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Comoving And Proper Distances
In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. ''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'' factors out the expansion of the universe, giving a distance that does not change in time due to the expansion of space (though this may change due to other, local factors, such as the motion of a galaxy within a cluster). 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 one to formulate the laws of physics using arbitrary coordinates, some coordinate choices are more natural or easier to work with. Com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Big Bang
The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the earliest known periods through its subsequent large-scale form. These models offer a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. The overall uniformity of the Universe, known as the flatness problem, is explained through cosmic inflation: a sudden and very rapid expansion of space during the earliest moments. However, physics currently lacks a widely accepted theory of quantum gravity that can successfully model the earliest conditions of the Big Bang. Crucially, these models are compatible with the Hubble–Lemaître law—the observation that the farther away a galaxy is, the faster it is mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cosmic Time
Cosmic time, or cosmological time, is the time coordinate commonly used in the Big Bang models of physical cosmology. Such time coordinate may be defined for a homogeneous, expanding universe so that the universe has the same density everywhere at each moment in time (the fact that this is possible means that the universe is, by definition, homogeneous). The clocks measuring cosmic time should move along the Hubble flow. Cosmic time t is a measure of time by a physical clock with zero peculiar velocity in the absence of matter over-/under-densities (to prevent time dilation due to relativistic effects or confusions caused by expansion of the universe). Unlike other measures of time such as temperature, redshift, particle horizon, or Hubble horizon, the cosmic time (similar and complementary to the comoving coordinates) is blind to the expansion of the universe. There are two main ways for establishing a reference point for the cosmic time. The most trivial way is to take the pr ... [...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] |
Cosmological Time
Cosmic time, or cosmological time, is the time coordinate commonly used in the Big Bang models of physical cosmology. Such time coordinate may be defined for a homogeneous, expanding universe so that the universe has the same density everywhere at each moment in time (the fact that this is possible means that the universe is, by definition, homogeneous). The clocks measuring cosmic time should move along the Hubble flow. Cosmic time t is a measure of time by a physical clock with zero peculiar velocity in the absence of matter over-/under-densities (to prevent time dilation due to relativistic effects or confusions caused by expansion of the universe). Unlike other measures of time such as temperature, redshift, particle horizon, or Hubble horizon, the cosmic time (similar and complementary to the comoving coordinates) is blind to the expansion of the universe. There are two main ways for establishing a reference point for the cosmic time. The most trivial way is to take the prese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expansion Of The Universe, Proper Distances (Animation)
Expansion may refer to: Arts, entertainment and media * '' L'Expansion'', a French monthly business magazine * ''Expansion'' (album), by American jazz pianist Dave Burrell, released in 2004 * ''Expansions'' (McCoy Tyner album), 1970 * ''Expansions'' (Lonnie Liston Smith album), 1975 * ''Expansión'' (Mexico), a Mexican news portal linked to CNN * Expansion (sculpture) (2004) Bronze sculpture illuminated from within * ''Expansión'' (Spanish newspaper), a Spanish economic daily newspaper published in Spain * Expansion pack in gaming, extra content for games, often simply "expansion" Science, technology, and mathematics * Expansion (geometry), stretching of geometric objects with flat sides * Expansion (model theory), in mathematical logic, a mutual converse of a reduct * Expansion card, in computing, a printed circuit board that can be inserted into an expansion slot * Expansion chamber, on a two-stroke engine, a tuned exhaust system that enhances power output * Expansion joi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also publishes 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. ... [...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 internationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, 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, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East Orang ... [...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) s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Integral
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be interpreted as 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speed Of Light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space. All forms of electromagnetic radiation, including visible light, travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects. Starlight viewed on Earth left the stars many years ago, allowing humans to study the history of the universe by viewing distant objects. When communicating with distant space probes, it can take minutes to hours for signals to travel from Earth to the spacecraft and vice versa. In computing, the speed of light fixes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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