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Misner Space
Misner space is an abstract mathematical spacetime, first described by Charles W. Misner. It is also known as the Lorentzian orbifold \mathbb^/\text. It is a simplified, two-dimensional version of the Taub–NUT spacetime. It contains a non-curvature singularity and is an important counterexample to various hypotheses in general relativity. Michio Kaku develops the following analogy for understanding the concept: "Misner space is an idealized space in which a room, for example, becomes the entire universe. For example, every point on the left wall of the room is identical to the corresponding point on the right wall, such that if you were to walk toward the left wall you will walk through the wall and appear from the right wall. This suggests that the left and right wall are joined, in some sense, as in a cylinder. The opposite walls are thus all identified with each other, and the ceiling is likewise identified with the floor. Misner space is often studied because it has the same ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive ''where'' and ''when'' events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity. In 1908, Hermann Minkowski presented a geometric interpretation of special relativity that fused time and the three spatial dimensions into a single four-dimensional continuum now known as Minkowski space. This interpretation proved vital t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles W
The F/V ''Charles W'', also known as Annie J Larsen, is a historic fishing schooner anchored in Petersburg, Alaska. At the time of its retirement in 2000, it was the oldest fishing vessel in the fishing fleet of Southeast Alaska, and the only known wooden fishing vessel in the entire state still in active service. Launched in 1907, she was first used in the halibut fisheries of Puget Sound and the Bering Sea as the ''Annie J Larsen''. In 1925 she was purchased by the Alaska Glacier Seafood Company, refitted for shrimp trawling, and renamed ''Charles W'' in honor of owner Karl Sifferman's father. The company was one of the pioneers of the local shrimp fishery, a business it began to phase out due to increasing competition in the 1970s. The ''Charles W'' was the last of the company's fleet of ships, which numbered twelve at its height. The boat was acquired in 2002 by the nonprofit Friends of the ''Charles W''. The boat was listed on the National Register of Historic Place ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentzian Manifold
In mathematical physics, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere non-degenerate bilinear form, nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of Positive-definite bilinear form, 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 Causal structure, timelike, null, and spacelike. Introduction Manifolds In differential geometry, a differentiable manifold is a space that 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 '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbifold
In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space that is locally a finite group quotient of a Euclidean space. Definitions of orbifold have been given several times: by Ichirō Satake in the context of automorphic forms in the 1950s under the name ''V-manifold''; by William Thurston in the context of the geometry of 3-manifolds in the 1970s when he coined the name ''orbifold'', after a vote by his students; and by André Haefliger in the 1980s in the context of Mikhail Gromov's programme on CAT(k) spaces under the name ''orbihedron''. Historically, orbifolds arose first as surfaces with singular points long before they were formally defined. One of the first classical examples arose in the theory of modular forms with the action of the modular group \mathrm(2,\Z) on the upper half-plane: a version of the Riemann–Roch theorem holds after the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taub–NUT Space
The Taub–NUT metric (,McGraw-Hill ''Science & Technology Dictionary'': "Taub NUT space" ) is an exact solutions in general relativity, exact solution to Einstein's equations. It may be considered a first attempt in finding the metric of a spinning black hole. It is sometimes also used in Homogeneity (physics), homogeneous but anisotropic cosmological models formulated in the framework of general relativity. The underlying Taub space was found by , and extended to a larger manifold by , whose initials form the "NUT" of "Taub–NUT". Description Taub's solution is an empty space solution of Einstein's equations with topology R×S3 and metric (or equivalently line element) :g =-dt^2/U(t) + 4l^2U(t)(d\psi+ \cos\theta d\phi)^2+(t^2+l^2)(d\theta^2+(\sin\theta)^2d\phi^2) where :U(t)=\frac and ''m'' and ''l'' are positive constants. Taub's metric has coordinate singularities at U=0, t=m+(m^2+l^2)^, and Newman, Tamburino and Unti showed how to extend the metric across these surfaces. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michio Kaku
Michio Kaku (; ; born January 24, 1947) is an American theoretical physicist, Science communication, science communicator, futurologist, and writer of popular-science. He is a professor of theoretical physics at the City College of New York and the CUNY Graduate Center. Kaku is the author of several books about physics and related topics and has made frequent appearances on radio, television, and film. He is also a regular contributor to his own blog, as well as other popular media outlets. For his efforts to bridge science and science fiction, he is a 2021 Sir Arthur Clarke Award, Sir Arthur Clarke Lifetime Achievement Awardee. His books ''Physics of the Impossible'' (2008), ''Physics of the Future'' (2011), ''The Future of the Mind'' (2014), and The God Equation, ''The God Equation: The Quest for a Theory of Everything'' (2021) became The New York Times Best Seller list, ''New York Times'' best sellers. Kaku has hosted several television specials for the BBC, the Discovery Chan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Penguin Books
Penguin Books Limited is a Germany, German-owned English publishing, publishing house. It was co-founded in 1935 by Allen Lane with his brothers Richard and John, as a line of the publishers the Bodley Head, only becoming a separate company the following year."About Penguin – company history" , Penguin Books. Penguin revolutionised publishing in the 1930s through its inexpensive paperbacks, sold through Woolworths (United Kingdom), Woolworths and other stores for Sixpence (British coin), sixpence, bringing high-quality fiction and non-fiction to the mass market. Its success showed that large audiences existed for several books. It also affected modern British popular culture significantly through its books concerning politics, the arts, and science. Penguin Books is now an imprint (trad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric (mathematics)
In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are a general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another. Since they are very general, metric spaces are a tool used in many different branches of mathematics. Many types of mathematical objects have a natural notion of distance and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 stro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
