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Nonlocality (other)
Nonlocality may refer to: * Action at a distance, the concept in physics of nonlocal interactions ** Principle of locality, the opposite of action at a distance * Quantum nonlocality, nonlocal phenomena in quantum mechanics * Nonlocal Lagrangian, a type of Lagrangian (a mathematical function) * Nonlocal operator, which maps functions on a topological space to functions, in such a way that the value of the output function at a given point cannot be determined solely from the values of the input function in any neighbourhood of any point. See also * Locality (other) * Nonlocal (other) {{disambig ru:Нелокальность ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Action At A Distance
In physics, action at a distance is the concept that an object can be affected without being physically touched (as in mechanical contact) by another object. That is, it is the non-local interaction of objects that are separated in space. Non-contact forces is action at a distance affecting specifically an object's motion. This term was used most often in the context of early theories of gravity and electromagnetism to describe how an object responds to the influence of distant objects. For example, Coulomb's law and Newton's law of universal gravitation are such early theories. More generally, "action at a distance" describes the failure of early atomistic and mechanistic theories which sought to reduce all physical interaction to collision. The exploration and resolution of this problematic phenomenon led to significant developments in physics, from the concept of a field, to descriptions of quantum entanglement and the mediator particles of the Standard Model. Electrici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Locality
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of instantaneous "action at a distance". Locality evolved out of the field theories of classical physics. The concept is that for an action at one point to have an influence at another point, something in the space between those points must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, carrying the influence. The special theory of relativity limits the speed at which all such influences can travel to the speed of light, c. Therefore, the principle of locality implies that an event at one point cannot cause a simultaneous result at another point. An event at point A cannot cause a result at point B in a time less than T=D/c, where D is the distance between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Nonlocality
In theoretical physics, quantum nonlocality refers to the phenomenon by which the measurement statistics of a multipartite quantum system do not admit an interpretation in terms of a local realistic theory. Quantum nonlocality has been experimentally verified under different physical assumptions. Any physical theory that aims at superseding or replacing quantum theory should account for such experiments and therefore cannot fulfill local realism; quantum nonlocality is a property of the universe that is independent of our description of nature. Quantum nonlocality does not allow for faster-than-light communication, and hence is compatible with special relativity and its universal speed limit of objects. Thus, quantum theory is local in the strict sense defined by special relativity and, as such, the term "quantum nonlocality" is sometimes considered a misnomer. Still, it prompts many of the foundational discussions concerning quantum theory. History Einstein, Podolsky and Rose ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlocal Lagrangian
In field theory, a nonlocal Lagrangian is a Lagrangian, a type of functional \mathcalphi(x) containing terms that are ''nonlocal'' in the fields \phi(x), i.e. not polynomials or functions of the fields or their derivatives evaluated at a single point in the space of dynamical parameters (e.g. space-time). Examples of such nonlocal Lagrangians might be: * \mathcal = \frac\big(\partial_x \phi(x)\big)^2 - \fracm^2 \phi(x)^2 + \phi(x) \int \frac \,d^ny. * \mathcal = -\frac\mathcal_\left(1 + \frac\right)\mathcal^. * S = \int dt \,d^dx \left psi^*\left(i\hbar \frac + \mu\right)\psi - \frac\nabla \psi^*\cdot \nabla \psi\right- \frac\int dt \,d^dx \,d^dy \, V(\mathbf - \mathbf) \psi^*(\mathbf) \psi(\mathbf) \psi^*(\mathbf) \psi(\mathbf). * The Wess–Zumino–Witten action. Actions obtained from nonlocal Lagrangians are called ''nonlocal actions''. The actions appearing in the fundamental theories of physics, such as the Standard Model, are local actions; nonlocal actions play a par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlocal Operator
In mathematics, a nonlocal operator is a mapping which maps functions on a topological space to functions, in such a way that the value of the output function at a given point cannot be determined solely from the values of the input function in any neighbourhood of any point. An example of a nonlocal operator is the Fourier transform. Formal definition Let X be a topological space, Y a set, F(X) a function space containing functions with domain X, and G(Y) a function space containing functions with domain Y. Two functions u and v in F(X) are called equivalent at x\in X if there exists a neighbourhood N of x such that u(x')=v(x') for all x'\in N. An operator A: F(X) \to G is said to be local if for every y\in Y there exists an x\in X such that Au(y) = Av(y) for all functions u and v in F(X) which are equivalent at x. A nonlocal operator is an operator which is not local. For a local operator it is possible (in principle) to compute the value Au(y) using only knowledge of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Locality (other)
Locality may refer to: * Locality (association), an association of community regeneration organizations in England * Locality (linguistics) * Locality (settlement) * Suburbs and localities (Australia), in which a locality is a geographic subdivision in rural areas of Australia Science * Locality (astronomy) * Locality of reference, in computer science * Locality (statistics) * Principle of locality, in physics See also * Local (other) Local may refer to: Geography and transportation * Local (train), a train serving local traffic demand * Local, Missouri, a community in the United States * Local government, a form of public administration, usually the lowest tier of administrat ... * Type locality (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlocal (other)
Nonlocal may refer to: * Action at a distance, direct interaction of physical objects that are not in proximity * Conjugated system (or nonlocalized bond), in chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in compounds with alternating single and multiple bonds, which in general may lower the overall energy of the molecule and increase stability * Nonlocal goto, an abstract representation of the control state of a computer program * Nonlocal Lagrangian, in field theory, a type of functional \mathcal L\phi(x) which contains terms which are nonlocal in the fields i.e. which are not polynomials or functions of the fields or their derivatives evaluated at a single point in the space of dynamical parameters (e.g. space-time) ** Other nonlocal relationships in physics, such as Pippard's nonlocal generalisation of the Londons' equations for superconductivity * Non-local means, an algorithm in image processing for image denoising * Non-local ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |