String theory

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. The name was proposed by Ingrid van Houten-Groeneveld who along with Cornelis Johannes van Houten and Tom Gehrels discovered the asteroid on September 24, 1960. 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). Honoring Spirit's great contribution to the exploration of Mars, the asteroid 37452 has been named Spirit. 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". Ephemeris data generated by JPL Horizons indicates that Opportunity would have been able to observe the transit from the start until local sunset at about 19:23 UTC Earth time, while Spirit would have been able to observe it from local sunrise at about 19:38 UTC Earth time until the end of the transit. 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. They were able to observe transits of Deimos across the Sun, but at 2' angular diameter, Deimos is about 20 times larger than Mercury's 6.1" angular diameter.

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. Theoretically, this could have been observed by both Spirit and Opportunity, however camera resolution did not permit seeing Mercury's 6.1" angular diameter. 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. A transit of Mercury from Mars took place on January 12, 2005 from about 14:45 UTC to 23:05 UTC. 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. Some of Spirit's star gazing was designed to look for a predicted meteor shower caused by Halley's Comet but no images of meteors have been formally released. Superstrings, D-strings or other stringy objects stretched to intergalactic scales would radiate gravitational waves, which could presumably be detected using experiments like LIGO. These observations included a "lunar" (or rather phobal) eclipse as Spirit watched Phobos disappear into Mars's shadow.

For example, astronomers have also detected a few cases of what might be string-induced gravitational lensing. In fall of 2005 Spirit took advantage of a favorable energy situation to make multiple nighttime observations of both of Mars' moons Phobos and Deimos. Older proposals for detecting cosmic strings could now be used to investigate superstring theory. It also took the only photo of Earth from another world in early March. As theorist Tom Kibble remarks, "string theory cosmologists have discovered cosmic strings lurking everywhere in the undergrowth". Spirit pointed its cameras towards the sky and observed a transit of the Sun by Mars' moon Deimos (see Transit of Deimos from Mars). 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").
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Such a stretched string would exhibit many of the properties of the old "cosmic" string variety, making the older calculations useful again. Spirit's total odometry as of sol 735 (January 27, 2006) was 6,279.01 meters (3.9 miles). 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. There has been a large effort to maximize driving prior to this. If such objects did exist, they must be few and far between. Spirit entered restricted sols on sol 715 and now is only able to drive every other day. 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. Spirit is making its way to "Home Plate", where it should receive adequate sunlight during the Martian winter.

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. On Sol 582, August 21, 2005, Spirit reached the summit of Husband Hill and acquired a 360 degree panorama picture. 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. Dust devils had previously been photographed by only the Pathfinder probe.

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. This also marks the first time dust devils had been spotted by either Spirit or Opportunity, easily one of the top highlights of the mission to date. 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. NASA scientists speculate a dust devil must have swept the solar panels clean, possibly significantly extending the duration of the mission. 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. On 9 March 2005 (probably during the Martian night), the rover's solar panel efficiency jumped from around 60% of what it had originally been to 93%, followed on 10 March by the sighting of dust devils. 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. Squyres said of the discovery, "We're still trying to work out what this means, but clearly, with this much salt around, water had a hand here".

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. The soil also contained a high amount of phosphorus in its composition, however not nearly as high as another rock sampled by Spirit, "Wishstone". 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. Spirit also investigated some targets along the way, including the soil target, "Paso Robles", which contained the highest amount of salt found on the red planet. 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. The scientists at this time were trying to conserve as much energy as possible for the climb. 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. By Sol 390 (Mid-February 2005), Spirit was advancing towards "Larry's Lookout", by driving up the hill backwards in reverse.

String theory remains to be verified. Spirit ground it with the RAT tool on Sol 373. 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. On Sol 371, Spirit arrived at a rock named "Peace" near the top of Cumberland Ridge. In either case, gravity acting in the hidden dimensions produces other non-gravitational forces such as electromagnetism. Slowly, Spirit has made its way around the summit of Husband Hill, and at Sol 344 was ready to climb over the newly designated "Cumberland Ridge" and into "Larry's Lookout" and "Tennessee Valley". Because it involves mathematical objects called D-branes, this is known as a braneworld theory. From Sols 239 to 262, Spirit powered down for solar conjunction.

