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.
. 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). They are expected to sign former BAR driver Takuma Sato to drive for their team, their engines would be supplied by Honda, and as of November 2005 they are in negotiations with former Minardi chief Paul Stoddart to buy chassis for their cars, which would be the 2002 Arrows model[14]. 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 team is named after its founder, Aguri Suzuki, who was a Formula One driver himself and participated in 88 races. 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. Another team, Super Aguri F1 is set to join the F1 course in 2006, after gaining the unanimous agreement of the ten existing team [13].

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. In 2006, the Faenza-based team will be run as a junior team named Scuderia Toro Rosso (initially known as Squadra Toro Rosso), although technically the team is a separate entity to Red Bull Racing. 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. Arguably, the final small team disappeared with the September 2005 purchase of Minardi by Red Bull. 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. The Williams team will cease their partnership with BMW as a result, instead opting to run Cosworth engines for 2006. Superstrings, D-strings or other stringy objects stretched to intergalactic scales would radiate gravitational waves, which could presumably be detected using experiments like LIGO. In June 2005, BMW bought a majority stake in Sauber and intends to run the team as a factory entry in 2006.

For example, astronomers have also detected a few cases of what might be string-induced gravitational lensing. For 2006, Jordan will be rebadged as Midland F1. Older proposals for detecting cosmic strings could now be used to investigate superstring theory. Jordan then signed deal to use Toyota engines, while Minardi continued to use Cosworth engines under Cosworth's new owners. As theorist Tom Kibble remarks, "string theory cosmologists have discovered cosmic strings lurking everywhere in the undergrowth". Jordan and Minardi both relied on Ford's Cosworth engines. 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"). Jaguar Racing was sold to Red Bull and is now known as Red Bull Racing.

Such a stretched string would exhibit many of the properties of the old "cosmic" string variety, making the older calculations useful again. The Ford Motor Company's decision to pull out of Formula One at the end of 2004 exposed the vulnerabilities of some small teams. 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. Drivers must make a final choice of dry-weather compound ahead of qualifying. If such objects did exist, they must be few and far between. Drivers also have access to slightly more tyres than in 2005 - seven sets of dry-weather, four sets of wet-weather and three sets of extreme-weather. 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. Also,the 2006 season will see the return of the tyre changes during the pitstops.The thinking behind this is that the reduced engine size will offset any performance gain.

For several years, cosmic strings were a popular model for explaining various cosmological phenomena, such as the way galaxies formed in the early Universe. [12]. Originally discussed in the 1980s, cosmic strings are a different type of object than the entities of superstring theories. These changes will be applicable for the 2006 season. In the early 2000s, string theorists revived interest in an older concept, the cosmic string. For the final period, lasting 20 minutes, the cars will be arranged on the grid in positions one to ten in the order of their times, the fastest occupying pole position. Eventually, scientists may be able to test string theory by observing cosmological phenomena which may be sensitive to string physics. The times for the ten remaining cars will be reset for the next session.

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. These cars will make up the grid in positions eleven to fifteen in the order of their times, the fastest occupying 11th position. 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. At the end of the second 15-minute period the slowest five cars can take no further part in qualifying. 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. The times for the fifteen remaining cars are reset for the next session. 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. These cars will make up the last five grid positions in the order of their times, the fastest occupying 16th position.

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. At the end of the first 15-minute period the slowest five cars can take no further part in qualifying. 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. All cars are permitted on the track. 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. Also, in 2005-10-24, the Formula One commission decided to switch the competition to the "KO" system. 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. [11].

String theory remains to be verified. These changes are due in 2007. 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. In 2005-10-05, the FIA proposal of enhancing overtaking won the support of the teams by agreeing about the new rear wing concept -that would eliminate the current single rear wing and replace it with two box-like wings, one behind each rear wheel. In either case, gravity acting in the hidden dimensions produces other non-gravitational forces such as electromagnetism. Over the coming years, radical changes will be made to the rules. Because it involves mathematical objects called D-branes, this is known as a braneworld theory. In the long run, the FIA intends to introduce greater restrictions on testing and the introduction of standardised electronic units and tires.

