelona and only reaching the last sixteen in the UEFA Champions League. If, however, one approaches the hose, one discovers that it contains a second dimension, its circumference. Beckham became a UNICEF goodwill amabassador in January 2005, having supported the charity for a number of years.[18]. This is akin to the 4 macroscopic dimensions we are accustomed to dealing with every day. The following month, the announcement of plans for the christening of the Beckhams' two children, including the construction of a fake Gothic chapel for £120,000 on the grounds of their Berkshire estate, were received with some ridicule, especially as neither are held to be strongly religious.

If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. In November 2004 it was reported that Real Madrid intended to offer Beckham a two-year extension to his contract, which would effectively keep him in Madrid for the remainder of his playing career. A standard analogy for this is to consider multidimensional space as a garden hose. The Football Association asked Beckham for an explanation of his actions and he admitted that he had "made a mistake" and apologised.[17]. Essentially these extra dimensions are compactified by causing them to loop back upon themselves. Beckham was due to receive a one-match suspension for his next caution, and picked up an injury which he knew would keep him out of England's next match, so he deliberately fouled Thatcher in order to serve his suspension in a match that he would have had to miss anyway. In 7 dimensions, they are termed G2 manifolds. Beckham made more headlines on 9 October when he admitted he had intentionally fouled Ben Thatcher in an England match against Wales in order to get himself booked.

The 6-dimensional model's resolution is achieved with Calabi-Yau spaces. Victoria and their children were in the house at the time, but security guards apprehended the man before he reached the house.[16]. The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable in our phenomenal experience. In July 2004, while David was in pre-season training in Spain, an intruder scaled a wall at the Beckhams' home while carrying a can of petrol. Physicists usually solve this problem in one of two different ways. England lost the shootout and went out of the competition. However, these models appear to contradict observed phenomena. He had a penalty saved in England's 2-1 defeat to France and missed another in a penalty shootout in the quarter final against Portugal.

(see technical details in the CERN preprint "Quantum Geometry of Bosonic Strings - Revisited"). Beckham played in all of England's matches at Euro 2004, but the tournament was a disappointment for him. In bosonic string theories, the 26 dimensions come from the Polyakov equation . Real Madrid finished the season in a diasppointing fourth place, and were knocked out of the UEFA Champions League at the quarter-final stage. More precisely, bosonic string theories are 26-dimensional, while superstring and M-theories turn out to involve 10 or 11 dimensions. Real Madrid denied rumours that they were interested in selling Beckham, and banned British reporters from access to the team. The only problem is that when the calculation is done, the universe's dimensionality is not four as one may expect (three axes of space and one of time), but twenty-six. Sources within the family told the Telegraph that Beckham would almost certainly be back in London.

This is roughly like saying that if an observer measures the distance between two points, then rotates by some angle and measures again, the observed distance only stays the same if the universe has a particular number of dimensions. Near the end of the 2003-04 season, The Daily Telegraph reported that Beckham's major sponsors were trying to arrange for him to return to England for the 2004-05 season. Technically, this happens because Lorentz invariance can only be satisfied in a certain number of dimensions. Beckham dismissed both accusations as "ludicrous".[15]. Instead, string theory allows one to compute the number of spacetime dimensions from first principles. A week later, the Malaysian-born Australian model Sarah Marbeck claimed that she had slept with Beckham on two occasions. The reason for the unobservability of the fifth dimension (its compactness) was suggested by the Swedish physicist Oskar Klein in 1926. Beckham had further problems in April 2004, when the British tabloid News of the World carried claims by his former personal assistant Rebecca Loos that he and Loos had had an extramarital affair.

The first person to add a fifth dimension to Einstein's four was the German mathematician Theodor Kaluza in 1919. Beckham immediately became a favourite with the Real Madrid supporters, scoring five times in his first 16 matches, but the team, whose club president expected them to win either the Spanish league or the Champions League each season, were not performing well. Nothing in Maxwell's theory of electromagnetism or Einstein's theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions "by hand". He chose to wear 23 instead, in tribute to Michael Jordan who had worn that number for the Chicago Bulls. One intriguing feature of string theory is that it predicts the number of dimensions which the universe should possess. Although Beckham had worn the number seven shirt for Manchester United and England, he was unable to wear it at Madrid as Raúl had the right to wear it written into his contract. Consequently, the minimum size of a string must be related to the string tension. It was reported that this tour would earn more money for the Beckhams than the first year of David's Real Madrid contract.

