What is 11th dimension? I mean why it is 11 not any other number .?

Question

I will be obliged if you will tell me about related topics like string theory. Don't attempt for any disposal of gabages in the answer if you don't know

Answer 1

What I know is that there are 3 dimensions that we can see - lenght, breadth and height.
One dimension we can feel - Time
6 dimensions which we cannot see or feel but they are present in subatomic level - in string level
The last dimension is to hold these 6 dimension together.
Hence there are 11 dimensions in all.

I have explained this answer in the most simplest of the languages. I have not put in any techinical data for easier understanding.

Answer 2

It's my understanding that string theory require a minimum of 11 (some say 10) dimensions to make sense. There is nothing in string theory that prevents more than 11 dimensions.

Answer 3

A lot of the physical universe just doesn't work out mathematically. Newtonian and Einsteinian physics, for example, are both accurate in their domains, but overall they disagree with each other in a three or four dimensional universe. In a 10, 11, or 26 dimensional universe, suddenly the numbers start making sense, even if the concept threatens to make out heads explode. Superstring theory seems to hold the answers, but as I'm no expert on it, I suggest you read about it in the following sources:

Answer 4

It took 11 dimensions to get satisfactory results from the math of string theory. The "satisfactory results" are the ability to describe the characteristics of weak, strong, electro-magnetic, and gravity forces under one theory. In other words, it took 11 dimensions to unify the four fundamental forces of this universe.

Other theories tried other dimensions; in some way or other, they failed to unify the four forces. Einstein used four dimensions, for example, but was never able to include gravity as one of the four forces in his theories. He died trying, but failed.

Answer 5

Mathematical dimensions, after the first 4 are different ways to define an object/point I.e. Weight, height color...nothing special.

Answer 6

It is 11 because string theory only works if it is.

Answer 7

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 point-like particles in theories of physics, in particular the problem of defining a sensible quantum theory of gravity. Studies of string theories have revealed that they predict not just strings, but also higher-dimensional objects.

The basic idea behind all string theories is that the fundamental constituents of reality are strings of extremely small scale (possibly Planck length, about 10-35 m) which vibrate at specific resonant frequencies. Thus, any particle should be thought of as a tiny vibrating object, rather than as a point. This object can vibrate in different modes (just like a guitar string can produce different notes), with every mode appearing as a different particle (electron, photon etc.). Strings can split and combine, which would appear as particles emitting and absorbing other particles, presumably giving rise to the known interactions between particles.

In addition to strings, string theories also include objects of higher dimensions, such as D-branes and NS-branes. Furthermore, all string theories predict the existence of degrees of freedom which are usually described as extra dimensions. String theory is thought to include some 10, 11 or 26 dimensions, depending on the specific theory and on the point of view.

Interest in string theory is driven largely by the hope that it will prove to be a consistent theory of quantum gravity or even a theory of everything. It can also naturally describe interactions similar to electromagnetism and the other forces of nature. Superstring theories include fermions, the building blocks of matter, and incorporate supersymmetry, a conjectured (but unobserved) symmetry of nature. It is not yet known whether string theory will be able to describe a universe with the precise collection of forces and particles that is observed, nor how much freedom the theory allows to choose those details.

String theory as a whole has not yet made falsifiable predictions that would allow it to be experimentally tested, though various planned observations and experiments could confirm some essential aspects of the theory, such as supersymmetry and extra dimensions. In addition, the full theory is not yet understood. For example, the theory does not yet have a satisfactory definition outside of perturbation theory; the quantum mechanics of branes (higher dimensional objects than strings) is not understood; the behavior of string theory in cosmological settings (time-dependent backgrounds) is still being worked out; finally, the principle by which string theory selects its vacuum state is a hotly contested topic

String theory is thought to be a certain limit of another, more profound theory - M-theory - which is only partly defined and is not well understood.

A key consequence of the theory is that there is no obvious operational way to probe distances shorter than the string length.

String theory was originally invented and explored, during the late 1960s and early 1970s, to explain some peculiarities of the behavior of hadrons (subatomic particles such as the proton and neutron which experience the strong nuclear force). In particular, Yoichiro Nambu (and later Lenny Susskind and Holger Nielsen) realized in 1970 that the dual resonance model of strong interactions could be explained by a quantum mechanical model of strings. This approach was abandoned as an alternative theory, quantum chromodynamics, gained experimental support.

During the mid-1970s it was discovered that the same mathematical formalism can be used to describe a theory of quantum gravity. This led to the development of bosonic string theory, which is still the version first taught to many students.

Between 1984 and 1986, physicists realized that string theory could describe all elementary particles and the interactions between them, and hundreds of them started to work on string theory as the most promising idea to unify theories of physics. This is known as the first superstring revolution.

