Elgin Baylor

Baylor ranked #11 on SLAM Magazine's Top 75 NBA Players of all time in 2003. 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. In 1977, Baylor was elected to the Basketball Hall of Fame and in 1980 he was named to the NBA 35th Anniversary All-Time Team and again in 1996, he was named to the NBA 50th Anniversary All-Time Team. 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). In 1986, Baylor was hired by the Los Angeles Clippers as the team's vice president of basketball operations, where he still is today. 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". In 1974, Baylor was hired to be an assistant coach and later the head coach for the New Orleans Jazz, but had a lackluster 86-135 record and retired following the 1978-79 season. 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.

He finished his career with an astonishing 23,149 points, 3,650 assists and 11,463 rebounds over 846 games. 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. Second, the Lakers went on to win the NBA Championship that season, something that Baylor never achieved. 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. First, the Lakers' next game after his retirement was the first of an NBA record of 33 consecutive wins. 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. His retirement resulted in two great ironies. Superstrings, D-strings or other stringy objects stretched to intergalactic scales would radiate gravitational waves, which could presumably be detected using experiments like LIGO.

Baylor finally retired during the 1971-72 season because of his nagging knee problems. For example, astronomers have also detected a few cases of what might be string-induced gravitational lensing. During Baylor's career, the Lakers were a consistently powerful team, but were continuously overshadowed by the Boston Celtics dynasty of the time. Older proposals for detecting cosmic strings could now be used to investigate superstring theory. Baylor began to be hampered with knee problems during the 1963-64 season and, while still a very powerful force, was never quite the same player, never averaging above 30 points per game again. As theorist Tom Kibble remarks, "string theory cosmologists have discovered cosmic strings lurking everywhere in the undergrowth". Baylor was a 10-time All-NBA First Team selection and went to the NBA All-Star Game 11 times. 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").

In 1959, Baylor won the NBA Rookie of the Year Award and from the 1960-61 to the 1962-63 seasons, he averaged 34.8, 38.3 and 34.0 points per game, leading the Lakers to the NBA Finals eight times (although never winning). Such a stretched string would exhibit many of the properties of the old "cosmic" string variety, making the older calculations useful again. Following his junior season, Baylor joined the Minneapolis Lakers for the 1958-1959 season and moving with them to Los Angeles in 1960. 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. Elgin Baylor played college basketball at the College of Idaho and Seattle University, leading the SU Chieftains to the NCAA championship game in 1958 (where they lost to the Kentucky Wildcats). If such objects did exist, they must be few and far between. Elgin Gay Baylor (born September 16, 1934 in Washington, DC) was one of the most graceful and acrobatic forwards to ever play the game of basketball playing 13 seasons for the NBA's Minneapolis and Los Angeles Lakers. 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.

For several years, cosmic strings were a popular model for explaining various cosmological phenomena, such as the way galaxies formed in the early Universe. Originally discussed in the 1980s, cosmic strings are a different type of object than the entities of superstring theories. In the early 2000s, string theorists revived interest in an older concept, the cosmic string. Eventually, scientists may be able to test string theory by observing cosmological phenomena which may be sensitive to string physics.

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. 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. 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. 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 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. 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. 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. 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.

String theory remains to be verified. 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 either case, gravity acting in the hidden dimensions produces other non-gravitational forces such as electromagnetism. Because it involves mathematical objects called D-branes, this is known as a braneworld theory.

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. 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.). In either case, the object has two spatial dimensions. 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.

(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. 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. If, however, one approaches the hose, one discovers that it contains a second dimension, its circumference. This is akin to the 4 macroscopic dimensions we are accustomed to dealing with every day.

If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. A standard analogy for this is to consider multidimensional space as a garden hose. Essentially these extra dimensions are compactified by causing them to loop back upon themselves. In 7 dimensions, they are termed G₂ manifolds.

The 6-dimensional model's resolution is achieved with Calabi-Yau spaces. 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. Physicists usually solve this problem in one of two different ways. However, these models appear to contradict observed phenomena.