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. Following Clovis came the targets of Ebenezer (Sols 226-235), Tetl (Sol 270), Uchben and Palinque (Sols 281-295), and Lutefisk (Sols 296-303). 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.). Clovis was ground and analyzed from Sol 210 to Sol 225. In either case, the object has two spatial dimensions. By Sol 203, Spirit had driven southward up the hill and arrived at the rock dubbed "Clovis". 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. From here, Spirit took a northernly path along the base of the hill towards the target Wooly Patch, which was studied from Sol 192 to Sol 199.

(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. Within Hank's Hollow was the strange looking rock dubbed "Pot of Gold". 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. Hank's Hollow was studied for 23 sols. If, however, one approaches the hose, one discovers that it contains a second dimension, its circumference. On Sol 159, Spirit reached the first of many targets at the base of the Columbia Hills called West Spur. This is akin to the 4 macroscopic dimensions we are accustomed to dealing with every day. A long, snaking sand dune stretches away from its southwestern side, and Spirit went around it.

If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. Lahonten is about 60 yards across and about 10 yards deep. A standard analogy for this is to consider multidimensional space as a garden hose. It then reached Lahonten crater on Sol 118, and drove along the rim until Sol 120. Essentially these extra dimensions are compactified by causing them to loop back upon themselves. The rover skirted the northern rim, and continued to the southeast. In 7 dimensions, they are termed G₂ manifolds. Missoula crater was not considered a high priority target due to the older rocks it contained.

The 6-dimensional model's resolution is achieved with Calabi-Yau spaces. The crater is roughly 100 yards across and 20 yards deep. 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. Spirit reached Missoula crater on Sol 105. Physicists usually solve this problem in one of two different ways. Spirit drove along the southern rim, tore up some sand dunes, and continued to the southwest towards the Columbia Hills. However, these models appear to contradict observed phenomena. JPL decided that it would be a bad idea to send the rover down into the crater, as they saw no targets of interest inside.

(see technical details in the CERN preprint "Quantum Geometry of Bosonic Strings - Revisited"). This crater is 150 yards across and about 30 yards deep. In bosonic string theories, the 26 dimensions come from the Polyakov equation . On 11 March 2004, the Spirit rover reached Bonneville crater after a 400 yard journey. More precisely, bosonic string theories are 26-dimensional, while superstring and M-theories turn out to involve 10 or 11 dimensions. (Press release). 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. If this interpretation holds true, the minerals were most likely dissolved in water, which was either carried inside the rock or interacted with it at a later stage, after it formed.

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. Louis, reported during a NASA press conference: "If we found this rock on Earth, we would say it is a volcanic rock that had a little fluid moving through it." In contrast to the rocks found by the twin rover Opportunity, this one was formed from magma and then acquired bright material in small crevices, which look like crystallized minerals. Technically, this happens because Lorentz invariance can only be satisfied in a certain number of dimensions. Ray Arvidson of Washington University, St. Instead, string theory allows one to compute the number of spacetime dimensions from first principles. Dr. The reason for the unobservability of the fifth dimension (its compactness) was suggested by the Swedish physicist Oskar Klein in 1926. On March 5, 2004, NASA announced that Spirit had found hints of water history on Mars in a rock dubbed "Humphrey".

The first person to add a fifth dimension to Einstein's four was the German mathematician Theodor Kaluza in 1919. Mimi could have been subjected to pressure either through burial or impact, or may have once been a dune that was cemented into flaky layers, a process that sometimes involves the action of water. 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". Mimi's flaky appearance leads scientists to a number of hypotheses. One intriguing feature of string theory is that it predicts the number of dimensions which the universe should possess. Mimi is only one of many features in the area known as "Stone Council", but looks very different from any rock that scientists have seen at the Gusev crater site so far. Consequently, the minimum size of a string must be related to the string tension. This color image taken by the Mars Exploration Rover Spirit's panoramic camera on Sol 40 is centered on an unusually flaky rock called Mimi.

