The Kaluza-Klein theory is striking because it has a particularly elegant presentation in terms of geometry. In a certain sense, it looks just like ordinary gravity in free space, except that it is phrased in five dimensions instead of four. Kaluza-Klein theory - The Einstein equations. The equations governing ordinary gravity in free space can be obtained from an action, by applying the variational principle to a certain action. Let M be a (pseudo-)Riemannian manifold, which may be taken as the spa ...

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Kaluza-Klein theory, Kaluza-Klein theory - Overview, Kaluza-Klein theory - Space-Time-Matter theory, Kaluza-Klein theory - Geometric interpretation, Kaluza-Klein theory - The Einstein equations, Kaluza-Klein theory - The Maxwell equations, Kaluza-Klein theory - The Kaluza-Klein geometry, Kaluza-Klein theory - Commentary and generalizations

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Kaluza-Klein theory, Kaluza-Klein theory - Overview, Kaluza-Klein theory - Space-Time-Matter theory, Kaluza-Klein theory - Geometric interpretation, Kaluza-Klein theory - The Einstein equations, Kaluza-Klein theory - The Maxwell equations, Kaluza-Klein theory - The Kaluza-Klein geometry, Kaluza-Klein theory - Commentary and generalizations

Read more here: » Kaluza-Klein theory: Encyclopedia II - Kaluza-Klein theory - Overview

One particular variant of Kaluza-Klein theory is Space-Time-Matter theory or induced matter theory, chiefly promogulated by Paul Wesson. In this version of the theory, it is noted that solutions to the equation RAB = 0 with RAB the five-dimensional Ricci curvature, may be re-expressed so that in four dimensions, these solutions satisfy Einstein's equations See also:

Kaluza-Klein theory, Kaluza-Klein theory - Overview, Kaluza-Klein theory - Space-Time-Matter theory, Kaluza-Klein theory - Geometric interpretation, Kaluza-Klein theory - The Einstein equations, Kaluza-Klein theory - The Maxwell equations, Kaluza-Klein theory - The Kaluza-Klein geometry, Kaluza-Klein theory - Commentary and generalizations

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Brane cosmology is a protoscience motivated by, but not rigorously derived from, superstring theory and M-theory. The idea is to solve problems in cosmology using speculative particle physics theories and in turn use cosmological observations to motivate ideas in string theory. The central idea is that our visible, four-dimensional universe is entirely restricted to a brane inside a higher-dimensional space, called the bulk. The additional dimensions may be taken to be compact, in which case the observed universe contains the e ...

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In physics, compactification plays an important part in string theory. In string theory, compactification refers to "curling up" the extra dimensions (six in the superstring theory), usually on Calabi-Yau spaces or on orbifolds. The mechanism behind this type of compactification is described by the Kaluza-Klein theory. See also compact dimension. The formulation of more precise versions of the meaning of compactification in this context has been promoted by discoveries such as the mysterious duality.

In common usage, the dimensions (from Latin "measured out") of an object are the parameters or measurements required to define its shape and size, that is, usually, its height, width, and length. In mathematics, the dimensions of a space are the parameters required to describe a particular object in this space. The dimension of a space is the number of these parameters. For example, locating a city on the Earth requires two parameters: longitude and latitude; the corresponding space has therefore two dimensions an ...

Including:

• Dimension - Physical dimensions
• Dimension - Spatial dimensions
• Dimension - Time
• Dimension - Additional dimensions
• Dimension - Units
• Dimension - Mathematical dimensions
• Dimension - Hamel dimension
• Dimension - Manifolds
• Dimension - Lebesgue covering dimension
• Dimension - Inductive dimension
• Dimension - Hausdorff dimension
• Dimension - Hilbert spaces
• Dimension - Krull dimension of commutative rings
• Dimension - Science fiction
• Dimension - Anaglyph
• Dimension - 3-D film
• Dimension - Modern 3-D films
• Dimension - More dimensions
• Dimension - Degrees of freedom
• Dimension - Other

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Main article: Einstein field equation Newtonian gravitation is now superseded by Einstein's theory of general relativity, in which gravitation is thought of as being due to a curved spacetime, caused by masses. The Einstein field equation - which describes how this curvature is produced by masses - is: ...

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Field equation, Field equation - Newton's theory of universal gravitation, Field equation - Laplace's equation, Field equation - Poisson's equation, Field equation - Einstein's field equation, Field equation - Maxwell's equations, Field equation - Kaluza-Klein field equations

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Main article: Maxwell's equations The electromagnetic force is best described by Maxwell's theory of electromagnetism. The field equations of classical electromagnetism are Maxwell's equations which describe how electromagnetic fields are produced from charged particles and are written in the framework of special relativity (which was devised to consistently describe ...

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Field equation, Field equation - Newton's theory of universal gravitation, Field equation - Laplace's equation, Field equation - Poisson's equation, Field equation - Einstein's field equation, Field equation - Maxwell's equations, Field equation - Kaluza-Klein field equations

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Supergravity was initially proposed as a four-dimensional theory in 1976, but was quickly expanded to Kaluza-Klein Supergravity by merging it with Kaluza-Klein theory. In this form, the 11-dimensional theory generated considerable excitement as the first potential candidate for the Theory of Everything. This excitement was built on four pillars: Werner Nahm showed that 11 dimensions was the largest number of dimensions consistent with a single graviton, and that a theory with more dimensions would also have particles with ...

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Supergravity, Supergravity - History, Supergravity - Failings of the 11-dimensional model support for 10 dimensions, Supergravity - Relation to superstrings

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The term 'string theory' properly refers to both the 26-dimensional bosonic string theories and to the 10-dimensional superstring theories created 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, qua ...

