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Comoving Distance
In standard cosmology, comoving distance and proper distance (or physical distance) are two closely related distance measures used by cosmologists to define distances between objects. ''Comoving distance'' factors out the expansion of the universe, giving a distance that does not change in time except due to local factors, such as the motion of a galaxy within a cluster. ''Proper distance'' roughly corresponds to where a distant object would be at a specific moment of cosmological time, which can change over time due to the expansion of the universe. Comoving distance and proper distance are defined to be equal at the present time. At other times, the Universe's expansion results in the proper distance changing, while the comoving distance remains constant. Comoving coordinates Although general relativity allows the formulation of the laws of physics using arbitrary coordinates, some coordinate choices are easier to work with. Comoving coordinates are an example of such a coor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Big Bang
The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. The uniformity of the universe, known as the horizon and flatness problems, is explained through cosmic inflation: a phase of accelerated expansion during the earliest stages. A wide range of empirical evidence strongly favors the Big Bang event, which is now essentially universally accepted.: "At the same time that observations tipped the balance definitely in favor of the relativistic big-bang theory, ..." Detailed measurements of the expansion rate of the universe place the Big Bang singularity at an estimated billion years ago, which is considered the age of the universe. Extrapolating this cosmic expansion backward in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proper Length
Proper length or rest length is the length of an object in the object's rest frame. The measurement of lengths is more complicated in the theory of relativity than in classical mechanics. In classical mechanics, lengths are measured based on the assumption that the locations of all points involved are measured simultaneously. But in the theory of relativity, the notion of simultaneity is dependent on the observer. A different term, proper distance, provides an invariant measure whose value is the same for all observers. ''Proper distance'' is analogous to proper time. The difference is that the proper distance is defined between two spacelike-separated events (or along a spacelike path), while the proper time is defined between two timelike-separated events (or along a timelike path). Proper length or rest length The ''proper length'' or ''rest length'' of an object is the length of the object measured by an observer which is at rest relative to it, by applying standard ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comoving Frame
A proper frame, or comoving frame, is a frame of reference that is attached to an object. The object in this frame is stationary within the frame, which is useful for many types of calculations. For example, a freely falling elevator is a proper frame for a free-falling object in the elevator, while the surface of the Earth is not. But, for an object on the Earth's surface, the Earth's surface is a proper frame while the falling elevator is not a proper frame. Proper frames can be inertial and non-inertial, as in the example above. The use of a proper frame is essential for the investigation of physical laws within the framework of general relativity. The term comoving frame is also a good description of a non-inertial frame, which is useful for many of the same uses as we mentioned previously. One advantage of proper frame and comoving frame is that the two frames must always maintain the same spatial position (i. "in the frame" - e.g. on the same frame of reference). This incl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Age Of The Universe
In physical cosmology, the age of the universe is the cosmological time, time elapsed since the Big Bang: 13.79 billion years. Astronomers have two different approaches to determine the age of the universe. One is based on a particle physics model of the early universe called Lambda-CDM model, Lambda-CDM, matched to measurements of the distant, and thus old features, like the cosmic microwave background. The other is based on the distance and relative velocity of a series or "ladder" of different kinds of stars, making it depend on local measurements late in the history of the universe. These two methods give slightly different values for the Hubble constant, which is then used in a formula to calculate the age. The range of the estimate is also within the range of the estimate for the List of oldest stars, oldest observed star in the universe. History In the 18th century, the concept that the age of Earth was millions, if not billions, of years began to appear. Nonetheless ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessment to form Cambridge University Press and Assessment under Queen Elizabeth II's approval in August 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it published over 50,000 titles by authors from over 100 countries. Its publications include more than 420 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also published Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. It also served as the King's Printer. Cambridge University Press, as part of the University of Cambridge, was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Science & Business Media
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second-largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American Multinational corporation, multinational Publishing, publishing company that focuses on academic publishing and instructional materials. The company was founded in 1807 and produces books, Academic journal, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, Technology, technical, and engineering subject areas, abandoning its literary interests. Wiley's son Joh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Null Geodesic
In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic. In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime geometry where the source of curvature is the stress–energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting a star is the projection of a geodesic of the curved four-dimensional (4-D) spacetime geometry around the star onto three-dimensional (3-D) space. Mathematical expression The full geodesic equation is +\Gamma^\mu _=0\ where ''s'' is a scalar parameter of motion (e.g. the proper time), and \Gamma^\mu _ are Christoffel symbols (sometimes called the affine connection coefficients or Levi-Civita connection coefficients) symme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Integral
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. the other being differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter. A definite integral computes the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an ''antiderivative'', a function whose derivat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedmann–Lemaître–Robertson–Walker Metric
The Friedmann–Lemaître–Robertson–Walker metric (FLRW; ) is a metric that describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not necessarily simply connected. The general form of the metric follows from the geometric properties of homogeneity and isotropy. Depending on geographical or historical preferences, the set of the four scientists – Alexander Friedmann, Georges Lemaître, Howard P. Robertson and Arthur Geoffrey Walker – are variously grouped as Friedmann, Friedmann–Robertson–Walker (FRW), Robertson–Walker (RW), or Friedmann–Lemaître (FL). When combined with Einstein's field equations the metric gives the Friedmann equation which has been developed into the ''Standard Model'' of modern cosmology, and the further developed Lambda-CDM model. Concept The metric is a consequence of assuming that the mass in the universe has constant density – homogeneity – and is the same in all direc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