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". Following up that glorious circular brushing — it's like back-to-back homers.". Classical intuition suggests that it might shrink to a single point, but this would violate Heisenberg's uncertainty principle. In fact, when we saw virtually a complete circle, I was thrilled beyond anything I could have ever dreamed. Its tension will tend to contract it into a smaller and smaller loop. "With the docile cutting parameters we set, I didn't think that it would cut this deep. Consider a closed loop of string, left to move through space without external forces. "The RAT performed beyond our expectations," beamed Steve Gorevan, of Honeybee Robotics, New York, lead scientist for the rock abrasion tools on both rovers.

The tension of a quantum string is closely related to its size. The rock abrasion tools on both Mars Exploration Rovers were supplied by Honeybee Robotics, New York, N.Y. For example, quantum strings have tension, much like regular strings made of twine; this tension is considered a fundamental parameter of the theory. This image was taken by Spirit's panoramic camera, providing a quick visual check of the success of the grinding. 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. The hole is 2.65 millimeters (0.1 inch) deep, exposing fresh interior material of the rock for close inspection with the rover's microscopic imager and two spectrometers on the robotic arm. Nowadays, 'string theory' usually refers to the supersymmetric variant while the earlier is given its full name, 'bosonic string theory'. 6, 2004.

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 Rock Abrasion Tool on NASA's Spirit rover ground off the surface of a patch 45.5 millimeters (1.8 inches) in diameter on a rock called Adirondack during Spirit's 34th sol on Mars, Feb. 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. The round, shallow depression in this image resulted from history's first grinding of a rock on Mars. (Several meanings of the "M" have been proposed; physicists joke that the true meaning will only be chosen when the theory is finally understood.). On 6 February (Sol 33), the rover was restored to its original working condition, and science activities resumed. These discoveries sparked the second superstring revolution. After realizing what the problem was, the engineers deleted some files, and eventually reformatted the entire flash memory system.

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. Most of these files contained unneeded in-flight data. Several other ground-breaking discoveries, such as the heterotic string, were made in 1985. NASA engineers finally came to the conclusion that there were too many files on the filesystem, which was a relatively minor problem. The anomaly is cancelled due to the Green-Schwarz mechanism. The engineers indicated that they had initially believed that this was a serious problem, and as a result, performed operations that only exacerbated the minor situation. 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 flash hardware was in fact believed to be working correctly but the file management module in the software was "not robust enough" for the operations the Spirit was engaged in when the problem occurred, indicating that the problem was caused by a software bug as opposed to faulty hardware.

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. Spirit communicated successfully at 120 bits per second for nearly an hour. String theories which include fermionic vibrations are now known as superstring theories; several different kinds have been described. In this mode, the rover obeyed commands about communicating and going into sleep mode. 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. Spirit was placed in "crippled mode," operating using RAM instead of flash. While bosons are a critical ingredient of the Universe, they are not its only constituents. On 24 January the rover repair team announced that the problem was with Spirit's flash memory and the software that wrote to it.

Additionally, as the name implies, the spectrum of particles contains only bosons, particles like the photon which obey particular rules of behavior. Indications were that the cause of the reset was not always perceived by the rover's diagnostics to be the same each time. Most importantly, the theory has a fundamental instability, believed to result in the decay of space-time itself. The processor was not resetting immediately, however, with a delay of up to an hour. However, the bosonic theory has problems. The rover had also been in a processor reset loop of some type since Wednesday, in which the processor would repeatedly wake, load the flight software, and uncover a condition that would cause it to reset. Not all modern string theories use both types; some incorporate only the closed variety. This suggested difficulties with the rover's high-gain antenna.

The two types of string behave in slightly different ways, yielding two spectra. Spirit was commanded to transmit engineering data, and on 23 January sent several short low-bitrate messages before finally transmitting 73 megabits via X band to Mars Odyssey. 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. This was described as a very serious anomaly, but potentially recoverable if it was a software or memory corruption issue rather than a serious hardware failure. The scale of notes, each corresponding to a different kind of particle, is termed the "spectrum" of the theory. The next day the rover radioed a 7.8 bit/s beep, confirming that it had received a transmission from Earth but indicating that the spacecraft believed it was in a fault mode. 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. On 21 January (Sol 18), Spirit abruptly ceased communicating with mission control.