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. However, some teams will be allowed to continue using the V10 with a rev limiter in order to cut costs. 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.). Beginning with the 2006 season, engine displacement will be decreased, a 2.4L V8 replacing the current 3.0L V10. In either case, the object has two spatial dimensions. Both the teams and the drivers are still unhappy with the qualifying system, however, and several alternative formats have been suggested for use from 2006 onwards.[10]. 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. This was ditched after complaints from spectators, who felt that the Saturday session was meaningless, and broadcasters, who did not want to broadcast so much Formula One on a Sunday.

(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. The current qualifying format, a single flying lap on race fuel, replaced one which was used for the first part of the 2005 season (until the 2005 European Grand Prix) which involved two separate sessions, one on Saturday and a second on Sunday morning, with the starting grid drawn up according to the fastest aggregate time of each driver. 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. These two issues, safety and cost, are paramount in all rule-change discussions, and the FIA has made public its intention to continue to modify the rules with these goals in mind. If, however, one approaches the hose, one discovers that it contains a second dimension, its circumference. In an attempt to reduce costs, a new rule requires each engine to be used for two consecutive races. This is akin to the 4 macroscopic dimensions we are accustomed to dealing with every day. In the interest of safety, the FIA instituted a number of rule changes at the start of the 2005 season, including restrictions on the changing of tyres.

If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. These newer circuits, however are generally agreed upon to meet the safety standards of modern Formula One better than the older ones. A standard analogy for this is to consider multidimensional space as a garden hose. His redesign of the Hockenheim circuit in Germany for example, while providing more capacity for grandstands and eliminating extremely long and dangerous straights, has been frowned upon by many who argue that part of the character of the Hockenheim circuits were the long and blinding straights into the Black Forest. Essentially these extra dimensions are compactified by causing them to loop back upon themselves. Several of the new circuits in F1, especially those designed by Herman Tilke, have been criticized as lacking the "flow" of such classics as Spa-Francorchamps and Imola. In 7 dimensions, they are termed G2 manifolds. The US Grand Prix has been offically scheduled to occur again at the Indianapolis Motor Speedway on July 2, 2006.

The 6-dimensional model's resolution is achieved with Calabi-Yau spaces. The future of the United States Grand Prix at Indianapolis Motor Speedway is also in doubt after only six cars started the 2005 race due to concerns about the safety of the supplied Michelin tyres. 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 inaugural Turkish Grand Prix took place in 2005 in IstanbulPark, and Ecclestone has asserted publicly that F1 will return to South Africa within five years.[7] He has also expressed interest in a Russian Grand Prix in Moscow or St Petersburg in the near future.[8] The European Union's ratification of laws prohibiting tobacco advertising went into effect on July 31, 2005, providing another incentive for the heavily tobacco-sponsored sport to find venues outside of Europe.[9]. Physicists usually solve this problem in one of two different ways. As of 2005, this expansion has resulted in the disappearance of only one race, the Austrian Grand Prix, which was last held in 2003; however, several teams have expressed their preference for a shorter calendar[6], and the future of such races as the British, European and San Marino Grands Prix has recently fallen into doubt. However, these models appear to contradict observed phenomena. In the interest of making the sport truer to its designation as a World Championship, FOM president Bernie Ecclestone has initiated and organized a number of Grands Prix in new countries and continues to discuss new future races.

(see technical details in the CERN preprint "Quantum Geometry of Bosonic Strings - Revisited"). The sport's rapid expansion into new areas of the globe also leaves some question as to which races will be cut. In bosonic string theories, the 26 dimensions come from the Polyakov equation . At present, the FIA has been taxed with the responsibility of making rules to combat the spiralling costs which affect the smaller teams and to ensure that the sport remains as safe as possible. More precisely, bosonic string theories are 26-dimensional, while superstring and M-theories turn out to involve 10 or 11 dimensions. However, viewing figures are seeing some signs of recovery due to the varied 2005 season, with the Canadian Grand Prix attracting the third largest global TV audience of any sporting event in 2005, behind only the Super Bowl and the UEFA Champions League final.[5]. 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. Viewing figures dropped, and fans expressed their loss of interest due to the dominance of Michael Schumacher and Ferrari.