In the 1990s, Edward Witten and others found strong evidence that the different superstring theories were different limits of a new 11-dimensional theory called M-theory. These discoveries sparked the second superstring revolution.

In the mid 1990s, Joseph Polchinski discovered that the theory requires the inclusion of higher-dimensional objects, called D-branes. These added an additional rich mathematical structure to the theory, and opened many possibilities for constructing realistic cosmological models in the theory.

In 1997 Juan Maldacena conjectured a relationship between string theory and a gauge theory called N=4 supersymmetric Yang-Mills theory. This conjecture, called the AdS/CFT correspondence has generated a great deal of interest in the field and is now well accepted. It is a concrete realization of the holographic principle, which has far-reaching implications for black holes, locality and information in physics, as well as the nature of the gravitational interaction. Through this relationship, string theory may be related in the future to quantum chromodynamics and lead, eventually, to a better understanding of the behavior of hadrons, thus returning to its original goal.

Most recently, the discovery of the string theory landscape, which suggests that string theory has an exponentially large number of inequivalent vacua, has led to much discussion of what string theory might eventually be expected to predict, and how cosmology can be incorporated into the theory.

String theory is formulated in terms of an action principle, either the Nambu-Goto action or the Polyakov action, which describes how strings move through space and time. Like springs, the strings want to contract to minimize their potential energy, but conservation of energy prevents them from disappearing, and instead they oscillate. By applying the ideas of quantum mechanics to strings it is possible to deduce the different vibrational modes of strings, and that each vibrational state appears to be a different particle. The mass of each particle, and the fashion with which it can interact, are determined by the way the string vibrates — the string can vibrate in many different modes, just like a guitar string can produce different notes. The different modes, each corresponding to a different kind of particle, make up the "spectrum" of the theory. Strings can split and combine, which would appear as particles emitting and absorbing other particles, presumably giving rise to the known interactions between particles.

String theory includes 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 different spectra. For example, in most string theories, one of the closed string modes is the graviton, and one of the open string modes is the photon. Because the two ends of an open string can always meet and connect, forming a closed string, there are no string theories without closed strings.

The earliest string model - the bosonic string, which incorporated only bosons, describe - in low enough energies - a quantum gravity theory, which also includes (if open strings are incorporated as well) gauge fields such as the photon (or, more generally, any Yang-Mills theory). However, this model has problems. Most importantly, the theory has a fundamental instability, believed to result in the decay (at least partially) of space-time itself. Additionally, as the name implies, the spectrum of particles contains only bosons, particles which, like the photon, obey particular rules of behavior. Roughly speaking, bosons are the constituents of radiation, but not of matter, which is made of fermions. Investigating how a string theory may include fermions in its spectrum led to the invention of supersymmetry, a mathematical relation between bosons and fermions. String theories which include fermionic vibrations are now known as superstring theories; several different kinds have been described, but all are now thought to be different limits of one theory (the M-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 is related to the string tension.

Imagine a point-like particle. If we draw a graph which depicts the progress of the particle as time passes by, the particle will draw a line in space-time. This line is called the particle's worldline. Now imagine a similar graph depicting the progress of a string as time passes by; the string (a one-dimensional object - a small line - by itself) will draw a surface (a two-dimensional manifold), known as the worldsheet. The different string modes (representing different particles, such as photon or graviton) are surface waves on this manifold.

A closed string looks like a small loop, so its worldsheet will look like a pipe, or - more generally - as a Riemannian manifold (a two-dimensional oriented surface) with no boundaries (i.e. no edge). An open string looks like a short line, so its worldsheet will look like a strip, or - more generally - as a Riemannian manifold with a boundary.

Strings can split and connect. This is reflected by the form of their worldsheet (more accurately, by its topology). For example, if a closed string splits, its worldsheet will look like a single pipe splitting (or connected) to two pipes (see drawing at the top of this page). If a closed string splits and its two parts later reconnect, its worldsheet will look like a single pipe splitting to two and then reconnecting, which also looks like torus connected to two pipes (one representing the ingoing string, and the other - the outgoing one). An open string doing the same thing will have its worldsheet looking like a ring connected to two strips.

Note that the process of a string splitting (or strings connecting) is a global process of the worldsheet, not a local one: locally, the worldsheet looks the same everywhere and it is not possible to determine a single point on the worldsheet where the splitting occurs. Therefore these processes are an integral part of the theory, and are described by the same dynamics that controls the string modes.

In some string theories (namely closed strings in Type I and string in some version of the bosonic string), strings can split and reconnect in an opposite orientation (as in a Möbius strip or a Klein bottle). These theories are called unoriented. Formally, the worldsheet in these theories is an unoriented surface.

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 general relativity was 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.