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String theory, String theory - History, String theory - Basic properties, String theory - Dualities, String theory - Extra dimensions, String theory - Problems, String theory - Popular culture, String theory - References and further reading, String theory - Footnote, String theory - Popular books and articles, String theory - Textbooks, String theory - External links

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The term 'string theory' properly refers to both the 26-dimensional bosonic string theories and to the 10-dimensional superstring theories created 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, qua ...

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String theory, String theory - History, String theory - Basic properties, String theory - Dualities, String theory - Extra dimensions, String theory - Problems, String theory - References and further reading, String theory - Footnote, String theory - Popular books and articles, String theory - Textbooks, String theory - External links

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This section requires some familiarity with classical or quantum field theory, and the use of Lagrangians. Definitions in this section: gauge group, gauge field, interaction Lagrangian, gauge boson Gauge theory - An example: Scalar On gauge theory. The following illustrates how local gauge invariance can be "derived" heuristically starting from global symmetry properties, and how it leads to an interactio ...

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Gauge theory, Gauge theory - A brief history, Gauge theory - A simple gauge symmetry example from electrodynamics, Gauge theory - Classical gauge theory, Gauge theory - An example: Scalar On gauge theory, Gauge theory - The Lagrangian for the gauge field, Gauge theory - A simple example: Electrodynamics, Gauge theory - Mathematical formalism, Gauge theory - Quantization of gauge theories, Gauge theory - Methods and aims, Gauge theory - Anomalies

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This section requires some familiarity with classical or quantum field theory, and the use of Lagrangians. Definitions in this section: gauge group, gauge field, interaction Lagrangian, gauge boson Gauge theory - An example: Scalar On gauge theory. The following illustrates how local gauge invariance can be "motivated" heuristically starting from global symmetry properties, and how it leads to an interactio ...

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Gauge theory, Gauge theory - A brief history, Gauge theory - A simple gauge symmetry example from electrodynamics, Gauge theory - Classical gauge theory, Gauge theory - An example: Scalar On gauge theory, Gauge theory - The Yang-Mills Lagrangian for the gauge field, Gauge theory - A simple example: Electrodynamics, Gauge theory - Mathematical formalism, Gauge theory - Quantization of gauge theories, Gauge theory - Methods and aims, Gauge theory - Anomalies

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The book The Elegant Universe by Brian Greene was adapted into a three-hour documentary for Nova. String theory is also a series of books based in the Star Trek: Voyager universe. ...

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String theory, String theory - History, String theory - Basic properties, String theory - Dualities, String theory - Extra dimensions, String theory - Problems, String theory - Popular culture, String theory - References and further reading, String theory - Footnote, String theory - Popular books and articles, String theory - Textbooks, String theory - External links

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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 nu ...

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String theory, String theory - History, String theory - Basic properties, String theory - Dualities, String theory - Extra dimensions, String theory - Problems, String theory - Popular culture, String theory - References and further reading, String theory - Footnote, String theory - Popular books and articles, String theory - Textbooks, String theory - External links

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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 fu ...

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String theory, String theory - History, String theory - Basic properties, String theory - Dualities, String theory - Extra dimensions, String theory - Problems, String theory - Popular culture, String theory - References and further reading, String theory - Footnote, String theory - Popular books and articles, String theory - Textbooks, String theory - External links

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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 nu ...

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String theory, String theory - History, String theory - Basic properties, String theory - Dualities, String theory - Extra dimensions, String theory - Problems, String theory - References and further reading, String theory - Footnote, String theory - Popular books and articles, String theory - Textbooks, String theory - External links

Read more here: » String theory: Encyclopedia II - String theory - History

The physical dimensions are the parameters required to answer to the question where and when happened or will happen some event; for instance: When did Napoleon die? — On the 5 May 1821 at Saint Helena (15°56′ S 5°42′ W). They play a fundamental role in our perception of the world around us. According to Immanuel Kant, we actually do not perceive them but they form the frame in which we perceive events; they form the a priori background in which events are perceived. ...

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Dimension, Dimension - Physical dimensions, Dimension - Spatial dimensions, Dimension - Time, Dimension - Additional dimensions, Dimension - Units, Dimension - Mathematical dimensions, Dimension - Hamel dimension, Dimension - Manifolds, Dimension - Lebesgue covering dimension, Dimension - Inductive dimension, Dimension - Hausdorff dimension, Dimension - Hilbert spaces, Dimension - Krull dimension of commutative rings, Dimension - Science fiction, Dimension - Anaglyph, Dimension - 3-D film, Dimension - Modern 3-D films, Dimension - More dimensions, Dimension - Degrees of freedom, Dimension - Other

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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 fu ...

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String theory, String theory - History, String theory - Basic properties, String theory - Dualities, String theory - Extra dimensions, String theory - Problems, String theory - References and further reading, String theory - Footnote, String theory - Popular books and articles, String theory - Textbooks, String theory - External links

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The definition of electrical ground in an electric circuit is an example of a gauge symmetry; when the voltages across all points in a circuit are raised by the same voltage, the circuit would still operate identically; as the voltage differences in the circuit are unchanged. A common illustration of this fact is the sight of a bird perched on a high voltage power line without electrocution, as the bird is insulated from ground. This is called a global gauge symmetryTrefil,1983See also:

Gauge theory, Gauge theory - A brief history, Gauge theory - A simple gauge symmetry example from electrodynamics, Gauge theory - Classical gauge theory, Gauge theory - An example: Scalar On gauge theory, Gauge theory - The Lagrangian for the gauge field, Gauge theory - A simple example: Electrodynamics, Gauge theory - Mathematical formalism, Gauge theory - Quantization of gauge theories, Gauge theory - Methods and aims, Gauge theory - Anomalies

Read more here: » Gauge theory: Encyclopedia II - Gauge theory - A simple gauge symmetry example from electrodynamics