The characteristic size of the string loop will be a balance between the tension force, acting to make it small, and the uncertainty effect, which keeps it "stretched". At the time the transfer was announced, Beckham and his wife were on a week-long tour of Asia promoting beauty products, chocolate, motor oil, and mobile phones. Classical intuition suggests that it might shrink to a single point, but this would violate Heisenberg's uncertainty principle. For example, Real Madrid shirts bearing his name and number sold out in Madrid on the day his transfer was completed and the club were expected to receive €624,000 for the sale of the shirts. Its tension will tend to contract it into a smaller and smaller loop. It was speculated that Real's desire to sign him came from the merchandising opportunities he would bring as well as from his football ability. Consider a closed loop of string, left to move through space without external forces. The transfer was completed on 1 July and made him the third Englishman to ever play for the club after Laurie Cunningham in the 1980s and Steve McManaman in the late 1990s to early 2000s.

The tension of a quantum string is closely related to its size. On June 17, 2003, Beckham signed a four-year contract with Real Madrid of Spain, potentially worth up to €35 million (£25 million, USD 41 million). For example, quantum strings have tension, much like regular strings made of twine; this tension is considered a fundamental parameter of the theory. He was still a first-choice player for England, however, and he was awarded an OBE for services to football on 13 June.[14]. While understanding the details of string and superstring theories requires considerable mathematical sophistication, some qualitative properties of quantum strings can be understood in a fairly intuitive fashion. Beckham scored the winning goal in their final match of the season. Nowadays, 'string theory' usually refers to the supersymmetric variant while the earlier is given its full name, 'bosonic string theory'. The incident led to a great deal of transfer speculation involving Beckham, with bookmakers offering odds on whether he or Ferguson would be first to leave the club.[13] Although the team had started the season badly, their results improved greatly from December onwards and they won the league.

The term 'string theory' properly refers to both the 26-dimensional bosonic string theories and to the 10-dimensional superstring theories discovered by adding supersymmetry. His relationship with his manager deteriorated further on 15 February 2003 when, in the changing room following a defeat to Arsenal, Alex Ferguson kicked a football boot which struck Beckham over the eye, causing a cut which required stitches. Many recent developments in the field relate to D-branes, objects which physicists discovered must also be included in any theory which includes open strings of the super string theory. Following an injury early in the 2002-03 season, Beckham was unable to regain his place in the team, with Ole Gunnar Solskjær having replaced him on the right side of midfield. (Several meanings of the "M" have been proposed; physicists joke that the true meaning will only be chosen when the theory is finally understood.). England were eventually knocked out of the tournament by Brazil in the Quarter-Finals. These discoveries sparked the second superstring revolution. Beckham scored the only goal of the match against Argentina, with a penalty.

In the 1990s, Edward Witten and others found strong evidence that the different superstring theories were different limits of an unknown 11-dimensional theory called M-theory. He was partially fit by the time of the 2002 World Cup and played in the first match against Sweden. Several other ground-breaking discoveries, such as the heterotic string, were made in 1985. [12]. The anomaly is cancelled due to the Green-Schwarz mechanism. The income from his new contract and the many endorsement deals he had made him the highest-paid player in the world at the time. This first superstring revolution was started by a discovery of anomaly cancellation in type I string theory by Michael Green and John Schwarz in 1984. The injury prevented Beckham from playing for United for the rest of the season, but he signed a three-year contract in May, following months of negotiations with the club, mostly concerning extra payments for his image rights.

Roughly between 1984 and 1986, physicists realized that string theory could describe all elementary particles and interactions between them, and hundreds of them started to work on string theory as the most promising idea to unify theories of physics. Those speculations were unfounded, though, and the accusations were never proved. String theories which include fermionic vibrations are now known as superstring theories; several different kinds have been described. There was speculation that the injury might have been caused deliberately, as the player who had injured Beckham was Argentinian Aldo Duscher and England and Argentina were due to meet in that year's World Cup [11]. Investigating how a string theory may include fermions in its spectrum led to supersymmetry, a mathematical relation between bosons and fermions which is now an independent area of study. On April 10, 2002, Beckham was injured during a Champions League match against Deportivo La Coruña, breaking the metatarsal bones of his left foot. While bosons are a critical ingredient of the Universe, they are not its only constituents. Shortly afterwards, he was voted the BBC Sports Personality of the Year for 2001.