Unlike general relativity, string theory allows one to compute the number of spacetime dimensions from first principles. Technically, this happens because for a different number of dimensions, the theory has a gauge anomaly. This can be understood by noting that in a consistent theory which includes a photon (technically, a particle carrying a force related to an unbroken gauge symmetry), it must be massless. The mass of the photon which is predicted by string theory depends on the energy of the string mode which represents the photon. This energy includes a contribution from Casimir effect, namely from quantum fluctuations in the string. The size of this contribution depends on the number of dimensions since for a larger number of dimensions, there are more possible fluctuations in the string position. Therefore, the photon will be massless — and the theory consistent — only for a particular number of dimensions.

When the calculation is done, the universe's dimensionality is not four as one may expect (three axes of space and one of time). 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. However, these results appear to contradict the observed four dimensional space-time.

Two different ways have been proposed to resolve this apparent contradiction. The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable in our phenomenal experience. In order to retain the supersymmetric properties of string theory, these spaces must be very special. The 6-dimensional model's resolution is achieved with Calabi-Yau spaces. In 7 dimensions, they are termed G2 manifolds. 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. Indeed, think of a ball small enough to enter the hose - but not too small. Throwing such a ball inside the hose, the ball would move more or less in one dimension; in any experiment we make by throwing such balls in the hose, the only important movement will be one-dimensional, that is, along the hose. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions (and a fly flying in it would move in three dimensions). This "extra dimension" is only visible within a relatively close range to the hose, or if one "throws in" small enough objects. Similarly, the extra compact dimensions are only visible at extremely small distances, or by experimenting with particles with extremely small wave lengths (of the order of the compact dimension's radius), which in quantum mechanics means very high energies (see wave-particle duality).

Another possibility is that we are stuck in a 3+1 dimensional (i.e. three spatial dimensions plus the time dimension) subspace of the full universe. This subspace is supposed to be a D-brane, hence this is known as a braneworld theory. Many people believe that some combination of the two ideas – compactification and branes – will ultimately yield the most realistic theory.

In either case, gravity acting in the hidden dimensions affects other non-gravitational forces such as electromagnetism. In fact, Kaluza and Klein's early work demonstrated that general relativity with five large dimensions and one small dimension actually predicts the existence of electromagnetism. However, because of the nature of Calabi-Yau manifolds, no new forces appear from the small dimensions, but their shape has a profound effect on how the forces between the strings appear in our four dimensional universe. 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. It is also possible to extract information regarding the hidden dimensions by precision tests of gravity, but so far these have only put upper limitations on the size of such hidden dimensions.

String theory remains to be verified. No version of string theory has yet made a prediction which differs from those made by other theories in a way that has been and can be checked experimentally. In this sense, string theory is still in a "larval stage": it is properly a mathematical theory but is not yet a physical theory. It possesses many features of mathematical interest and 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 have asked if it even deserves to be called a scientific theory: it is not yet falsifiable in the sense of Popper.

For example, while supersymmetry is now seen as a vital ingredient of string theory, supersymmetric models with no obvious connection to string theory are also studied. Therefore, if supersymmetry were detected at the Large Hadron Collider it would not be seen as a direct confirmation of the theory. More importantly, if supersymmetry were not detected, there are vacua in string theory in which supersymmetry would only be seen at much higher energies, so its absence would not falsify string theory. By contrast, 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.

One hope for testing string theory is that a better understanding of how string theory deals with singularities and time-dependent backgrounds would allow physicists to understand the predictions of string theory for the big bang, and see how cosmic inflation can be incorporated into the theory. This has led to some deep theoretical progress, and some early models of string cosmology, such as brane inflation, trans-Planckian effects, string gas cosmology and the ekpyrotic universe, but fundamental progress must be made before it is understood what, if any, distinctive predictions the theory makes for cosmology. A recent popular suggestion is that brane inflation may produce cosmic strings which could be observed through their gravitational radiation, or lensing of distant galaxies or the cosmic microwave background.

On a more mathematical level, another problem is that, like many quantum field theories, 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 non-perturbative definition of the theory is still lacking.

Another problem is that the vacuum structure of the theory, called the string theory landscape, is not well understood. As string theory is presently understood, it appears to contain an exponentially large number of distinct vacua, perhaps 10500 or more. Each of these corresponds to a different universe, with a different collection of particles and forces. What principle, if any, can be used to select among these vacua is not widely agreed upon. While there are no known continuous parameters in the theory, there is a very large discretuum (coined in contradistinction to continuum) of possible universes, which may be radically different from each other. Some physicists believe this is a benefit of the theory, as it may allow a natural anthropic explanation of the observed values of physical constants, in particular the small value of the cosmological constant. However, such explanations are not usually regarded as scientific in the Popperian sense.