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Tipler Cylinder
A Tipler cylinder, also called a Tipler time machine, is a hypothetical object theorized to be a potential mode of time travel—although results have shown that a Tipler cylinder could only allow time travel if its length were infinite or with the existence of negative energy. Discovery The Tipler cylinder was discovered as a solution to the equations of general relativity by Willem Jacob van Stockum in 1936 and Kornel Lanczos in 1924, but not recognized as allowing closed timelike curves until an analysis by Frank Tipler Available in GIF format here: page123
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Hypothetical
A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous observations that cannot satisfactorily be explained with the available scientific theories. Even though the words "hypothesis" and "theory" are often used interchangeably, a scientific hypothesis is not the same as a scientific theory. A working hypothesis is a provisionally accepted hypothesis proposed for further research in a process beginning with an educated guess or thought. A different meaning of the term ''hypothesis'' is used in formal logic, to denote the antecedent of a proposition; thus in the proposition "If ''P'', then ''Q''", ''P'' denotes the hypothesis (or antecedent); ''Q'' can be called a consequent. ''P'' is the assumption in a (possibly counterfactual) ''What If'' question. The adjective ''hypothetical'', meaning "ha ...
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Pseudo-Riemannian Manifold
In differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed. Every tangent space of a pseudo-Riemannian manifold is a pseudo-Euclidean vector space. A special case used in general relativity is a four-dimensional Lorentzian manifold for modeling spacetime, where tangent vectors can be classified as timelike, null, and spacelike. Introduction Manifolds In differential geometry, a differentiable manifold is a space which is locally similar to a Euclidean space. In an ''n''-dimensional Euclidean space any point can be specified by ''n'' real numbers. These are called the coordinates of the point. An ''n''-dimensional differentiable manifold is a generalisation of ''n''-dimensional Euclidean space. In a manifold it may only be possibl ...
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Steins;Gate
''Steins;Gate'' is a 2009 science fiction visual novel game developed by 5pb. and Nitroplus. It is the second game in the ''Science Adventure'' series, following ''Chaos;Head''. The story follows a group of students as they discover and develop technology that gives them the means to change the past. The gameplay in ''Steins;Gate'' includes branching scenarios with courses of interaction. ''Steins;Gate'' was released for the Xbox 360 on October 15, 2009. The game was ported to Windows on August 26, 2010, PlayStation Portable on June 23, 2011, iOS on August 25, 2011, PlayStation 3 on May 24, 2012, PlayStation Vita on March 14, 2013, and Android on June 27, 2013. The game is described by the development team as a . JAST USA released the PC version in North America on March 31, 2014, both digitally and as a physical collector's edition, while PQube released the PS3 and Vita versions in North America and Europe in 2015. Additionally, the iOS version was released in English on Sept ...
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Cauchy Horizon
In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem (a particular boundary value problem of the theory of partial differential equations). One side of the horizon contains closed space-like geodesics and the other side contains closed time-like geodesics. The concept is named after Augustin-Louis Cauchy. Under the averaged weak energy condition (AWEC), Cauchy horizons are inherently unstable. However, cases of AWEC violation, such as the Casimir effect caused by periodic boundary conditions, do exist, and since the region of spacetime inside the Cauchy horizon has closed timelike curves it is subject to periodic boundary conditions. If the spacetime inside the Cauchy horizon violates AWEC, then the horizon becomes stable and frequency boosting effects would be canceled out by the tendency of the spacetime to act as a divergent lens. Were this conjecture to be shown empirically true, it would provide a counter-example to the str ...
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Quantum Gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, such as neutron stars. Three of the four fundamental forces of physics are described within the framework of quantum mechanics and quantum field theory. The current understanding of the fourth force, gravity, is based on Albert Einstein's general theory of relativity, which is formulated within the entirely different framework of classical physics. However, that description is incomplete: describing the gravitational field of a black hole in the general theory of relativity leads physical quantities, such as the spacetime curvature, to diverge at the center of the black hole. This signals the breakdown of the general theory of relativity and the need for a theory that ...