Additionally, as the name implies, the spectrum of particles contains only bosons, particles like the photon which obey particular rules of behavior. With Teddy Sheringham being fouled some eight yards outside the Greek penalty area, England was awarded a free-kick and Beckham ensured England's qualification by with a curling strike of the kind which had become his trademark. Most importantly, the theory has a fundamental instability, believed to result in the decay of space-time itself. England needed to win or draw the match in order to qualify for the World Cup, but were losing 2–1 with little time remaining. However, the bosonic theory has problems. The final step in Beckham's conversion from villain to hero happened in England's 2–2 draw against Greece on 6 October 2001. Not all modern string theories use both types; some incorporate only the closed variety. He helped England to qualify for the 2002 World Cup Finals, with their performances including an impressive 5–1 victory over Germany in Munich.

The two types of string behave in slightly different ways, yielding two spectra. Following Kevin Keegan's resignation as England manager in October 2000, Beckham was promoted to team captain by the caretaker manager Peter Taylor, and then kept the role under new manager Sven-Göran Eriksson. These early models included both open strings, which have two distinct endpoints, and closed strings, where the endpoints are joined to make a complete loop. The abuse that Beckham was receiving from English supporters peaked during England's 3–2 defeat by Portugal in Euro 2000, when a group of England supporters taunted him throughout the match with chants including "we hope your kid dies of cancer".[9] Beckham responded with a one-fingered gesture and, while the gesture attracted some criticism, many of the newspapers that had previously encouraged his vilification asked their readers to stop abusing him.[10]. The scale of notes, each corresponding to a different kind of particle, is termed the "spectrum" of the theory. He later criticised Beckham in an updated edition of his 1999 autobiography, claiming he hadn't been "fair to his team mates".[8] Beckham had a good season for his club, though, and helped United to win the Premier League by a record margin. The mass the particle has, and the fashion with which it can interact, are determined by the way the string vibrates—in essence, by the "note" which the string sounds. He responded by fining Beckham the maximum amount that was permitted (two weeks' wages – then £50,000) and dropping him for a crucial match against United's rivals Leeds United.

By applying the ideas of quantum mechanics to the Polyakov action—a procedure known as quantization—one can deduce that each string can vibrate in many different ways, and that each vibrational state appears to be a different particle. In 2000, the club gave Beckham permission to miss training to look after his son Brooklyn, who had gastroenteritis, but Ferguson was furious when Victoria Beckham was photographed at a London Fashion Week event on the same night, and he realised that Beckham would have been able to train if Victoria had looked after Brooklyn that day. Bosonic string theory is formulated in terms of the Polyakov action, a mathematical quantity which can be used to predict how strings move through space and time. The relationship between Ferguson and Beckham began to deteriorate, possibly as a result of Beckham's fame and commitments away from football. It is now hoped that string theory or some descendant of it will provide a fundamental understanding of the quarks themselves.). It was suggested in the press that his wife was a bad influence on him, and that it might be in United's interests to sell him,[7] but his manager publicly backed him and he stayed at the club. (The original need for a viable theory of hadrons has been fulfilled by quantum chromodynamics, the theory of quarks and their interactions. Despite Beckham's achievements in the 1998-99 season, he was still unpopular among opposition fans and many journalists, and he was heavily criticised after being sent off for a deliberate foul in Manchester United's World Club Championship match against Necaxa.

This led to the development of bosonic string theory, which is still the version first taught to many students. 437 staff were employed for the wedding reception, which was estimated to have cost UK£500,000.[6]. Schwarz and Scherk argued that string theory had failed to catch on because physicists had underestimated its scope. They were later accused of bad taste after photographs showed that they had sat on thrones for the ceremony. Then, in 1974, John Schwarz and Joel Scherk studied the messenger-like patterns of string vibration and found that their properties exactly matched those of the gravitational force’s hypothetical messenger particle -- graviton. The media were kept away from the ceremony as the Beckhams had a deal with OK! Magazine giving them exclusive rights for photographs. The scientific community soon lost interest in string theory, and the standard model, with its particles and fields, remained unthreatened. Beckham's teammate Gary Neville was the best man, and Brooklyn was the ring bearer.