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. Formula One went through a difficult period in the early 2000s. Technically, this happens because Lorentz invariance can only be satisfied in a certain number of dimensions. Whilst circuit safety is of prime importance, this can often be achieved without the reduction of the modern circuit to parade route status. Instead, string theory allows one to compute the number of spacetime dimensions from first principles. An ongoing complaint of long time F1 fans is the emasculation of the world's greatest circuits in order to satisfy sometimes arbitrary demands from the FIA. The reason for the unobservability of the fifth dimension (its compactness) was suggested by the Swedish physicist Oskar Klein in 1926. These were mostly aimed at better matching the speed of a car with both the available space to slow down in before reaching a barrier and the ability of those barriers to safely absorb the energy of a crash.

The first person to add a fifth dimension to Einstein's four was the German mathematician Theodor Kaluza in 1919. This is an ongoing task – after the deaths of Ayrton Senna and Roland Ratzenberger at Imola during the 1994 season, the FIA mandated further changes to circuits. 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". Whereas in the 1950s a driver was lucky to find a strategically placed bale of straw to absorb an impact, modern Formula One circuits feature large run-off areas, gravel traps and tire barriers to reduce the risk of injury in crashes. One intriguing feature of string theory is that it predicts the number of dimensions which the universe should possess. Circuit design to protect the safety of drivers is becoming increasingly sophisticated, as exemplified by the new track in Bahrain, designed – like most of F1's new circuits – by Hermann Tilke. Consequently, the minimum size of a string must be related to the string tension. Three-time World champion Nelson Piquet famously described racing in Monaco as "riding a bicycle around your living room.".

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". The glamour and history of the Monaco race are the primary reasons why the circuit is still in use, since it is thought not to meet the strict safety requirements imposed on other tracks. Classical intuition suggests that it might shrink to a single point, but this would violate Heisenberg's uncertainty principle. Several other circuits are also completely or partially laid out on public roads, such as Spa-Francorchamps. Its tension will tend to contract it into a smaller and smaller loop. The only real street circuit is the Circuit de Monaco, used for the Monaco Grand Prix, although races in other urban locations come and go (Las Vegas and Detroit, for example) and proposals for such races are often discussed – most recently for London. Consider a closed loop of string, left to move through space without external forces. Most of the circuits currently in use are specially constructed for competition.

The tension of a quantum string is closely related to its size. Also particularly lamented are the circuits at Zandvoort in the Netherlands and Kyalami in South Africa, neither of which are now used by F1. For example, quantum strings have tension, much like regular strings made of twine; this tension is considered a fundamental parameter of the theory. Many corners have become well known in their own right, such as the high-speed Eau Rouge at Spa-Francorchamps, and before the addition of chicanes to tame it, the Tamburello corner at Imola and the Curva Grande at Monza, as well as in recent years the thirteenth turn at Indianapolis (road course configuration), known as the fastest corner in the sport. 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. Those few circuits that run anticlockwise (and therefore have predominantly left handed corners) can cause drivers neck problems due to the enormous lateral forces generated by F1 cars pulling their heads in the opposite direction to normal. Nowadays, 'string theory' usually refers to the supersymmetric variant while the earlier is given its full name, 'bosonic string theory'. The layout of the rest of the circuit varies widely, although in most cases the circuit runs in a clockwise direction.

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. The pit lane, where the drivers stop for fuel during the race, and where the teams work on the cars before the race, is normally located next to the starting grid. 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. A typical circuit usually features a stretch of straight road on which the starting grid is situated. (Several meanings of the "M" have been proposed; physicists joke that the true meaning will only be chosen when the theory is finally understood.). The Bahrain Grand Prix, along with other new races in China and Turkey, present new opportunities for the growth and evolution of the Formula One Grand Prix franchise whilst new facilities also raise the bar for other Formula One racing venues around the world. These discoveries sparked the second superstring revolution. One of the newest races on the Grand Prix, held in Bahrain, represents Formula One's first penetration into the Middle East with a high tech purpose-built desert track.

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. It has always taken place at Monza, with one exception in 1980 when it took place at Imola (which now hosts the San Marino Grand Prix). Several other ground-breaking discoveries, such as the heterotic string, were made in 1985. The only other race to have been included in every World Championship season is the Italian Grand Prix. The anomaly is cancelled due to the Green-Schwarz mechanism. The British Grand Prix, for example, though held every year since 1950, alternated between Brands Hatch and Silverstone from 1963 to 1986. 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 grands prix, some of which have a history that predates the Formula One World Championship, are not always held on the same circuit every year.