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Chronology Protection Conjecture
The chronology protection conjecture is a hypothesis first proposed by Stephen Hawking that laws of physics beyond those of standard general relativity prevent time travel on all but microscopic scales - even when the latter theory states that it should be possible (such as in scenarios where faster than light travel is allowed). The permissibility of time travel is represented mathematically by the existence of closed timelike curves in some solutions to the field equations of general relativity. The chronology protection conjecture should be distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting the causal violation (also known as chronology violation). Etymology In a 1992 paper, Hawking uses the metaphorical device of a "Chronology Protection Agency" as a personification of the aspects of physics that make time travel impossible at macroscopic scales, thus apparently ...
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Exotic Matter
There are several proposed types of exotic matter: * Hypothetical particles and states of matter that have "exotic" physical properties that would violate known laws of physics, such as a particle having a negative mass. * Hypothetical particles and states of matter that have not yet been encountered, but whose properties would be within the realm of mainstream physics if found to exist. * Several particles whose existence has been experimentally confirmed that are conjectured to be exotic hadrons and within the Standard Model. * States of matter that are not commonly encountered, such as Bose–Einstein condensates, fermionic condensates, nuclear matter, quantum spin liquid, string-net liquid, supercritical fluid, color-glass condensate, quark–gluon plasma, Rydberg matter, Rydberg polaron, photonic matter, and time crystal but whose properties are entirely within the realm of mainstream physics. * Forms of matter that are poorly understood, such as dark matter and mirror ma ...
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Weak Energy Condition
In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is a generalization of the statement "the energy density of a region of space cannot be negative" in a relativistically-phrased mathematical formulation. There are multiple possible alternative ways to express such a condition such that can be applied to the matter content of the theory. The hope is then that any reasonable matter theory will satisfy this condition or at least will preserve the condition if it is satisfied by the starting conditions. Energy conditions are not physical constraints , but are rather mathematically imposed boundary conditions that attempt to capture a belief that "energy should be positive". Many energy conditions are known to not correspond to physical reality—for example, the observable effects of dark energy are well-known to violate the strong energy condition. In general relativity, energy conditions are often used (and required) i ...
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Dust Solution
In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has ''positive mass density'' but ''vanishing pressure''. Dust solutions are an important special case of fluid solutions in general relativity. Dust model A pressureless perfect fluid can be interpreted as a model of a configuration of ''dust particles'' that locally move in concert and interact with each other only gravitationally, from which the name is derived. For this reason, dust models are often employed in cosmology as models of a toy universe, in which the dust particles are considered as highly idealized models of galaxies, clusters, or superclusters. In astrophysics, dust models have been employed as models of gravitational collapse. Dust solutions can also be used to model finite rotating disks of dust grains; some examples are ...
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Van Stockum Dust
In general relativity, the van Stockum dust is an exact solution of the Einstein field equations in which the gravitational field is generated by dust rotating about an axis of cylindrical symmetry. Since the density of the dust is ''increasing'' with distance from this axis, the solution is rather artificial, but as one of the simplest known solutions in general relativity, it stands as a pedagogically important example. This solution is named after Willem Jacob van Stockum, who rediscovered it in 1937 independently of a much earlier discovery by Cornelius Lanczos in 1924. It is currently recommended that the solution be referred to as the Lanczos–van Stockum dust. Derivation One way of obtaining this solution is to look for a cylindrically symmetric perfect fluid solution in which the fluid exhibits ''rigid rotation''. That is, we demand that the world lines of the fluid particles form a timelike congruence having nonzero vorticity but vanishing expansion and shear. (In ...
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Rotating Black Hole
A rotating black hole is a black hole that possesses angular momentum. In particular, it rotates about one of its axes of symmetry. All celestial objects – planets, stars ( Sun), galaxies, black holes – spin. Types of black holes There are four known, exact, black hole solutions to the Einstein field equations, which describe gravity in general relativity. Two of those rotate: the Kerr and Kerr–Newman black holes. It is generally believed that every black hole decays rapidly to a stable black hole; and, by the no-hair theorem, that (except for quantum fluctuations) stable black holes can be completely described at any moment in time by these 11 numbers: * mass-energy ''M'', * linear momentum ''P'' (three components), * angular momentum ''J'' (three components), * position ''X'' (three components), * electric charge ''Q''. These numbers represent the conserved attributes of an object which can be determined from a distance by examining its electromagnetic and grav ...
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