But even after physicists understood the physical explanation for Veneziano’s insight, the string description of the strong force made many predictions that directly contradicted experimental findings. The wedding attracted enormous media coverage. By representing nuclear forces as vibrating, one-dimensional strings, these physicists showed how Euler’s function accurately described those forces. He married Victoria at Luttrellstown Castle, Ireland on 4 July 1999. In 1970, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind unveiled the physics beneath Euler’s strictly theoretical formula. Both of the goals came from corners taken by Beckham, and this, combined with his performances over the rest of the season, led to him finishing runner up for 1999's European Footballer of the Year award. Veneziano applied the Euler beta function to the strong force, but no one could explain why it worked. United were losing the Champions League final 1–0 at the end of normal time, but won the trophy by scoring two goals in stoppage time.

Veneziano found that a 200-year-old formula created by Swiss mathematician Leonhard Euler (the Euler beta function) perfectly matched modern data on the strong force. Beckham played in United's FA Cup final win over Newcastle and played in centre-midfield for the UEFA Champions League final as United's first choice centre-midfielders were suspended for the match. In 1968, theoretical physicist Gabriele Veneziano was trying to understand the strong nuclear force when he made a startling discovery. Beckham scored their equaliser and United went on to win the match and the league. No simple model of the hadron, such as picturing it as a set of smaller particles held together by spring-like forces, was able to explain these relationships. United needed to win their final league match of the season at home to Tottenham Hotspur to ensure they would win the league championship, but Tottenham took an early lead in the match. In particle-accelerator experiments, physicists observed that the spin of a hadron is never larger than a certain multiple of the square of its energy. On a more positive note for Beckham, Victoria gave birth to their first child Brooklyn on 4 March 1999.

String theory was originally invented to explain peculiarities of hadron (subatomic particle which experiences the strong nuclear force) behavior. United's supporters had mostly forgiven him for the problems he'd had with England, and were frequently heard to chant "Argentina" in response to the other supporters' taunts. . Throughout the season, Beckham was jeered by opposition supporters whenever he touched the ball, but he consistently played well and his crossing provided a significant number of goals for United's forwards Dwight Yorke and Andy Cole. String theory has also led to insight into supersymmetric gauge theories, which will be tested at the new Large Hadron Collider experiment. There had been speculation that the criticism that he had received after being sent off in the World Cup would lead to him leaving England, but he decided to stay at Manchester United. Work on string theory has led to advances in mathematics, mainly in algebraic geometry. In the 1998–99 season, he was part of the United team that won the "treble" — Premier League, FA Cup and Champions League, a unique feat in English football.

String theory as a whole has not yet made falsifiable predictions that would allow it to be experimentally tested, though various special corners of the theory are accessible to planned observations and experiments. Many supporters and journalists blamed Beckham for England's elimination and he became the target of severe criticism and abuse, including the hanging of an effigy outside a London pub, and the Daily Mirror newspaper printing a dartboard with a picture of him in the middle.[5]. It is not yet known whether string theory is able to describe a universe with the precise collection of forces and matter that is observed, nor how much freedom to choose those details the theory will allow. Simeone later admitted to trying to get Beckham sent off by over-reacting to the kick and then, along with other members of his team, waving imaginary red cards at the referee, urging him to send Beckham off.[4] The match finished in a draw and England were eliminated in a penalty shootout. Superstring theories include fermions, the building blocks of matter, and incorporate supersymmetry. As Beckham lay on the pitch he held out his right leg as Simeone backed into it and fell over. It is a possible solution of the quantum gravity problem, and in addition to gravity it can naturally describe interactions similar to electromagnetism and the other forces of nature. In the second round of that competition, he received a red card in England's match against Argentina, for kicking out at Diego Simeone following a foul challenge by the Argentine.

Interest in string theory is driven largely by the hope that it will prove to be a theory of everything. He was picked for their third match against Colombia, which England needed to win to ensure their progress in the tournament, and played well, scoring one of his trademark free kicks in a 2–0 victory. Study of string theories has revealed that they require not just strings but other objects, variously including points, membranes, and higher-dimensional objects. Beckham had played in all of England's qualifying matches for the 1998 World Cup and travelled with the England squad to the finals in France, but the team's manager Glenn Hoddle publicly accused him of not concentrating on the tournament,[3] and he didn't start in either of England's first two matches. For this reason, string theories are able to avoid problems associated with the presence of pointlike particles in a physical theory. United started the season well, but their results deteriorated when several players became injured and they finished the season in second place. String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles) that are the basis of the Standard Model of particle physics. Their relationship attracted a great deal of media interest.

In 1998, Beckham started dating the Spice Girl Victoria Adams and was pictured wearing a sarong while they were on holiday together. He was voted PFA Young Player of the Year by his peers. He became an automatic first-choice player at United that season, scoring a series of blistering goals and sublime free kicks, thus helping them to retain their league championship. Beckham's name was frequently mentioned in the press, and he made his first appearance for the England national football team on 1 September 1996 in a world cup qualifying a match against Moldova.

Sky Sports' commentator Martin Tyler's words "You'll see that over and over again" proved prophetic as the goal was voted Premier League 'Goal of the Decade' in 2003. With United 2–0 ahead, Beckham noticed that Wimbledon's goalkeeper Neil Sullivan was standing a long way out of his goal, and hit a shot from the halfway line that floated over the goalkeeper and into the net. In August 1996, Beckham became something of a household name when he scored a spectacular goal in a match against Wimbledon. Beckham became a regular player in the team and helped them to win the Premiership and FA Cup double that season, scoring the winner in the semi-final against Chelsea and also supplying the corner kick cross that Eric Cantona scored with a volley from in the FA Cup Final.

The criticism of Ferguson increased when United started the season with a 3–1 defeat at Aston Villa F.C.[2], with Beckham scoring United's only goal of the game, but many of the doubters were won over when the team won their next five matches. United manager Alex Ferguson had large confidence in the club's young players and when three of his first-team players left the club at the end of the 1994-95 season, he made the decision to let the youth team players replace them instead of buying players from other clubs. He went to Preston North End on loan in the 1994-95 season to get some first team experience, then made his first Premier League appearance for Manchester United on 2 April 1995, in a goalless draw against Leeds. United reached the final of the Youth Cup again the following year, with Beckham playing in their defeat by Leeds United, and he won another medal in 1994 when the club's reserve team won their league.

He had his first appearance for United's first team that year, as a substitute in a League Cup match against Brighton & Hove Albion, and signed his first professional contract shortly afterwards. These players later helped the club to win the FA Youth Cup in May 1992, with Beckham scoring in the second leg of the final against Crystal Palace. He was part of an exceptionally talented group of young players at the club, including the future internationals Paul Scholes, Nicky Butt, Ryan Giggs Phil Neville and Gary Neville. He signed schoolboy forms at United on his fourteenth birthday in 1989, then signed a Youth Training Scheme contract on 8 July 1991.

The young Beckham had trials with Leyton Orient and attended Tottenham Hotspur's school of excellence, but once Manchester United offered him a place there was no doubting which club he would go to. He was Manchester United's mascot for a match against West Ham United in 1986. At the age of eleven, he attended one of Bobby Charlton's soccer schools in Manchester and won the chance to take part in a training session at FC Barcelona in a talent competition. David was a strong cross-country runner who regularly finished first in his age group in the Essex cross-country championships, but he had inherited his parents' love of Manchester United and his main passion was football.

Both have also obtained matching tattoos from the Song of Songs that says, in Hebrew: “I am for my beloved, and my beloved is for me, who grazes sheep in rose-like pastures.”) The Beckhams were fanatical Manchester United supporters, who would regularly travel to Old Trafford by coach and frequently went to away games. (Presently, Beckham and his wife have embraced the mystic Jewish offshoot of Kabbalah. In his first autobiography My World, which was serialised in OK! Magazine, David was quoted as saying; "I've probably had more contact with Judaism than with any other religion." Beckham is Jewish on his maternal grandfather's side. Beckham was born in Leytonstone, east London, the son of Ted Beckham (a kitchen fitter) and Sandra West (a hairdresser).

. Beckham's relationship with and marriage to the former Spice Girl Victoria (née Adams) has contributed towards him becoming a major celebrity away from football, and his name was searched for on Google more than that of any other sporting personality in 2003 and 2004.[1] The Beckhams have three sons, Brooklyn, born March 4, 1999, Romeo, born September 1, 2002, and Cruz, born February 20, 2005. As of November 2005, Beckham has had 5 different coaches in Real Madrid and failed to win any major trophies with his struggling new team. While his performances for Real Madrid have attracted praise, the team itself has been in turmoil.

His relationship with the club's manager Sir Alex Ferguson began to deteriorate, though, and although he won further league championships with United in 2000 and 2001, he left the club to join Real Madrid in 2003. Beckham became a figure of public hatred among many English football supporters, but he continued to play well and helped United win the league, FA Cup, and UEFA Champions League the following year. He was soon selected to play for England, but after winning another league medal in 1997, he was sent off in a World Cup match against Argentina for kicking Diego Simeone. By 1995, he had established himself as a first-team player at United and won Premier League and FA Cup winners' medals with the club in 1996.

He signed schoolboy forms for Manchester United in 1989, became a trainee in 1991 and signed a professional contract with them soon after making his first first-team appearance in 1992. He is also famed for his celebrity lifestyle trappings, media attention and marketing potential. He currently plays for Real Madrid and as captain of the English national team, especially noted for the quality of his crossing and ability to hit free-kicks and corners, particularly from long-range. David Robert Joseph Beckham OBE (born May 2, 1975 in Leytonstone, London) is an English footballer, widely regarded as the most famous player in the sport.

^  Managing My Life 137. The others are Paolo Maldini, Gary Neville and Raúl. ^  As of December 2005. URL accessed on October 9, 2005..

UNICEF official website. ^  David Beckham, Goodwill Ambassador. URL accessed on October 6, 2005.. BBC News, 14 October 2004.

^  FA wants explanation from Beckham. URL accessed on October 9, 2005.. Manchester Online, 20 July 2004. ^  Intruder alert for Victoria Beckham.

URL accessed on October 7, 2005.. BBC News, 20 May 2004. ^  Beckham to stay in Spain. URL accessed on October 6, 2005..

BBC News, 13 June 2003. ^  Beckham's pride at OBE. URL accessed on October 6, 2005.. BBC News, 18 February 2003.

^  Will Becks give Man Utd the boot?. URL accessed on October 7, 2005.. BBC News, May 2002. ^  Beckham signs new contract.

URL accessed on October 7, 2005.. ESPN Socernet, 2 April 2002. ^  Did 'hatchet man' target Beckham?. URL accessed on October 4, 2005..

BBC News, 14 June 2000. ^  Media sympathy for Beckham's gesture. URL accessed on October 4, 2005.. New Statesman, 26 June 2000.

Leader — Play games behind closed doors. ^  A reference to Brooklyn. ^  Quoted in The Boss 468. URL accessed on October 6, 2005..

BBC News, 7 January 2000. ^  Man Utd's flawed genius?. URL accessed on December 2, 2005.. BBC News, 5 July 1999.

^  Wedded spice. URL accessed on October 6, 2005.. Article on official UEFA website. ^  Beckham's Darkest Hour.

URL accessed on October 26, 2005.. Rediff Sports, 19 May 2002. ^  Simeone admits trying to get Beckham sent off. URL accessed on October 5, 2005..

Dispatch Online, 29 June 1998. ^  Beckham Blasts Hoddle. Beckham scored United's goal from a distance of around 30 metres. ^  The most famous comment was Alan Hansen's "You can't win anything with kids.", quoted in The Boss 405.

URL accessed on October 9, 2005.. Google.com. URL accessed on October 9, 2005., 2004 Year-End Google Zeitgeist. Google.com.

^  2003 Year-End Google Zeitgeist. New Statesman. Manchester Online. ESPN Soccernet.

Dispatch Online. BBC News. URL accessed on October 3, 2005.. Biography on fifa.com.

URL accessed on October 3, 2005.. Biography on manutd.com. ISBN 0-340-72855-8.. Managing My Life — My Autobiography, Hodder & Stoughton.

Ferguson, Alex; McIlvanney, Hugh (1999). ISBN 0-7434-2991-5.. The Boss — The Many Sides of Alex Ferguson, Pocket Books. Crick, Michael (2003).

ISBN 0060570938.. Beckham: Both Feet on the Ground, HarperCollins. Beckham, David; Watt, Tom (2003). ISBN 0340792701..

Beckham: My World, Hodder & Stoughton Ltd. Beckham, David; Freeman, Dean (2001). ISBN 0007157320.. David Beckham: My Side, HarperCollinsWillow.

Beckham, David (2002).