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Quantum spacetime

Quantum spacetime
In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra. The choice of that algebra still varies from theory to theory. As a result of this change some variables that are usually continuous may become discrete. Physical reasons have been given to believe that physical spacetime is a quantum spacetime. are already noncommutative, obey the Heisenberg uncertainty principle, and are continuous. Again, physical spacetime is expected to be quantum because physical coordinates are already slightly noncommutative. Both arguments are based on pure gravity and quantum theory, and they limit the measurement of time by the only time constant in pure quantum gravity, the Planck time. Quantum spacetimes are often described mathematically using the noncommutative geometry of Connes, quantum geometry, or quantum groups. and the time variable Related:  docs

Planck constant Plaque at the Humboldt University of Berlin: "Max Planck, discoverer of the elementary quantum of action h, taught in this building from 1889 to 1928." In 1905 the value (E), the energy of a charged atomic oscillator, was theoretically associated with the energy of the electromagnetic wave itself, representing the minimum amount of energy required to form an electromagnetic field (a "quantum"). Further investigation of quanta revealed behaviour associated with an independent unit ("particle") as opposed to an electromagnetic wave and was eventually given the term photon. The Planck relation now describes the energy of each photon in terms of the photon's frequency. This energy is extremely small in terms of ordinary experience. Since the frequency , wavelength λ, and speed of light c are related by λν = c, the Planck relation for a photon can also be expressed as The above equation leads to another relationship involving the Planck constant. Value[edit] Significance of the value[edit]

Glueball In particle physics, a glueball is a hypothetical composite particle.[1] It consists solely of gluon particles, without valence quarks. Such a state is possible because gluons carry color charge and experience the strong interaction. Glueballs are extremely difficult to identify in particle accelerators, because they mix with ordinary meson states.[2] Theoretical calculations show that glueballs should exist at energy ranges accessible with current collider technology. Properties of glueballs[edit] In principle, it is theoretically possible for all properties of glueballs to be calculated exactly and derived directly from the equations and fundamental physical constants of quantum chromodynamics (QCD) without further experimental input. Constituent Particles and Color Charge[edit] Theoretical studies of glueballs have focused on glueballs consisting of either two gluons or three gluons, by analogy to mesons and baryons that have two and three quarks respectively. Electric Charge[edit]

Quantum geometry In theoretical physics, quantum geometry is the set of new mathematical concepts generalizing the concepts of geometry whose understanding is necessary to describe the physical phenomena at very short distance scales (comparable to Planck length). At these distances, quantum mechanics has a profound effect on physics. Quantum gravity[edit] In an alternative approach to quantum gravity called loop quantum gravity (LQG), the phrase "quantum geometry" usually refers to the formalism within LQG where the observables that capture the information about the geometry are now well defined operators on a Hilbert space. It is possible (but considered unlikely) that this strictly quantized understanding of geometry will be consistent with the quantum picture of geometry arising from string theory. Another, quite successful, approach, which tries to reconstruct the geometry of space-time from "first principles" is Discrete Lorentzian quantum gravity. Quantum states as differential forms[edit]

Quantum Mechanics and Reality, by Thomas J McFarlane © Thomas J. McFarlane 1995www.integralscience.org Most traditional [spiritual] paths were developed in prescientific cultures. Consequently, many of their teachings are expressed in terms of cosmologies or world views which we no longer find relevant. . .The question then naturally arises: Is it possible to incorporate both science and mysticism into a single, coherent world view? The primary purpose of this essay is to explain how quantum mechanics shows that the materialistic common sense notion of reality is an illusion, i.e., that the objective existence of the world is an illusion. The appearance of an objective world distinguishable from a subjective self is but the imaginary form in which Consciousness Perfectly Realizes Itself. Now listen to Niels Bohr, the pioneer of 20th century physics: An independent reality, in the ordinary physical sense, can neither be ascribed to the phenomena nor to the agencies of observation. [3] To quote Bohr and Heisenberg once more,

Quantum entanglement Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently – instead, a quantum state may be given for the system as a whole. Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky and Nathan Rosen,[1] describing what came to be known as the EPR paradox, and several papers by Erwin Schrödinger shortly thereafter.[2][3] Einstein and others considered such behavior to be impossible, as it violated the local realist view of causality (Einstein referred to it as "spooky action at a distance"),[4] and argued that the accepted formulation of quantum mechanics must therefore be incomplete. History[edit] However, they did not coin the word entanglement, nor did they generalize the special properties of the state they considered. Concept[edit] Meaning of entanglement[edit] Apparent paradox[edit] The hidden variables theory[edit]

Wick rotation In physics, Wick rotation, named after Gian-Carlo Wick, is a method of finding a solution to a mathematical problem in Minkowski space from a solution to a related problem in Euclidean space by means of a transformation that substitutes an imaginary-number variable for a real-number variable. This transformation is also used to find solutions to problems in quantum mechanics and other areas. Overview[edit] Wick rotation is motivated by the observation that the Minkowski metric [with (−1, +1, +1, +1) convention for the metric tensor] and the four-dimensional Euclidean metric are equivalent if one permits the coordinate t to take on imaginary values. , sometimes yields a problem in real Euclidean coordinates x, y, z, which is easier to solve. Statistical and quantum mechanics[edit] Wick rotation connects statistical mechanics to quantum mechanics by replacing inverse temperature with imaginary time . . is , where is Boltzmann's constant. is, up to a normalizing constant, under a Hamiltonian . where

Schrödinger equation In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of some physical system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger.[1] In classical mechanics, the equation of motion is Newton's second law, and equivalent formulations are the Euler–Lagrange equations and Hamilton's equations. In quantum mechanics, the analogue of Newton's law is Schrödinger's equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). The concept of a state vector is a fundamental postulate of quantum mechanics. In the standard interpretation of quantum mechanics, the wave function is the most complete description that can be given to a physical system. Equation[edit] Time-dependent equation[edit] The form of the Schrödinger equation depends on the physical situation (see below for special cases). Implications[edit]

Robot Un article de Wikipédia, l'encyclopédie libre. Cet article concerne les robots matériels. Pour les robots purement logiciels, voir Bot informatique. Le robot Nao, un humanoïde, développé pour interagir avec les gens. Le robot Actroid-DER, un Androïde, développé pour assurer des fonctions d'accueil du public, a été présenté à l’Expo Aichi 2005. Un robot est un dispositif mécatronique (alliant mécanique, électronique et informatique) accomplissant automatiquement soit des tâches qui sont généralement dangereuses, pénibles, répétitives ou impossibles pour les humains, soit des tâches plus simples mais en les réalisant mieux que ce que ferait un être humain. En dépit de leur coût élevé à l'époque (faute de microprocesseurs puissants produits en masse), les robots se sont imposés dès le début des années 1970 pour certaines tâches comme la peinture des carrosseries automobiles, en atmosphère de vapeurs toxiques. La science des robots se nomme la robotique. Étymologie[modifier | modifier le code]

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