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. For example, every year two grands prix take place in Germany, one of which is known as the European Grand Prix. String theories which include fermionic vibrations are now known as superstring theories; several different kinds have been described. If a single country hosts multiple grands prix in a year, they receive different names. 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. Traditionally, each nation has hosted a single grand prix that carries the name of the country. While bosons are a critical ingredient of the Universe, they are not its only constituents. The current nineteen races are spread over the continents of Europe, Asia, Oceania, North America, and South America.

Additionally, as the name implies, the spectrum of particles contains only bosons, particles like the photon which obey particular rules of behavior. Asia (Japan in 1976) and Oceania (Australia in 1985) followed. Most importantly, the theory has a fundamental instability, believed to result in the decay of space-time itself. Argentina hosted the first South American grand prix in 1953, and Morocco hosted the first African World Championship race in 1958. However, the bosonic theory has problems. The F1 championship gradually expanded to other non-European countries as well. Not all modern string theories use both types; some incorporate only the closed variety. Six of the original seven races took place in Europe; the only non-European race that counted towards the World Championship in 1950 was the Indianapolis 500, which, due to lack of participation by F1 teams, since it required cars with different specifications from the other races, was later replaced by the United States Grand Prix.

The two types of string behave in slightly different ways, yielding two spectra. Though the number of races had stayed at sixteen or seventeen since the 1980s, it reached nineteen in 2005. 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. Only seven races comprised the inaugural 1950 season; over the years the calendar has more than doubled in size. The scale of notes, each corresponding to a different kind of particle, is termed the "spectrum" of the theory. The number of Grands Prix held in a season has varied over the years. 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. Jochen Rindt has the distinction of having been the only posthumous World Champion.

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. Michael Schumacher holds the record for having won the most Drivers' Championships (seven) and Ferrari holds the record for having won the most Constructors' Championships (fourteen). 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. As privateer teams quickly folded in the early 1990s, numbers were frequently shuffled around, until the current system was adopted in 1996. It is now hoped that string theory or some descendant of it will provide a fundamental understanding of the quarks themselves.). For many years, for example, Ferrari held numbers 27 & 28, regardless of their finishing position in the world championship. (The original need for a viable theory of hadrons has been fulfilled by quantum chromodynamics, the theory of quarks and their interactions. Before 1996, only the world championship winning driver and his team generally swapped numbers with the previous champion – the remainder held their numbers from prior years, as they had been originally set at the start of the 1974 season.

This led to the development of bosonic string theory, which is still the version first taught to many students. The number 13 has not been used since 1974, before which it was occasionally assigned at the discretion of individual race organizers. Schwarz and Scherk argued that string theory had failed to catch on because physicists had underestimated its scope. In this case the drivers for the team of the previous year's champion are given numbers 0 and 2. 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. There have been exceptions to this rule, such as in 1993 and 1994, when the current World Drivers' Champion was no longer competing in Formula One. The scientific community soon lost interest in string theory, and the standard model, with its particles and fields, remained unthreatened. Numbers are then assigned according to each team's position in the previous season's World Constructors' Championship.

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 previous season's World Drivers' Champion is designated number 1, with his teammate given number 2. By representing nuclear forces as vibrating, one-dimensional strings, these physicists showed how Euler’s function accurately described those forces. Each car is assigned a number. In 1970, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind unveiled the physics beneath Euler’s strictly theoretical formula. As a consequence, constructors desiring to enter Formula One often prefer to buy an existing team: B.A.R.'s purchase of Tyrrell and Midland's purchase of Jordan allowed both of these teams to sidestep the large deposit. Veneziano applied the Euler beta function to the strong force, but no one could explain why it worked. Entering a new team in the Formula One World Championship requires a £25 million (about US$50 million) up-front payment to the FIA, which is then repaid to the team over the course of the season.

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. Although teams rarely disclose information about their budgets, it is estimated that they range from US$75 million to US$500 million each. In 1968, theoretical physicist Gabriele Veneziano was trying to understand the strong nuclear force when he made a startling discovery. Ferrari is the only still-active team which competed in 1950, and as of 2005 only ten teams remain on the grid, each fielding two cars. 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 fact, such was the scarcity of competitive cars for much of the first decade of Formula One that Formula Two cars were admitted to fill the grids. 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. The sport's 1950 debut season saw eighteen teams compete, but due to high costs many dropped out quickly.

