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Background Independence
Background independence is a condition in theoretical physics that requires the defining equations of a theory to be independent of the actual shape of the spacetime and the value of various fields within the spacetime. In particular this means that it must be possible not to refer to a specific coordinate system—the theory must be coordinate-free. In addition, the different spacetime configurations (or backgrounds) should be obtained as different solutions of the underlying equations. Description Background independence is a loosely defined property of a theory of physics. Roughly speaking, it limits the number of mathematical structures used to describe space and time that are put in place "by hand". Instead, these structures are the result of dynamical equations, such as Einstein field equations, so that one can determine from first principles what form they should take. Since the form of the metric determines the result of calculations, a theory with background independence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert Einstein was concerned wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superselection
In quantum mechanics, superselection extends the concept of selection rules. Superselection rules are postulated rules forbidding the preparation of quantum states that exhibit coherence between eigenstates of certain observables. It was originally introduced by Wick, Wightman, and Wigner to impose additional restrictions to quantum theory beyond those of selection rules. Mathematically speaking, two quantum states \psi_1 and \psi_2 are separated by a selection rule if \langle \psi_1 , H , \psi_2 \rangle = 0 for the given Hamiltonian H , while they are separated by a superselection rule if \langle \psi_1 , A , \psi_2 \rangle = 0 for ''all ''physical observables A . Because no observable connects \langle \psi_1 , and , \psi_2 \rangle they cannot be put into a quantum superposition \alpha , \psi_1 \rangle + \beta , \psi_2 \rangle , and/or a quantum superposition cannot be distinguished from a classical mixture of the two states. It also implies that there is a cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open Court Publishing Company
The Open Court Publishing Company is a publisher with offices in Chicago and LaSalle, Illinois. It is part of the Carus Publishing Company of Peru, Illinois. History Open Court was founded in 1887 by Edward C. Hegeler of the Matthiessen-Hegeler Zinc Company, at one time the largest producer of zinc in the United States. Hegeler intended for the firm to serve the purpose of discussing religious and psychological problems on the principle that the scientific world-conception should be applied to religion. Its first managing editor was Paul Carus, Hegeler's son-in-law through his marriage to engineer Mary Hegeler Carus.Fields 1992, pg. 138 For the first 80 years of its existence, the company had its offices in the Hegeler Carus Mansion. Open Court specializes in philosophy, science, and religion. It was one of the first academic presses in the country, as well as one of the first publishers of inexpensive editions of the classics. It also published the journals ''Open Court'' a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kluwer Academic
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, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Pittsburgh Press
The University of Pittsburgh Press is a scholarly publishing house and a major American university press, part of the University of Pittsburgh. The university and the press are located in Pittsburgh, Pennsylvania, in the United States. The press publishes several series in the humanities and social sciences, including Illuminations—Cultural Formations of the Americas; Pitt Latin American Series; Pitt Series in Russian and East European Studies, Pittsburgh Series in Composition, Literary, and Culture; Pittsburgh/Konstanz Series in Philosophy and History of Science; Culture, Politics, and the Built Environment; Central Eurasia in Context, and Latinx and Latin American Profiles. The press is especially known for literary publishing, particularly its Pitt Poetry Series, the Agnes Lynch Starrett Poetry Prize, and the Drue Heinz Literature Prize. The press also publishes the winner of the annual Donald Hall Prize, awarded by the Association of Writers & Writing Programs and the winne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advanced Science Letters
× ''Advanced Science Letters'' is a peer-reviewed scientific journal published by American Scientific Publishers. The editor-in-chief is Hari Singh Nalwa. Publishing formats include full papers, short communications, and special sections consisting of various formats. The journal was established in June 2008, and is published by American Scientific Publishers, a company identified by Jeffrey Beall as a predatory publisher. Although the journal received a 2010 impact factor of 1.253, it ceased to be indexed the following year. The journal was discontinued in 2019. Scope Coverage includes joining basic and applied original research across multiple disciplines. These are the physical sciences, biological sciences (including health sciences and medicine), computer sciences (including information science), agriculture sciences, geosciences, and environmental sciences (including environmental engineering Environmental engineering is a professional engineering discipline that enco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate-free
A coordinate-free, or component-free, treatment of a scientific theory or mathematical topic develops its concepts on any form of manifold without reference to any particular coordinate system. Benefits Coordinate-free treatments generally allow for simpler systems of equations and inherently constrain certain types of inconsistency, allowing greater mathematical elegance at the cost of some abstraction from the detailed formulae needed to evaluate these equations within a particular system of coordinates. In addition to elegance, coordinate-free treatments are crucial in certain applications for proving that a given definition is well formulated. For example, for a vector space V with basis v_1, ..., v_n, it may be tempting to construct the dual space V^* as the formal span of the symbols v_1^*, ..., v_n^* with bracket \langle \sum \alpha_i v_i , \sum \beta_i v_i^* \rangle := \sum \alpha_i \beta_i, but it is not immediately clear that this construction is independent of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called Quantum, quanta) of their underlying quantum field (physics), fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian (field theory), Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory (quantum mechanics), perturbation theory in quantum mechanics. History Quantum field theory emerged from the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loop Quantum Gravity
Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a force. As a theory LQG postulates that the structure of Spacetime, space and time is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale above the order of a Planck length, approximately 10−35 meters, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic hypothesis, atomic structure. The areas of research, which involves about 30 research groups worldwide, share the basic physical assumptions and the mathematical description of q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Causal Dynamical Triangulation
Causal dynamical triangulation (abbreviated as CDT) theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, is an approach to quantum gravity that, like loop quantum gravity, is background independent. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves. There is evidence that at large scales CDT approximates the familiar 4-dimensional spacetime, but shows spacetime to be 2-dimensional near the Planck scale, and reveals a fractal structure on slices of constant time. These interesting results agree with the findings of Lauscher and Reuter, who use an approach called Quantum Einstein Gravity, and with other recent theoretical work. Introduction Near the Planck scale, the structure of spacetime itself is supposed to be constantly changing due to quantum fluctuations and topological fluctuations. CDT theory uses a triangulation process which varies dynamically an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the ' is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations. Newton's law of universal gravitation, which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Twist (mathematics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity (mathematics), continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopy, homotopies. A property that is invariant under such deformations is a topological property. Basic exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