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. This, however, is only the tip of the iceberg, as this image, received on 6 January 2004, is about one eighth of a single pancam panorama and isn't stereo. 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. There are actually 12 million pixels in this image, it's 4,000 high by 3,000 wide. It is now hoped that string theory or some descendant of it will provide a fundamental understanding of the quarks themselves.). "We're seeing a panoramic mosaic of four pancam images high by three wide," said camera designer Jim Bell of Cornell. (The original need for a viable theory of hadrons has been fulfilled by quantum chromodynamics, the theory of quarks and their interactions. It is the highest resolution image ever taken on the surface of another planet.

This led to the development of bosonic string theory, which is still the version first taught to many students. To the right is the first color image of Mars taken by the panoramic camera on the Mars Exploration Rover Spirit. Schwarz and Scherk argued that string theory had failed to catch on because physicists had underestimated its scope. "Just as the ancient mariners used sextants for 'shooting the Sun,' as they called it, we were successfully able to shoot the Sun with our panorama camera, then use that information to point the antenna," said JPL's Matt Wallace, mission manger. 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. It is 9 meters (30 feet) across and about 12 meters (40 feet) north of the lander. The scientific community soon lost interest in string theory, and the standard model, with its particles and fields, remained unthreatened. NASA scientists were very interested in this crater.

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. "Sleepy Hollow," a shallow depression in the Mars ground near NASA's Spirit rover, was targeted as an early destination when the rover drove off its lander platform. By representing nuclear forces as vibrating, one-dimensional strings, these physicists showed how Euler’s function accurately described those forces. An archive of approximately weekly updates on the rover's status can be found at Spirit Update Archive (NASA/JPL site). In 1970, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind unveiled the physics beneath Euler’s strictly theoretical formula. The following paragraphs discuss the more notable findings. Veneziano applied the Euler beta function to the strong force, but no one could explain why it worked. A detailed but incomplete chronology of events and discoveries may be found in the Spirit rover timeline entry.

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. The mission received several extensions and by January, 2006 had passed 720 sols. In 1968, theoretical physicist Gabriele Veneziano was trying to understand the strong nuclear force when he made a startling discovery. The primary surface mission for Spirit was planned to last 90 sols. 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. (NASA has submitted these geographical feature names to the IAU for approval.).

String theory was originally invented to explain peculiarities of hadron (subatomic particle which experiences the strong nuclear force) behavior. On February 2, the astronauts on Columbia's final mission were further memorialized when NASA named a set of hills to the east of the landing site the Columbia Hills Complex, denoting seven peaks in that area Anderson, Brown, Chawla, Clark, Husband, McCool and Ramon. . On January 27 NASA memorialized the crew of Apollo 1 by naming three hills to the north of "Columbia Memorial Station" as the Apollo 1 Hills. String theory has also led to insight into supersymmetric gauge theories, which will be tested at the new Large Hadron Collider experiment. The MER team named the landing site "Columbia Memorial Station," in honor of the seven astronauts killed in the Space Shuttle Columbia disaster. Work on string theory has led to advances in mathematics, mainly in algebraic geometry. A panorama [2] shows a slightly rolling surface, littered with small rocks, with hills on the horizon up to 27 km away.

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. The rover, parachute, heat shield and several bounce marks are visible in a picture taken by Mars Global Surveyor. 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. Spirit landed in Gusev crater about 10 km from the center of the target ellipse at latitude 14.5718° S ± 30 meters, longitude 175.4785° E ± 0.5 meters [1]. 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. Spirit was named by a winning entry in a student essay competiton—see Naming of Spirit and Opportunity.

Interest in string theory is driven largely by the hope that it will prove to be a theory of everything. Her twin Opportunity landed successfully on Mars on January 24, 2004. Study of string theories has revealed that they require not just strings but other objects, variously including points, membranes, and higher-dimensional objects. She successfully landed on Mars at 04:35 Ground UTC on January 4, 2004 and has operated successfully for over one full Martian year and two Earth years. For this reason, string theories are able to avoid problems associated with the presence of pointlike particles in a physical theory. Spirit (official designation: MER-A) is the first of the two Mars Exploration Rover missions. 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.