String theory was originally invented to explain peculiarities of hadron (subatomic particle which experiences the strong nuclear force) behavior. The only remaining commercial engine manufacturer is Cosworth. . Others, such as DaimlerChrysler, provide engines and sponsorship for privately owned teams in return for prominent advertisement on their team clothing and car livery. String theory has also led to insight into supersymmetric gauge theories, which will be tested at the new Large Hadron Collider experiment. Honda has also recently gained control over what was once British American Racing. Work on string theory has led to advances in mathematics, mainly in algebraic geometry. After having virtually disappeared by the early 1980s, factory teams made a comeback in the 1990s and 2000s, with Toyota, Ferrari (FIAT), and Renault owning their own teams and BMW following suit by purchasing the former Sauber team.

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. As the manufacturers' deep pockets and engineering ability took over, these collaborations largely died out in favour of the present system in which a manufacturer supports a single team. 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. Companies such as Climax, Repco, Cosworth, Hart, Judd and Supertec, which had no direct team affiliation, often sold engines to teams who could not afford to manufacture them. Superstring theories include fermions, the building blocks of matter, and incorporate supersymmetry. Early manufacturer involvement came in the form of a "factory team" (that is, one owned and staffed by a major car company), such as those of Alfa Romeo, Ferrari (FIAT) or Renault. 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 its early years, Formula One teams sometimes also built their engines, though this became less common with the increased involvement of major car manufacturers such as BMW, DaimlerChrysler, Renault, Toyota, and Honda, whose large budgets rendered privately built engines less competitive (and redundant).

Interest in string theory is driven largely by the hope that it will prove to be a theory of everything. This requirement distinguishes the sport from series such as IRL, Champ Cars, and NASCAR, which allow teams to purchase chassis, and "spec series" such as GP2, which require all cars be kept to an identical specification. Study of string theories has revealed that they require not just strings but other objects, variously including points, membranes, and higher-dimensional objects. Formula One teams must build the chassis in which they compete, and consequently the terms "team" and "constructor" are more or less interchangeable. For this reason, string theories are able to avoid problems associated with the presence of pointlike particles in a physical theory. The winner of the two annual championships are the driver and the team who have accumulated the most points at the end of the season. 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. The FIA awards points to the top eight drivers and their respective teams of a grand prix on a 10-8-6-5-4-3-2-1 basis (the race winner receives ten points, the first runner-up eight, and so on).

Throughout the race, drivers may make one or more pit stops in order to refuel, although they are currently not allowed to change tires unless the change is essential (for instance, due to a puncture). Races are a little over 300 kilometres (180 miles) long and are limited to two hours, though in practice they usually last about ninety minutes. A light system above the track then signals the start of the race. As long as he moves off and at least one car is behind him, he can retake his original position.

If a driver stalls before the parade lap, and the rest of the field passes him, then he must start from the back of the grid. The race begins with a warm-up formation lap, after which the cars assemble on the starting grid in the order they qualified. After these practice sessions, a qualifying session consisting of one "flying lap" (whereby the driver is given an empty track to set his time on, with time measured from a rolling start) determines a driver's position on the starting grid for Sunday's race, with the fastest driver during qualifying given "pole position" and the slowest driver starting last. Third drivers are allowed to run on Fridays for teams that finished the preceding season in 5th place or lower.

A Formula One Grand Prix event spans an entire weekend, beginning with two free practices on Friday, and two free practices on Saturday. The effects on the already low viewing figures are to be seen as the sound produced by V8 engines is expected to be different and perhaps not as loud as their V10 counterparts. The new 2.4 litre 8 Cylinder Formula is set to be introduced as early as the beginning of 2006 season allowing smaller teams to run rpm-limited V10 3-litre engines. Other Championship winning engines are those from Mercedes Benz, BMW, Porsche and Ford Cosworth.

but not only Renault was successful, Ferrari and specially Honda enjoyed great success with multiple championships with several teams, most notable McLaren and by a lesser extent Williams with whom Honda engines reached the highest levels of power in F1 history in the late 80's exceeding, in some circumstances, the 1200 bhp limit in qualifying. Renault was innovative during this period producing out of the standard designs as the 111º 10 cylinder engine for the 2003 RS23. At the end the statistics show a raw supremacy of the Renault engines having clinched several championships as engine suppliers and their first ever Drivers and Constructors Championships in a 100% Renault car in 2005. The year 2005 marks the end of an era, the end of the 10 cylinder powerplants which saw both normally aspirated and supercharged engines being deployed in F1 cars for more than two decades.