(see technical details in the CERN preprint "Quantum Geometry of Bosonic Strings - Revisited"). In bosonic string theories, the 26 dimensions come from the Polyakov equation . More precisely, bosonic string theories are 26-dimensional, while superstring and M-theories turn out to involve 10 or 11 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.

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. Technically, this happens because Lorentz invariance can only be satisfied in a certain number of dimensions. Instead, string theory allows one to compute the number of spacetime dimensions from first principles. The reason for the unobservability of the fifth dimension (its compactness) was suggested by the Swedish physicist Oskar Klein in 1926.

The first person to add a fifth dimension to Einstein's four was the German mathematician Theodor Kaluza in 1919. 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". One intriguing feature of string theory is that it predicts the number of dimensions which the universe should possess. Consequently, the minimum size of a string must be related to the string tension.

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". Classical intuition suggests that it might shrink to a single point, but this would violate Heisenberg's uncertainty principle. Its tension will tend to contract it into a smaller and smaller loop. Consider a closed loop of string, left to move through space without external forces.

The tension of a quantum string is closely related to its size. For example, quantum strings have tension, much like regular strings made of twine; this tension is considered a fundamental parameter of the 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. Nowadays, 'string theory' usually refers to the supersymmetric variant while the earlier is given its full name, 'bosonic string theory'.

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. 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. (Several meanings of the "M" have been proposed; physicists joke that the true meaning will only be chosen when the theory is finally understood.). These discoveries sparked the second superstring revolution.

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. Several other ground-breaking discoveries, such as the heterotic string, were made in 1985. The anomaly is cancelled due to the Green-Schwarz mechanism. 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.

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. String theories which include fermionic vibrations are now known as superstring theories; several different kinds have been described. 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. While bosons are a critical ingredient of the Universe, they are not its only constituents.

Additionally, as the name implies, the spectrum of particles contains only bosons, particles like the photon which obey particular rules of behavior. Most importantly, the theory has a fundamental instability, believed to result in the decay of space-time itself. However, the bosonic theory has problems. Not all modern string theories use both types; some incorporate only the closed variety.

The two types of string behave in slightly different ways, yielding two spectra. 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 scale of notes, each corresponding to a different kind of particle, is termed the "spectrum" of the theory. 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.

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. 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. It is now hoped that string theory or some descendant of it will provide a fundamental understanding of the quarks themselves.). (The original need for a viable theory of hadrons has been fulfilled by quantum chromodynamics, the theory of quarks and their interactions.

This led to the development of bosonic string theory, which is still the version first taught to many students. Schwarz and Scherk argued that string theory had failed to catch on because physicists had underestimated its scope. 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 scientific community soon lost interest in string theory, and the standard model, with its particles and fields, remained unthreatened.

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. By representing nuclear forces as vibrating, one-dimensional strings, these physicists showed how Euler’s function accurately described those forces. In 1970, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind unveiled the physics beneath Euler’s strictly theoretical formula. Veneziano applied the Euler beta function to the strong force, but no one could explain why it worked.

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. In 1968, theoretical physicist Gabriele Veneziano was trying to understand the strong nuclear force when he made a startling discovery. 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 particle-accelerator experiments, physicists observed that the spin of a hadron is never larger than a certain multiple of the square of its energy.

String theory was originally invented to explain peculiarities of hadron (subatomic particle which experiences the strong nuclear force) behavior. . String theory has also led to insight into supersymmetric gauge theories, which will be tested at the new Large Hadron Collider experiment. Work on string theory has led to advances in mathematics, mainly in algebraic geometry.

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. 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. Superstring theories include fermions, the building blocks of matter, and incorporate supersymmetry. 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.

Interest in string theory is driven largely by the hope that it will prove to be a theory of everything. Study of string theories has revealed that they require not just strings but other objects, variously including points, membranes, and higher-dimensional objects. For this reason, string theories are able to avoid problems associated with the presence of pointlike particles in a physical 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.