# Duality

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## Duality (physics)

The state of having two natures, which is often applied in physics. The classic example is wave-particle duality. The elementary constituents of nature—electrons, quarks, photons, gravitons, and so on—behave in some respects like particles and in others like waves.

Duality is often used in a more precise sense. It indicates that two seemingly different, theoretical descriptions of a physical system are actually mathematically equivalent. Such an occurrence is very useful. Various properties and phenomena are clearer in one or the other of the descriptions, and calculations that are difficult or impossible in one description may be simple in the other. In the case of wave-particle duality, the wave description corresponds to a theory of quantized fields, where the field variables are governed by an uncertainty principle. The particle description corresponds to a Feynman integral over all particle paths in spacetime. The quantized-field and path integral theories sound very different but are mathematically equivalent, making identical predictions. See Feynman integral, Quantum field theory, Quantum mechanics, Uncertainty principle, Wave mechanics

#### Weak-strong duality

In some systems, there is weak-strong duality, meaning that when the coupling constant g of the original description is large that of the dual description, g, is small; for example g = 1/g. When g is large, so the interactions in the original description are strong and the perturbation theory in this description is highly inaccurate, then perturbation theory in the dual description gives a very accurate description.

#### Duality in superstring theory

It is believed that a complete theory of all particles and interactions must be based on quantization of one-dimensional objects (loops) rather than points: this is superstring theory. In superstring theory there is again the problem that perturbation theory is the main tool, giving an incomplete description of the physics. The situation has greatly improved with the discovery that weak-strong duality is a general property of string theory. In fact, there are five known string theories, and all are dual to one another. A notable feature in string theory is that in addition to strings and solitons, duality requires certain other objects as well: D-branes, which are local disturbances to which strings become fixed. Remarkably, the same methods have also been used to solve some long-standing problems regarding the quantum mechanics of black holes. See Quantum gravitation;, Superstring theory

References in periodicals archive ?
The Last Judgment and Anastasis scenes that exist on the wall paintings of Chora Monastery Church involve the dualities of good and bad, the other world and this world and masculine-feminine.
The other main current of opinion, historically led by Niels Bohr, tends to believe that the dualities.
Marketers realize that this growing target will respond to a multicultural approach that recognizes the dualities and the unique needs of their communities.
String dualities invite comparison to a waltz: "So S-duality is like Fred Astaire dancing with a slimy alien--Sorry Fred.
The project explored dualities and ambiguities of inside and outside, under and over which are reiterated in both the Chapel and the Ruskin Library.
Branes, for instance, are like strings with any number of dimensions, and string dualities are "a duality relation between two apparently different string theories, or between two apparently different constructions in string theory.
Their articles of personal adornment responded to the inherent axial nature of the body with the dualities of arms and legs, laws of symmetry and proportion.
Neither rebus nor narrative, Lapthisophon's walls presented streams of dualities, speculations raised and dismissed, information abutting its own rebuttal.
Once, most people thought that artificial-natural, human-machine, organic and constructed, were dualities .

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