It was introduced in many countries over the years, but was shut down after the 2002 season for financial reasons. Bernievision offered the viewer several simultaneous feeds (such as super signal, on-board, top of field, backfield, highlights, pit lane, timing), which were produced with cameras, technical equipment and staff different from those used for the conventional coverage. Ecclestone experimented with a digital television package (known colloquially as Bernievision), which was launched at the 1996 German Grand Prix in cooperation with German digital television service "DF1". During the early 2000s, Bernie Ecclestone's Formula One Administration created a number of trademarks, an official logo, and an official website for the sport in an attempt to give it a corporate identity.

[3] In 2005, the United States Grand Prix at Indianapolis saw only three out of ten teams race in a bizarre mishap when it turned out that the Michelin tires for the other seven teams could not be safely used on the surface of the track, causing them to pull out [4] when the FIA refused a change for safety reasons, insisting on keeping to the letter of the regulations. The ensuing scandal saw Ferrari slapped with a fine by the FIA, who also banned any further use of team orders in the new rules and regulations. At the Austrian Grand Prix in 2002, Rubens Barrichello, Schumacher's teammate at Ferrari who was leading the race, was ordered to allow Schumacher to overtake him. The first few years of the 21st century in F1 also saw some controversies and scandals.

In 2005, drivers were no longer allowed to change tires during the race, unless the tires are deemed to be dangerously worn. Other new restrictions included one making it mandatory for each engine to last two races; a driver that had to have his engine replaced would be penalised by starting at a lower position in the starting grid of the race. Another new regulation made drivers start each race with the same level of fuel they had during qualifying, introducing a new tactical element to each team's strategy. Most notably, the qualifying format has changed several times since 2003.

Meanwhile, several changes to the rules were made in a bid to improve the on-track action and cut spiralling costs. In the rulebook, several driver aids returned due in part to developments that allowed teams to evade the FIA "restrictions". Michael Schumacher had been world champion for more than 1,800 days. Ferrari's championship streak finally came to an end on September 25, 2005 when Fernando Alonso clinched the 2005 championship with a third place finish at the Brazilian Grand Prix to become the youngest champion to date, replacing previous record holder Emerson Fittipaldi of Brazil.

Juan Pablo Montoya driving for Williams also came close in 2003. Despite Ferrari's dominance, Kimi Räikkönen driving for McLaren had a theoretical chance of claiming the championship in 2003 right until the end of the season at the Japanese Grand Prix. Later that year he became the youngest ever winner of a Grand Prix when he took the chequered flag in Hungary. In 2003 Fernando Alonso became the youngest ever pole sitter by qualifying first at Malaysia.

His record now stands at 7 championships. In 2002, Schumacher also set a new record by claiming the championship earlier in the season than any previous driver by winning the French Grand Prix in July that year.[2] In 2003, Schumacher claimed his sixth championship title, beating the earlier record-holder, Juan Manuel Fangio with five championships. In 2001, Schumacher set the new record for the most Grands Prix ever won; the earlier record holder was Alain Prost, with 51 wins to his name. The early 2000s were dominated by Michael Schumacher and a resurgent Ferrari.

Many records have been broken in the 21st century especially in the hands of German Michael Schumacher and recently the young Spaniard Fernando Alonso. This has prompted former Jordan owner Eddie Jordan to say that the days of competitive privateers are over.[1]. Since 1990, 28 teams have pulled out of Formula One. Financial troubles forced several teams to withdraw.

This increased financial burden, combined with four teams' dominance (largely funded by big car manufacturers such as DaimlerChrysler), caused the poorer independent teams to struggle not only to remain competitive, but to stay in business. Due to the technological advances of the 1990s, the cost of competing in Formula One rose dramatically. Drivers from McLaren, Williams, Renault (formerly Benetton) and Ferrari, dubbed the "Big Four", have won every World Championship from 1984 to the present day. The FIA vowed to improve the sport's safety standards; since that weekend, no driver has died on the track during a race.

