Domain Wall (string Theory)
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Domain Wall (string Theory)
In string theory, a domain wall is a theoretical (d−1)-dimensional singularity. A domain wall is meant to represent an object of codimension one embedded into space (a defect in space localized in one spatial dimension). For example, D8-branes are domain walls in type II string theory. In M-theory, the existence of Horava–Witten domain walls, "ends of the world" that carry an E8 gauge theory, is important for various relations between superstring theory and M-theory. If domain walls exist, their interactions are hypothesized to emit gravitational waves that would be detectable by LIGO and similar experiments. See also * Topological defect * Cosmic string *Membrane (M-theory) In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions. Branes are dynamical objects which can propagate through spacetime accordi ... * Gravitational singularity References ...
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String Theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. String theory has contributed a number of advances to mathematical physics, which have been applied to a variety of problems in black hole physics, early universe cosmology, nuclear physics, and conde ...
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Gravitational Waves
Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that Wave propagation, propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as waves similar to Electromagnetic radiation, electromagnetic waves but the gravitational equivalent. Gravitational waves were later #History, predicted in 1916 by Albert Einstein on the basis of his General relativity, general theory of relativity as ripples in spacetime. Later he refused to accept gravitational waves. Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, since that law is predicated on the assumption that Speed of gravity, physical interactions propagate instantaneously (at infinite ...
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Large-scale Structure Of The Cosmos
The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. There may be 2 trillion galaxies in the observable universe, although that number was reduced in 2021 to only several hundred billion based on data from '' New Horizons''. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe is a spherical region centered on the observer and is unique for every unique observational position. The word ''observable'' in this sense does not refer to the capability of modern technology to detect light or other information from an object, or whether there is anything to be detected. It refers to the ...
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Hypothetical Astronomical Objects
Various unknown astronomical objects have been hypothesized throughout recorded history. For example, in the 5th century BCE, the philosopher Philolaus defined a hypothetical astronomical object which he called the "Central Fire", around which he proposed other celestial bodies (including the Sun) moved.Marco Ceccarelli, ''Distinguished Figures in Mechanism and Machine Science'' (2007), p. 124. Types of hypothetical astronomical objects Hypothetical astronomical objects have been speculated to exist both inside and outside of the Solar System, and speculation has included different kinds of stars, planets, and other astronomical objects. * For hypothetical astronomical objects in the Solar System, see: List of hypothetical Solar System objects * For hypothetical stars, see: Hypothetical star * For hypothetical brown dwarfs, see: List of brown dwarfs * For hypothetical black holes, see: Hypothetical black hole * For extrasolar moons, all of which are currently hypothetical, see ...
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Membrane (M-theory)
In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions. Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge. Mathematically, branes can be represented within categories, and are studied in pure mathematics for insight into homological mirror symmetry and noncommutative geometry. ''p''-branes A point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one. In addition to point particles and strings, it is possible to consider higher-dimensional branes. A ''p''-dimensional brane is generally called "''p''-brane". The term "''p''-brane" was coined by M. J. Duff ''et al.'' in 1988; "brane" comes from the word "membrane" which refers to a two-dimensional brane. A ''p''-brane sweeps out a ...
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Cosmic String
Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry-breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simply connected. Their existence was first contemplated by the theoretical physicist Tom Kibble in the 1970s. The formation of cosmic strings is somewhat analogous to the imperfections that form between crystal grains in solidifying liquids, or the cracks that form when water freezes into ice. The phase transitions leading to the production of cosmic strings are likely to have occurred during the earliest moments of the universe's evolution, just after cosmological inflation, and are a fairly generic prediction in both quantum field theory and string theory models of the early universe. Theories containing cosmic strings In string theory, the role of cosmic strings can be played by the fundamental strings (or F-strings) themselves that defin ...
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Topological Defect
A topological soliton occurs when two adjoining structures or spaces are in some way "out of phase" with each other in ways that make a seamless transition between them impossible. One of the simplest and most commonplace examples of a topological soliton occurs in old-fashioned coiled telephone handset cords, which are usually coiled clockwise. Years of picking up the handset can end up coiling parts of the cord in the opposite counterclockwise direction, and when this happens there will be a distinctive larger loop that separates the two directions of coiling. This odd looking transition loop, which is neither clockwise nor counterclockwise, is an excellent example of a topological soliton. No matter how complex the context, anything that qualifies as a topological soliton must at some level exhibit this same simple issue of reconciliation seen in the twisted phone cord example. Topological solitons arise with ease when creating the crystalline semiconductors used in modern elect ...
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LIGO
The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Two large observatories were built in the United States with the aim of detecting gravitational waves by laser interferometry. These observatories use mirrors spaced four kilometers apart which are capable of detecting a change of less than one ten-thousandth the charge diameter of a proton. (that is, to Proxima Centauri at ). The initial LIGO observatories were funded by the United States National Science Foundation (NSF) and were conceived, built and are operated by Caltech and MIT. They collected data from 2002 to 2010 but no gravitational waves were detected. The Advanced LIGO Project to enhance the original LIGO detectors began in 2008 and continues to be supported by the NSF, with important contributions from the United Kingdom's Science ...
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Superstring Theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. 'Superstring theory' is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that accounts for both fermions and bosons and incorporates supersymmetry to model gravity. Since the second superstring revolution, the five superstring theories are regarded as different limits of a single theory tentatively called M-theory. Background The deepest problem in theoretical physics is harmonizing the theory of general relativity, which describes gravitation and applies to large-scale structures (stars, galaxies, super clusters), with quantum mechanics, which describes the other three fundamental forces acting on the atomic scale. The development of a quantum field theory of a force invariably results in infinite possibilities. Physicists developed ...
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Gravitational Singularity
A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravitational field, gravity is so intense that spacetime itself breaks down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where" or "when". Gravitational singularities exist at a junction between general relativity and quantum mechanics; therefore, the properties of the singularity cannot be described without an established theory of quantum gravity. Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of gravity, remains a difficult problem. A singularity in general relativity can be defined by the Curvature invariant (general relativity), scalar invariant Curvature of Riemannian manifolds, curvature becoming Infinity, infinite or, better, by a Geodesics in general relativity, geodesic being Geodesic manifold#Non-examples, incom ...
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Gauge Theory
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups). The term ''gauge'' refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called ''gauge transformations'', form a Lie group—referred to as the ''symmetry group'' or the ''gauge group'' of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the ''gauge field''. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called ''gauge invariance''). When such a theory is quantized, the quanta of the gauge fields are called '' gauge bosons ...
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E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8. The designation E8 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled A''n'', B''n'', C''n'', D''n'', and five exceptional cases labeled G2, F4, E6, E7, and E8. The E8 algebra is the largest and most complicated of these exceptional cases. Basic description The Lie group E8 has dimension 248. Its rank, which is the dimension of its maximal torus, is eight. Therefore, the vectors of the root system are in eight-dimensional Euclidean space: they are described explicitly later in this article. The Weyl group of E8, which is the group of symmetries of the maximal torus which are induced by conjugations in the whole group, has order 2357 = . The compact group E8 is unique ...
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