Tragically, Ayrton Senna died in a crash at the 1994 San Marino Grand Prix having taken over Prost's lead drive at Williams that year. The rivalry between racing legends Senna and Prost became F1's central focus in 1988, and continued until Prost retired at the end of 1993. Honda and McLaren dominated much of the 1980s, whilst Renault-powered Williams drivers won several world championships in the mid 1990s, with a McLaren comeback in the late 1990s. On the track, the McLaren and Williams teams dominated the 1980s and 1990s.

The teams signed a second Concorde Agreement in 1992 and a third in 1997, which is due to expire on the last day of 2007. However, many observers felt that the ban on driver aids was a ban in name only as the FIA did not have the technology or the methods to eliminate these features from competition. The FIA, due to complaints that technology was determining the outcome of races more than driver skill, banned many such aids in 1994. Some, like active suspension, were primarily developed for the track and later made their way to the showroom.

Some were borrowed from contemporary road cars. In the early 1990s, teams started introducing electronic driver aids such as power steering, traction control, and semi-automatic gearboxes. To reduce engine power output and thus speeds, the FIA limited fuel tank capacity in 1984 and boost pressures in 1988 before banning turbocharged engines in 1989. These cars were and still are the most powerful open-wheel circuit racing cars ever.

In later years, notably 1987, the Formula One turbo cars produced in excess of 1,000 bhp in racing trim (and perhaps as much as 1,250 bhp in qualifying trim). By then, however, turbocharged engines, which Renault had pioneered in 1977, were producing over 700 bhp (520 kW) and were essential to be competitive. The FIA imposed a ban on ground effect aerodynamics in 1983. 1981 saw the signing of the first Concorde Agreement, a contract which bound the teams to compete until its expiration and assured them a share of the profits from the sale of television rights, bringing an end to the FISA-FOCA War and contributing to Bernie Ecclestone's eventual complete financial control of the sport, after much negotiation.

The formation of the Federation Internationale du Sport Automobile in 1979 set off the FISA-FOCA War, during which FISA and its president Jean Marie Balestre clashed repeatedly with the Formula One Constructors Association over television profits and technical regulations. In the late 1970s Lotus introduced ground effect aerodynamics that provided enormous downforce and greatly increased cornering speeds (though the concept had previously been tested by Jim Hall's Chaparral IndyCar team in the 1960s). Aerodynamic downforce slowly gained importance in car design from the appearance of aerofoils in the late 1960s. In 1968, Lotus painted an Imperial Tobacco livery on their cars, thus introducing sponsorship to the sport.

In 1962, Lotus introduced a car with aluminium sheet chassis called a monocoque in place of the traditional tubular chassis; this proved to be the next major technological breakthrough since the introduction of mid-engined cars. Between Jim Clark, Jackie Stewart, Jack Brabham, Graham Hill, and Denny Hulme, British teams and Commonwealth drivers won twelve world championships between 1962 and 1973. However, when Colin Chapman entered F1 as a chassis designer and later founder of Lotus, British racing green came to dominate the field for the next decade. The first British World Champion was Mike Hawthorn, who drove a Ferrari to the title in 1958.

By 1961, all competitors had switched to mid-engined cars. Jack Brabham, champion in 1959 and 1960, soon proved the new design's superiority. The first major technological development, Cooper's re-introduction of mid-engined cars (following Porsche's pioneering and all-conquering Auto Unions of the 1930s), which evolved from the company's successful Formula 3 designs, occurred in the 1950s. Fangio is remembered for dominating Formula One's first decade and has long been considered the "grand master" of Formula One.

Though Britain's Stirling Moss was able to compete regularly, he was never able to win the World Championship. However, Fangio won the title in 1951 and four more in the next six years, his streak interrupted by two-time champion Alberto Ascari of Ferrari. The inaugural Formula One World Championship was won by Italian Giuseppe Farina in his Alfa Romeo in 1950, barely defeating his Argentine teammate Juan Manuel Fangio. The sport's title, Formula One, indicates that it is intended to be the most advanced and most competitive of the many racing formulae.

Non-championship Formula One races were held for many years, but due to the rising cost of competition, the last of these occurred in the early 1980s. A championship for constructors followed in 1958. A number of Grand Prix racing organisations laid out rules for a World Championship before World War II, but due to the suspension of racing during the war, the World Drivers Championship was not formalised until 1947, and was first run in 1950. The Formula One series has its roots in the European Grand Prix motor racing (q.v. for pre-1947 history) of the 1920s and 1930s.

. Its present President is Max Mosley, and is generally promoted and controlled by the official commercial rights holder Bernie Ecclestone through a variety of corporate entities. The sport is regulated by the Fédération Internationale de l'Automobile,with its headquarters in Place de la Concorde, Paris. In recent years, it has also become known for glamour.

As the world's most expensive sport, its economic impact is significant, and its financial and political battles are widely observed. Europe is Formula One's traditional centre and remains its leading market; however, Grands Prix have been held all over the world, and with new races in Bahrain, China, Malaysia and Turkey, its scope is continually expanding. The cars race at speeds often in excess of 300 km/h (185 mph) with engines that produce, as of 2005, around 950 bhp at just over 19000 rpm. It consists of a series of races, known as Grands Prix, held on purpose-built circuits or closed city streets, whose results determine two annual World Championships, one for drivers and one for constructors.

Formula One, abbreviated to F1 and also known as Grand Prix racing, is the highest class of single-seat open-wheel formula auto racing. Parragon. The Concise Encyclopedia of Formula One. Tremayne, David & Hughes, Mark (1999).

BBC Sport. (June 19, 2005). Seven teams boycott US Grand Prix. Referenced 5 January 2006.

F1 third biggest global TV draw. Retrieved 1 September 2005. BBC Sport. Schumacher makes history (2002).

Retrieved 1 September 2005. itv.com/f1. Sauber: 19 races is too many (2004). The Sportstar.

It was Ferrari all the way. 28, 2002). (Dec. Rajan, Sanjay.

Retrieved 1 September 2005. itv.com/f1. Mexican GP back on track (2005). Carlton.

The Guide to 2005 FIA Formula One World Championship : The World's Bestselling Grand Prix Guide. Jones, Bruce (2005). Retrieved 1 September 2005. itv.com/f1.

Jordan: Privateer era is over (2005). Includes foreword by Martin Brundle. Carlton. The Official ITV Sport Guide: Formula One Grand Prix 2003.

Jones, Bruce (2003). Parragon. Formula One: The Complete Stats and Records of Grand Prix Racing. Jones, Bruce (1998).

Hodder & Stoughton. The Ultimate Encyclopedia of Formula One. Jones, Bruce (1997). Retrieved 25 October 2004.

The Official Formula 1 Website. Insight. (2004). Parragon. 55-84).

In, 100 Years of Change: Speed and Power (pp. Grand Prix Motor Racing. Gross, Nigel et al (1999). Retrieved 23 October 2004.

Federation Internationale de l'Automobile. Formula One Regulations. (2004). Retrieved 25 October 2004. Federation Internationale de l'Automobile.

FIA Archive. (2004). Retrieved 1 September 2005. itv.com/f1. Drivers suggest qualifying plan (2005).

Retrieved 1 September 2005. itv.com/f1. Confusion over tobacco laws (2005). Retrieved 1 September 2005.

itv.com/f1. Bernie promises Russian race (2005). Retrieved 1 September 2005. itv.com/f1.

Bernie in South Africa pledge (2004). Retrieved 1 September 2005. itv.com/f1. Bernie confident of Indy future (2005).

Motorbooks International. The Complete Book of Formula One. Arron, Simon & Hughes, Mark (2003). ^  Super Aguri could run Arrows cars from BBC Sport, published 23 November 2005.

^  F1 gives Super Aguri green light from BBC Sport, published 21 December 2005. ^  Drivers suggest qualifying plan. ^  Bernie confident of Indy future. ^  Confusion over tobacco laws.

^  Bernie promises Russian race. ^  Bernie in South Africa pledge. ^  Mexican GP back on track. ^  Sauber: 19 races is too many.

^  Seven teams boycott US Grand Prix. ^  F1 third biggest global TV draw referenced from ITV-F1, published 31 December 2005. ^  It was Ferrari all the way. ^  Schumacher makes history.

^  Jordan: Privateer era is over. ^  Red Bull confirms Minardi purchase.